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Answer test results
This page exposes the results of running answer tests on STACK test cases. This page is automatically generated from the STACK unit tests and is designed to show question authors what answer tests actually do. This includes cases where answer tests currentl fail, which gives a negative expected mark. Comments and further test cases are very welcome.
AlgEquiv
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| AlgEquiv | 1/0 |
1 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATAlgEquiv_STACKERROR_SAns. | ||
| AlgEquiv | 1 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATAlgEquiv_STACKERROR_TAns. | ||
| AlgEquiv | (x-1)^2 |
-1 | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | ATAlgEquivTEST_FAILED-Empty SA. | |||
| AlgEquiv | x^2 |
-1 | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question. | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question. | ATAlgEquivTEST_FAILED-Empty TA. | |||
| AlgEquiv | x-1)^2 |
(x-1)^2 |
-1 | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | ATAlgEquivTEST_FAILED-Empty SA. | ||
| See docs on subscripts and different atoms. | ||||||||
| AlgEquiv | x1 |
x_1 |
0 | |||||
| AlgEquiv | x_1 |
x[1] |
0 | |||||
| AlgEquiv | x[1] |
x1 |
0 | |||||
| Predicates | ||||||||
| AlgEquiv | integerp(3) |
true |
1 | ATLogic_True. | ||||
| AlgEquiv | integerp(3.1) |
true |
0 | |||||
| AlgEquiv | integerp(3) |
false |
0 | |||||
| AlgEquiv | integerp(3) |
true |
1 | ATLogic_True. | ||||
| AlgEquiv | lowesttermsp(x^2/x) |
true |
1 | ATLogic_True. | ||||
| AlgEquiv | lowesttermsp(-y/-x) |
true |
1 | ATLogic_True. | ||||
| AlgEquiv | lowesttermsp((x^2-1)/(x-1)) |
true |
0 | |||||
| AlgEquiv | lowesttermsp((x^2-1)/(x+2)) |
true |
1 | ATLogic_True. | ||||
| Case sensitivity | ||||||||
| AlgEquiv | X |
x |
0 | ATAlgEquiv_WrongCase. | ||||
| AlgEquiv | exdowncase(X) |
x |
1 | |||||
| AlgEquiv | exdowncase((X-1)^2) |
x^2-2*x+1 |
1 | |||||
| Permutations of variables (To do: a dedicated answer test with feedback) | ||||||||
| AlgEquiv | Y=1+X |
y=1+x |
0 | ATEquation_default | ||||
| AlgEquiv | v+w+x+y+z |
a+b+c+A+B |
0 | |||||
| Numbers | ||||||||
| AlgEquiv | 4^(-1/2) |
1/2 |
1 | |||||
| AlgEquiv | 4^(1/2) |
sqrt(4) |
1 | |||||
| Mix of floats and rational numbers | ||||||||
| AlgEquiv | 0.5 |
1/2 |
1 | |||||
| AlgEquiv | 0.33 |
1/3 |
0 | |||||
| AlgEquiv | 452 |
4.52*10^2 |
0 | |||||
| AlgEquiv | 5.1e-2 |
51/1000 |
1 | |||||
| AlgEquiv | 0.333333333333333 |
1/3 |
0 | |||||
| AlgEquiv | (0.5+x)*2 |
2*x+1 |
1 | |||||
| Complex numbers | ||||||||
| AlgEquiv | sqrt(-1) |
%i |
1 | |||||
| AlgEquiv | %i |
e^(i*pi/2) |
1 | |||||
| AlgEquiv | (4*sqrt(3)*%i+4)^(1/5) |
8^(1/5)*(cos(%pi/15)+%i*sin(%p i/15)) |
1 | |||||
| AlgEquiv | (4*sqrt(3)*%i+4)^(1/5) |
rectform((4*sqrt(3)*%i+4)^(1/5 )) |
1 | |||||
| AlgEquiv | (4*sqrt(3)*%i+4)^(1/5) |
polarform((4*sqrt(3)*%i+4)^(1/ 5)) |
1 | |||||
| AlgEquiv | %i/sqrt(x) |
sqrt(-1/x) |
1 | |||||
| Infinity | ||||||||
| AlgEquiv | inf |
inf |
1 | |||||
| AlgEquiv | inf |
-inf |
0 | |||||
| AlgEquiv | 2*inf |
inf |
0 | |||||
| AlgEquiv | 0*inf |
0 |
1 | |||||
| Powers and roots | ||||||||
| AlgEquiv | x^(1/2) |
sqrt(x) |
1 | |||||
| AlgEquiv | x |
sqrt(x^2) |
0 | |||||
| AlgEquiv | abs(x) |
sqrt(x^2) |
1 | |||||
| AlgEquiv | 1/abs(x)^(1/3) |
(abs(x)^(1/3)/abs(x))^(1/2) |
1 | |||||
| AlgEquiv | sqrt((x-3)*(x-5)) |
sqrt(x-3)*sqrt(x-5) |
0 | |||||
| AlgEquiv | 1/sqrt(x) |
sqrt(1/x) |
1 | |||||
| AlgEquiv | x-1 |
(x^2-1)/(x+1) |
1 | |||||
| AlgEquiv | 2^((1/5.1)*t) |
2^((1/5.1)*t) |
1 | |||||
| AlgEquiv | 2^((1/5.1)*t) |
2^(0.196078431373*t) |
0 | |||||
| AlgEquiv | a^b*a^c |
a^(b+c) |
1 | |||||
| AlgEquiv | (a^b)^c |
a^(b*c) |
0 | |||||
| AlgEquiv | (assume(a>0),(a^b)^c) |
a^(b*c) |
1 | |||||
| AlgEquiv | (assume(x>2),6*((x-2)^2)^k) |
6*(x-2)^(2*k) |
1 | |||||
| AlgEquiv | signum(-3) |
-1 |
1 | |||||
| AlgEquiv | 6*((x-2)^3)^k |
6*(x-2)^(3*k) |
1 | |||||
| AlgEquiv | (4*sqrt(3)*%i+4)^(1/5) |
6^(1/5)*cos(%pi/15)-6^(1/5)*%i *sin(%pi/15) |
0 | |||||
| AlgEquiv | 2+2*sqrt(3+x) |
2+sqrt(12+4*x) |
1 | |||||
| AlgEquiv | 6*e^(6*(y^2+x^2))+72*x^2*e^(6* (y^2+x^2)) |
(72*x^2+6)*e^(6*(y^2+x^2)) |
1 | |||||
| Expressions with subscripts | ||||||||
| AlgEquiv | a1 |
a_1 |
0 | |||||
| AlgEquiv | rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2)) |
rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2)) |
1 | |||||
| AlgEquiv | rho*z*V/(4*pi*epsilon[1]*(R^2+ z^2)^(3/2)) |
rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2)) |
0 | |||||
| AlgEquiv | sqrt(k/m)*sqrt(m/k) |
1 |
1 | |||||
| AlgEquiv | (2*pi)/(k/m)^(1/2) |
(2*pi)/(k/m)^(1/2) |
1 | |||||
| AlgEquiv | (2*pi)*(m/k)^(1/2) |
(2*pi)/(k/m)^(1/2) |
1 | |||||
| AlgEquiv | sqrt(2*x/10+1) |
sqrt((2*x+10)/10) |
1 | |||||
| AlgEquiv | ((x+3)^2*(x+3))^(1/3) |
((x+3)*(x^2+6*x+9))^(1/3) |
1 | |||||
| Need to factor internally. | ||||||||
| AlgEquiv | ((x+3)^2*(x+3))^(1/3) |
((x+3)*(x^2+6*x+9))^(1/3) |
1 | |||||
| Polynomials and rational function | ||||||||
| AlgEquiv | (x-1)^2 |
x^2-2*x+1 |
1 | |||||
| AlgEquiv | (x-1)*(x^2+x+1) |
x^3-1 |
1 | |||||
| AlgEquiv | (x-1)^(-2) |
1/(x^2-2*x+1) |
1 | |||||
| AlgEquiv | 1/(4*x-(%pi+sqrt(2))) |
1/(x+1) |
0 | |||||
| AlgEquiv | (x-a)^6000 |
(x-a)^6000 |
1 | |||||
| AlgEquiv | (a-x)^6000 |
(x-a)^6000 |
1 | |||||
| AlgEquiv | (4*a-x)^6000 |
(x-4*a)^6000 |
1 | |||||
| AlgEquiv | (x-a)^6000 |
(x-a)^5999 |
0 | |||||
| AlgEquiv | (k+8)/(k^2+4*k-12) |
(k+8)/(k^2+4*k-12) |
1 | |||||
| AlgEquiv | (k+7)/(k^2+4*k-12) |
(k+8)/(k^2+4*k-12) |
0 | |||||
| AlgEquiv | -(2*k+6)/(k^2+4*k-12) |
-(2*k+6)/(k^2+4*k-12) |
1 | |||||
| AlgEquiv | 1/n-1/(n+1) |
1/(n*(n+1)) |
1 | |||||
| AlgEquiv | 0.5*x^2+3*x-1 |
x^2/2+3*x-1 |
1 | |||||
| AlgEquiv | 14336000000*x^13+250265600000* x^12+1862860800000*x^11+762392 5760000*x^10+18290677760000*x^ 9+24744757985280*x^8+145672123 51488*x^7-3267871272960*x^6-64 08053107200*x^5+670406720000*x ^4+1179708800000*x^3-429244800 000*x^2+56696000000*x-26800000 00 |
512*(2*x+5)^7*(5*x-1)^5*(70*x+ 67) |
1 | |||||
| AlgEquiv | 14336000000*x^13+250265600000* x^12+1862860800000*x^11+762392 5760000*x^10+18290677760000*x^ 9+24744757985280*x^8+145672123 51488*x^7-3267871272960*x^6-64 08053107200*x^5+670406720000*x ^4+1179708800000*x^3-429244800 000*x^2+56696000000*x-26800000 01 |
512*(2*x+5)^7*(5*x-1)^5*(70*x+ 67) |
0 | |||||
| AlgEquiv | 14336000000*x^13 |
512*(2*x+5)^7*(5*x-1)^5*(70*x+ 67) |
0 | |||||
| Trig functions | ||||||||
| AlgEquiv | cos(x) |
cos(-x) |
1 | |||||
| AlgEquiv | cos(x)^2+sin(x)^2 |
1 |
1 | |||||
| AlgEquiv | cos(x+y) |
cos(x)*cos(y)-sin(x)*sin(y) |
1 | |||||
| AlgEquiv | cos(x+y) |
cos(x)*cos(y)+sin(x)*sin(y) |
0 | |||||
| AlgEquiv | cos(x#pm#y) |
cos(x)*cos(y)-(#pm#sin(x)*sin( y)) |
1 | ATLogic_True. | ||||
| AlgEquiv | sin(x#pm#y) |
sin(x)*cos(y)#pm#cos(x)*sin(y) |
1 | ATLogic_True. | ||||
| AlgEquiv | sin(x#pm#y) |
cos(x)*sin(y)#pm#sin(x)*cos(y) |
0 | |||||
| AlgEquiv | 2*cos(x)^2-1 |
cos(2*x) |
1 | |||||
| AlgEquiv | 1.0*cos(1200*%pi*x) |
cos(1200*%pi*x) |
1 | |||||
| AlgEquiv | diff(tan(10*x)^2,x) |
cos(6*x) |
0 | |||||
| AlgEquiv | exp(%i*%pi) |
-1 |
1 | |||||
| AlgEquiv | 2*cos(2*x)+x+1 |
-sin(x)^2+3*cos(x)^2+x |
1 | |||||
| AlgEquiv | (2*sec(2*t)^2-2)/2 |
-(sin(4*t)^2-2*sin(4*t)+cos(4* t)^2-1)*(sin(4*t)^2+2*sin(4*t) +cos(4*t)^2-1)/(sin(4*t)^2+cos (4*t)^2+2*cos(4*t)+1)^2 |
1 | |||||
| AlgEquiv | 1+cosec(3*x) |
1+csc(3*x) |
1 | |||||
| AlgEquiv | 1/(1+exp(-2*x)) |
tanh(x)/2+1/2 |
1 | |||||
| AlgEquiv | 1+cosech(3*x) |
1+csch(3*x) |
1 | |||||
| AlgEquiv | -4*sec(4*z)^2*sin(6*z)-6*tan(4 *z)*cos(6*z) |
-4*sec(4*z)^2*sin(6*z)-6*tan(4 *z)*cos(6*z) |
1 | |||||
| AlgEquiv | -4*sec(4*z)^2*sin(6*z)-6*tan(4 *z)*cos(6*z) |
4*sec(4*z)^2*sin(6*z)+6*tan(4* z)*cos(6*z) |
0 | |||||
| AlgEquiv | csc(6*x)^2*(7*sin(6*x)*cos(7*x )-6*cos(6*x)*sin(7*x)) |
-(6*cos(6*x)*sin(7*x)-7*sin(6* x)*cos(7*x))/sin(6*x)^2 |
1 | |||||
| AlgEquiv | csc(6*x)^2*(7*sin(6*x)*cos(7*x )-6*cos(6*x)*sin(7*x)) |
(6*cos(6*x)*sin(7*x)-7*sin(6*x )*cos(7*x))/sin(6*x)^2 |
0 | |||||
| AlgEquiv | -(7*x^6+4*x^3)/sin(7*y+x^7+x^4 +1)^2 |
-(7*x^6+4*x^3)*csc(7*y+x^7+x^4 +1)^2 |
1 | |||||
| AlgEquiv | sin((2*%pi*n-%pi)/2) |
-cos(n*%pi) |
1 | |||||
| AlgEquiv | sin(x/2)/(1+tan(x)*tan(x/2)) |
sin(x/2)*cos(x) |
1 | |||||
| AlgEquiv | (declare(n,integer),trigrat(si n((2*%pi*n-%pi)/2))) |
-(-1)^n |
1 | |||||
| AlgEquiv | ! | cot(%pi/20)+cot(%pi/24)-cot(%p i/10) |
sqrt(1)+sqrt(2)+sqrt(3)+sqrt(4 )+sqrt(5)+sqrt(6) |
-3 | ||||
| AlgEquiv | trigeval(cot(%pi/20)+cot(%pi/2 4)-cot(%pi/10)) |
sqrt(1)+sqrt(2)+sqrt(3)+sqrt(4 )+sqrt(5)+sqrt(6) |
1 | |||||
| AlgEquiv | ! | sin([1/8,1/6, 1/4, 1/3, 1/2, 1 ]*%pi) |
[sqrt(2-sqrt(2))/2,1/2,1/sqrt( 2),sqrt(3)/2,1,0] |
-3 | The entries underlined in red below are those that are incorrect. \[\left[ {\color{red}{\underline{\sin \left( \frac{\pi}{8} \right)}}} , \frac{1}{2} , \frac{1}{\sqrt{2}} , \frac{\sqrt{3}}{2} , 1 , 0 \right] \] | (ATList_wrongentries 1). | ||
| AlgEquiv | trigeval(sin([1/8,1/6, 1/4, 1/ 3, 1/2, 1]*%pi)) |
[sqrt(2-sqrt(2))/2,1/2,1/sqrt( 2),sqrt(3)/2,1,0] |
1 | |||||
| AlgEquiv | 1+x |
taylor(1/(1-x),x,0,1) |
1 | |||||
| AlgEquiv | 1 |
taylor(1/(1-x),x,0,1) |
0 | |||||
| Logarithms | ||||||||
| AlgEquiv | log(a^2*b) |
2*log(a)+log(b) |
1 | |||||
| AlgEquiv | (2*log(2*x)+x)/(2*x) |
(log(2*x)+2)/(2*sqrt(x)) |
0 | |||||
| AlgEquiv | log(abs((x^2-9))) |
log(abs(x-3))+log(abs(x+3)) |
0 | |||||
| AlgEquiv | lg(10^x) |
x |
1 | |||||
| AlgEquiv | lg(3^x,3) |
x |
1 | |||||
| AlgEquiv | lg(a^x,a) |
x |
1 | |||||
| AlgEquiv | 1+lg(27,3) |
4 |
1 | |||||
| AlgEquiv | 1+lg(27,3) |
3 |
0 | |||||
| AlgEquiv | lg(1/8,2) |
-3 |
1 | |||||
| AlgEquiv | lg(root(x,n)) |
lg(x,10)/n |
1 | |||||
| AlgEquiv | log(root(x,n)) |
lg(x,10)/n |
0 | |||||
| AlgEquiv | x^log(y) |
y^log(x) |
1 | |||||
| Hyperbolic trig | ||||||||
| AlgEquiv | e^1-e^(-1) |
2*sinh(1) |
1 | |||||
| Lists | ||||||||
| AlgEquiv | x |
[1,2,3] |
0 | Your answer should be a list, but is not. Note that the syntax to enter a list is to enclose the comma separated values with square brackets. | ATAlgEquiv_SA_not_list. | |||
| AlgEquiv | [1,2] |
[1,2,3] |
0 | Your list should have \(3\) elements, but it actually has \(2\). | ATList_wronglen. | |||
| AlgEquiv | [1,2,4] |
[1,2,3] |
0 | The entries underlined in red below are those that are incorrect. \[\left[ 1 , 2 , {\color{red}{\underline{4}}} \right] \] | (ATList_wrongentries 3). | |||
| AlgEquiv | [1,x>2] |
[1,2<x] |
1 | |||||
| AlgEquiv | [1,2,[2-x<0,{1,2,2,2, 1,3}]
] |
[1,2,[2-x<0,{1,2}]] |
0 | The entries underlined in red below are those that are incorrect. \[\left[ 1 , 2 , \left[ 2-x < 0 , \left \{1 , 2 , 3 \right \} \right] \right] \] | (ATList_wrongentries 3: (ATList_wrongentries 2: ATSet_wrongsz)). | |||
| AlgEquiv | [(k+8)/(k^2+4*k-12),-(2*k+6)/( k^2+4*k-12)] |
[(k+8)/(k^2+4*k-12),-(2*k+6)/( k^2+4*k-12)] |
1 | |||||
| AlgEquiv | [1,2] |
ntuple(1,2) |
0 | Your answer should be an expression, not an equation, inequality, list, set or matrix. | ATAlgEquiv_SA_not_expression. | |||
| Rounding of floats | ||||||||
| AlgEquiv | round(0.5) |
0.0 |
1 | |||||
| AlgEquiv | round(1.5) |
2.0 |
1 | |||||
| AlgEquiv | round(2.5) |
2.0 |
1 | |||||
| AlgEquiv | round(12.5) |
12.0 |
1 | |||||
| AlgEquiv | significantfigures(0.5,1) |
0.5 |
1 | |||||
| AlgEquiv | significantfigures(1.5,1) |
2.0 |
1 | |||||
| AlgEquiv | significantfigures(2.5,1) |
3.0 |
1 | |||||
| AlgEquiv | significantfigures(3.5,1) |
4.0 |
1 | |||||
| AlgEquiv | significantfigures(11.5,2) |
12.0 |
1 | |||||
| AlgEquiv | 1500 |
scientific_notation(1500,3) |
1 | |||||
| AlgEquiv | 1500 |
displaysci(1.5,2,3) |
1 | |||||
| AlgEquiv | [3,3.1,3.14,3.142,3.1416,3.141 59,3.141593,3.1415927] |
makelist(significantfigures(%p i,i),i,8) |
1 | |||||
| Sets | ||||||||
| AlgEquiv | x |
{1,2,3} |
0 | Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets. | ATAlgEquiv_SA_not_set. | |||
| AlgEquiv | co(1,2) |
{1,2,3} |
0 | Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets. | ATAlgEquiv_SA_not_set. | |||
| AlgEquiv | {1,2} |
{1,2,3} |
0 | Your set should have \(3\) different elements, but it actually has \(2\). | ATSet_wrongsz. | |||
| AlgEquiv | {2/4, 1/3} |
{1/2, 1/3} |
1 | |||||
| AlgEquiv | {A[1],A[2],A[4]} |
{A[1],A[2],A[3]} |
0 | The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{A_{4} \right \}\] | ATSet_wrongentries. | |||
| AlgEquiv | {A[1],A[2],A[3]} |
{A[1],A[2],A[3]} |
1 | |||||
| AlgEquiv | {1,2,4} |
{1,2,3} |
0 | The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{4 \right \}\] | ATSet_wrongentries. | |||
| AlgEquiv | {1,x>4} |
{4<x, 1} |
1 | |||||
| AlgEquiv | {x-1=0,x>1 and 5>x} |
{x>1 and x<5,x=1} |
1 | |||||
| AlgEquiv | {x-1=0,x>1 and 5>x} |
{x>1 and x<5,x=2} |
0 | The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{x-1=0 \right \}\] | ATSet_wrongentries. | |||
| AlgEquiv | {x-1=0,x>1 and 5>x} |
{x>1 and x<3,x=1} |
0 | The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{5-x > 0\,{\mbox{ and }}\, x-1 > 0 \right \}\] | ATSet_wrongentries. | |||
| Equivalence for elements of sets is different from expressions: see docs. | ||||||||
| AlgEquiv | ! | {-sqrt(2)/sqrt(3)} |
{-2/sqrt(6)} |
-3 | The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{-\frac{\sqrt{2}}{\sqrt{3}} \right \}\] | ATSet_wrongentries. | ||
| AlgEquiv | ! | {[-sqrt(2)/sqrt(3),0],[2/sqrt(
6),0]} |
{[2/sqrt(6),0],[-2/sqrt(6),0]} |
-3 | The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{\left[ -\frac{\sqrt{2}}{\sqrt{3}} , 0 \right] \right \}\] | ATSet_wrongentries. | ||
| AlgEquiv | ev(radcan({-sqrt(2)/sqrt(3)}),
simp) |
ev(radcan({-2/sqrt(6)}),simp) |
1 | |||||
| AlgEquiv | ev(radcan(ratsimp({(-sqrt(10)/
2)-2,sqrt(10)/2-2},algebraic:t
rue)),simp) |
ev(radcan(ratsimp({(-sqrt(5)/s
qrt(2))-2,sqrt(5)/sqrt(2)-2},a
lgebraic:true)),simp) |
1 | |||||
| AlgEquiv | {(2-2^(5/2))/2,(2^(5/2)+2)/2} |
{1-2^(3/2),2^(3/2)+1} |
0 | The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{\frac{2-2^{\frac{5}{2}}}{2} , \frac{2^{\frac{5}{2}}+2}{2} \right \}\] | ATSet_wrongentries. | |||
| AlgEquiv | ev(radcan({(2-2^(5/2))/2,(2^(5
/2)+2)/2}),simp) |
{1-2^(3/2),2^(3/2)+1} |
1 | |||||
| AlgEquiv | {(x-a)^6000} |
{(a-x)^6000} |
0 | The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{{\left(x-a\right)}^{6000} \right \}\] | ATSet_wrongentries. | |||
| AlgEquiv | {(k+8)/(k^2+4*k-12),-(2*k+6)/(
k^2+4*k-12)} |
{(k+8)/(k^2+4*k-12),-(2*k+6)/(
k^2+4*k-12)} |
1 | |||||
| Matrices | ||||||||
| AlgEquiv | matrix([1,2],[2,3]) |
matrix([1,2],[2,3]) |
1 | |||||
| AlgEquiv | matrix([1,2],[2,3]) |
matrix([1,2,3],[2,3,3]) |
0 | Your matrix should be \(2\) by \(3\), but it is actually \(2\) by \(2\). | ATMatrix_wrongsz_columns. | |||
| AlgEquiv | matrix([1,2],[2,3]) |
matrix([1,2],[2,5]) |
0 | The entries underlined in red below are those that are incorrect. \[ \left[\begin{array}{cc} 1 & 2 \\ 2 & {\color{red}{\underline{3}}} \end{array}\right]\] | ATMatrix_wrongentries. | |||
| AlgEquiv | matrix([0.33,1],[1,1]) |
matrix([0.333,1],[1,1]) |
0 | The entries underlined in red below are those that are incorrect. \[ \left[\begin{array}{cc} {\color{red}{\underline{0.33}}} & 1 \\ 1 & 1 \end{array}\right]\] | ATMatrix_wrongentries. | |||
| AlgEquiv | matrix([x+x,2],[2,x*x]) |
matrix([2*x,2],[2,x^2]) |
1 | |||||
| AlgEquiv | matrix([epsilon[0],2],[2,x^2]) |
matrix([epsilon[0],2],[2,x^2]) |
1 | |||||
| AlgEquiv | matrix([epsilon[2],2],[2,x^2]) |
matrix([epsilon[0],2],[2,x^3]) |
0 | The entries underlined in red below are those that are incorrect. \[ \left[\begin{array}{cc} {\color{red}{\underline{\varepsilon_{2}}}} & 2 \\ 2 & {\color{red}{\underline{x^2}}} \end{array}\right]\] | ATMatrix_wrongentries. | |||
| AlgEquiv | matrix([x>4,{1,x^2}],[[1,2]
,[1,3]]) |
matrix([4-x<0,{x^2, 1}],[[1
,2],[1,3]]) |
1 | |||||
| AlgEquiv | matrix([x>4,{1,x^2}],[[1,2]
,[1,3]]) |
matrix([4-x<0,{x^2, 1}],[[1
,2],[1,4]]) |
0 | The entries underlined in red below are those that are incorrect. \[ \left[\begin{array}{cc} x > 4 & \left \{1 , x^2 \right \} \\ \left[ 1 , 2 \right] & \left[ 1 , {\color{red}{\underline{3}}} \right] \end{array}\right]\] | ATMatrix_wrongentries. | |||
| Vectors | ||||||||
| AlgEquiv | a |
stackvector(a) |
0 | |||||
| Equations | ||||||||
| AlgEquiv | 1 |
x=1 |
0 | Your answer should be an equation, but is not. | ATAlgEquiv_SA_not_equation. | |||
| AlgEquiv | x=1 |
x=1 |
1 | ATEquation_sides | ||||
| AlgEquiv | 1=x |
1=x |
1 | ATEquation_sides | ||||
| AlgEquiv | 1=x |
x=1 |
1 | ATEquation_sides_op | ||||
| AlgEquiv | 1=1 |
1=x |
0 | ATEquation_default | ||||
| AlgEquiv | 1=1 |
x=1 |
0 | ATEquation_default | ||||
| AlgEquiv | x=2 |
x=1 |
0 | ATEquation_lhs_notrhs | ||||
| AlgEquiv | 2=x |
x=1 |
0 | ATEquation_default | ||||
| AlgEquiv | x=x |
y=y |
1 | ATEquation_zero | ||||
| AlgEquiv | x+y=1 |
y=1-x |
1 | |||||
| AlgEquiv | 2*x+2*y=1 |
y=0.5-x |
1 | ATEquation_ratio | ||||
| AlgEquiv | 1/x+1/y=2 |
y = x/(2*x-1) |
1 | ATEquation_ratio | ||||
| AlgEquiv | y=sin(2*x) |
y/2=cos(x)*sin(x) |
1 | ATEquation_ratio | ||||
| AlgEquiv | y=(x-a)^6000 |
y=(x-a)^6000 |
1 | ATEquation_sides | ||||
| AlgEquiv | y=(x-a)^5999 |
y=(x-a)^6000 |
0 | ATEquation_lhs_notrhs | ||||
| AlgEquiv | y=(a-x)^6000 |
y=(x-a)^6000 |
1 | ATEquation_sides | ||||
| AlgEquiv | y=(a-x)^5999 |
y=(x-a)^5999 |
0 | ATEquation_lhs_notrhs | ||||
| AlgEquiv | y=(a-x)^59999 |
y=(x-a)^5999 |
0 | ATEquation_lhs_notrhs | ||||
| AlgEquiv | x+y=i |
y=i-x |
1 | |||||
| AlgEquiv | (1+%i)*(x+y)=0 |
y=-x |
1 | |||||
| AlgEquiv | s^2*%e^(s*t)=0 |
s^2=0 |
0 | ATEquation_default | ||||
| AlgEquiv | 0=-x+y/A+(y-z)/B |
0=x-y/A-(y-z)/B |
1 | |||||
| AlgEquiv | x^6000-x^6001=x^5999 |
x^5999*(1-x+x^2)=0 |
1 | ATEquation_ratio | ||||
| AlgEquiv | x^6000-x^6001=x^5999 |
x^5999*(1-x+x^3)=0 |
0 | ATEquation_default | ||||
| AlgEquiv | 258552*x^7*(81*x^8+1)^398 |
x^3*(x^4+1)^399 |
0 | |||||
| AlgEquiv | Ia*(R1+R2+R3)-Ib*R3=0 |
-Ia*(R1+R2+R3)+Ib*R3=0 |
1 | |||||
| AlgEquiv | a=0 or b=0 |
a*b=0 |
1 | ATEquation_sides | ||||
| AlgEquiv | a*b=0 |
a=0 or b=0 |
1 | ATEquation_sides | ||||
| AlgEquiv | a*x=a*y |
x=y |
0 | ATEquation_default | ||||
| AlgEquiv | a*x=a*y |
a=0 or x=y |
1 | ATEquation_ratio | ||||
| Unary Equations | ||||||||
| AlgEquiv | 1 |
stackeq(1) |
1 | |||||
| AlgEquiv | stackeq(1) |
1 |
1 | |||||
| AlgEquiv | stackeq(1) |
0 |
0 | |||||
| Equations: Loose/gain roots with nth powers of each side. | ||||||||
| AlgEquiv | x=y |
x^2=y^2 |
0 | ATEquation_default | ||||
| AlgEquiv | (x-2)^2=0 |
x=2 |
0 | ATEquation_default | ||||
| AlgEquiv | 4*x^2-71*x+220 = 0 or 14*x^2-9 1*x+140 = 0 |
x = 5/2 or x = 4 or x = 55/4 |
0 | ATEquation_default | ||||
| AlgEquiv | 4*x^2-71*x+220 = 0 or 14*x^2-9 1*x+140 = 0 |
x = 5/2 or x = 4 or x=4 or x = 55/4 |
1 | ATEquation_sides | ||||
| AlgEquiv | x^2=4 |
x=2 or x=-2 |
1 | ATEquation_ratio | ||||
| AlgEquiv | a^3*b^3=0 |
a=0 or b=0 |
0 | ATEquation_default | ||||
| AlgEquiv | a^3*b^3=0 |
a*b=0 |
0 | ATEquation_default | ||||
| AlgEquiv | (x-y)*(x+y)=0 |
x^2=y^2 |
1 | ATEquation_ratio | ||||
| AlgEquiv | x=1 |
(x-1)^3=0 |
0 | ATEquation_default | ||||
| AlgEquiv | sqrt(x)=sqrt(y) |
x=y |
0 | ATEquation_default | ||||
| AlgEquiv | x=sqrt(a) |
x^2=a |
0 | ATEquation_default | ||||
| AlgEquiv | (x-sqrt(a))*(x+sqrt(a))=0 |
x^2=a |
1 | ATEquation_ratio | ||||
| AlgEquiv | (x-%i*sqrt(a))*(x+%i*sqrt(a))= 0 |
x^2=-a |
1 | ATEquation_ratio | ||||
| AlgEquiv | (x-%i*sqrt(abs(a)))*(x+%i*sqrt (abs(a)))=0 |
x^2=-abs(a) |
1 | ATEquation_ratio | ||||
| AlgEquiv | y=sqrt(1-x^2) |
x^2+y^2=1 |
0 | ATEquation_default | ||||
| AlgEquiv | (y-sqrt(1-x^2))*(y+sqrt(1-x^2) )=0 |
x^2+y^2=1 |
1 | ATEquation_ratio | ||||
| AlgEquiv | (y-sqrt((1-x)*(1+x)))*(y+sqrt( (1-x)*(1+x)))=0 |
x^2+y^2=1 |
1 | ATEquation_ratio | ||||
| AlgEquiv | (x-1)*(x+1)*(y-1)*(y+1)=0 |
y^2+x^2=1+x^2*y^2 |
1 | ATEquation_ratio | ||||
| Equations: edge cases. Teacher must enter an equation, all or none here. | ||||||||
| AlgEquiv | all |
x=x |
1 | ATEquation_zero | ||||
| AlgEquiv | true |
x=x |
1 | ATEquation_zero | ||||
| AlgEquiv | x=x |
all |
1 | ATEquation_zero | ||||
| AlgEquiv | all |
all |
1 | ATEquation_zero | ||||
| AlgEquiv | true |
all |
1 | ATEquation_zero | ||||
| AlgEquiv | a=a |
x=x |
1 | ATEquation_zero | ||||
| AlgEquiv | false |
x=x |
0 | ATEquation_zero_fail | ||||
| AlgEquiv | false |
all |
0 | ATEquation_zero_fail | ||||
| AlgEquiv | none |
all |
0 | ATEquation_zero_fail | ||||
| AlgEquiv | all |
none |
0 | ATEquation_empty_fail | ||||
| AlgEquiv | 2=3 |
1=4 |
1 | ATEquation_empty | ||||
| AlgEquiv | none |
1=2 |
1 | ATEquation_empty | ||||
| AlgEquiv | false |
1=2 |
1 | ATEquation_empty | ||||
| AlgEquiv | none |
none |
1 | ATEquation_empty | ||||
| AlgEquiv | false |
none |
1 | ATEquation_empty | ||||
| AlgEquiv | 3=0 |
none |
1 | ATEquation_empty | ||||
| AlgEquiv | 0=3 |
none |
1 | ATEquation_empty | ||||
| AlgEquiv | all |
1=2 |
0 | ATEquation_empty_fail | ||||
| AlgEquiv | true |
1=2 |
0 | ATEquation_empty_fail | ||||
| AlgEquiv | {} |
1=2 |
0 | Your answer should be an equation, but is not. | ATAlgEquiv_SA_not_equation. | |||
| AlgEquiv | [] |
1=2 |
0 | Your answer should be an equation, but is not. | ATAlgEquiv_SA_not_equation. | |||
| AlgEquiv | {} |
none |
0 | Your answer should be an equation, inequality or a logical combination of many of these, but is not. | ATAlgEquiv_SA_not_logic. | |||
| Sets of real numbers | ||||||||
| AlgEquiv | x^2 |
cc(1,3) |
0 | Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals. | ATAlgEquiv_SA_not_realset. | |||
| AlgEquiv | %union(oo(1,2),oo(3,4)) |
%union(oo(1,2),oo(3,4)) |
1 | ATRealSet_true. | ||||
| AlgEquiv | %union(oc(1,2),co(2,3)) |
oo(1,3) |
1 | ATRealSet_true. | ||||
| AlgEquiv | %union(oc(1,2),co(2,3)) |
cc(1,3) |
0 | ATRealSet_false. | ||||
| AlgEquiv | {-1,1} |
%union({-1,1}) |
1 | ATRealSet_true. | ||||
| AlgEquiv | {1,3} |
cc(1,3) |
0 | ATRealSet_false. | ||||
| AlgEquiv | %intersection(oc(-1,1),co(1,2) ) |
%union({1}) |
1 | ATRealSet_true. | ||||
| AlgEquiv | oo(-inf,1) |
oo(-inf,1) |
1 | ATRealSet_true. | ||||
| AlgEquiv | oo(-1,inf) |
oo(0,inf) |
0 | ATRealSet_false. | ||||
| AlgEquiv | %union(oc(-inf,0),oo(-1,4)) |
oo(-inf,4) |
1 | ATRealSet_true. | ||||
| AlgEquiv | %union(oo(-inf,1),oo(-1,inf)) |
oo(-inf,inf) |
1 | ATRealSet_true. | ||||
| AlgEquiv | all |
oo(-inf,inf) |
1 | ATRealSet_true. | ||||
| AlgEquiv | co(1,2) |
1 <= x nounand x<2 |
0 | Your answer should be an equation, inequality or a logical combination of many of these, but is not. | ATAlgEquiv_SA_not_logic. | |||
| AlgEquiv | 1 <= x nounand x<2 |
co(1,2) |
0 | Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals. | ATAlgEquiv_SA_not_realset. | |||
| AlgEquiv | minf <= x |
co(minf,inf) |
0 | Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals. | ATAlgEquiv_SA_not_realset. | |||
| AlgEquiv | -inf <= x |
co(minf,inf) |
0 | Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals. | ATAlgEquiv_SA_not_realset. | |||
| AlgEquiv | x <= inf |
oc(minf,inf) |
0 | Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals. | ATAlgEquiv_SA_not_realset. | |||
| AlgEquiv | minf <= x |
oo(minf,inf) |
0 | Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals. | ATAlgEquiv_SA_not_realset. | |||
| AlgEquiv | single_variable_solver_real(mi nf <= x) |
co(minf,inf) |
1 | ATRealSet_true. | ||||
| AlgEquiv | single_variable_solver_real(-i nf <= x) |
co(minf,inf) |
1 | ATRealSet_true. | ||||
| AlgEquiv | single_variable_solver_real(x <= inf) |
oc(minf,inf) |
1 | ATRealSet_true. | ||||
| AlgEquiv | single_variable_solver_real(mi nf <= x) |
oo(minf,inf) |
0 | ATRealSet_false. | ||||
| Complex numbers | ||||||||
| AlgEquiv | a=b/%i |
%i*a=b |
1 | ATEquation_num_i | ||||
| AlgEquiv | b/%i=a |
%i*a=b |
1 | ATEquation_num_i | ||||
| AlgEquiv | b=a/%i |
%i*a=b |
0 | ATEquation_lhs_notrhs_op | ||||
| AlgEquiv | a*(2+%i)=b |
a=b/(2+%i) |
1 | ATEquation_ratio | ||||
| AlgEquiv | a*(2+%i)=b |
a=b*(2-%i)/5 |
1 | ATEquation_num_i | ||||
| AlgEquiv | a*(2+%i)=b |
a=b*(2-%i)/4 |
0 | ATEquation_default | ||||
| AlgEquiv | i |
disp_complex(0,1) |
0 | |||||
| Absolute value in equations | ||||||||
| AlgEquiv | abs(x)=abs(y) |
x=y |
0 | ATEquation_default | ||||
| AlgEquiv | abs(x)=abs(y) |
x=y or x=-y |
1 | |||||
| AlgEquiv | abs(x)=abs(y) |
(x-y)*(x+y)=0 |
1 | |||||
| Functions | ||||||||
| AlgEquiv | f(x):=1/0 |
f(x):=x^2 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | TEST_FAILED | ||
| AlgEquiv | 1 |
f(x):=x^2 |
0 | Your answer should be a function, defined using the operator :=, but is not. | ATAlgEquiv_SA_not_function. | |||
| AlgEquiv | f(x)=x^2 |
f(x):=x^2 |
0 | Your answer should be a function, defined using the operator :=, but is not. | ATAlgEquiv_SA_not_function. | |||
| AlgEquiv | f(x):=x^2 |
f(x,y):=x^2+y^2 |
0 | ATFunction_length_args. ATFunction_false. | ||||
| AlgEquiv | f(x):=x^2 |
f(x)=x^2 |
0 | Your answer should be an equation, but is not. | ATAlgEquiv_SA_not_equation. | |||
| AlgEquiv | f(x):=x^2 |
f(x):=x^2 |
1 | ATFunction_true. | ||||
| AlgEquiv | f(x):=x^2 |
f(x):=sin(x) |
0 | ATFunction_false. | ||||
| AlgEquiv | g(x):=x^2 |
f(x):=x^2 |
0 | ATFunction_wrongname. ATFunction_true. | ||||
| AlgEquiv | f(y):=y^2 |
f(x):=x^2 |
1 | ATFunction_arguments_different. ATFunction_true. | ||||
| AlgEquiv | f(a,b):=a^2+b^2 |
f(x,y):=x^2+y^2 |
1 | ATFunction_arguments_different. ATFunction_true. | ||||
| Inequalities | ||||||||
| AlgEquiv | 1 |
x>1 |
0 | Your answer should be an inequality, but is not. | ATAlgEquiv_SA_not_inequality. | |||
| AlgEquiv | x=1 |
x>1 and x<5 |
0 | You have entered an equation, but an equation is not expected here. You may have typed something like "y=2*x+1" when you only needed to type "2*x+1". | ATAlgEquiv_TA_not_equation. | |||
| AlgEquiv | x<1 |
x>1 |
0 | Your inequality appears to be backwards. | ATInequality_backwards. | |||
| AlgEquiv | 1<x |
x>1 |
1 | |||||
| AlgEquiv | a<b |
b>a |
1 | |||||
| AlgEquiv | 2<2*x |
x>1 |
1 | |||||
| AlgEquiv | -2>-2*x |
x>1 |
1 | |||||
| AlgEquiv | x>1 |
x<=1 |
0 | Your inequality should not be strict! Your inequality appears to be backwards. | ATInequality_strict. ATInequality_backwards. | |||
| AlgEquiv | x>=2 |
x<2 |
0 | Your inequality should be strict, but is not! Your inequality appears to be backwards. | ATInequality_nonstrict. ATInequality_backwards. | |||
| AlgEquiv | x>=1 |
x>2 |
0 | Your inequality should be strict, but is not! | ATInequality_nonstrict. | |||
| AlgEquiv | x>1 |
x>1 |
1 | |||||
| AlgEquiv | x>=1 |
x>=1 |
1 | |||||
| AlgEquiv | x>2 |
x>1 |
0 | |||||
| AlgEquiv | 1<x |
x>1 |
1 | |||||
| AlgEquiv | 2*x>=x^2 |
x^2<=2*x |
1 | |||||
| AlgEquiv | 2*x>=x^2 |
x^2<=2*x |
1 | |||||
| AlgEquiv | 3*x^2<9*a |
x^2-3*a<0 |
1 | |||||
| AlgEquiv | x^2>4 |
x>2 or x<-2 |
1 | ATLogic_True. | ||||
| AlgEquiv | 1<x or x<-3 |
x<-3 or 1<x |
1 | ATLogic_True. | ||||
| AlgEquiv | 1<x or x<-3 |
x<-1 or 3<x |
0 | |||||
| AlgEquiv | x>1 and x<5 |
x>1 and x<5 |
1 | ATLogic_True. | ||||
| AlgEquiv | x>1 and x<5 |
5>x and 1<x |
1 | ATLogic_True. | ||||
| AlgEquiv | not (x<=2 and -2<=x) |
x>2 or -2>x |
1 | ATLogic_True. | ||||
| AlgEquiv | x>2 or -2>x |
not (x<=2 and -2<=x) |
1 | ATLogic_True. | ||||
| AlgEquiv | x>=1 or 1<=x |
x>=1 |
1 | |||||
| AlgEquiv | x>=1 and x<=1 |
x=1 |
1 | ATInequality_solver. | ||||
| AlgEquiv | (x>4 and x<5) or (x<- 4 and x>-5) or (x+5>0 an d x<-4) |
(x>-5 and x<-4) or (x> ;4 and x<5) |
1 | ATLogic_True. | ||||
| AlgEquiv | (x>4 and x<5) or (x<- 4 and x>-5) or (x+5>0 an d x<-4) |
(x>-5 and x<-4) or (x> ;8 and x<5) |
0 | |||||
| AlgEquiv | (x < 0 nounor x >= 1) no unand x <= 3 |
x < 0 or (x >= 1 and x & lt;= 3) |
1 | ATLogic_True. | ||||
| AlgEquiv | (x < 0 nounor x >= 1) no unand x <= 3 |
x < 0 or x >= 1 and x &l t;= 3 |
1 | ATLogic_True. | ||||
| AlgEquiv | (x < 0 nounor x >= 1) no unand x <= 3 |
x < 0 or (x >= 1 and x & lt;= 3) |
1 | ATLogic_True. | ||||
| AlgEquiv | (x < 0 nounor x >= 1) no unand x <= 3 |
(x < 0 or x >= 1) and x <= 3 |
1 | ATLogic_True. | ||||
| AlgEquiv | (x < 0 nounor x >= 1) no unand x <= 3 |
x < 0 or (x >= 1 and x & lt;= 3) |
1 | ATLogic_True. | ||||
| AlgEquiv | natural_domain(1/x^2) |
natural_domain(1/x) |
1 | ATRealSet_true. | ||||
| AlgEquiv | x^4>=0 |
x^2>=0 |
1 | |||||
| AlgEquiv | x^4>=16 |
x^2>=4 |
1 | |||||
| AlgEquiv | x^4>=16 |
x^2>=4 |
1 | |||||
| AlgEquiv | -3<=x |
-3<=x nounand x<=3 |
0 | |||||
| AlgEquiv | {2,-2} |
x>2 nounor -2>x |
0 | Your answer should be an equation, inequality or a logical combination of many of these, but is not. | ATAlgEquiv_SA_not_logic. | |||
| AlgEquiv | x^2<4 |
x<2 nounand x>-2 |
1 | ATLogic_Solver_True. | ||||
| AlgEquiv | x^2<6 |
x<2 nounand x>-2 |
0 | |||||
| AlgEquiv | x>1 nounand x<-1 |
false |
1 | ATLogic_Solver_True. | ||||
| AlgEquiv | x>1 nounand x<3 |
true |
0 | |||||
| AlgEquiv | x>1 nounor x<3 |
true |
1 | ATLogic_Solver_True. | ||||
| AlgEquiv | x>1 nounor x<3 |
all |
1 | ATLogic_Solver_True. | ||||
| AlgEquiv | abs(x)<1 |
abs(x)<1 |
1 | |||||
| AlgEquiv | abs(x)<1 |
abs(x)<2 |
0 | |||||
| AlgEquiv | abs(x)<1 |
abs(x)>1 |
0 | Your inequality appears to be backwards. | ATInequality_backwards. | |||
| AlgEquiv | ! | abs(x)<2 |
-2<x and x<2 |
-3 | ||||
| AlgEquiv | ! | -2<x and x<2 |
abs(x)<2 |
-3 | ||||
| AlgEquiv | abs(x)<2 |
-1<x and x<1 |
0 | |||||
| AlgEquiv | x^2<=9 |
abs(x)<3 |
0 | |||||
| AlgEquiv | ! | x^2<=9 |
abs(x)<=3 |
-3 | ||||
| AlgEquiv | ! | x^6<1 |
abs(x)<1 |
-3 | ||||
| AlgEquiv | ! | abs(x)>1 |
x<-1 or x>1 |
-3 | ||||
| AlgEquiv | minf < x |
minf <= x |
0 | Your inequality should not be strict! | ATInequality_strict. | |||
| AlgEquiv | x>minf |
minf < x |
1 | |||||
| AlgEquiv | x>-inf |
minf < x |
1 | |||||
| AlgEquiv | x<2*inf |
x<inf |
0 | |||||
| AlgEquiv | minf < x nounand x <1 |
x<1 |
1 | |||||
| AlgEquiv | minf < x nounand x <1 |
x<2 |
0 | |||||
| Maxima and infinity | ||||||||
| AlgEquiv | 2*inf |
inf |
0 | |||||
| AlgEquiv | -inf |
minf |
0 | |||||
| Not equal to | ||||||||
| AlgEquiv | x#1 |
x#1 |
1 | ATLogic_True. | ||||
| AlgEquiv | x#(1+1) |
x#2 |
1 | ATLogic_True. | ||||
| AlgEquiv | 1#x |
x#1 |
1 | ATLogic_True. | ||||
| AlgEquiv | x#2 |
x-2#0 |
1 | ATLogic_True. | ||||
| AlgEquiv | [x#2] |
[x-2#0] |
1 | |||||
| AlgEquiv | x-3#0 |
x#2 |
0 | |||||
| AlgEquiv | x#2 |
x<2 nounor x>2 |
1 | ATLogic_Solver_True. | ||||
| AlgEquiv | x^2-3#1 |
x<-2 nounor (x<-2 and x& lt;2) nounor 2<x |
0 | |||||
| AlgEquiv | x^2-3#1 |
x<-2 nounor (-2<x and x& lt;2) nounor 2<x |
1 | ATLogic_Solver_True. | ||||
| AlgEquiv | x#1 |
x#0 |
0 | |||||
| Surds | ||||||||
| AlgEquiv | sqrt(12) |
2*sqrt(3) |
1 | |||||
| AlgEquiv | sqrt(11+6*sqrt(2)) |
3+sqrt(2) |
1 | |||||
| AlgEquiv | (19601-13860*sqrt(2))^(7/4) |
(5*sqrt(2)-7)^7 |
1 | |||||
| AlgEquiv | (19601-13861*sqrt(2))^(7/4) |
(5*sqrt(2)-7)^7 |
0 | |||||
| AlgEquiv | (19601-13861*sqrt(2))^(7/4) |
(5*sqrt(2)-7)^7 |
0 | |||||
| AlgEquiv | sqrt(2*log(26)+4-2*log(2)) |
sqrt(2*log(13)+4) |
1 | |||||
| AlgEquiv | sqrt(2)*sqrt(3)+2*(sqrt(2/3))* x-(2/3)*(sqrt(2/3))*x^2+(4/9)* (sqrt(2/3))*x^3 |
4*sqrt(6)*x^3/27-(2*sqrt(6)*x^ 2)/9+(2*sqrt(6)*x)/3+sqrt(6) |
1 | |||||
| Factorials and binomials | ||||||||
| AlgEquiv | (n+1)*n! |
(n+1)! |
1 | |||||
| AlgEquiv | n/n! |
1/(n-1)! |
1 | |||||
| AlgEquiv | n/n! |
1/(n+1)! |
0 | |||||
| AlgEquiv | n!/(k!*(n-k)!) |
binomial(n,k) |
1 | |||||
| AlgEquiv | ! | binomial(n,k)+binomial(n,k+1) |
binomial(n+1,k+1) |
-3 | ||||
| AlgEquiv | binomial(n,k)+binomial(n,k+1) |
binomial(n+1,k) |
0 | |||||
| AlgEquiv | binomial(n,k) |
binomial(n,n-k) |
1 | |||||
| AlgEquiv | 175!*56!/(55!*176!) |
17556/55176 |
1 | |||||
| Unevaluated derviatives | ||||||||
| AlgEquiv | 3*s*diff(q(s),s) |
3*s*diff(q(s),s) |
1 | |||||
| Sums and products | ||||||||
| AlgEquiv | sum(k^n,n,0,3) |
sum(k^n,n,0,3) |
1 | |||||
| AlgEquiv | 1+k+k^2+k^3 |
sum(k^n,n,0,3) |
1 | |||||
| AlgEquiv | 1+k+k^2 |
sum(k^n,n,0,3) |
0 | |||||
| AlgEquiv | n*(n+1)*(2*n+1)/6 |
sum(k^2,k,1,n) |
1 | |||||
| AlgEquiv | sum((k+1)^2,k,0,n-1) |
sum(k^2,k,1,n) |
1 | |||||
| AlgEquiv | product(cos(k*x),k,1,3) |
product(cos(k*x),k,1,3) |
1 | |||||
| AlgEquiv | cos(x)*cos(2*x)*cos(3*x) |
product(cos(k*x),k,1,3) |
1 | |||||
| AlgEquiv | cos(x)*cos(2*x) |
product(cos(k*x),k,1,3) |
0 | |||||
| Scientific units are ignored | ||||||||
| AlgEquiv | 9.81*m/s^2 |
stackunits(9.81,m/s^2) |
1 | |||||
| AlgEquiv | 6*stackunits(1,m) |
stackunits(6,m) |
1 | |||||
| AlgEquiv | stackunits(2,m)^2 |
stackunits(4,m^2) |
1 | |||||
| AlgEquiv | stackunits(2,s)^2 |
stackunits(4,m^2) |
0 | |||||
| Maxima does not simplify -inf (I agree!) | ||||||||
| AlgEquiv | -inf |
minf |
0 | |||||
| These currently fail | ||||||||
| AlgEquiv | ! | 2/%i*ln(sqrt((1+z)/2)+%i*sqrt( (1-z)/2)) |
-%i*ln(z+%i*sqrt(1-z^2)) |
-3 | ||||
| AlgEquiv | ! | abs(x^2-4)/(abs(x-2)*abs(x+2)) |
1 |
-3 | ||||
| AlgEquiv | ! | abs(x^2-4) |
abs(x-2)*abs(x+2) |
-3 | ||||
| AlgEquiv | ! | (-1)^n*cos(x)^n |
(-cos(x))^n |
-3 | ||||
| AlgEquiv | ! | (sqrt(108)+10)^(1/3)-(sqrt(108 )-10)^(1/3) |
2 |
-3 | ||||
| AlgEquiv | ! | (sqrt(2+sqrt(2))+sqrt(2-sqrt(2 )))/(2*sqrt(2)) |
sqrt(sqrt(2)+2)/2 |
-3 | ||||
| AlgEquiv | ! | sqrt(2*x*sqrt(x^2+1)+2*x^2+1)- sqrt(x^2+1)-x |
0 |
-3 | ||||
| AlgEquiv | ! | (77+20*sqrt(13))^(1/6)-(77-20* sqrt(13))^(1/6) |
1 |
-3 | ||||
| AlgEquiv | ! | (930249+416020*sqrt(5))^(1/30) -(930249-416020*sqrt(5))^(1/30 ) |
1 |
-3 | ||||
| AlgEquiv | ! | cos(2*%pi/17) |
(-1+sqrt(17)+sqrt(34-2*sqrt(17 )))/16+(2*sqrt(17+3*sqrt(17)-s qrt(34-2*sqrt(17))-2*sqrt(34+2 *sqrt(17))))/16 |
-3 | ||||
| AlgEquiv | ! | (41-sqrt(511))/2 |
(sqrt((4*(cos((1/2*(acos((61/1 040*sqrt(130)))-atan(11/3))))) ^(2))+21)-(2*cos((1/2*(acos((6 1/1040*sqrt(130)))-atan(11 / 3 ))))))^(2) |
-3 | ||||
| AlgEquiv | ! | a*(1+sqrt(2))=b |
a=b*(sqrt(2)-1)/3 |
-3 | ATEquation_default | |||
| This is only equivalent for x>=0... | ||||||||
| AlgEquiv | ! | atan(1/2) |
%pi/2-atan(2) |
-3 | ||||
| This is true for all x... | ||||||||
| AlgEquiv | ! | asinh(x) |
ln(x+sqrt(x^2+1)) |
-3 | ||||
| Logical expressions | ||||||||
| AlgEquiv | true and false |
false |
1 | ATLogic_True. | ||||
| AlgEquiv | true or false |
false |
0 | |||||
| AlgEquiv | A and B |
B and A |
1 | ATLogic_True. | ||||
| AlgEquiv | A and B |
C and A |
0 | |||||
| AlgEquiv | A and B=C |
C=B and A |
1 | ATLogic_True. | ||||
| AlgEquiv | A and (B and C) |
A and B and C |
1 | ATLogic_True. | ||||
| AlgEquiv | A and (B or C) |
A and (B or C) |
1 | ATLogic_True. | ||||
| AlgEquiv | (A and B) or (A and C) |
A and (B or C) |
1 | ATLogic_True. | ||||
| AlgEquiv | -(b#pm#sqrt(b^2-4*a*c)) |
-b#pm#sqrt(b^2-4*a*c) |
1 | ATLogic_True. | ||||
| AlgEquiv | x=-b#pm#c^2 |
x=c^2-b or x=-c^2-b |
1 | ATLogic_True. | ||||
| AlgEquiv | x#pm#a = y#pm#b |
x#pm#a = y#pm#b |
1 | ATEquation_sides | ||||
| AlgEquiv | x#pm#a = y#pm#b |
x#pm#a = y#pm#c |
0 | ATEquation_lhs_notrhs | ||||
| AlgEquiv | not(A) and not(B) |
not(A or B) |
1 | ATLogic_True. | ||||
| AlgEquiv | not(A) and not(B) |
not(A and B) |
0 | |||||
| AlgEquiv | not(A) or B |
boolean_form(A implies B) |
1 | |||||
| AlgEquiv | not(A) or B |
A implies B |
1 | ATLogic_True. | ||||
| AlgEquiv | not(A) and B |
A implies B |
0 | |||||
| AlgEquiv | (not A and B) or (not B and A) |
A xor B |
1 | ATLogic_True. | ||||
| AlgEquiv | (A and B) or (not A and not B) |
A xnor B |
1 | ATLogic_True. | ||||
| AlgEquiv | {not(A) or B,A and B} |
{A implies B,A and B} |
0 | The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{{\rm not}\left( A \right)\,{\mbox{ or }}\, B \right \}\] | ATSet_wrongentries. | |||
| AlgEquiv | {A implies B,A and B} |
{not(A) and B,A and B} |
0 | The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{A\,{\mbox{ implies }}\, B \right \}\] | ATSet_wrongentries. | |||
| Differential equations | ||||||||
| AlgEquiv | diff(x^2,x) |
2*x |
1 | |||||
| AlgEquiv | diff(x^2,x) |
'diff(x^2,x) |
1 | |||||
| AlgEquiv | noundiff(x^2,x) |
2*x |
1 | |||||
| AlgEquiv | diff(y,x) |
0 |
1 | |||||
| AlgEquiv | noundiff(y,x) |
0 |
1 | |||||
| AlgEquiv | diff(y(x),x) |
0 |
0 | |||||
| AlgEquiv | diff(y(x),x) |
diff(y,x) |
0 | |||||
| AlgEquiv | diff(y,x) |
diff(y,x,2) |
1 | |||||
| Basic support for strings | ||||||||
| AlgEquiv | "Hello" |
"Hello" |
1 | ATAlgEquiv_String | ||||
| AlgEquiv | "hello" |
"Hello" |
0 | ATAlgEquiv_String | ||||
| AlgEquiv | W |
"Hello" |
0 | Your answer should be a string, but is not. | ATAlgEquiv_SA_not_string. | |||
| AlgEquiv | "Hello" |
x^2 |
0 | Your answer should be an expression, not an equation, inequality, list, set or matrix. | ATAlgEquiv_SA_not_expression. | |||
AlgEquivNouns
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| AlgEquivNouns | 1/0 |
1 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATAlgEquivNouns_STACKERROR_SAns. | ||
| AlgEquivNouns | 1 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATAlgEquivNouns_STACKERROR_TAns. | ||
| AlgEquivNouns | (x-1)^2 |
-1 | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | ATAlgEquivNounsTEST_FAILED-Empty SA. | |||
| AlgEquivNouns | x^2 |
-1 | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question. | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question. | ATAlgEquivNounsTEST_FAILED-Empty TA. | |||
| AlgEquivNouns | x-1)^2 |
(x-1)^2 |
-1 | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | ATAlgEquivNounsTEST_FAILED-Empty SA. | ||
| AlgEquivNouns | diff(x^2,x) |
2*x |
1 | |||||
| AlgEquivNouns | diff(x^2,x) |
'diff(x^2,x) |
0 | |||||
| AlgEquivNouns | diff(x^2,x) |
'diff(x^2,x) |
0 | |||||
| AlgEquivNouns | 'diff(y,x) |
noundiff(y,x) |
1 | |||||
| AlgEquivNouns | diff(y,x) |
0 |
1 | |||||
| AlgEquivNouns | 'diff(y,x) |
0 |
0 | |||||
| AlgEquivNouns | noundiff(y,x) |
0 |
0 | |||||
| AlgEquivNouns | diff(y(x),x) |
0 |
0 | |||||
| AlgEquivNouns | 'diff(y,x,1) |
'diff(y,x,2) |
0 | |||||
| AlgEquivNouns | 'diff(y(x),x) |
'diff(y,x) |
0 | |||||
| AlgEquivNouns | subst(y,y(x),'diff(y,x)+y =1) |
'diff(y,x)+y=1 |
1 | ATEquation_sides | ||||
| AlgEquivNouns | subst(y,y(x),'diff(y(x),x )+y(x)=1) |
'diff(y,x)+y=1 |
1 | ATEquation_sides | ||||
| AlgEquivNouns | subst(y(x),y,'diff(y,x)+y =1) |
'diff(y(x),x)+y(x)=1 |
1 | ATEquation_sides | ||||
| AlgEquivNouns | subst(y(x),y,'diff(y,x)+y =1) |
'diff(y,x)+y=1 |
0 | ATEquation_default | ||||
| AlgEquivNouns | subst(y(x),y,'diff(y(x),x )+y(x)=1) |
'diff(y,x)+y=1 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. subst: cannot substitute y(x) for operator y in expression y(x) | ATAlgEquivNouns_STACKERROR_SAns. | ||
| AlgEquivNouns | y_x |
'diff(y,x) |
0 | |||||
| Partials | ||||||||
| AlgEquivNouns | noundiff(f,x,1,y,1) |
noundiff(noundiff(f,x),y) |
1 | |||||
| AlgEquivNouns | noundiff(noundiff(f,y),x) |
noundiff(noundiff(f,x),y) |
1 | |||||
| AlgEquivNouns | noundiff(noundiff(f,x),x) |
noundiff(f,x,2) |
1 | |||||
| Differential equations | ||||||||
| AlgEquivNouns | noundiff(H,x,2) = -R/T |
noundiff(H,x,2) + R/T = 0 |
1 | ATEquation_ratio | ||||
| AlgEquivNouns | 'diff(H,x,2) = -R/T |
noundiff(H,x,2) + R/T = 0 |
1 | ATEquation_ratio | ||||
| AlgEquivNouns | y(t)=int(s^2,s,0,t) |
y(t)=t^3/3 |
1 | ATEquation_sides | ||||
| AlgEquivNouns | y(t)='int(s^2,s,0,t) |
y(t)=t^3/3 |
0 | ATEquation_lhs_notrhs | ||||
| AlgEquivNouns | y(t)='int(s^2,s,0,t) |
y(t)=nounint(s^2,s,0,t) |
1 | ATEquation_sides | ||||
| Logic nouns are still evaluated | ||||||||
| AlgEquivNouns | true nounand false |
false |
1 | ATLogic_True. | ||||
SubstEquiv
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| SubstEquiv | 1/0 |
x^2-2*x+1 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATSubstEquiv_STACKERROR_SAns. | ||
| SubstEquiv | x^2 |
x^2-2*x+1 |
[1/0] |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATSubstEquiv_STACKERROR_Opt. | |
| SubstEquiv | x^2 |
x^2-2*x+1 |
x |
-1 | The option to this answer test must be a list. This is an error. Please contact your teacher. | ATSubstEquiv_Opt_List. | ||
| SubstEquiv | x^2+1 |
x^2+1 |
1 | |||||
| SubstEquiv | x^2+1 |
x^3+1 |
0 | |||||
| SubstEquiv | x^2+1 |
x^3+1 |
0 | |||||
| SubstEquiv | X^2+1 |
x^2+1 |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ X=x \right] \] | ATSubstEquiv_Subst [X = x]. | |||
| SubstEquiv | x^2+y |
a^2+b |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ x=a , y=b \right] \] | ATSubstEquiv_Subst [x = a,y = b]. | |||
| SubstEquiv | x^2+y/z |
a^2+c/b |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ x=a , y=c , z=b \right] \] | ATSubstEquiv_Subst [x = a,y = c,z = b]. | |||
| SubstEquiv | y=x^2 |
a^2=b |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ x=a , y=b \right] \] | ATSubstEquiv_Subst [x = a,y = b]. | |||
| SubstEquiv | {x=1,y=2} |
{x=2,y=1} |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ x=y , y=x \right] \] | ATSubstEquiv_Subst [x = y,y = x]. | |||
| Where a variable is also a function name. | ||||||||
| SubstEquiv | cos(a*x)/(x*(ln(x))) |
cos(a*y)/(y*(ln(y))) |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ a=a , x=y \right] \] | ATSubstEquiv_Subst [a = a,x = y]. | |||
| SubstEquiv | cos(a*x)/(x*(ln(x))) |
cos(x*a)/(a*(ln(a))) |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ a=x , x=a \right] \] | ATSubstEquiv_Subst [a = x,x = a]. | |||
| SubstEquiv | cos(a*x)/(x*(ln(x))) |
cos(a*x)/(x(ln(x))) |
0 | |||||
| SubstEquiv | cos(a*x)/(x*(ln(x))) |
cos(a*y)/(y(ln(y))) |
0 | |||||
| SubstEquiv | x+1>y |
y+1>x |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ x=y , y=x \right] \] | ATSubstEquiv_Subst [x = y,y = x]. | |||
| SubstEquiv | x+1>y |
x<y+1 |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ x=y , y=x \right] \] | ATSubstEquiv_Subst [x = y,y = x]. | |||
| Matrices | ||||||||
| SubstEquiv | matrix([1,A^2+A+1],[2,0]) |
matrix([1,x^2+x+1],[2,0]) |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ A=x \right] \] | ATSubstEquiv_Subst [A = x]. | |||
| SubstEquiv | matrix([B,A^2+A+1],[2,C]) |
matrix([y,x^2+x+1],[2,z]) |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ A=x , B=y , C=z \right] \] | ATSubstEquiv_Subst [A = x,B = y,C = z]. | |||
| SubstEquiv | matrix([B,A^2+A+1],[2,C]) |
matrix([y,x^2+x+1],[2,x]) |
0 | The entries underlined in red below are those that are incorrect. \[ \left[\begin{array}{cc} {\color{red}{\underline{B}}} & {\color{red}{\underline{A^2+A+1}}} \\ 2 & {\color{red}{\underline{C}}} \end{array}\right]\] | ATMatrix_wrongentries. | |||
| Lists | ||||||||
| SubstEquiv | [x^2+1,x^2] |
[A^2+1,A^2] |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ x=A \right] \] | ATSubstEquiv_Subst [x = A]. | |||
| SubstEquiv | [x^2-1,x^2] |
[A^2+1,A^2] |
0 | The entries underlined in red below are those that are incorrect. \[\left[ {\color{red}{\underline{x^2-1}}} , {\color{red}{\underline{x ^2}}} \right] \] | (ATList_wrongentries 1, 2). | |||
| SubstEquiv | [A,B,C] |
[B,C,A] |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ A=B , B=C , C=A \right] \] | ATSubstEquiv_Subst [A = B,B = C,C = A]. | |||
| SubstEquiv | [A,B,C] |
[B,B,A] |
0 | The entries underlined in red below are those that are incorrect. \[\left[ {\color{red}{\underline{A}}} , B , {\color{red}{\underline{C }}} \right] \] | (ATList_wrongentries 1, 3). | |||
| SubstEquiv | [1,[A,B],C] |
[1,[a,b],C] |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ A=a , B=b , C=C \right] \] | ATSubstEquiv_Subst [A = a,B = b,C = C]. | |||
| Sets | ||||||||
| SubstEquiv | {x^2+1,x^2} |
{A^2+1,A^2} |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ x=A \right] \] | ATSubstEquiv_Subst [x = A]. | |||
| SubstEquiv | {x^2-1,x^2} |
{A^2+1,A^2} |
0 | The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{x^2-1 , x^2 \right \}\] | ATSet_wrongentries. | |||
| SubstEquiv | {A+1,B^2,C} |
{B,C+1,A^2} |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ A=C , B=A , C=B \right] \] | ATSubstEquiv_Subst [A = C,B = A,C = B]. | |||
| SubstEquiv | {1,{A,B},C} |
{1,{a,b},C} |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ A=a , B=b , C=C \right] \] | ATSubstEquiv_Subst [A = a,B = b,C = C]. | |||
| SubstEquiv | A*cos(t)+B*sin(t) |
P*cos(t)+Q*sin(t) |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ A=P , B=Q , t=t \right] \] | ATSubstEquiv_Subst [A = P,B = Q,t = t]. | |||
| SubstEquiv | A*cos(t)+B*sin(t) |
P*cos(x)+Q*sin(x) |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ A=P , B=Q , t=x \right] \] | ATSubstEquiv_Subst [A = P,B = Q,t = x]. | |||
| Fix some variables. | ||||||||
| SubstEquiv | A*cos(t)+B*sin(t) |
P*cos(x)+Q*sin(x) |
[x] |
0 | ||||
| SubstEquiv | A*cos(t)+B*sin(t) |
P*cos(x)+Q*sin(x) |
[t] |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ A=P , B=Q , t=x \right] \] | ATSubstEquiv_Subst [A = P,B = Q,t = x]. | ||
| SubstEquiv | A*cos(t)*e^x+B*sin(t)*e^x+C*si n(2*x)+D*cos(2*x) |
P*cos(t)*e^x+Q*sin(t)*e^x+R*si n(2*x)+S*cos(2*x) |
[x,t] |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ A=P , B=Q , C=R , D=S \right] \] | ATSubstEquiv_Subst [A = P,B = Q,C = R,D = S]. | ||
| SubstEquiv | sqrt(2*g*y) |
sqrt(2*g*x) |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ g=g , y=x \right] \] | ATSubstEquiv_Subst [g = g,y = x]. | |||
| SubstEquiv | sqrt(2*g*y) |
sqrt(2*g*x) |
[g] |
1 | Your answer would be correct if you used the following substitution of variables. \[\left[ y=x \right] \] | ATSubstEquiv_Subst [y = x]. | ||
EqualComAss
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| EqualComAss | 1/0 |
0 |
-1 | ATEqualComAss_STACKERROR_SAns. | ||||
| EqualComAss | 0 |
1/0 |
-1 | ATEqualComAss_STACKERROR_TAns. | ||||
| Numbers | ||||||||
| EqualComAss | 2/4 |
1/2 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | 3^2 |
8 |
0 | ATEqualComAss (AlgEquiv-false). | ||||
| EqualComAss | 3^2 |
9 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | cos(0) |
1 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | 4^(1/2) |
2 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | 1/3^(1/2) |
(1/3)^(1/2) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | sqrt(3)/3 |
(1/3)^(1/2) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | sqrt(3) |
3^(1/2) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | 2*sqrt(2) |
sqrt(8) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | 2*2^(1/2) |
sqrt(8) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | sqrt(2)/4 |
1/sqrt(8) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | 1/sqrt(2) |
2^(1/2)/2 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | 4.0 |
4 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Case sensitivity | ||||||||
| EqualComAss | X |
x |
0 | ATEqualComAss (AlgEquiv-false)ATAlgEquiv_WrongCase. | ||||
| EqualComAss | exdowncase(X) |
x |
1 | |||||
| EqualComAss | exdowncase((X-1)^2) |
x^2-2*x+1 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | exdowncase(X^2-2*X+1) |
x^2-2*x+1 |
1 | |||||
| Powers | ||||||||
| EqualComAss | a^2/b^3 |
a^2*b^(-3) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | lg(a^x,a) |
x |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | x^(2/4) |
x^(1/2) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Simple polynomials | ||||||||
| EqualComAss | 1+2*x |
x*2+1 |
1 | |||||
| EqualComAss | 1+x |
2*x+1 |
0 | ATEqualComAss (AlgEquiv-false). | ||||
| EqualComAss | 1+x+x |
2*x+1 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | (x+y)+z |
z+x+y |
1 | |||||
| EqualComAss | x*x |
x^2 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | (x+5)*x |
x*(5+x) |
1 | |||||
| EqualComAss | x*(x+5) |
5*x+x^2 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | (1-x)^2 |
(x-1)^2 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | (a-x)^6000 |
(x-a)^6000 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Expressions with subscripts | ||||||||
| EqualComAss | rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2)) |
rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2)) |
1 | |||||
| EqualComAss | rho*z*V/(4*pi*epsilon[1]*(R^2+ z^2)^(3/2)) |
rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2)) |
0 | ATEqualComAss (AlgEquiv-false). | ||||
| Unary minus | ||||||||
| EqualComAss | -1+2 |
2-1 |
1 | |||||
| EqualComAss | -1*2+3*4 |
3*4-1*2 |
1 | |||||
| EqualComAss | (-1*2)+3*4 |
10 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | -1*2+3*4 |
3*4-1*2 |
1 | |||||
| EqualComAss | x*(-y) |
-x*y |
1 | |||||
| EqualComAss | x*(-y) |
-(x*y) |
1 | |||||
| EqualComAss | (-x)*(-x) |
x*x |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | (-x)*(-x) |
x^2 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | -1/4*%pi*i |
-(%i*%pi)/4 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Rational expressions | ||||||||
| EqualComAss | 1/2 |
3/6 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | 1/(1+2*x) |
1/(2*x+1) |
1 | |||||
| EqualComAss | 2/(4+2*x) |
1/(x+2) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | (a*b)/c |
a*(b/c) |
1 | |||||
| EqualComAss | ((x+1)/(x*(x-1)))*(x-1) |
((x+1)*(x-1))/(x*(x-1)) |
1 | |||||
| EqualComAss | (-x)/y |
-(x/y) |
1 | |||||
| EqualComAss | x/(-y) |
-(x/y) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | -1/(1-x) |
1/(x-1) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | 1/2*1/x |
1/(2*x) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | (k+8)/(k^2+4*k-12) |
(k+8)/(k^2+4*k-12) |
1 | |||||
| EqualComAss | (k+8)/(k^2+4*k-12) |
(k+8)/((k-2)*(k+6)) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | (k+7)/(k^2+4*k-12) |
(k+8)/(k^2+4*k-12) |
0 | ATEqualComAss (AlgEquiv-false). | ||||
| EqualComAss | -(2*k+6)/(k^2+4*k-12) |
-(2*k+6)/(k^2+4*k-12) |
1 | |||||
| EqualComAss | (a+b)/1 |
(b+a)/1 |
1 | |||||
| No simplicifcation here | ||||||||
| EqualComAss | 1*x |
x |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | 23+0*x |
23 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | x+0 |
x |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | x^1 |
x |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | (1/2)*(a+b) |
(a+b)/2 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | 1/3*logbase(27,6) |
logbase(27,6)/3 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | 1/3*lg(27,6) |
lg(27,6)/3 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | lg(root(x, n)) |
lg(x, 10)/n |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | exp(x) |
%e^x |
1 | |||||
| EqualComAss | exp(x)^2 |
%e^(2*x) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | exp(x)^2 |
(%e^(x))^2 |
1 | |||||
| EqualComAss | 1/3*i |
i/3 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Complex numbers | ||||||||
| EqualComAss | %i |
e^(i*pi/2) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | (4*sqrt(3)*%i+4)^(1/5) |
rectform((4*sqrt(3)*%i+4)^(1/5 )) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | (4*sqrt(3)*%i+4)^(1/5) |
8^(1/5)*(cos(%pi/15)+%i*sin(%p i/15)) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | (4*sqrt(3)*%i+4)^(1/5) |
polarform((4*sqrt(3)*%i+4)^(1/ 5)) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Equations | ||||||||
| EqualComAss | y=x |
x=y |
1 | |||||
| EqualComAss | x+1 |
y=2*x+1 |
0 | Your answer should be an equation, but is not. | ATEqualComAss ATAlgEquiv_SA_not_equation. | |||
| EqualComAss | y=1+2*x |
y=2*x+1 |
1 | |||||
| EqualComAss | y=x+x+1 |
y=1+2*x |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Logic | ||||||||
| EqualComAss | A and B |
B and A |
1 | |||||
| EqualComAss | A or B |
B or A |
1 | |||||
| EqualComAss | A or B |
B and A |
0 | ATEqualComAss (AlgEquiv-false). | ||||
| EqualComAss | not(true) |
false |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Sets | ||||||||
| EqualComAss | {2*x+1,2} |
{2, 1+x*2} |
1 | |||||
| EqualComAss | 2 |
{2} |
0 | Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets. | ATEqualComAss ATAlgEquiv_SA_not_set. | |||
| EqualComAss | {2*x+1, 1+1} |
{2, 1+x*2} |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | {1,2} |
{1,{2}} |
0 | ATEqualComAss (AlgEquiv-false)ATSet_wrongentries. | ||||
| EqualComAss | {4,3} |
{3,4} |
1 | |||||
| EqualComAss | {4,4} |
{4} |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | {-1,1,-1} |
{-1,-1,1} |
1 | |||||
| EqualComAss | {-1,1,-1} |
{-1,1} |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Lists | ||||||||
| EqualComAss | [2*x+1,2] |
[1+x*2,2] |
1 | |||||
| EqualComAss | [x+x+1, 1+1] |
[1+x*2,2] |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Matrices | ||||||||
| EqualComAss | matrix([1,2],[2,3]) |
matrix([1,2],[2,3]) |
1 | |||||
| EqualComAss | matrix([1,2],[2,3]) |
matrix([1,2,3],[2,3,3]) |
0 | ATEqualComAss (AlgEquiv-false)ATMatrix_wrongsz_columns. | ||||
| EqualComAss | matrix([1,2],[2,3]) |
matrix([1,2],[2,5]) |
0 | ATEqualComAss (AlgEquiv-false)ATMatrix_wrongentries. | ||||
| EqualComAss | matrix([1,2],[2,2+1]) |
matrix([1,2],[2,3]) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | matrix([x+x, 1],[1, 1]) |
matrix([2*x, 1],[1, 1]) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Sums and products | ||||||||
| EqualComAss | sum(k^n,n,0,3) |
sum(k^n,n,0,3) |
1 | |||||
| EqualComAss | 1+k+k^2+k^3 |
sum(k^n,n,0,3) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | sum(k,k,0,1+n) |
sum(k,k,0,n+1) |
1 | |||||
| EqualComAss | (n+1)*(n+2)/2 |
sum(k,k,0,n+1) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | product(cos(k*x),k,1,3) |
product(cos(k*x),k,1,3) |
1 | |||||
| EqualComAss | cos(x)*cos(2*x)*cos(3*x) |
product(cos(k*x),k,1,3) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Inequalities are not commutative under this test | ||||||||
| EqualComAss | -6/5 > x |
x < -6/5 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | x<1 and -3<x |
-3<x and x<1 |
1 | |||||
| EqualComAss | 1>x and -3<x |
-3<x and x<1 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | make_less_ineq(-6/5 > x) |
x < -6/5 |
1 | |||||
| EqualComAss | make_less_ineq(1>x and -3&l t;x) |
-3<x and x<1 |
1 | |||||
| EqualComAss | make_less_ineq(6/3 > x) |
x < 2 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| Unary Equations | ||||||||
| EqualComAss | 1 |
stackeq(1) |
1 | |||||
| EqualComAss | stackeq(1) |
1 |
1 | |||||
| EqualComAss | stackeq(1+1) |
2 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | stackeq(1) |
0 |
0 | ATEqualComAss (AlgEquiv-false). | ||||
| EqualComAss | lowesttermsp(1/3) |
true |
1 | |||||
| EqualComAss | lowesttermsp(2/6) |
true |
0 | ATEqualComAss (AlgEquiv-false). | ||||
| EqualComAss | lowesttermsp(x^2/x) |
true |
0 | ATEqualComAss (AlgEquiv-false). | ||||
| EqualComAss | lowesttermsp(-y/-x) |
true |
0 | ATEqualComAss (AlgEquiv-false). | ||||
| EqualComAss | lowesttermsp((x^2-1)/(x-1)) |
true |
0 | ATEqualComAss (AlgEquiv-false). | ||||
| EqualComAss | lowesttermsp((x^2-1)/(x+2)) |
true |
1 | |||||
| Bad things in denominators | ||||||||
| EqualComAss | rationalized(1+sqrt(3)/3) |
true |
1 | |||||
| EqualComAss | rationalized(1+1/sqrt(3)) |
[sqrt(3)] |
1 | |||||
| EqualComAss | rationalized(1/sqrt(3)) |
[sqrt(3)] |
1 | |||||
| EqualComAss | rationalized(1/sqrt(2)+i/sqrt( 2)) |
[sqrt(2),sqrt(2)] |
1 | |||||
| EqualComAss | rationalized(sqrt(2)/2+1/sqrt( 3)) |
[sqrt(3)] |
1 | |||||
| EqualComAss | rationalized(1/sqrt(2)+1/sqrt( 3)) |
[sqrt(2),sqrt(3)] |
1 | |||||
| EqualComAss | rationalized(1/(1+i)) |
[i] |
1 | |||||
| EqualComAss | rationalized(1/(1+1/root(3,2)) ) |
[root(3,2)] |
1 | |||||
| Differential Equations | ||||||||
| EqualComAss | diff(y,x) |
0 |
1 | |||||
| EqualComAss | diff(x^2,x) |
2*x |
1 | |||||
| EqualComAss | noundiff(x^2,x) |
2*x |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | diff(y,x) |
'diff(y,x) |
0 | ATEqualComAss (AlgEquiv-true). | ||||
| EqualComAss | noundiff(y,x) |
'diff(y,x) |
1 | |||||
| EqualComAss | 'diff(y(x),x) |
'diff(y(x),x,1) |
1 | |||||
| EqualComAss | noundiff(y(x),x)=-x/4 |
4*noundiff(y(x),x)+x=0 |
0 | ATEqualComAss (AlgEquiv-true). | ||||
EqualComAssRules
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| EqualComAssRules | 1/0 |
0 |
[] |
-1 | ATEqualComAssRules_STACKERROR_SAns. | |||
| EqualComAssRules | 0 |
1/0 |
[] |
-1 | ATEqualComAssRules_STACKERROR_TAns. | |||
| EqualComAssRules | 0+a |
a |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test. | STACKERROR_OPTION. | ||
| EqualComAssRules | 0+a |
a |
x |
-1 | The option to this answer test must be a non-empty list of supported rules. This is an error. Please contact your teacher. | ATEqualComAssRules_Opt_List. | ||
| EqualComAssRules | 0+a |
a |
[x] |
-1 | The option to this answer test must be a non-empty list of supported rules. This is an error. Please contact your teacher. | ATEqualComAssRules_Opt_Wrong. | ||
| EqualComAssRules | 0+a |
a |
[intMul,intFac] |
-1 | The option to this answer test contains incompatible rules. This is an error. Please contact your teacher. | ATEqualComAssRules_Opt_Incompatible. | ||
| Basic cases | ||||||||
| EqualComAssRules | 1+1 |
3 |
[zeroAdd] |
0 | ATEqualComAssRules (AlgEquiv-false). | |||
| EqualComAssRules | 1+1 |
2 |
[zeroAdd] |
0 | ||||
| EqualComAssRules | 1+1 |
2 |
[testdebug,zero Add] |
0 | ATEqualComAssRules: [1 nounadd 1,2]. | |||
| EqualComAssRules | 0+a |
a |
[zeroAdd] |
1 | ||||
| EqualComAssRules | a+0 |
a |
[zeroAdd] |
1 | ||||
| EqualComAssRules | 1*a |
a |
[testdebug,zero Add] |
0 | ATEqualComAssRules: [1 nounmul a,a]. | |||
| EqualComAssRules | 1*a |
a |
[oneMul] |
1 | ||||
| EqualComAssRules | 1*a |
a |
ID_TRANS |
1 | ||||
| EqualComAssRules | a/1 |
a |
ID_TRANS |
1 | ||||
| EqualComAssRules | 0*a |
0 |
ID_TRANS |
1 | ||||
| EqualComAssRules | 0-1*i |
-i |
ID_TRANS |
1 | ||||
| EqualComAssRules | 0-i |
-i |
ID_TRANS |
1 | ||||
| EqualComAssRules | 2+1*i |
2+i |
ID_TRANS |
1 | ||||
| EqualComAssRules | x^0+x^1/1+x^2/2+x^3/3!+x^4/4! |
1+x+x^2/2+x^3/3!+x^4/4! |
ID_TRANS |
1 | ||||
| EqualComAssRules | %e^x |
exp(x) |
[testdebug,ID_T RANS] |
1 | ATEqualComAssRules: [%e nounpow x,%e nounpow x]. | |||
| EqualComAssRules | 12*%e^((2*(%pi/2)*%i)/2) |
12*exp(%i*(%pi/2)) |
ID_TRANS |
0 | ||||
| EqualComAssRules | 12*%e^((2*(%pi/2)*%i)/2) |
12*exp(%i*(%pi/2)) |
[ID_TRANS,[negN eg,negDiv,negOr d],[recipMul,di vDiv,divCancel] ,[intAdd,intMul ,intPow]] |
1 | ||||
| EqualComAssRules | 0^(1-1) |
0 |
ID_TRANS |
0 | ATEqualComAssRules_STACKERROR_SAns. | |||
| EqualComAssRules | 0*a |
0 |
delete(zeroMul, ID_TRANS) |
0 | ||||
| EqualComAssRules | -(-a) |
a |
[negNeg] |
1 | ||||
| EqualComAssRules | -(-(-a)) |
-a |
[negNeg] |
1 | ||||
| EqualComAssRules | -(-(-a)) |
a |
[testdebug,negN eg] |
0 | ATEqualComAssRules (AlgEquiv-false). | |||
| EqualComAssRules | 3/(-x) |
-3/x |
ID_TRANS |
0 | ||||
| EqualComAssRules | 3/(-x) |
-3/x |
[testdebug,ID_T RANS] |
0 | ATEqualComAssRules: [3 nounmul UNARY_RECIP UNARY_MINUS nounmul x,UNARY_MINUS nounmul 3 nounmul UNARY_RECIP x]. | |||
| EqualComAssRules | -x*(x+1) |
x*(-x-1) |
[negDist] |
1 | ||||
| EqualComAssRules | -x*(x-1) |
x*(1-x) |
NEG_TRANS |
1 | ||||
| EqualComAssRules | -x*(x-1) |
x*(1-x) |
NEG_TRANS |
1 | ||||
| EqualComAssRules | -5*x*(3-x) |
5*x*(x-3) |
NEG_TRANS |
1 | ||||
| EqualComAssRules | -x*(x-1)*(x+1) |
x*(x-1)*(-x-1) |
NEG_TRANS |
1 | ||||
| EqualComAssRules | -x*(x-1)*(x+1) |
x*(1-x)*(x+1) |
NEG_TRANS |
1 | ||||
| EqualComAssRules | -x*(y-1)*(x-1) |
x*(1-x)*(y-1) |
NEG_TRANS |
1 | ||||
| EqualComAssRules | -x*(y-1)*(x-1) |
x*(x-1)*(1-y) |
NEG_TRANS |
1 | ||||
| EqualComAssRules | (x-y)*(y-x) |
-(x-y)*(x-y) |
NEG_TRANS |
1 | ||||
| EqualComAssRules | (x-y)*(y-x) |
-(x-y)^2 |
[testdebug,NEG_ TRANS] |
0 | ATEqualComAssRules: [UNARY_MINUS nounmul (x nounadd UNARY_MINUS nounmul y) nounmul (x nounadd UNARY_MINUS nounmul y),UNARY_MINUS nounmul (x nounadd UNARY_MINUS nounmul y) nounpow 2]. | |||
| EqualComAssRules | -x*(x-1)*(x+1) |
x*(1-x)*(x+1) |
[testdebug,negD ist,negNeg] |
0 | ATEqualComAssRules: [x nounmul (UNARY_MINUS nounmul 1 nounadd UNARY_MINUS nounmul x) nounmul (x nounadd UNARY_MINUS nounmul 1),x nounmul (1 nounadd UNARY_MINUS nounmul x) nounmul (1 nounadd x)]. | |||
| EqualComAssRules | -x*(y-1)*(x-1) |
x*(x-1)*(1-y) |
[testdebug,negD ist,negNeg] |
0 | ATEqualComAssRules: [x nounmul (1 nounadd UNARY_MINUS nounmul x) nounmul (y nounadd UNARY_MINUS nounmul 1),x nounmul (1 nounadd UNARY_MINUS nounmul y) nounmul (x nounadd UNARY_MINUS nounmul 1)]. | |||
| EqualComAssRules | 3/(-x) |
-3/x |
[negDiv] |
1 | ||||
| EqualComAssRules | 3/(-x) |
ev(-3,simp)/x |
[negDiv] |
1 | ||||
| EqualComAssRules | (-a)/(-x) |
-(-a/x) |
[testdebug,ID_T RANS] |
0 | ATEqualComAssRules: [UNARY_MINUS nounmul a nounmul UNARY_RECIP UNARY_MINUS nounmul x,UNARY_MINUS nounmul UNARY_MINUS nounmul a nounmul UNARY_RECIP x]. | |||
| EqualComAssRules | (-a)/(-x) |
-(-a/x) |
[negDiv] |
1 | ||||
| EqualComAssRules | (-a)/(-x) |
a/x |
[testdebug,negD iv] |
0 | ATEqualComAssRules: [UNARY_MINUS nounmul UNARY_MINUS nounmul a nounmul UNARY_RECIP x,a nounmul UNARY_RECIP x]. | |||
| EqualComAssRules | (-a)/(-x) |
a/x |
[negDiv,negNeg] |
1 | ||||
| EqualComAssRules | 1/(-x) |
(-1)/x |
[negDiv] |
1 | ||||
| EqualComAssRules | 1/(-x) |
ev(-1,simp)/x |
[negDiv] |
1 | ||||
| EqualComAssRules | (2/-3)*(x-y) |
-(2/3)*(x-y) |
[negDiv] |
1 | ||||
| EqualComAssRules | (2/-3)*(x-y) |
(2/3)*(y-x) |
[negDiv] |
0 | ||||
| EqualComAssRules | (2/-3)*(x-y) |
(2/3)*(y-x) |
[negDiv,negOrd] |
1 | ||||
| EqualComAssRules | -2/(1-x) |
2/(x-1) |
[testdebug,negD iv] |
0 | ATEqualComAssRules: [UNARY_MINUS nounmul 2 nounmul UNARY_RECIP (1 nounadd UNARY_MINUS nounmul x),2 nounmul UNARY_RECIP (x nounadd UNARY_MINUS nounmul 1)]. | |||
| EqualComAssRules | 1/2*3/x |
3/(2*x) |
[testdebug,ID_T RANS] |
0 | ATEqualComAssRules: [3 nounmul (UNARY_RECIP 2) nounmul UNARY_RECIP x,3 nounmul UNARY_RECIP 2 nounmul x]. | |||
| EqualComAssRules | 1/2*3/x |
3/(2*x) |
[ID_TRANS,recip Mul] |
1 | ||||
| EqualComAssRules | 5/2*3/x |
15/(2*x) |
[testdebug,ID_T RANS,recipMul] |
0 | ATEqualComAssRules: [3 nounmul 5 nounmul UNARY_RECIP 2 nounmul x,15 nounmul UNARY_RECIP 2 nounmul x]. | |||
| EqualComAssRules | -(x-y) |
y-x |
[negOrd] |
1 | ||||
| EqualComAssRules | 5/2*3/x |
15/(2*x) |
[ID_TRANS,recip Mul,intMul] |
1 | ||||
| EqualComAssRules | (3+2)*x+x |
5*x+x |
[ID_TRANS,intAd d] |
1 | ||||
| EqualComAssRules | (3-5)*x+x |
-2*x+x |
[ID_TRANS,intAd d] |
1 | ||||
| EqualComAssRules | 7*x*(-3*x) |
-21*x*x |
[ID_TRANS,intMu l] |
1 | ||||
| EqualComAssRules | (-7*x)*(-3*x) |
21*x*x |
[testdebug,ID_T RANS,intMul] |
0 | ATEqualComAssRules: [UNARY_MINUS nounmul UNARY_MINUS nounmul 21 nounmul x nounmul x,21 nounmul x nounmul x]. | |||
| EqualComAssRules | (-7*x)*(-3*x) |
21*x*x |
[ID_TRANS,intMu l,negNeg] |
1 | ||||
| ev(a/b/c, simp)=a/(b*c) | ||||||||
| EqualComAssRules | a/b/c |
a/(b*c) |
[testdebug,ID_T RANS] |
0 | ATEqualComAssRules: [a nounmul (UNARY_RECIP b) nounmul UNARY_RECIP c,a nounmul UNARY_RECIP b nounmul c]. | |||
| EqualComAssRules | a/b/c |
a/(b*c) |
[ID_TRANS,recip Mul] |
1 | ||||
| EqualComAssRules | (a/b)/c |
a/(b*c) |
[ID_TRANS,recip Mul] |
1 | ||||
| ev(a/(b/c), simp)=(a*c)/b | ||||||||
| EqualComAssRules | a/(b/c) |
(a*c)/b |
[testdebug,ID_T RANS] |
0 | ATEqualComAssRules: [a nounmul UNARY_RECIP b nounmul UNARY_RECIP c,a nounmul c nounmul UNARY_RECIP b]. | |||
| EqualComAssRules | a/(b/c) |
(a*c)/b |
[testdebug,ID_T RANS,recipMul] |
0 | ATEqualComAssRules: [a nounmul UNARY_RECIP b nounmul UNARY_RECIP c,a nounmul c nounmul UNARY_RECIP b]. | |||
| EqualComAssRules | a/(b/c) |
(a*c)/b |
[ID_TRANS,divDi v] |
1 | ||||
| EqualComAssRules | A*a/(B*b/c) |
A*(a*c)/(B*b) |
[ID_TRANS,divDi v] |
1 | ||||
| EqualComAssRules | A*a/(B*b/c)*1/d |
A*(a*c)/(B*b)*1/d |
[ID_TRANS,divDi v] |
1 | ||||
| EqualComAssRules | D*A*a/(B*b/c)*1/d |
A*(a*c)/(B*b)*D/d |
[ID_TRANS,divDi v] |
1 | ||||
| EqualComAssRules | A*a/(B*b/c)*1/d |
A*(a*c)/(B*b*d) |
[testdebug,ID_T RANS,divDiv] |
0 | ATEqualComAssRules: [A nounmul a nounmul c nounmul (UNARY_RECIP B nounmul b) nounmul UNARY_RECIP d,A nounmul a nounmul c nounmul UNARY_RECIP B nounmul b nounmul d]. | |||
| EqualComAssRules | A*a/(B*b/c)*1/d |
A*(a*c)/(B*b*d) |
[ID_TRANS,divDi v,recipMul] |
1 | ||||
| EqualComAssRules | A/(B/(C/D)) |
A*C/(B*D) |
[testdebug,ID_T RANS,divDiv] |
0 | ATEqualComAssRules: [A nounmul C nounmul (UNARY_RECIP B) nounmul UNARY_RECIP D,A nounmul C nounmul UNARY_RECIP B nounmul D]. | |||
| EqualComAssRules | A/(B/(C/D)) |
A*C/(B*D) |
[ID_TRANS,divDi v,recipMul] |
1 | ||||
| EqualComAssRules | 18 |
2*3^2 |
[intFac] |
1 | ||||
| EqualComAssRules | 0+%i*(-(1/27)) |
-(%i/27) |
[[zeroAdd,zeroM ul,oneMul,onePo w,idPow,zeroPow ,zPow,oneDiv],[ negNeg,negDiv,n egOrd],[recipMu l,divDiv,divCan cel],[intAdd,in tMul,intPow]] |
1 | ||||
| EqualComAssRules | x=sqrt(3)+2 |
x=3^(1/2)+2 |
[ID_TRANS,sqrtR em] |
1 | ||||
| EqualComAssRules | x=sqrt(3)+2 nounor x=-sqrt(3)- 2 |
x=3^(1/2)+2 nounor x=-3^(1/2)- 2 |
ID_TRANS |
0 | ||||
| EqualComAssRules | x=sqrt(3)+2 nounor x=-sqrt(3)- 2 |
x=3^(1/2)+2 nounor x=-3^(1/2)- 2 |
[ID_TRANS,sqrtR em] |
1 | ||||
| EqualComAssRules | x=sqrt(3)+2 nounor x=-sqrt(3)+ 7 |
x=3^(1/2)+2 nounor x=-3^(1/2)- 2 |
[ID_TRANS,sqrtR em] |
0 | ATEqualComAssRules (AlgEquiv-false)ATEquation_default. | |||
| EqualComAssRules | 1/sqrt(3) |
1/3^(1/2) |
[ID_TRANS,sqrtR em] |
1 | ||||
| EqualComAssRules | 1/sqrt(3) |
3^(-1/2) |
[ID_TRANS,sqrtR em] |
0 | ||||
CasEqual
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| CasEqual | 1/0 |
x^2-2*x+1 |
-1 | ATCASEqual_STACKERROR_SAns. | ||||
| CasEqual | x |
1/0 |
-1 | ATCASEqual_STACKERROR_TAns. | ||||
| CasEqual | 0.5 |
1/2 |
x |
0 | ATCASEqual (AlgEquiv-true). | |||
| CasEqual | x=1 |
1 |
0 | You have entered an equation, but an equation is not expected here. You may have typed something like "y=2*x+1" when you only needed to type "2*x+1". | ATCASEqual ATAlgEquiv_TA_not_equation. | |||
| Case sensitivity | ||||||||
| CasEqual | a |
A |
0 | ATCASEqual_false. | ||||
| CasEqual | exdowncase(X^2-2*X+1) |
x^2-2*x+1 |
1 | ATCASEqual_true. | ||||
| Numbers | ||||||||
| CasEqual | 4^(-1/2) |
1/2 |
0 | ATCASEqual (AlgEquiv-true). | ||||
| CasEqual | ev(4^(-1/2),simp) |
ev(1/2,simp) |
1 | ATCASEqual_true. | ||||
| CasEqual | 2^2 |
4 |
0 | ATCASEqual (AlgEquiv-true). | ||||
| Powers | ||||||||
| CasEqual | a^2/b^3 |
a^2*b^(-3) |
0 | ATCASEqual (AlgEquiv-true). | ||||
| Expressions with subscripts | ||||||||
| CasEqual | rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2)) |
rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2)) |
1 | ATCASEqual_true. | ||||
| CasEqual | rho*z*V/(4*pi*epsilon[1]*(R^2+ z^2)^(3/2)) |
rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2)) |
0 | ATCASEqual_false. | ||||
| Mix of floats and rational numbers | ||||||||
| CasEqual | 0.5 |
1/2 |
0 | ATCASEqual (AlgEquiv-true). | ||||
| CasEqual | x^(1/2) |
sqrt(x) |
0 | ATCASEqual (AlgEquiv-true). | ||||
| CasEqual | ev(x^(1/2),simp) |
ev(sqrt(x),simp) |
1 | ATCASEqual_true. | ||||
| CasEqual | abs(x) |
sqrt(x^2) |
0 | ATCASEqual (AlgEquiv-true). | ||||
| CasEqual | ev(abs(x),simp) |
ev(sqrt(x^2),simp) |
1 | ATCASEqual_true. | ||||
| CasEqual | x-1 |
(x^2-1)/(x+1) |
0 | ATCASEqual (AlgEquiv-true). | ||||
| Polynomials and rational function | ||||||||
| CasEqual | x+x |
2*x |
0 | ATCASEqual (AlgEquiv-true). | ||||
| CasEqual | ev(x+x,simp) |
ev(2*x,simp) |
1 | ATCASEqual_true. | ||||
| CasEqual | x+x^2 |
x^2+x |
0 | ATCASEqual (AlgEquiv-true). | ||||
| CasEqual | ev(x+x^2,simp) |
ev(x^2+x,simp) |
1 | ATCASEqual_true. | ||||
| CasEqual | (x-1)^2 |
x^2-2*x+1 |
0 | ATCASEqual (AlgEquiv-true). | ||||
| CasEqual | (x-1)^(-2) |
1/(x^2-2*x+1) |
0 | ATCASEqual (AlgEquiv-true). | ||||
| CasEqual | 1/n-1/(n+1) |
1/(n*(n+1)) |
0 | ATCASEqual (AlgEquiv-true). | ||||
| Trig functions | ||||||||
| CasEqual | cos(x) |
cos(-x) |
0 | ATCASEqual (AlgEquiv-true). | ||||
| CasEqual | ev(cos(x),simp) |
ev(cos(-x),simp) |
1 | ATCASEqual_true. | ||||
| CasEqual | cos(x)^2+sin(x)^2 |
1 |
0 | ATCASEqual (AlgEquiv-true). | ||||
| CasEqual | 2*cos(x)^2-1 |
cos(2*x) |
0 | ATCASEqual (AlgEquiv-true). | ||||
| Predicate function wrapper | ||||||||
| CasEqual | imag_numberp(2*%i) |
true |
1 | ATCASEqual_true. | ||||
| CasEqual | imag_numberp(%e^(%i*%pi/2)) |
true |
1 | ATCASEqual_true. | ||||
| CasEqual | imag_numberp(2) |
false |
1 | ATCASEqual_true. | ||||
| CasEqual | imag_numberp(%e^(%pi/2)) |
false |
1 | ATCASEqual_true. | ||||
| CasEqual | complex_exponentialp(3*%e^(%i* %pi/6)) |
true |
1 | ATCASEqual_true. | ||||
| CasEqual | complex_exponentialp(3) |
true |
1 | ATCASEqual_true. | ||||
| CasEqual | complex_exponentialp(%e^(%i*%p i/6)) |
true |
1 | ATCASEqual_true. | ||||
| CasEqual | complex_exponentialp(%e^%i) |
true |
1 | ATCASEqual_true. | ||||
| CasEqual | complex_exponentialp(%e^(%pi/6 )) |
true |
1 | ATCASEqual_true. | ||||
| CasEqual | complex_exponentialp(3+%i) |
false |
1 | ATCASEqual_true. | ||||
| CasEqual | complex_exponentialp(%e^(%i)/4 ) |
true |
1 | ATCASEqual_true. | ||||
| CasEqual | complex_exponentialp(3*exp(%i* %pi/6)) |
true |
1 | ATCASEqual_true. | ||||
| CasEqual | integerp(-1) |
true |
0 | ATCASEqual_false. | ||||
| CasEqual | integerp(ev(-1,simp)) |
true |
1 | ATCASEqual_true. | ||||
SameType
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| SameType | 1/0 |
1 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATSameType_STACKERROR_SAns. | ||
| SameType | 1 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATSameType_STACKERROR_TAns. | ||
| Numbers | ||||||||
| SameType | 4^(-1/2) |
1/2 |
1 | |||||
| Lists | ||||||||
| SameType | x |
[1,2,3] |
0 | |||||
| SameType | [1,2] |
[1,2,3] |
1 | |||||
| SameType | [1,x>2] |
[1,2<x] |
1 | |||||
| SameType | [1,x,3] |
[1,2<x,4] |
0 | |||||
| Sets | ||||||||
| SameType | x |
{1,2,3} |
0 | |||||
| SameType | {1,2} |
{1,2,3} |
1 | |||||
| Matrices | ||||||||
| SameType | matrix([1,2],[2,3]) |
matrix([1,2],[2,3]) |
1 | |||||
| SameType | [[1,2],[2,3]] |
matrix([1,2],[2,3]) |
0 | |||||
| SameType | matrix([1,2],[2,3]) |
matrix([1,2,3],[2,3,3]) |
1 | |||||
| SameType | matrix([x>4,{1,x^2}],[[1,2]
,[1,3]]) |
matrix([4-x<0,{x^2, 1}],[[1
,2],[1,3]]) |
1 | |||||
| SameType | matrix([x>4,[1,x^2]],[[1,2] ,[1,3]]) |
matrix([4-x<0,{x^2, 1}],[[1
,2],[1,4]]) |
0 | |||||
| Equations | ||||||||
| SameType | 1 |
x=1 |
0 | |||||
| SameType | x=1 |
x=1 |
1 | |||||
| Inequalities | ||||||||
| SameType | 1 |
x>1 |
0 | |||||
| SameType | x>2 |
x>1 |
1 | |||||
| SameType | x>1 |
x>=1 |
1 | |||||
| SameType | x>1 and x<3 |
x>=1 |
1 | |||||
| SameType | {x>1,x<3} |
x>=1 |
0 | |||||
| SameType | sqrt(2)*sqrt(3)+2*(sqrt(2/3))* x-(2/3)*(sqrt(2/3))*x^2+(4/9)* (sqrt(2/3))*x^3 |
4*sqrt(6)*x^3/27-(2*sqrt(6)*x^ 2)/9+(2*sqrt(6)*x)/3+sqrt(6) |
1 | |||||
SysEquiv
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Basic tests | ||||||||
| SysEquiv | 1/0 |
[(x-1)*(x+1)=0] |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATSysEquiv_STACKERROR_SAns. | ||
| SysEquiv | [(x-1)*(x+1)=0] |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATSysEquiv_STACKERROR_TAns. | ||
| SysEquiv | 1 |
[(x-1)*(x+1)=0] |
0 | Your answer should be a list, but it is not! | ATSysEquiv_SA_not_list. | |||
| SysEquiv | [(x-1)*(x+1)=0] |
1 |
0 | The teacher's answer is not a list. Please contact your teacher. | ATSysEquiv_SB_not_list. | |||
| SysEquiv | [1] |
[90=v*t,90=(v+5)*(t-1/4)] |
0 | Your answer should be a list of equations, but it is not! | ATSysEquiv_SA_not_eq_list. | |||
| SysEquiv | [(x-1)*(x+1)=0] |
[1] |
0 | The teacher's answer is not a list of equations, but should be. | ATSysEquiv_SB_not_eq_list. | |||
| SysEquiv | [x^2] |
[(x-1)*(x+1)=0] |
0 | Your answer should be a list of equations, but it is not! | ATSysEquiv_SA_not_eq_list. | |||
| SysEquiv | [90=v*t^t,90=(v+5)*(t-1/4)] |
[90=v*t,90=(v+5)*(t-1/4)] |
0 | One or more of your equations is not a polynomial! | ATSysEquiv_SA_not_poly_eq_list. | |||
| SysEquiv | [90=v*t,90=(v+5)*(t-1/4)] |
[90=v*t^t,90=(v+5)*(t-1/4)] |
0 | The Teacher's answer should be a list of polynomial equations, but is not. Please contact your teacher. | ATSysEquiv_SB_not_poly_eq_list. | |||
| Tests of equivalence | ||||||||
| SysEquiv | [x^2=1] |
[(x-1)*(x+1)=0] |
1 | |||||
| SysEquiv | [x^2+y^2=4,y=x] |
[y=x,y^2=2] |
1 | |||||
| SysEquiv | [x^2+y^2=2,y=x] |
[y=x,y^2=2] |
0 | The entries underlined in red below are those that are incorrect. \[\left[ {\color{red}{\underline{y^2+x^2=2}}} , y=x \right] \] | ATSysEquiv_SA_system_overdetermined. | |||
| SysEquiv | [x=1] |
[(x-1)*(x+1)=0,(x-1)*(x-3)=0] |
1 | ATSysEquiv_SA_Completely_solved. | ||||
| SysEquiv | [3*a+b-c=2, a-b+2*c=5,b+c=5] |
[a=1,b=2,c=3] |
1 | |||||
| SysEquiv | [a=1,b=2,c=3] |
[3*a+b-c=2, a-b+2*c=5,b+c=5] |
1 | ATSysEquiv_SA_Completely_solved. | ||||
| SysEquiv | [x^2=1] |
[(x-1)*(x+1)*(x-2)=0] |
0 | The entries underlined in red below are those that are incorrect. \[\left[ {\color{red}{\underline{x^2=1}}} \right] \] | ATSysEquiv_SA_system_overdetermined. | |||
| SysEquiv | [x=1,y=-1] |
[(x-1)*(y+1)=0] |
0 | ATSysEquiv_SA_Not_completely_solved. | ||||
| SysEquiv | [x=1] |
[(x-1)*(x+1)=0] |
0 | ATSysEquiv_SA_Not_completely_solved. | ||||
| SysEquiv | [x=1] |
[(x-1)*(x+1)*y=0] |
0 | ATSysEquiv_SA_Not_completely_solved. | ||||
| SysEquiv | [90=v*t,90=(v+5)*(t-1/4)] |
[90=v*t,90=(v+5)*(t-1/4)] |
1 | |||||
| SysEquiv | [90=v*t,90=(v+5)*(t*x-1/4)] |
[90=v*t,90=(v+5)*(t-1/4)] |
0 | Your answer includes too many variables! | ATSysEquiv_SA_extra_variables. | |||
| SysEquiv | [90=v*t,90=(v+5)*(t-1/4)] |
[90=v*t,90=(v+5)*(t*x-1/4)] |
0 | Your answer is missing one or more variables! | ATSysEquiv_SA_missing_variables. | |||
| SysEquiv | [90=v*t] |
[90=v*t,90=(v+5)*(t-1/4)] |
0 | The equations in your system appear to be correct, but you need others besides. | ATSysEquiv_SA_system_underdetermined. | |||
| SysEquiv | [90=v*t,90=(v+5)*(t-1/4),90=(v +6)*(t-1/5)] |
[90=v*t,90=(v+5)*(t-1/4)] |
0 | The entries underlined in red below are those that are incorrect. \[\left[ 90=t\cdot v , 90=\left(t-\frac{1}{4}\right)\cdot \left(v+5 \right) , {\color{red}{\underline{90=\left(t-\frac{1}{5}\right) \cdot \left(v+6\right)}}} \right] \] | ATSysEquiv_SA_system_overdetermined. | |||
| SysEquiv | [90=v*t,90=(v+5)*(t-1/4),90=(v +6)*(t-1/5),90=(v+7)*(t-1/4),9 0=(v+8)*(t-1/3)] |
[90=v*t,90=(v+5)*(t-1/4)] |
0 | The entries underlined in red below are those that are incorrect. \[\left[ 90=t\cdot v , 90=\left(t-\frac{1}{4}\right)\cdot \left(v+5 \right) , {\color{red}{\underline{90=\left(t-\frac{1}{5}\right) \cdot \left(v+6\right)}}} , {\color{red}{\underline{90=\left(t- \frac{1}{4}\right)\cdot \left(v+7\right)}}} , {\color{red} {\underline{90=\left(t-\frac{1}{3}\right)\cdot \left(v+8\right)}}} \right] \] | ATSysEquiv_SA_system_overdetermined. | |||
| Wrong variables | ||||||||
| SysEquiv | [b^2=a,a=9] |
[x^2=y,y=9] |
0 | Your answer uses the wrong variables! | ATSysEquiv_SA_wrong_variables. | |||
| SysEquiv | [x^2=4] |
[x^2=4,y=9] |
0 | Your answer is missing one or more variables! | ATSysEquiv_SA_missing_variables. | |||
| SysEquiv | [d=90,d=v*t,d=(v+5)*(t-1/4)] |
[90=v*t,90=(v+5)*(t-1/4)] |
0 | Your answer includes too many variables! | ATSysEquiv_SA_extra_variables. | |||
| SysEquiv | stack_eval_assignments([d=90,d =v*t,d=(v+5)*(t-1/4)]) |
[90=v*t,90=(v+5)*(t-1/4)] |
1 | |||||
Sets
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Sets | {1/0} |
{0} |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATSets_STACKERROR_SAns. | ||
| Sets | {0} |
{1/0} |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATSets_STACKERROR_TAns. | ||
| Sets | x |
{1,2,3} |
0 | Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets. | ATSets_SA_not_set. | |||
| Sets | {1,2} |
x |
0 | The "Sets" answer test expects its second argument to be a set. This is an error. Please contact your teacher. | ATSets_SB_not_set. | |||
| Sets | {1,2} |
{1,2,3} |
0 | The following are missing from your set. \[\left \{3 \right \}\] | ATSets_missingentries. | |||
| Sets | {1,2,4} |
{1,2} |
0 | These entries should not be elements of your set. \[\left \{4 \right \}\] | ATSets_wrongentries. | |||
| Sets | {1,2,2+2} |
{1,2} |
0 | These entries should not be elements of your set. \[\left \{4 \right \}\] | ATSets_wrongentries. | |||
| Sets | {5,1,2,4} |
{1,2,3} |
0 | These entries should not be elements of your set. \[\left \{4 , 5 \right \}\] The following are missing from your set. \[\left \{3 \right \}\] | ATSets_wrongentries. ATSets_missingentries. | |||
| Sets | {2/4, 1/3} |
{1/2, 1/3} |
1 | |||||
| Duplicate entries | ||||||||
| Sets | {1,2,1} |
{1,2} |
1 | Your set appears to contain duplicate entries! | ATSets_duplicates. | |||
| Sets | {1,2,1+1} |
{1,2} |
1 | Your set appears to contain duplicate entries! | ATSets_duplicates. | |||
| Sets | {1,2,1+1} |
{1,2,3} |
0 | Your set appears to contain duplicate entries! The following are missing from your set. \[\left \{3 \right \}\] | ATSets_duplicates. ATSets_missingentries. | |||
| Sets | {(x-a)^6000} |
{(a-x)^6000} |
0 | These entries should not be elements of your set. \[\left \{{\left(x-a\right)}^{6000} \right \}\] The following are missing from your set. \[\left \{{\left(a-x\right)}^{6000} \right \}\] | ATSets_wrongentries. ATSets_missingentries. | |||
Expanded
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Expanded | 1/0 |
0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATExpanded_STACKERROR_SAns. | ||
| Expanded | x>2 |
x^2-2*x+1 |
0 | Your answer should be an expression, not an equation, inequality, list, set or matrix. | ATExpanded_SA_not_expression. | |||
| Expanded | x^2-1 |
0 |
1 | ATExpanded_TRUE. | ||||
| Expanded | 2*(x-1) |
0 |
0 | ATExpanded_FALSE. | ||||
| Expanded | (x-1)*(x+1) |
0 |
0 | ATExpanded_FALSE. | ||||
| Expanded | (x-a)*(x-b) |
0 |
0 | ATExpanded_FALSE. | ||||
| Expanded | x^2-(a+b)*x+a*b |
0 |
0 | ATExpanded_FALSE. | ||||
| Expanded | x^2-a*x-b*x+a*b |
0 |
1 | ATExpanded_TRUE. | ||||
| Expanded | cos(2*x) |
0 |
1 | ATExpanded_TRUE. | ||||
| Expanded | p+1 |
0 |
1 | ATExpanded_TRUE. | ||||
| Expanded | (p+1)*(p-1) |
0 |
0 | ATExpanded_FALSE. | ||||
| Expanded | 3+2*sqrt(3) |
0 |
1 | ATExpanded_TRUE. | ||||
| Expanded | 3+sqrt(12) |
0 |
1 | ATExpanded_TRUE. | ||||
| Expanded | (1+sqrt(5))*(1-sqrt(3)) |
0 |
0 | ATExpanded_FALSE. | ||||
| This fails, but you are never going to ask students to do this anyway... | ||||||||
| Expanded | ! | (a-x)^6000 |
0 |
-2 | ATExpanded_TRUE. | |||
FacForm
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| FacForm | 1/0 |
0 |
x |
-1 | ATFacForm_STACKERROR_SAns. | |||
| FacForm | 0 |
1/0 |
x |
-1 | ATFacForm_STACKERROR_TAns. | |||
| FacForm | 0 |
0 |
1/0 |
-1 | ATFacForm_STACKERROR_Opt. | |||
| Trivial cases | ||||||||
| FacForm | 2 |
2 |
x |
1 | ATFacForm_int_true. | |||
| FacForm | 6 |
6 |
x |
1 | ATFacForm_int_true. | |||
| FacForm | 1/3 |
1/3 |
x |
1 | ATFacForm_true. | |||
| FacForm | 3*x^2 |
3*x^2 |
x |
1 | ATFacForm_true. | |||
| FacForm | 4*x^2 |
4*x^2 |
x |
1 | ATFacForm_true. | |||
| Linear integer factors | ||||||||
| FacForm | 2*(x-1) |
2*x-2 |
x |
1 | ATFacForm_true. | |||
| FacForm | 2*x-2 |
2*x-2 |
x |
0 | Your answer is not factored. You need to take out a common factor. | ATFacForm_notfactored. | ||
| FacForm | 2*(x+1) |
2*x-2 |
x |
0 | Your answer is factored, well done. Note that your answer is not algebraically equivalent to the correct answer. You must have done something wrong. | ATFacForm_isfactored. ATFacForm_notalgequiv. | ||
| FacForm | 2*x+2 |
2*x-2 |
x |
0 | Your answer is not factored. You need to take out a common factor. Note that your answer is not algebraically equivalent to the correct answer. You must have done something wrong. | ATFacForm_notfactored. ATFacForm_notalgequiv. | ||
| FacForm | 2*(x+0.5) |
2*x+1 |
x |
1 | ATFacForm_default_true. | |||
| Linear factors | ||||||||
| FacForm | t*(2*x+1) |
t*(2*x+1) |
x |
1 | ATFacForm_true. | |||
| FacForm | t*x+t |
t*(x+1) |
x |
0 | Your answer is not factored. | ATFacForm_notfactored. | ||
| FacForm | 6*s*t+10*s |
2*s*(3*t+5) |
t |
0 | Your answer is not factored. | ATFacForm_notfactored. | ||
| Quadratic, with no const | ||||||||
| FacForm | 2*x*(x-3) |
2*x^2-6*x |
x |
1 | ATFacForm_true. | |||
| FacForm | 2*(x^2-3*x) |
2*x*(x-3) |
x |
0 | Your answer is not factored. You could still do some more work on the term \(x^2-3\cdot x\). | ATFacForm_notfactored. | ||
| FacForm | x*(2*x-6) |
2*x*(x-3) |
x |
0 | Your answer is not factored. You could still do some more work on the term \(2\cdot x-6\). You need to take out a common factor. | ATFacForm_notfactored. | ||
| Quadratic | ||||||||
| FacForm | (x+2)*(x+3) |
(x+2)*(x+3) |
x |
1 | ATFacForm_true. | |||
| FacForm | (x+2)*(2*x+6) |
2*(x+2)*(x+3) |
x |
0 | Your answer is not factored. You could still do some more work on the term \(2\cdot x+6\). You need to take out a common factor. | ATFacForm_notfactored. | ||
| FacForm | (z*x+z)*(2*x+6) |
2*z*(x+1)*(x+3) |
x |
0 | Your answer is not factored. You could still do some more work on the term \(z\cdot x+z\). You could still do some more work on the term \(2\cdot x+6\). You need to take out a common factor. | ATFacForm_notfactored. | ||
| FacForm | (x+t)*(x-t) |
x^2-t^2 |
x |
1 | ATFacForm_true. | |||
| FacForm | t^2-1 |
(t-1)*(t+1) |
t |
0 | Your answer is not factored. | ATFacForm_notfactored. | ||
| FacForm | t^2+1 |
t^2+1 |
t |
1 | ATFacForm_true. | |||
| FacForm | v^2+1 |
v^2+1 |
v |
1 | ATFacForm_true. | |||
| FacForm | v^2-1 |
v^2-1 |
v |
0 | Your answer is not factored. | ATFacForm_notfactored. | ||
| FacForm | -(3*w-4*v+9*u)*(3*w+4*v-u) |
-(3*w-4*v+9*u)*(3*w+4*v-u) |
v |
1 | ATFacForm_true. | |||
| FacForm | -6*k*(4*b-k-1) |
6*k*(1+k-4*b) |
k |
1 | ATFacForm_default_true. | |||
| FacForm | -2*3*k*(4*b-k-1) |
6*k*(1+k-4*b) |
k |
1 | ATFacForm_true. | |||
| FacForm | -(6*k*(4*b-k-1)) |
6*k*(1+k-4*b) |
k |
1 | ATFacForm_default_true. | |||
| FacForm | -(6*a*(4*b-a-1)) |
6*a*(1+a-4*b) |
a |
1 | ATFacForm_true. | |||
| FacForm | -(6*a*(4*b-a-1)) |
6*a*(-(4*b)+a+1) |
a |
1 | ATFacForm_true. | |||
| FacForm | x*(x-4+4/x) |
x^2-4*x+4 |
x |
0 | Your answer is not factored. You could still do some more work on the term \(x-4+\frac{4}{x}\). This term is expected to be a polynomial, but is not. | ATFacForm_notfactored. | ||
| These are delicate cases! | ||||||||
| FacForm | (2-x)*(3-x) |
(x-2)*(x-3) |
x |
1 | ATFacForm_true. | |||
| FacForm | (1-x)^2 |
(x-1)^2 |
x |
1 | ATFacForm_true. | |||
| FacForm | (1-x)*(1-x) |
(x-1)^2 |
x |
1 | ATFacForm_true. | |||
| FacForm | -(1-x)^2 |
-(x-1)^2 |
x |
1 | ATFacForm_true. | |||
| FacForm | (1-x)^2 |
(x-1)^2 |
x |
1 | ATFacForm_true. | |||
| FacForm | 4*(1-x/2)^2 |
(x-2)^2 |
x |
1 | ATFacForm_default_true. | |||
| FacForm | -3*(x-4)*(x+1) |
-3*x^2+9*x+12 |
x |
1 | ATFacForm_true. | |||
| FacForm | 3*(-x+4)*(x+1) |
-3*x^2+9*x+12 |
x |
1 | ATFacForm_true. | |||
| FacForm | 3*(4-x)*(x+1) |
-3*x^2+9*x+12 |
x |
1 | ATFacForm_true. | |||
| Cubics | ||||||||
| FacForm | (x-1)*(x^2+x+1) |
x^3-1 |
x |
1 | ATFacForm_true. | |||
| FacForm | x^3-x+1 |
x^3-x+1 |
x |
1 | ATFacForm_true. | |||
| FacForm | 7*x^3-7*x+7 |
7*(x^3-x+1) |
x |
0 | Your answer is not factored. You need to take out a common factor. | ATFacForm_notfactored. | ||
| FacForm | (1-x)*(2-x)*(3-x) |
-x^3+6*x^2-11*x+6 |
x |
1 | ATFacForm_true. | |||
| FacForm | (2-x)*(2-x)*(3-x) |
-x^3+7*x^2-16*x+12 |
x |
1 | ATFacForm_true. | |||
| FacForm | (2-x)^2*(3-x) |
-x^3+7*x^2-16*x+12 |
x |
1 | ATFacForm_true. | |||
| FacForm | (x^2-4*x+4)*(3-x) |
-x^3+7*x^2-16*x+12 |
x |
0 | Your answer is not factored. You could still do some more work on the term \(x^2-4\cdot x+4\). | ATFacForm_notfactored. | ||
| FacForm | (x^2-3*x+2)*(3-x) |
-x^3+6*x^2-11*x+6 |
x |
0 | Your answer is not factored. You could still do some more work on the term \(x^2-3\cdot x+2\). | ATFacForm_notfactored. | ||
| FacForm | 3*y^3-6*y^2-24*y |
3*(y-4)*y*(y+2) |
y |
0 | Your answer is not factored. You need to take out a common factor. | ATFacForm_notfactored. | ||
| FacForm | 3*(y^3-2*y^2-8*y) |
3*(y-4)*y*(y+2) |
y |
0 | Your answer is not factored. You could still do some more work on the term \(y^3-2\cdot y^2-8\cdot y\). | ATFacForm_notfactored. | ||
| FacForm | 3*y*(y^2-2*y-8) |
3*(y-4)*y*(y+2) |
y |
0 | Your answer is not factored. You could still do some more work on the term \(y^2-2\cdot y-8\). | ATFacForm_notfactored. | ||
| FacForm | 3*(y^2-4*y)*(y+2) |
3*(y-4)*y*(y+2) |
y |
0 | Your answer is not factored. You could still do some more work on the term \(y^2-4\cdot y\). | ATFacForm_notfactored. | ||
| FacForm | (y-4)*y*(3*y+6) |
3*(y-4)*y*(y+2) |
y |
0 | Your answer is not factored. You could still do some more work on the term \(3\cdot y+6\). You need to take out a common factor. | ATFacForm_notfactored. | ||
| FacForm | (a-x)^6000 |
(a-x)^6000 |
x |
1 | ATFacForm_true. | |||
| FacForm | (x-a)^6000 |
(a-x)^6000 |
x |
1 | ATFacForm_true. | |||
| Needs flattening | ||||||||
| FacForm | 2*a*(a*b-1) |
2*a*(a*b-1) |
a |
1 | ATFacForm_true. | |||
| FacForm | (2*a)*(a*b-1) |
2*a*(a*b-1) |
a |
1 | ATFacForm_true. | |||
| FacForm | 3*x*(7*y-3)*(7*y+3) |
3*x*(7*y-3)*(7*y+3) |
x |
1 | ATFacForm_true. | |||
| FacForm | 3*x*(7*y-3)*(7*y+3) |
3*x*(7*y-3)*(7*y+3) |
y |
1 | ATFacForm_true. | |||
| Not polynomials in a variable | ||||||||
| FacForm | (sin(x)+1)*(sin(x)-1) |
sin(x)^2-1 |
sin(x) |
1 | ATFacForm_true. | |||
| FacForm | (cos(t)-sqrt(2))^2 |
cos(t)^2-2*sqrt(2)*cos(t)+2 |
cos(t) |
1 | ATFacForm_true. | |||
| FacForm | 7 |
7 |
x |
1 | ATFacForm_int_true. | |||
| Factors over other fields | ||||||||
| FacForm | 24*(x-1/4) |
24*x-6 |
x |
1 | ATFacForm_default_true. | |||
| FacForm | (x-sqrt(2))*(x+sqrt(2)) |
x^2-2 |
x |
1 | ATFacForm_true. | |||
| FacForm | x^2-2 |
x^2-2 |
x |
1 | ATFacForm_true. | |||
| FacForm | (%i*x-2*%i) |
%i*(x-2) |
x |
0 | Your answer is not factored. | ATFacForm_notfactored. | ||
| FacForm | %i*(x-2) |
(%i*x-2*%i) |
x |
1 | ATFacForm_true. | |||
| FacForm | (x-%i)*(x+%i) |
x^2+1 |
x |
1 | ATFacForm_true. | |||
| FacForm | (x-1)*(x+(1+sqrt(3)*%i)/2)*(x+ (1-sqrt(3)*%i)/2) |
x^3-1 |
x |
1 | ATFacForm_default_true. | |||
CompSquare
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| CompSquare | 1/0 |
0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test. | STACKERROR_OPTION. | ||
| CompSquare | 1/0 |
0 |
x |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATCompSquare_STACKERROR_SAns. | |
| CompSquare | 0 |
1/0 |
x |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATCompSquare_STACKERROR_TAns. | |
| CompSquare | 0 |
0 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATCompSquare_STACKERROR_Opt. | |
| Category errors. | ||||||||
| CompSquare | 1 |
(x-1)^2+1 |
x |
0 | Your answer should depend on the variable \(x\) but it does not! | ATCompSquare_SA_not_depend_var. | ||
| CompSquare | (t-1)^2+1 |
(x-1)^2+1 |
x |
0 | Your answer should depend on the variable \(x\) but it does not! | ATCompSquare_SA_not_depend_var. | ||
| CompSquare | (x-1)^2+1=0 |
(x-1)^2+1 |
x |
0 | Your answer should be an expression, not an equation, inequality, list, set or matrix. | ATCompSquare_STACKERROR_LIST. | ||
| CompSquare | sin(x-1)+a-1 |
(x-1)^2+1 |
x |
0 | ATCompSquare_false_not_AlgEquiv. | |||
| Trivial cases | ||||||||
| CompSquare | 1 |
1 |
x |
1 | ATCompSquare_true_trivial. | |||
| CompSquare | x-a |
x-a |
x |
1 | ATCompSquare_true_trivial. | |||
| CompSquare | x^2 |
x^2 |
x |
1 | ATCompSquare_true. | |||
| CompSquare | x^2-1 |
(x-1)*(x+1) |
x |
1 | ATCompSquare_true. | |||
| CompSquare | (x-1)^2*k |
(x-1)^2*k |
x |
1 | ATCompSquare_true. | |||
| CompSquare | (x-1)^2/k |
(x-1)^2/k |
x |
1 | ATCompSquare_true. | |||
| Normal cases | ||||||||
| CompSquare | (x-1)^2+1 |
(x-1)^2+1 |
x |
1 | ATCompSquare_true. | |||
| CompSquare | (1-x)^2+1 |
(x-1)^2+1 |
x |
1 | ATCompSquare_true. | |||
| CompSquare | (X-1)^2+1 |
(x-1)^2+1 |
x |
0 | Your answer should depend on the variable \(x\) but it does not! | ATCompSquare_SA_not_depend_var. | ||
| CompSquare | 9*(x-1)^2+1 |
(3*x-3)^2+1 |
x |
1 | ATCompSquare_true. | |||
| CompSquare | -(x-1)^2 |
-(x-1)^2 |
x |
1 | ATCompSquare_true. | |||
| CompSquare | -(1-x)^2 |
-(x-1)^2 |
x |
1 | ATCompSquare_true. | |||
| CompSquare | -(x-1)^2+3 |
-(x-1)^2+3 |
x |
1 | ATCompSquare_true. | |||
| CompSquare | -(1-x)^2+3 |
-(x-1)^2+3 |
x |
1 | ATCompSquare_true. | |||
| CompSquare | -4*(x-1)^2+3 |
-4*(x-1)^2+3 |
x |
1 | ATCompSquare_true. | |||
| CompSquare | -4*(x-1)^2+3 |
-(2*x-2)^2+3 |
x |
1 | ATCompSquare_true. | |||
| CompSquare | 3-4*(x-1)^2 |
-(2*x-2)^2+3 |
x |
1 | ATCompSquare_true. | |||
| CompSquare | (x-1)^2+1 |
(x+1)^2+1 |
x |
0 | Your answer appears to be in the correct form, but is not equivalent to the correct answer. | ATCompSquare_true_not_AlgEquiv. | ||
| CompSquare | (x-a^2)^2+1+b |
(x-a^2)^2+1+b |
x |
1 | ATCompSquare_true. | |||
| CompSquare | x^2-2*x+2 |
(x-1)^2+1 |
x |
0 | The completed square is of the form \( a(\cdots\cdots)^2 + b\) where \(a\) and \(b\) do not depend on your variable. More than one of your summands appears to depend on the variable in your answer. | ATCompSquare_false_no_summands. | ||
| CompSquare | x+1 |
(x-1)^2+1 |
x |
0 | ATCompSquare_false_not_AlgEquiv. | |||
| CompSquare | a*(x-1)^2+1 |
a*(x-1)^2+1 |
x |
1 | ATCompSquare_true. | |||
| CompSquare | -a*(x-1)^2+1 |
1-a*(x-1)^2 |
x |
1 | ATCompSquare_true. | |||
| Not simple variable | ||||||||
| CompSquare | (sin(x)-1)^2+1 |
(sin(x)-1)^2+1 |
sin(x) |
1 | ATCompSquare_true. | |||
| CompSquare | (x^2-1)^2+1 |
(x^2-1)^2+1 |
x^2 |
1 | ATCompSquare_true. | |||
| CompSquare | (y-1)^2+1 |
(y-1)^2+1 |
y |
1 | ATCompSquare_true. | |||
| CompSquare | (y+1)^2+1 |
(y-1)^2+1 |
y |
0 | Your answer appears to be in the correct form, but is not equivalent to the correct answer. | ATCompSquare_true_not_AlgEquiv. | ||
| CompSquare | (x-1)^2+1 |
(sin(x)-1)^2+1 |
sin(x) |
0 | Your answer should depend on the variable \({\it facdum}\) but it does not! | ATCompSquare_SA_not_depend_var. | ||
PropLogic
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| PropLogic | 1/0 |
0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATPropLogic_STACKERROR_SAns. | ||
| PropLogic | 0 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATPropLogic_STACKERROR_TAns. | ||
| PropLogic | true |
true |
1 | |||||
| PropLogic | true |
false |
0 | |||||
| PropLogic | A implies B |
not(A) or B |
1 | |||||
| PropLogic | (a and b and c) xor (a and b) xor (a and c) xor a xor true |
(a implies b) or c |
1 | |||||
Equiv
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Equiv | x |
[x^2=4,x=2 or x=-2] |
-1 | The first argument to the Equiv answer test should be a list, but the test failed. Please contact your teacher. | ATEquiv_SA_not_list. | |||
| Equiv | [x^2=4,x=2 or x=-2] |
x |
-1 | The second argument to the Equiv answer test should be a list, but the test failed. Please contact your teacher. | ATEquiv_SB_not_list. | |||
| Equiv | [1/0] |
[x^2=4,x=2 or x=-2] |
-1 | ATEquiv_STACKERROR_SAns. | ||||
| Equiv | [x^2=4,x=2 or x=-2] |
[1/0] |
-1 | ATEquiv_STACKERROR_TAns. | ||||
| Equiv | [x^2=4,x=2 or x=-2] |
[x^2=4,x=2 or x=-2] |
1 | \[\begin{array}{lll} &x^2=4& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ or }}\, x=-2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [x^2=4,x=#pm#2,x=2 and x=-2] |
[x^2=4,x=2 or x=-2] |
0 | \[\begin{array}{lll} &x^2=4& \cr \color{green}{\Leftrightarrow}&x= \pm 2& \cr \color{red}{\mbox{and/or confusion!}}&\left\{\begin{array}{l}x=2\cr x=-2\cr \end{array}\right.& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR,ANDOR) | |||
| Equiv | [x^2=4,x=2] |
[x^2=4,x=2 or x=-2] |
0 | \[\begin{array}{lll} &x^2=4& \cr \color{red}{\Leftarrow}&x=2& \cr \end{array}\] | (EMPTYCHAR,IMPLIEDCHAR) | |||
| Equiv | [x^2=4,x=2] |
[x^2=4,x=2] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&x^2=4& \cr \color{green}{\Leftrightarrow}&x=2& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [x^2=4,x^2-4=0,(x-2)*(x+2)=0,x =2 or x=-2] |
[x^2=4,x=2 or x=-2] |
1 | \[\begin{array}{lll} &x^2=4& \cr \color{green}{\Leftrightarrow}&x^2-4=0& \cr \color{green}{\Leftrightarrow}&\left(x-2\right)\cdot \left(x+2\right)=0& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ or }}\, x=-2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^2=4,x= #pm#2, x=2 or x=-2] |
[x^2=4,x=2 or x=-2] |
1 | \[\begin{array}{lll} &x^2=4& \cr \color{green}{\Leftrightarrow}&x= \pm 2& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ or }}\, x=-2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^2-6*x+9=0,x=3] |
[x^2-6*x+9=0,x=3] |
1 | \[\begin{array}{lll} &x^2-6\cdot x+9=0& \cr \color{green}{\mbox{(Same roots)}}&x=3& \cr \end{array}\] | (EMPTYCHAR,SAMEROOTS) | |||
| Equiv | [] |
[] |
1 | \[\begin{array}{lll} &\left[ \right] & \cr \end{array}\] | (EMPTYCHAR) | |||
| Equiv | [x^2=-1] |
[] |
1 | \[\begin{array}{lll} &x^2=-1& \cr \end{array}\] | (EMPTYCHAR) | |||
| Equiv | [x=x,all] |
[] |
1 | \[\begin{array}{lll} &x=x& \cr \color{green}{\Leftrightarrow}&\mathbb{R}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [x=x,true] |
[] |
1 | \[\begin{array}{lll} &x=x& \cr \color{green}{\Leftrightarrow}&\mathbf{True}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [x=x,false] |
[] |
0 | \[\begin{array}{lll} &x=x& \cr \color{red}{?}&\mathbf{False}& \cr \end{array}\] | (EMPTYCHAR,QMCHAR) | |||
| Equiv | [1=1,all] |
[] |
1 | \[\begin{array}{lll} &1=1& \cr \color{green}{\Leftrightarrow}&\mathbb{R}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [1=1,true] |
[] |
1 | \[\begin{array}{lll} &1=1& \cr \color{green}{\Leftrightarrow}&\mathbf{True}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [0=0,all] |
[] |
1 | \[\begin{array}{lll} &0=0& \cr \color{green}{\Leftrightarrow}&\mathbb{R}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [0=0,true] |
[] |
1 | \[\begin{array}{lll} &0=0& \cr \color{green}{\Leftrightarrow}&\mathbf{True}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [1=2,false] |
[] |
1 | \[\begin{array}{lll} &1=2& \cr \color{green}{\Leftrightarrow}&\mathbf{False}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [1=2,none] |
[] |
1 | \[\begin{array}{lll} &1=2& \cr \color{green}{\Leftrightarrow}&\emptyset& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [1=2,{}] |
[] |
1 | \[\begin{array}{lll} &1=2& \cr \color{green}{\Leftrightarrow}&\left \{ \right \}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [1=2,[]] |
[] |
1 | \[\begin{array}{lll} &1=2& \cr \color{green}{\Leftrightarrow}&\left[ \right] & \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [x=1,X=1] |
[] |
0 | \[\begin{array}{lll} &x=1& \cr \color{red}{?}&X=1& \cr \end{array}\] | (EMPTYCHAR,QMCHAR) | |||
| Equiv | [1/(x^2+1)=1/((x+%i)*(x-%i)),t rue] |
[] |
1 | \[\begin{array}{lll} &\frac{1}{x^2+1}=\frac{1}{\left(x+\mathrm{i}\right)\cdot \left(x-\mathrm{i}\right)}& \cr \color{green}{\Leftrightarrow}&\mathbf{True}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [2^2,stackeq(4)] |
[] |
1 | \[\begin{array}{lll} &2^2& \cr \color{green}{\checkmark}&=4& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK) | |||
| Equiv | [2^2,stackeq(3)] |
[] |
0 | \[\begin{array}{lll} &2^2& \cr \color{red}{\Rightarrow}&=3& \cr \end{array}\] | (EMPTYCHAR,IMPLIESCHAR) | |||
| Equiv | [2^2,4] |
[] |
1 | \[\begin{array}{lll} &2^2& \cr \color{green}{\Leftrightarrow}&4& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [2^2,3] |
[] |
0 | \[\begin{array}{lll} &2^2& \cr \color{red}{\Rightarrow}&3& \cr \end{array}\] | (EMPTYCHAR,IMPLIESCHAR) | |||
| Equiv | [lg(64,4),lg(4^3,4),3*lg(4,4), 3] |
[] |
1 | \[\begin{array}{lll} &\log_{4}\left(64\right)& \cr \color{green}{\Leftrightarrow}&\log_{4}\left(4^3\right)& \cr \color{green}{\Leftrightarrow}&3\cdot \log_{4}\left(4\right)& \cr \color{green}{\Leftrightarrow}&3& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [lg(64,4),stackeq(lg(4^3,4)),s tackeq(3*lg(4,4)),stackeq(3)] |
[] |
1 | \[\begin{array}{lll} &\log_{4}\left(64\right)& \cr \color{green}{\checkmark}&=\log_{4}\left(4^3\right)& \cr \color{green}{\checkmark}&=3\cdot \log_{4}\left(4\right)& \cr \color{green}{\checkmark}&=3& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK) | |||
| Equiv | [x=1 or x=2,x=1 or 2] |
[] |
0 | \[\begin{array}{lll} &x=1\,{\mbox{ or }}\, x=2& \cr \color{red}{\mbox{Missing assignments}}&x=1\,{\mbox{ or }}\, 2& \cr \end{array}\] | (EMPTYCHAR,MISSINGVAR) | |||
| Equiv | [x=1 or x=2,x=1 and x=2] |
[] |
0 | \[\begin{array}{lll} &x=1\,{\mbox{ or }}\, x=2& \cr \color{red}{\mbox{and/or confusion!}}&\left\{\begin{array}{l}x=1\cr x=2\cr \end{array}\right.& \cr \end{array}\] | (EMPTYCHAR,ANDOR) | |||
| Equiv | [x=1 and y=2,x=1 or y=2] |
[] |
0 | \[\begin{array}{lll} &\left\{\begin{array}{l}x=1\cr y=2\cr \end{array}\right.& \cr \color{red}{\mbox{and/or confusion!}}&x=1\,{\mbox{ or }}\, y=2& \cr \end{array}\] | (EMPTYCHAR,ANDOR) | |||
| Equiv | [a=b,a^2=b^2] |
[] |
0 | \[\begin{array}{lll} &a=b& \cr \color{red}{\Rightarrow}&a^2=b^2& \cr \end{array}\] | (EMPTYCHAR,IMPLIESCHAR) | |||
| Equiv | [a=b,sqrt(a)=sqrt(b)] |
[] |
0 | \[\begin{array}{lll} &a=b& \cr \color{red}{\Leftarrow}&\sqrt{a}=\sqrt{b}& \cr \end{array}\] | (EMPTYCHAR,IMPLIEDCHAR) | |||
| Equiv | [a^2=b^2,a=b] |
[] |
0 | \[\begin{array}{lll} &a^2=b^2& \cr \color{red}{\Leftarrow}&a=b& \cr \end{array}\] | (EMPTYCHAR,IMPLIEDCHAR) | |||
| Equiv | [a^2=b^2,a=b or a=-b] |
[] |
1 | \[\begin{array}{lll} &a^2=b^2& \cr \color{green}{\Leftrightarrow}&a=b\,{\mbox{ or }}\, a=-b& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [a^2=b^2,a= #pm#b,a= b or a=-b ] |
[] |
1 | \[\begin{array}{lll} &a^2=b^2& \cr \color{green}{\Leftrightarrow}&a= \pm b& \cr \color{green}{\Leftrightarrow}&a=b\,{\mbox{ or }}\, a=-b& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [9*x^2/2-81*x/2+90=5*x^2/2-5*x -20 nounor 9*x^2/2-81*x/2+90=- (5*x^2/2-5*x-20),9*x^2-81*x+18 0=5*x^2-10*x-40 nounor 9*x^2-8 1*x+180=-5*x^2+10*x+40,4*x^2-7 1*x+220=0 nounor 14*x^2-91*x+1 40=0,x=(71 #pm# sqrt(71^2-4*4* 220))/(2*4) nounor x=(91 #pm# sqrt(91^2-4*14*140))/(2*14),x= 55/4 nounor x=4 nounor x=5/2] |
[] |
1 | \[\begin{array}{lll} &\frac{9\cdot x^2}{2}-\frac{81\cdot x}{2}+90=\frac{5\cdot x^2}{2}-5\cdot x-20\,{\mbox{ or }}\, \frac{9\cdot x^2}{2}-\frac{81\cdot x}{2}+90=-\left(\frac{5\cdot x^2}{2}-5\cdot x-20\right)& \cr \color{green}{\Leftrightarrow}&9\cdot x^2-81\cdot x+180=5\cdot x^2-10\cdot x-40\,{\mbox{ or }}\, 9\cdot x^2-81\cdot x+180=-5\cdot x^2+10\cdot x+40& \cr \color{green}{\Leftrightarrow}&4\cdot x^2-71\cdot x+220=0\,{\mbox{ or }}\, 14\cdot x^2-91\cdot x+140=0& \cr \color{green}{\Leftrightarrow}&x=\frac{{71 \pm \sqrt{71^2-4\cdot 4\cdot 220}}}{2\cdot 4}\,{\mbox{ or }}\, x=\frac{{91 \pm \sqrt{91^2-4\cdot 14\cdot 140}}}{2\cdot 14}& \cr \color{green}{\mbox{(Same roots)}}&x=\frac{55}{4}\,{\mbox{ or }}\, x=4\,{\mbox{ or }}\, x=\frac{5}{2}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR,SAMEROOTS) | |||
| Equiv | [a=b,abs(a)=abs(b),a=b] |
[] |
0 | \[\begin{array}{lll} &a=b& \cr \color{red}{\Rightarrow}&\left| a\right| =\left| b\right| & \cr \color{red}{\Leftarrow}&a=b& \cr \end{array}\] | (EMPTYCHAR,IMPLIESCHAR,IMPLIEDCHAR) | |||
| Equiv | [abs(a)=abs(b),a=b or a=-b] |
[] |
1 | \[\begin{array}{lll} &\left| a\right| =\left| b\right| & \cr \color{green}{\Leftrightarrow}&a=b\,{\mbox{ or }}\, a=-b& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [abs(a)=abs(b),a^2=b^2] |
[] |
1 | \[\begin{array}{lll} &\left| a\right| =\left| b\right| & \cr \color{green}{\Leftrightarrow}&a^2=b^2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [x^3=8,x=2] |
[] |
0 | \[\begin{array}{lll} &x^3=8& \cr \color{red}{\Leftarrow}&x=2& \cr \end{array}\] | (EMPTYCHAR,IMPLIEDCHAR) | |||
| Equiv | [x^3=8,x=2] |
[] |
[assumereal] |
1 | \[\begin{array}{lll}\color{blue}{(\mathbb{R})}&x^3=8& \cr \color{green}{\Leftrightarrow}\, \color{blue}{(\mathbb{R})}&x=2& \cr \end{array}\] | (ASSUMEREALVARS, EQUIVCHARREAL) | ||
| Equiv | [abs(x-1/2)+abs(x+1/2)=2,abs(x )=1] |
[] |
1 | \[\begin{array}{lll} &\left| x-\frac{1}{2}\right| +\left| x+\frac{1}{2}\right| =2& \cr \color{green}{\Leftrightarrow}&\left| x\right| =1& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [a^2=9 and a>0,a=3] |
[] |
1 | \[\begin{array}{lll} &\left\{\begin{array}{l}a^2=9\cr a > 0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&a=3& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [T=2*pi*sqrt(L/g),T^2=4*pi^2*L /g,g=4*pi^2*L/T^2] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&T=2\cdot \pi\cdot \sqrt{\frac{L}{g}}& \cr \color{green}{\Leftrightarrow}&T^2=\frac{4\cdot \pi^2\cdot L}{g}& \cr \color{green}{\Leftrightarrow}&g=\frac{4\cdot \pi^2\cdot L}{T^2}& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR, EQUIVCHAR) | ||
| Equiv | [a=b,a^2=b^2] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&a=b& \cr \color{green}{\Leftrightarrow}&a^2=b^2& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [a=b,sqrt(a)=sqrt(b)] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&a=b& \cr \color{green}{\Leftrightarrow}&\sqrt{a}=\sqrt{b}& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [a^2=b^2,a=b] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&a^2=b^2& \cr \color{green}{\Leftrightarrow}&a=b& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [a^2=b^2,a=b or a=-b] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&a^2=b^2& \cr \color{green}{\Leftrightarrow}&a=b\,{\mbox{ or }}\, a=-b& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [a=b,abs(a)=abs(b)] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&a=b& \cr \color{green}{\Leftrightarrow}&\left| a\right| =\left| b\right| & \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [abs(a)=abs(b),a=b] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&\left| a\right| =\left| b\right| & \cr \color{green}{\Leftrightarrow}&a=b& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [abs(a)=abs(b),a=-b] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&\left| a\right| =\left| b\right| & \cr \color{green}{\Leftrightarrow}&a=-b& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [abs(a)=abs(b),a=b or a=-b] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&\left| a\right| =\left| b\right| & \cr \color{green}{\Leftrightarrow}&a=b\,{\mbox{ or }}\, a=-b& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [x=abs(-2),x=2] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&x=\left| -2\right| & \cr \color{green}{\Leftrightarrow}&x=2& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [abs(a)=abs(b),a^2=b^2] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&\left| a\right| =\left| b\right| & \cr \color{green}{\Leftrightarrow}&a^2=b^2& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [x^2=9,x=#pm#3,x=3 or x=-3,x=3 ] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&x^2=9& \cr \color{green}{\Leftrightarrow}&x= \pm 3& \cr \color{green}{\Leftrightarrow}&x=3\,{\mbox{ or }}\, x=-3& \cr \color{green}{\Leftrightarrow}&x=3& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | ||
| Equiv | [x^2=9,x=3] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&x^2=9& \cr \color{green}{\Leftrightarrow}&x=3& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [x^2=2,x=#pm#sqrt(2),x=sqrt(2) or x=-sqrt(2)] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&x^2=2& \cr \color{green}{\Leftrightarrow}&x= \pm \sqrt{2}& \cr \color{green}{\Leftrightarrow}&x=\sqrt{2}\,{\mbox{ or }}\, x=-\sqrt{2}& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR, EQUIVCHAR) | ||
| Equiv | [x^2=2,x=sqrt(2)] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&x^2=2& \cr \color{green}{\Leftrightarrow}&x=\sqrt{2}& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [x^2 = a^2-b,x = sqrt(a^2-b)] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&x^2=a^2-b& \cr \color{green}{\Leftrightarrow}&x=\sqrt{a^2-b}& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
| Equiv | [2*(x-3) = 4*x-3*(x+2),2*x-6=x -6,x=0] |
[] |
1 | \[\begin{array}{lll} &2\cdot \left(x-3\right)=4\cdot x-3\cdot \left(x+2\right)& \cr \color{green}{\Leftrightarrow}&2\cdot x-6=x-6& \cr \color{green}{\Leftrightarrow}&x=0& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [2*(x-3) = 5*x-3*(x+2),2*x-6=2 *x-6,0=0,all] |
[] |
1 | \[\begin{array}{lll} &2\cdot \left(x-3\right)=5\cdot x-3\cdot \left(x+2\right)& \cr \color{green}{\Leftrightarrow}&2\cdot x-6=2\cdot x-6& \cr \color{green}{\Leftrightarrow}&0=0& \cr \color{green}{\Leftrightarrow}&\mathbb{R}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [2*(x-3) = 5*x-3*(x+1),2*x-6=2
*x-3,0=3,{}] |
[] |
1 | \[\begin{array}{lll} &2\cdot \left(x-3\right)=5\cdot x-3\cdot \left(x+1\right)& \cr \color{green}{\Leftrightarrow}&2\cdot x-6=2\cdot x-3& \cr \color{green}{\Leftrightarrow}&0=3& \cr \color{green}{\Leftrightarrow}&\left \{ \right \}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [a^2=b^2,a^2-b^2=0,(a-b)*(a+b) =0,a=b or a=-b] |
[] |
1 | \[\begin{array}{lll} &a^2=b^2& \cr \color{green}{\Leftrightarrow}&a^2-b^2=0& \cr \color{green}{\Leftrightarrow}&\left(a-b\right)\cdot \left(a+b\right)=0& \cr \color{green}{\Leftrightarrow}&a=b\,{\mbox{ or }}\, a=-b& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [a^3=b^3,a^3-b^3=0,(a-b)*(a^2+ a*b+b^2)=0,(a-b)=0,a=b] |
[] |
0 | \[\begin{array}{lll} &a^3=b^3& \cr \color{green}{\Leftrightarrow}&a^3-b^3=0& \cr \color{green}{\Leftrightarrow}&\left(a-b\right)\cdot \left(a^2+a\cdot b+b^2\right)=0& \cr \color{red}{\Leftarrow}&a-b=0& \cr \color{green}{\Leftrightarrow}&a=b& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR,IMPLIEDCHAR, EQUIVCHAR) | |||
| Equiv | [a^3=b^3,a^3-b^3=0,(a-b)*(a^2+ a*b+b^2)=0,(a-b)=0 or (a^2+a*b +b^2)=0, a=b or (a+(1+%i*sqrt( 3))/2*b)*(a+(1-%i*sqrt(3))/2*b )=0, a=b or a=-(1+%i*sqrt(3))/ 2*b or a=-(1-%i*sqrt(3))/2*b] |
[] |
1 | \[\begin{array}{lll} &a^3=b^3& \cr \color{green}{\Leftrightarrow}&a^3-b^3=0& \cr \color{green}{\Leftrightarrow}&\left(a-b\right)\cdot \left(a^2+a\cdot b+b^2\right)=0& \cr \color{green}{\Leftrightarrow}&a-b=0\,{\mbox{ or }}\, a^2+a\cdot b+b^2=0& \cr \color{green}{\Leftrightarrow}&a=b\,{\mbox{ or }}\, \left(a+\frac{1+\mathrm{i}\cdot \sqrt{3}}{2}\cdot b\right)\cdot \left(a+\frac{1-\mathrm{i}\cdot \sqrt{3}}{2}\cdot b\right)=0& \cr \color{green}{\Leftrightarrow}&a=b\,{\mbox{ or }}\, a=\frac{-\left(1+\mathrm{i}\cdot \sqrt{3}\right)}{2}\cdot b\,{\mbox{ or }}\, a=\frac{-\left(1-\mathrm{i}\cdot \sqrt{3}\right)}{2}\cdot b& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^2-x=30,x^2-x-30=0,(x-6)*(x+ 5)=0,x-6=0 or x+5=0,x=6 or x=- 5] |
[] |
1 | \[\begin{array}{lll} &x^2-x=30& \cr \color{green}{\Leftrightarrow}&x^2-x-30=0& \cr \color{green}{\Leftrightarrow}&\left(x-6\right)\cdot \left(x+5\right)=0& \cr \color{green}{\Leftrightarrow}&x-6=0\,{\mbox{ or }}\, x+5=0& \cr \color{green}{\Leftrightarrow}&x=6\,{\mbox{ or }}\, x=-5& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^2=2,x^2-2=0,(x-sqrt(2))*(x+ sqrt(2))=0,x=sqrt(2) or x=-sqr t(2)] |
[] |
1 | \[\begin{array}{lll} &x^2=2& \cr \color{green}{\Leftrightarrow}&x^2-2=0& \cr \color{green}{\Leftrightarrow}&\left(x-\sqrt{2}\right)\cdot \left(x+\sqrt{2}\right)=0& \cr \color{green}{\Leftrightarrow}&x=\sqrt{2}\,{\mbox{ or }}\, x=-\sqrt{2}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^2=2,x=#pm#sqrt(2),x=sqrt(2) or x=-sqrt(2)] |
[] |
1 | \[\begin{array}{lll} &x^2=2& \cr \color{green}{\Leftrightarrow}&x= \pm \sqrt{2}& \cr \color{green}{\Leftrightarrow}&x=\sqrt{2}\,{\mbox{ or }}\, x=-\sqrt{2}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [(2*x-7)^2=(x+1)^2,(2*x-7)^2 - (x+1)^2=0,(2*x-7+x+1)*(2*x-7-x -1)=0,(3*x-6)*(x-8)=0,x=2 or x =8] |
[] |
1 | \[\begin{array}{lll} &{\left(2\cdot x-7\right)}^2={\left(x+1\right)}^2& \cr \color{green}{\Leftrightarrow}&{\left(2\cdot x-7\right)}^2-{\left(x+1\right)}^2=0& \cr \color{green}{\Leftrightarrow}&\left(2\cdot x-7+x+1\right)\cdot \left(2\cdot x-7-x-1\right)=0& \cr \color{green}{\Leftrightarrow}&\left(3\cdot x-6\right)\cdot \left(x-8\right)=0& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ or }}\, x=8& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^2-6*x=-9,(x-3)^2=0,x-3=0,x= 3] |
[] |
1 | \[\begin{array}{lll} &x^2-6\cdot x=-9& \cr \color{green}{\Leftrightarrow}&{\left(x-3\right)}^2=0& \cr \color{green}{\mbox{(Same roots)}}&x-3=0& \cr \color{green}{\Leftrightarrow}&x=3& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR,SAMEROOTS, EQUIVCHAR) | |||
| Equiv | [(2*x-7)^2=(x+1)^2,sqrt((2*x-7 )^2)=sqrt((x+1)^2),2*x-7=x+1,x =8] |
[] |
0 | \[\begin{array}{lll} &{\left(2\cdot x-7\right)}^2={\left(x+1\right)}^2& \cr \color{green}{\Leftrightarrow}&\sqrt{{\left(2\cdot x-7\right)}^2}=\sqrt{{\left(x+1\right)}^2}& \cr \color{red}{\Leftarrow}&2\cdot x-7=x+1& \cr \color{green}{\Leftrightarrow}&x=8& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR,IMPLIEDCHAR, EQUIVCHAR) | |||
| Equiv | [x^2-10*x+9 = 0, (x-5)^2-16 = 0, (x-5)^2 =16, x-5 =#pm#4, x- 5 =4 or x-5=-4, x = 1 or x = 9 ] |
[] |
1 | \[\begin{array}{lll} &x^2-10\cdot x+9=0& \cr \color{green}{\Leftrightarrow}&{\left(x-5\right)}^2-16=0& \cr \color{green}{\Leftrightarrow}&{\left(x-5\right)}^2=16& \cr \color{green}{\Leftrightarrow}&x-5= \pm 4& \cr \color{green}{\Leftrightarrow}&x-5=4\,{\mbox{ or }}\, x-5=-4& \cr \color{green}{\Leftrightarrow}&x=1\,{\mbox{ or }}\, x=9& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^2-2*p*x-q=0,x^2-2*p*x=q,x^2 -2*p*x+p^2=q+p^2,(x-p)^2=q+p^2 ,x-p=#pm#sqrt(q+p^2),x-p=sqrt( q+p^2) or x-p=-sqrt(q+p^2),x=p +sqrt(q+p^2) or x=p-sqrt(q+p^2 )] |
[] |
1 | \[\begin{array}{lll} &x^2-2\cdot p\cdot x-q=0& \cr \color{green}{\Leftrightarrow}&x^2-2\cdot p\cdot x=q& \cr \color{green}{\Leftrightarrow}&x^2-2\cdot p\cdot x+p^2=q+p^2& \cr \color{green}{\Leftrightarrow}&{\left(x-p\right)}^2=q+p^2& \cr \color{green}{\Leftrightarrow}&x-p= \pm \sqrt{q+p^2}& \cr \color{green}{\Leftrightarrow}&x-p=\sqrt{q+p^2}\,{\mbox{ or }}\, x-p=-\sqrt{q+p^2}& \cr \color{green}{\Leftrightarrow}&x=p+\sqrt{q+p^2}\,{\mbox{ or }}\, x=p-\sqrt{q+p^2}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^2-10*x+7=0,(x-5)^2-18=0,(x- 5)^2=sqrt(18)^2,(x-5)^2-sqrt(1 8)^2=0,(x-5-sqrt(18))*(x-5+sqr t(18))=0,x=5-sqrt(18) or x=5+s qrt(18)] |
[] |
1 | \[\begin{array}{lll} &x^2-10\cdot x+7=0& \cr \color{green}{\Leftrightarrow}&{\left(x-5\right)}^2-18=0& \cr \color{green}{\Leftrightarrow}&{\left(x-5\right)}^2={\sqrt{18}}^2& \cr \color{green}{\Leftrightarrow}&{\left(x-5\right)}^2-{\sqrt{18}}^2=0& \cr \color{green}{\Leftrightarrow}&\left(x-5-\sqrt{18}\right)\cdot \left(x-5+\sqrt{18}\right)=0& \cr \color{green}{\Leftrightarrow}&x=5-\sqrt{18}\,{\mbox{ or }}\, x=5+\sqrt{18}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [9*x^2/2-81*x/2+90=5*x^2/2-5*x -20,4*x^2-71*x+220 = 0,x = (71 #pm# 39)/8,x=55/4 nounor x=4] |
[] |
1 | \[\begin{array}{lll} &\frac{9\cdot x^2}{2}-\frac{81\cdot x}{2}+90=\frac{5\cdot x^2}{2}-5\cdot x-20& \cr \color{green}{\Leftrightarrow}&4\cdot x^2-71\cdot x+220=0& \cr \color{green}{\Leftrightarrow}&x=\frac{{71 \pm 39}}{8}& \cr \color{green}{\Leftrightarrow}&x=\frac{55}{4}\,{\mbox{ or }}\, x=4& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^2+2*a*x = 0, x*(x+2*a)=0, ( x+a-a)*(x+a+a)=0, (x+a)^2-a^2= 0] |
[] |
1 | \[\begin{array}{lll} &x^2+2\cdot a\cdot x=0& \cr \color{green}{\Leftrightarrow}&x\cdot \left(x+2\cdot a\right)=0& \cr \color{green}{\Leftrightarrow}&\left(x+a-a\right)\cdot \left(x+a+a\right)=0& \cr \color{green}{\Leftrightarrow}&{\left(x+a\right)}^2-a^2=0& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^3-1=0,(x-1)*(x^2+x+1)=0,x=1 ] |
[] |
0 | \[\begin{array}{lll} &x^3-1=0& \cr \color{green}{\Leftrightarrow}&\left(x-1\right)\cdot \left(x^2+x+1\right)=0& \cr \color{red}{\Leftarrow}&x=1& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR,IMPLIEDCHAR) | |||
| Equiv | [x^3-1=0,(x-1)*(x^2+x+1)=0,x=1 or x^2+x+1=0,x=1 or x = -(sqr t(3)*%i+1)/2 or x=(sqrt(3)*%i- 1)/2] |
[] |
1 | \[\begin{array}{lll} &x^3-1=0& \cr \color{green}{\Leftrightarrow}&\left(x-1\right)\cdot \left(x^2+x+1\right)=0& \cr \color{green}{\Leftrightarrow}&x=1\,{\mbox{ or }}\, x^2+x+1=0& \cr \color{green}{\Leftrightarrow}&x=1\,{\mbox{ or }}\, x=\frac{-\left(\sqrt{3}\cdot \mathrm{i}+1\right)}{2}\,{\mbox{ or }}\, x=\frac{\sqrt{3}\cdot \mathrm{i}-1}{2}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [a*x^2+b*x+c=0 or a=0,a^2*x^2+ a*b*x+a*c=0,(a*x)^2+b*(a*x)+a* c=0, (a*x)^2+b*(a*x)+b^2/4-b^2 /4+a*c=0,(a*x+b/2)^2-b^2/4+a*c =0,(a*x+b/2)^2=b^2/4-a*c, a*x+ b/2= #pm#sqrt(b^2/4-a*c),a*x=- b/2+sqrt(b^2/4-a*c) or a*x=-b/ 2-sqrt(b^2/4-a*c), (a=0 or x=( -b+sqrt(b^2-4*a*c))/(2*a)) or (a=0 or x=(-b-sqrt(b^2-4*a*c)) /(2*a)), a^2=0 or x=(-b+sqrt(b ^2-4*a*c))/(2*a) or x=(-b-sqrt (b^2-4*a*c))/(2*a)] |
[] |
1 | \[\begin{array}{lll} &a\cdot x^2+b\cdot x+c=0\,{\mbox{ or }}\, a=0& \cr \color{green}{\Leftrightarrow}&a^2\cdot x^2+a\cdot b\cdot x+a\cdot c=0& \cr \color{green}{\Leftrightarrow}&{\left(a\cdot x\right)}^2+b\cdot \left(a\cdot x\right)+a\cdot c=0& \cr \color{green}{\Leftrightarrow}&{\left(a\cdot x\right)}^2+b\cdot \left(a\cdot x\right)+\frac{b^2}{4}-\frac{b^2}{4}+a\cdot c=0& \cr \color{green}{\Leftrightarrow}&{\left(a\cdot x+\frac{b}{2}\right)}^2-\frac{b^2}{4}+a\cdot c=0& \cr \color{green}{\Leftrightarrow}&{\left(a\cdot x+\frac{b}{2}\right)}^2=\frac{b^2}{4}-a\cdot c& \cr \color{green}{\Leftrightarrow}&a\cdot x+\frac{b}{2}= \pm \sqrt{\frac{b^2}{4}-a\cdot c}& \cr \color{green}{\Leftrightarrow}&a\cdot x=-\frac{b}{2}+\sqrt{\frac{b^2}{4}-a\cdot c}\,{\mbox{ or }}\, a\cdot x=-\frac{b}{2}-\sqrt{\frac{b^2}{4}-a\cdot c}& \cr \color{green}{\Leftrightarrow}&a=0\,{\mbox{ or }}\, x=\frac{-b+\sqrt{b^2-4\cdot a\cdot c}}{2\cdot a}\,{\mbox{ or }}\, \left(a=0\,{\mbox{ or }}\, x=\frac{-b-\sqrt{b^2-4\cdot a\cdot c}}{2\cdot a}\right)& \cr \color{green}{\Leftrightarrow}&a^2=0\,{\mbox{ or }}\, x=\frac{-b+\sqrt{b^2-4\cdot a\cdot c}}{2\cdot a}\,{\mbox{ or }}\, x=\frac{-b-\sqrt{b^2-4\cdot a\cdot c}}{2\cdot a}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [a*x^2+b*x=-c,4*a^2*x^2+4*a*b* x+b^2=b^2-4*a*c,(2*a*x+b)^2=b^ 2-4*a*c,2*a*x+b=#pm#sqrt(b^2-4 *a*c),2*a*x=-b#pm#sqrt(b^2-4*a *c),x=(-b#pm#sqrt(b^2-4*a*c))/ (2*a)] |
[] |
0 | \[\begin{array}{lll} &a\cdot x^2+b\cdot x=-c& \cr \color{red}{\Rightarrow}&4\cdot a^2\cdot x^2+4\cdot a\cdot b\cdot x+b^2=b^2-4\cdot a\cdot c& \cr \color{green}{\Leftrightarrow}&{\left(2\cdot a\cdot x+b\right)}^2=b^2-4\cdot a\cdot c& \cr \color{green}{\Leftrightarrow}&2\cdot a\cdot x+b= \pm \sqrt{b^2-4\cdot a\cdot c}& \cr \color{green}{\Leftrightarrow}&2\cdot a\cdot x={-b \pm \sqrt{b^2-4\cdot a\cdot c}}& \cr \color{red}{?}&x=\frac{{-b \pm \sqrt{b^2-4\cdot a\cdot c}}}{2\cdot a}& \cr \end{array}\] | (EMPTYCHAR,IMPLIESCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR,QMCHAR) | |||
| Equiv | [a*x^2+b*x=-c or a=0,4*a^2*x^2 +4*a*b*x+b^2=b^2-4*a*c,(2*a*x+ b)^2=b^2-4*a*c,2*a*x+b=#pm#sqr t(b^2-4*a*c),2*a*x=-b#pm#sqrt( b^2-4*a*c),x=(-b#pm#sqrt(b^2-4 *a*c))/(2*a) or a=0] |
[] |
1 | \[\begin{array}{lll} &a\cdot x^2+b\cdot x=-c\,{\mbox{ or }}\, a=0& \cr \color{green}{\Leftrightarrow}&4\cdot a^2\cdot x^2+4\cdot a\cdot b\cdot x+b^2=b^2-4\cdot a\cdot c& \cr \color{green}{\Leftrightarrow}&{\left(2\cdot a\cdot x+b\right)}^2=b^2-4\cdot a\cdot c& \cr \color{green}{\Leftrightarrow}&2\cdot a\cdot x+b= \pm \sqrt{b^2-4\cdot a\cdot c}& \cr \color{green}{\Leftrightarrow}&2\cdot a\cdot x={-b \pm \sqrt{b^2-4\cdot a\cdot c}}& \cr \color{green}{\Leftrightarrow}&x=\frac{{-b \pm \sqrt{b^2-4\cdot a\cdot c}}}{2\cdot a}\,{\mbox{ or }}\, a=0& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [sqrt(3*x+4) = 2+sqrt(x+2), 3* x+4=4+4*sqrt(x+2)+(x+2),x-1=2* sqrt(x+2),x^2-2*x+1 = 4*x+8,x^ 2-6*x-7 = 0,(x-7)*(x+1) = 0,x= 7 or x=-1] |
[] |
0 | \[\begin{array}{lll} &\sqrt{3\cdot x+4}=2+\sqrt{x+2}&{\color{blue}{{x \in {\left[ -\frac{4}{3},\, \infty \right)}}}}\cr \color{red}{\Rightarrow}&3\cdot x+4=4+4\cdot \sqrt{x+2}+\left(x+2\right)&{\color{blue}{{x \in {\left[ -2,\, \infty \right)}}}}\cr \color{green}{\Leftrightarrow}&x-1=2\cdot \sqrt{x+2}&{\color{blue}{{x \in {\left[ -2,\, \infty \right)}}}}\cr \color{red}{\Rightarrow}&x^2-2\cdot x+1=4\cdot x+8& \cr \color{green}{\Leftrightarrow}&x^2-6\cdot x-7=0& \cr \color{green}{\Leftrightarrow}&\left(x-7\right)\cdot \left(x+1\right)=0& \cr \color{green}{\Leftrightarrow}&x=7\,{\mbox{ or }}\, x=-1& \cr \end{array}\] | (EMPTYCHAR,IMPLIESCHAR, EQUIVCHAR,IMPLIESCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [sqrt(3*x+4) = 2+sqrt(x+2), 3* x+4=4+4*sqrt(x+2)+(x+2),x-1=2* sqrt(x+2),x^2-2*x+1 = 4*x+8,x^ 2-6*x-7 = 0,(x-7)*(x+1) = 0,x= 7 or x=-1,x=7] |
[] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&\sqrt{3\cdot x+4}=2+\sqrt{x+2}&{\color{blue}{{x \in {\left[ 0,\, \infty \right)}}}}\cr \color{green}{\Leftrightarrow}&3\cdot x+4=4+4\cdot \sqrt{x+2}+\left(x+2\right)&{\color{blue}{{x \in {\left[ 0,\, \infty \right)}}}}\cr \color{green}{\Leftrightarrow}&x-1=2\cdot \sqrt{x+2}&{\color{blue}{{x \in {\left[ 0,\, \infty \right)}}}}\cr \color{green}{\Leftrightarrow}&x^2-2\cdot x+1=4\cdot x+8& \cr \color{green}{\Leftrightarrow}&x^2-6\cdot x-7=0& \cr \color{green}{\Leftrightarrow}&\left(x-7\right)\cdot \left(x+1\right)=0& \cr \color{green}{\Leftrightarrow}&x=7\,{\mbox{ or }}\, x=-1& \cr \color{green}{\Leftrightarrow}&x=7& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | ||
| Equiv | [x*(x-1)*(x-2)=0,x*(x-1)=0,x*( x-1)*(x-2)=0,x*(x^2-2)=0] |
[] |
0 | \[\begin{array}{lll} &x\cdot \left(x-1\right)\cdot \left(x-2\right)=0& \cr \color{red}{\Leftarrow}&x\cdot \left(x-1\right)=0& \cr \color{red}{\Rightarrow}&x\cdot \left(x-1\right)\cdot \left(x-2\right)=0& \cr \color{red}{?}&x\cdot \left(x^2-2\right)=0& \cr \end{array}\] | (EMPTYCHAR,IMPLIEDCHAR,IMPLIESCHAR,QMCHAR) | |||
| Equiv | [x^2-6*x=-9,x=3] |
[] |
1 | \[\begin{array}{lll} &x^2-6\cdot x=-9& \cr \color{green}{\mbox{(Same roots)}}&x=3& \cr \end{array}\] | (EMPTYCHAR,SAMEROOTS) | |||
| Equiv | [x=1 nounor x=-2 nounor x=1,x^ 3-3*x=-2,x=1 nounor x=-2] |
[] |
1 | \[\begin{array}{lll} &x=1\,{\mbox{ or }}\, x=-2\,{\mbox{ or }}\, x=1& \cr \color{green}{\Leftrightarrow}&x^3-3\cdot x=-2& \cr \color{green}{\mbox{(Same roots)}}&x=1\,{\mbox{ or }}\, x=-2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR,SAMEROOTS) | |||
| Equiv | [9*x^3-24*x^2+13*x=2,x=1/3 nou nor x=2] |
[] |
1 | \[\begin{array}{lll} &9\cdot x^3-24\cdot x^2+13\cdot x=2& \cr \color{green}{\mbox{(Same roots)}}&x=\frac{1}{3}\,{\mbox{ or }}\, x=2& \cr \end{array}\] | (EMPTYCHAR,SAMEROOTS) | |||
| Equiv | [(x-2)^43*(x+1/3)^60=0,(3*x+1) ^4*(x-2)^2=0,x=-1/3 nounor x=2 ] |
[] |
1 | \[\begin{array}{lll} &{\left(x-2\right)}^{43}\cdot {\left(x+\frac{1}{3}\right)}^{60}=0& \cr \color{green}{\mbox{(Same roots)}}&{\left(3\cdot x+1\right)}^4\cdot {\left(x-2\right)}^2=0& \cr \color{green}{\mbox{(Same roots)}}&x=\frac{-1}{3}\,{\mbox{ or }}\, x=2& \cr \end{array}\] | (EMPTYCHAR,SAMEROOTS,SAMEROOTS) | |||
| Equiv | [2^x=4,x*log(2)=log(4),x=log(2 ^2)/log(2),x=2*log(2)/log(2),x =2] |
[] |
1 | \[\begin{array}{lll} &2^{x}=4& \cr \color{green}{\Leftrightarrow}&x\cdot \ln \left( 2 \right)=\ln \left( 4 \right)& \cr \color{green}{\Leftrightarrow}&x=\frac{\ln \left( 2^2 \right)}{\ln \left( 2 \right)}& \cr \color{green}{\Leftrightarrow}&x=\frac{2\cdot \ln \left( 2 \right)}{\ln \left( 2 \right)}& \cr \color{green}{\Leftrightarrow}&x=2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^log(y),stackeq(e^(log(x)*lo g(y))),stackeq(e^(log(y)*log(x ))),stackeq(y^log(x))] |
[] |
1 | \[\begin{array}{lll} &x^{\ln \left( y \right)}& \cr \color{green}{\checkmark}&=e^{\ln \left( x \right)\cdot \ln \left( y \right)}& \cr \color{green}{\checkmark}&=e^{\ln \left( y \right)\cdot \ln \left( x \right)}& \cr \color{green}{\checkmark}&=y^{\ln \left( x \right)}& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK) | |||
| Equiv | [lg(x+17,3)-2=lg(2*x,3),lg(x+1 7,3)-lg(2*x,3)=2,lg((x+17)/(2* x),3)=2,(x+17)/(2*x)=3^2,(x+17 )=18*x,17*x=17,x=1] |
[] |
1 | \[\begin{array}{lll} &\log_{3}\left(x+17\right)-2=\log_{3}\left(2\cdot x\right)&{\color{blue}{{x \in {\left( 0,\, \infty \right)}}}}\cr \color{green}{\Leftrightarrow}&\log_{3}\left(x+17\right)-\log_{3}\left(2\cdot x\right)=2&{\color{blue}{{x \in {\left( 0,\, \infty \right)}}}}\cr \color{green}{\Leftrightarrow}&\log_{3}\left(\frac{x+17}{2\cdot x}\right)=2& \cr \color{green}{\log(?)}&\frac{x+17}{2\cdot x}=3^2&{\color{blue}{{x \not\in {\left \{0 \right \}}}}}\cr \color{green}{\Leftrightarrow}&x+17=18\cdot x& \cr \color{green}{\Leftrightarrow}&17\cdot x=17& \cr \color{green}{\Leftrightarrow}&x=1& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR,EQUIVLOG, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [a=logbase(9,3),3^a=9,3^a=3^2, a=2] |
[] |
1 | \[\begin{array}{lll} &a=\log_{3}\left(9\right)& \cr \color{green}{\Leftrightarrow}&3^{a}=9& \cr \color{green}{\Leftrightarrow}&3^{a}=3^2& \cr \color{green}{\Leftrightarrow}&a=2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x=(1+y/n)^n,x^(1/n)=(1+y/n),y /n=x^(1/n)-1,y=n*(x^(1/n)-1)] |
[] |
0 | \[\begin{array}{lll} &x={\left(1+\frac{y}{n}\right)}^{n}& \cr \color{red}{?}&x^{\frac{1}{n}}=1+\frac{y}{n}& \cr \color{green}{\Leftrightarrow}&\frac{y}{n}=x^{\frac{1}{n}}-1& \cr \color{green}{\Leftrightarrow}&y=n\cdot \left(x^{\frac{1}{n}}-1\right)& \cr \end{array}\] | (EMPTYCHAR,QMCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [a^3=b^3,a^3-b^3=0,(a-b)*(a^2+ a*b+b^2)=0,(a-b)=0,a=b] |
[] |
[assumereal] |
0 | \[\begin{array}{lll}\color{blue}{(\mathbb{R})}&a^3=b^3& \cr \color{green}{\Leftrightarrow}&a^3-b^3=0& \cr \color{green}{\Leftrightarrow}&\left(a-b\right)\cdot \left(a^2+a\cdot b+b^2\right)=0& \cr \color{red}{\Leftarrow}&a-b=0& \cr \color{green}{\Leftrightarrow}&a=b& \cr \end{array}\] | (ASSUMEREALVARS, EQUIVCHAR, EQUIVCHAR,IMPLIEDCHAR, EQUIVCHAR) | ||
| Equiv | [x^3-1=0,(x-1)*(x^2+x+1)=0,x=1 ] |
[] |
[assumereal] |
1 | \[\begin{array}{lll}\color{blue}{(\mathbb{R})}&x^3-1=0& \cr \color{green}{\Leftrightarrow}&\left(x-1\right)\cdot \left(x^2+x+1\right)=0& \cr \color{green}{\Leftrightarrow}\, \color{blue}{(\mathbb{R})}&x=1& \cr \end{array}\] | (ASSUMEREALVARS, EQUIVCHAR, EQUIVCHARREAL) | ||
| Equiv | [x^4=2,x^4-2=0,(x^2-sqrt(2))*( x^2+sqrt(2))=0,x^2=sqrt(2),x=# pm# 2^(1/4)] |
[] |
[assumereal] |
1 | \[\begin{array}{lll}\color{blue}{(\mathbb{R})}&x^4=2& \cr \color{green}{\Leftrightarrow}&x^4-2=0& \cr \color{green}{\Leftrightarrow}&\left(x^2-\sqrt{2}\right)\cdot \left(x^2+\sqrt{2}\right)=0& \cr \color{green}{\Leftrightarrow}\, \color{blue}{(\mathbb{R})}&x^2=\sqrt{2}& \cr \color{green}{\Leftrightarrow}&x= \pm 2^{\frac{1}{4}}& \cr \end{array}\] | (ASSUMEREALVARS, EQUIVCHAR, EQUIVCHAR, EQUIVCHARREAL, EQUIVCHAR) | ||
| Equiv | [6*x-12=3*(x-2),6*x-12+3*(x-2) =0,9*x-18=0,x=2] |
[] |
1 | \[\begin{array}{lll} &6\cdot x-12=3\cdot \left(x-2\right)& \cr \color{green}{\Leftrightarrow}&6\cdot x-12+3\cdot \left(x-2\right)=0& \cr \color{green}{\Leftrightarrow}&9\cdot x-18=0& \cr \color{green}{\Leftrightarrow}&x=2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^2-6*x+9=0,x^2-6*x=-9,x*(x-6 )=3*-3,x=3 or x-6=-3,x=3] |
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1 | \[\begin{array}{lll} &x^2-6\cdot x+9=0& \cr \color{green}{\Leftrightarrow}&x^2-6\cdot x=-9& \cr \color{green}{\Leftrightarrow}&x\cdot \left(x-6\right)=3\cdot \left(-3\right)& \cr \color{green}{\Leftrightarrow}&x=3\,{\mbox{ or }}\, x-6=-3& \cr \color{green}{\mbox{(Same roots)}}&x=3& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR,SAMEROOTS) | |||
| Equiv | [(x+3)*(2-x)=4,x+3=4 or (2-x)= 4,x=1 or x=-2] |
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1 | \[\begin{array}{lll} &\left(x+3\right)\cdot \left(2-x\right)=4& \cr \color{green}{\Leftrightarrow}&x+3=4\,{\mbox{ or }}\, 2-x=4& \cr \color{green}{\Leftrightarrow}&x=1\,{\mbox{ or }}\, x=-2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [(x-p)*(x-q)=0,x^2-p*x-q*x+p*q =0,1+q-x-p-p*q+p*x+x+q*x-x^2=1 -p+q,(1+q-x)*(1-p+x)=1-p+q,(1+ q-x)=1-p+q or (1-p+x)=1-p+q,x= p or x=q] |
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1 | \[\begin{array}{lll} &\left(x-p\right)\cdot \left(x-q\right)=0& \cr \color{green}{\Leftrightarrow}&x^2-p\cdot x+\left(-q\right)\cdot x+p\cdot q=0& \cr \color{green}{\Leftrightarrow}&1+q-x-p+\left(-p\right)\cdot q+p\cdot x+x+q\cdot x-x^2=1-p+q& \cr \color{green}{\Leftrightarrow}&\left(1+q-x\right)\cdot \left(1-p+x\right)=1-p+q& \cr \color{green}{\Leftrightarrow}&1+q-x=1-p+q\,{\mbox{ or }}\, 1-p+x=1-p+q& \cr \color{green}{\Leftrightarrow}&x=p\,{\mbox{ or }}\, x=q& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [a=b, a^2=a*b, a^2-b^2=a*b-b^2 , (a-b)*(a+b)=b*(a-b), a+b=b, 2*a=a, 1=2] |
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0 | \[\begin{array}{lll} &a=b& \cr \color{red}{\Rightarrow}&a^2=a\cdot b& \cr \color{green}{\Leftrightarrow}&a^2-b^2=a\cdot b-b^2& \cr \color{green}{\Leftrightarrow}&\left(a-b\right)\cdot \left(a+b\right)=b\cdot \left(a-b\right)& \cr \color{red}{\Leftarrow}&a+b=b& \cr \color{green}{\Leftrightarrow}&2\cdot a=a& \cr \color{red}{\Leftarrow}&1=2& \cr \end{array}\] | (EMPTYCHAR,IMPLIESCHAR, EQUIVCHAR, EQUIVCHAR,IMPLIEDCHAR, EQUIVCHAR,IMPLIEDCHAR) | |||
| Equiv | [a=b or a=0, a^2=a*b, a^2-b^2= a*b-b^2, (a-b)*(a+b)=b*(a-b), a+b=b or a-b=0, 2*a=a or a=b, 2=1 or a=0 or a=b, a=0 or a=b] |
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1 | \[\begin{array}{lll} &a=b\,{\mbox{ or }}\, a=0& \cr \color{green}{\Leftrightarrow}&a^2=a\cdot b& \cr \color{green}{\Leftrightarrow}&a^2-b^2=a\cdot b-b^2& \cr \color{green}{\Leftrightarrow}&\left(a-b\right)\cdot \left(a+b\right)=b\cdot \left(a-b\right)& \cr \color{green}{\Leftrightarrow}&a+b=b\,{\mbox{ or }}\, a-b=0& \cr \color{green}{\Leftrightarrow}&2\cdot a=a\,{\mbox{ or }}\, a=b& \cr \color{green}{\Leftrightarrow}&2=1\,{\mbox{ or }}\, a=0\,{\mbox{ or }}\, a=b& \cr \color{green}{\Leftrightarrow}&a=0\,{\mbox{ or }}\, a=b& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [(x^2-4)/(x-2)=0,(x-2)*(x+2)/( x-2)=0,x+2=0,x=-2] |
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1 | \[\begin{array}{lll} &\frac{x^2-4}{x-2}=0&{\color{blue}{{x \not\in {\left \{2 \right \}}}}}\cr \color{green}{\Leftrightarrow}&\frac{\left(x-2\right)\cdot \left(x+2\right)}{x-2}=0& \cr \color{green}{\Leftrightarrow}&x+2=0& \cr \color{green}{\Leftrightarrow}&x=-2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [(x^2-4)/(x-2)=0,(x^2-4)=0,(x- 2)*(x+2)=0,x=-2 or x=2] |
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0 | \[\begin{array}{lll} &\frac{x^2-4}{x-2}=0&{\color{blue}{{x \not\in {\left \{2 \right \}}}}}\cr \color{red}{\Rightarrow}&x^2-4=0& \cr \color{green}{\Leftrightarrow}&\left(x-2\right)\cdot \left(x+2\right)=0& \cr \color{green}{\Leftrightarrow}&x=-2\,{\mbox{ or }}\, x=2& \cr \end{array}\] | (EMPTYCHAR,IMPLIESCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [5*x/(2*x+1)-3/(x+1) = 1,5*x*( x+1)-3*(2*x+1)=(x+1)*(2*x+1),5 *x^2+5*x-6*x-3=2*x^2+3*x+1,3*x ^2-4*x-4=0,(x-2)*(3*x+2)=0,x=2 or x=-2/3] |
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1 | \[\begin{array}{lll} &\frac{5\cdot x}{2\cdot x+1}-\frac{3}{x+1}=1&{\color{blue}{{x \not\in {\left \{-1 , -\frac{1}{2} \right \}}}}}\cr \color{green}{\Leftrightarrow}&5\cdot x\cdot \left(x+1\right)-3\cdot \left(2\cdot x+1\right)=\left(x+1\right)\cdot \left(2\cdot x+1\right)& \cr \color{green}{\Leftrightarrow}&5\cdot x^2+5\cdot x-6\cdot x-3=2\cdot x^2+3\cdot x+1& \cr \color{green}{\Leftrightarrow}&3\cdot x^2-4\cdot x-4=0& \cr \color{green}{\Leftrightarrow}&\left(x-2\right)\cdot \left(3\cdot x+2\right)=0& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ or }}\, x=\frac{-2}{3}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [(x+10)/(x-6)-5= (4*x-40)/(13- x),(x+10-5*(x-6))/(x-6)= (4*x- 40)/(13-x), (4*x-40)/(6-x)= (4 *x-40)/(13-x),6-x= 13-x,6= 13] |
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0 | \[\begin{array}{lll} &\frac{x+10}{x-6}-5=\frac{4\cdot x-40}{13-x}&{\color{blue}{{x \not\in {\left \{6 , 13 \right \}}}}}\cr \color{green}{\Leftrightarrow}&\frac{x+10-5\cdot \left(x-6\right)}{x-6}=\frac{4\cdot x-40}{13-x}&{\color{blue}{{x \not\in {\left \{6 , 13 \right \}}}}}\cr \color{green}{\Leftrightarrow}&\frac{4\cdot x-40}{6-x}=\frac{4\cdot x-40}{13-x}&{\color{blue}{{x \not\in {\left \{6 , 13 \right \}}}}}\cr \color{red}{?}&6-x=13-x& \cr \color{green}{\Leftrightarrow}&6=13& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR,QMCHAR, EQUIVCHAR) | |||
| Equiv | [(x+5)/(x-7)-5= (4*x-40)/(13-x ),(x+5-5*(x-7))/(x-7)= (4*x-40 )/(13-x), (4*x-40)/(7-x)= (4*x -40)/(13-x),7-x= 13-x,7= 13] |
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0 | \[\begin{array}{lll} &\frac{x+5}{x-7}-5=\frac{4\cdot x-40}{13-x}&{\color{blue}{{x \not\in {\left \{7 , 13 \right \}}}}}\cr \color{green}{\Leftrightarrow}&\frac{x+5-5\cdot \left(x-7\right)}{x-7}=\frac{4\cdot x-40}{13-x}&{\color{blue}{{x \not\in {\left \{7 , 13 \right \}}}}}\cr \color{green}{\Leftrightarrow}&\frac{4\cdot x-40}{7-x}=\frac{4\cdot x-40}{13-x}&{\color{blue}{{x \not\in {\left \{7 , 13 \right \}}}}}\cr \color{red}{\Leftarrow}&7-x=13-x& \cr \color{green}{\Leftrightarrow}&7=13& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR,IMPLIEDCHAR, EQUIVCHAR) | |||
| Equiv | [(x+5)/(x-7)-5= (4*x-40)/(13-x ),(x+5-5*(x-7))/(x-7)= (4*x-40 )/(13-x), (4*x-40)/(7-x)= (4*x -40)/(13-x),7-x= 13-x or 4*x-4 0=0,7= 13 or 4*x=40,x=10] |
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1 | \[\begin{array}{lll} &\frac{x+5}{x-7}-5=\frac{4\cdot x-40}{13-x}&{\color{blue}{{x \not\in {\left \{7 , 13 \right \}}}}}\cr \color{green}{\Leftrightarrow}&\frac{x+5-5\cdot \left(x-7\right)}{x-7}=\frac{4\cdot x-40}{13-x}&{\color{blue}{{x \not\in {\left \{7 , 13 \right \}}}}}\cr \color{green}{\Leftrightarrow}&\frac{4\cdot x-40}{7-x}=\frac{4\cdot x-40}{13-x}&{\color{blue}{{x \not\in {\left \{7 , 13 \right \}}}}}\cr \color{green}{\Leftrightarrow}&7-x=13-x\,{\mbox{ or }}\, 4\cdot x-40=0& \cr \color{green}{\Leftrightarrow}&7=13\,{\mbox{ or }}\, 4\cdot x=40& \cr \color{green}{\Leftrightarrow}&x=10& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [a*x^2+b*x+c=0,a=0 nounand b=0 nounand c=0,a*x^2+b*x+c=0] |
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1 | \[\begin{array}{lll} &a\cdot x^2+b\cdot x+c=0& \cr \color{green}{\equiv (\cdots ? x)}&\left\{\begin{array}{l}a=0\cr b=0\cr c=0\cr \end{array}\right.& \cr \color{green}{(\cdots ? x)\equiv}&a\cdot x^2+b\cdot x+c=0& \cr \end{array}\] | (EMPTYCHAR,EQUATECOEFFLOSS(x),EQUATECOEFFGAIN(x)) | |||
| Equiv | [a*x^2+b*x+c=A*x^2+B*x+C,a=A n ounand b=B nounand c=C,a*x^2+b *x+c=A*x^2+B*x+C] |
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1 | \[\begin{array}{lll} &a\cdot x^2+b\cdot x+c=A\cdot x^2+B\cdot x+C& \cr \color{green}{\equiv (\cdots ? x)}&\left\{\begin{array}{l}a=A\cr b=B\cr c=C\cr \end{array}\right.& \cr \color{green}{(\cdots ? x)\equiv}&a\cdot x^2+b\cdot x+c=A\cdot x^2+B\cdot x+C& \cr \end{array}\] | (EMPTYCHAR,EQUATECOEFFLOSS(x),EQUATECOEFFGAIN(x)) | |||
| Equiv | [(x-1)*(x+4), stackeq(x^2-x+4* x-4),stackeq(x^2+3*x-4)] |
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1 | \[\begin{array}{lll} &\left(x-1\right)\cdot \left(x+4\right)& \cr \color{green}{\checkmark}&=x^2-x+4\cdot x-4& \cr \color{green}{\checkmark}&=x^2+3\cdot x-4& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK) | |||
| Equiv | [(x-1)*(x+4), stackeq(x^2-x+4* x-4),stackeq(x^2+3*x-4)] |
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1 | \[\begin{array}{lll} &\left(x-1\right)\cdot \left(x+4\right)& \cr \color{green}{\checkmark}&=x^2-x+4\cdot x-4& \cr \color{green}{\checkmark}&=x^2+3\cdot x-4& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK) | |||
| Equiv | [x^2-2,stackeq((x-sqrt(2))*(x+ sqrt(2)))] |
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1 | \[\begin{array}{lll} &x^2-2& \cr \color{green}{\checkmark}&=\left(x-\sqrt{2}\right)\cdot \left(x+\sqrt{2}\right)& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK) | |||
| Equiv | [x^2+4,stackeq((x-2*i)*(x+2*i) )] |
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1 | \[\begin{array}{lll} &x^2+4& \cr \color{green}{\checkmark}&=\left(x-2\cdot \mathrm{i}\right)\cdot \left(x+2\cdot \mathrm{i}\right)& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK) | |||
| Equiv | [x^2+2*a*x,x^2+2*a*x+a^2-a^2,( x+a)^2-a^2] |
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1 | \[\begin{array}{lll} &x^2+2\cdot a\cdot x& \cr \color{green}{\Leftrightarrow}&x^2+2\cdot a\cdot x+a^2-a^2& \cr \color{green}{\Leftrightarrow}&{\left(x+a\right)}^2-a^2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^2+2*a*x,stackeq(x^2+2*a*x+a ^2-a^2),stackeq((x+a)^2-a^2)] |
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1 | \[\begin{array}{lll} &x^2+2\cdot a\cdot x& \cr \color{green}{\checkmark}&=x^2+2\cdot a\cdot x+a^2-a^2& \cr \color{green}{\checkmark}&={\left(x+a\right)}^2-a^2& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK) | |||
| Equiv | [(y-z)/(y*z)+(z-x)/(z*x)+(x-y) /(x*y),(x*(y-z)+y*(z-x)+z*(x-y ))/(x*y*z),0] |
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1 | \[\begin{array}{lll} &\frac{y-z}{y\cdot z}+\frac{z-x}{z\cdot x}+\frac{x-y}{x\cdot y}& \cr \color{green}{\Leftrightarrow}&\frac{x\cdot \left(y-z\right)+y\cdot \left(z-x\right)+z\cdot \left(x-y\right)}{x\cdot y\cdot z}& \cr \color{green}{\Leftrightarrow}&0& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [(y-z)/(y*z)+(z-x)/(z*x)+(x-y) /(x*y),stackeq((x*(y-z)+y*(z-x )+z*(x-y))/(x*y*z)),stackeq(0) ] |
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1 | \[\begin{array}{lll} &\frac{y-z}{y\cdot z}+\frac{z-x}{z\cdot x}+\frac{x-y}{x\cdot y}& \cr \color{green}{\checkmark}&=\frac{x\cdot \left(y-z\right)+y\cdot \left(z-x\right)+z\cdot \left(x-y\right)}{x\cdot y\cdot z}& \cr \color{green}{\checkmark}&=0& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK) | |||
| Equiv | [2*(a^2*b^2+b^2*c^2+c^2*a^2)-( a^4+b^4+c^4),stackeq(4*a^2*b^2 -(a^4+b^4+c^4+2*a^2*b^2-2*b^2* c^2-2*c^2*a^2)),stackeq((2*a*b )^2-(b^2+a^2-c^2)^2,(2*a*b+b^2 +a^2-c^2)*(2*a*b-b^2-a^2+c^2)) ,stackeq(((a+b)^2-c^2)*(c^2-(a -b)^2)),stackeq((a+b+c)*(a+b-c )*(c+a-b)*(c-a+b))] |
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1 | \[\begin{array}{lll} &2\cdot \left(a^2\cdot b^2+b^2\cdot c^2+c^2\cdot a^2\right)-\left(a^4+b^4+c^4\right)& \cr \color{green}{\checkmark}&=4\cdot a^2\cdot b^2-\left(a^4+b^4+c^4+2\cdot a^2\cdot b^2-2\cdot b^2\cdot c^2-2\cdot c^2\cdot a^2\right)& \cr \color{green}{\checkmark}&={\left(2\cdot a\cdot b\right)}^2-{\left(b^2+a^2-c^2\right)}^2& \cr \color{green}{\checkmark}&=\left({\left(a+b\right)}^2-c^2\right)\cdot \left(c^2-{\left(a-b\right)}^2\right)& \cr \color{green}{\checkmark}&=\left(a+b+c\right)\cdot \left(a+b-c\right)\cdot \left(c+a-b\right)\cdot \left(c-a+b\right)& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK) | |||
| Equiv | [abs(x-1/2)+abs(x+1/2)-2,stack eq(abs(x)-1)] |
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0 | \[\begin{array}{lll} &\left| x-\frac{1}{2}\right| +\left| x+\frac{1}{2}\right| -2& \cr \color{red}{?}&=\left| x\right| -1& \cr \end{array}\] | (EMPTYCHAR,QMCHAR) | |||
| Equiv | [11*sqrt(abs(x)+1)=25-x,11^2*( abs(x)+1)=(25-x)^2,11^2*abs(x) =(25-x)^2-11^2,11^4*x^2=((25-x )^2-11^2)^2, ((25-x)^2-11^2)^2 -11^4*x^2=0,((25-x)^2-11^2-11^ 2*x)*((25-x)^2-11^2+11^2*x)=0, (x^2-50*x+504-121*x)*(x^2-50*x +504+121*x)=0, (x-168)*(x-3)*( x+8)*(x+63)=0] |
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0 | \[\begin{array}{lll} &11\cdot \sqrt{\left| x\right| +1}=25-x& \cr \color{red}{?}&11^2\cdot \left(\left| x\right| +1\right)={\left(25-x\right)}^2& \cr \color{green}{\Leftrightarrow}&11^2\cdot \left| x\right| ={\left(25-x\right)}^2-11^2& \cr \color{green}{\Leftrightarrow}&11^4\cdot x^2={\left({\left(25-x\right)}^2-11^2\right)}^2& \cr \color{green}{\Leftrightarrow}&{\left({\left(25-x\right)}^2-11^2\right)}^2-11^4\cdot x^2=0& \cr \color{green}{\Leftrightarrow}&\left({\left(25-x\right)}^2-11^2+\left(-11^2\right)\cdot x\right)\cdot \left({\left(25-x\right)}^2-11^2+11^2\cdot x\right)=0& \cr \color{green}{\Leftrightarrow}&\left(x^2-50\cdot x+504-121\cdot x\right)\cdot \left(x^2-50\cdot x+504+121\cdot x\right)=0& \cr \color{green}{\Leftrightarrow}&\left(x-168\right)\cdot \left(x-3\right)\cdot \left(x+8\right)\cdot \left(x+63\right)=0& \cr \end{array}\] | (EMPTYCHAR,QMCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [1/(x^2+1)=1/((x+%i)*(x-%i)), stackeq(1/(2*%i)*(1/(x-%i)-1/( x+%i)))] |
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1 | \[\begin{array}{lll}\color{green}{\checkmark}&\frac{1}{x^2+1}=\frac{1}{\left(x+\mathrm{i}\right)\cdot \left(x-\mathrm{i}\right)}& \cr \color{green}{\checkmark}&=\frac{1}{2\cdot \mathrm{i}}\cdot \left(\frac{1}{x-\mathrm{i}}-\frac{1}{x+\mathrm{i}}\right)& \cr \end{array}\] | (CHECKMARK, CHECKMARK) | |||
| Equiv | [((a-b)/(a^2+a*b))/((a^2-2*a*b +b^2)/(a^4-b^4)),stackeq(((a-b )*(a-b)*(a+b)*(a^2+b^2))/(a*(a +b)*(a-b)^2)),stackeq((a^2+b^2 )/a),stackeq(a+b^2/a)] |
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1 | \[\begin{array}{lll} &\frac{\frac{a-b}{a^2+a\cdot b}}{\frac{a^2-2\cdot a\cdot b+b^2}{a^4-b^4}}& \cr \color{green}{\checkmark}&=\frac{\left(a-b\right)\cdot \left(a-b\right)\cdot \left(a+b\right)\cdot \left(a^2+b^2\right)}{a\cdot \left(a+b\right)\cdot {\left(a-b\right)}^2}& \cr \color{green}{\checkmark}&=\frac{a^2+b^2}{a}& \cr \color{green}{\checkmark}&=a+\frac{b^2}{a}& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK) | |||
| Equiv | [a^4+4*b^4,stackeq((a^2)^2+4*a ^2*b^2+(2*b^2)^2-4*a^2*b^2),st ackeq((a^2+2*b^2)^2-(2*a*b)^2) ,stackeq((2*b^2-2*a*b+a^2)*(2* b^2+2*a*b+a^2))] |
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1 | \[\begin{array}{lll} &a^4+4\cdot b^4& \cr \color{green}{\checkmark}&={\left(a^2\right)}^2+4\cdot a^2\cdot b^2+{\left(2\cdot b^2\right)}^2-4\cdot a^2\cdot b^2& \cr \color{green}{\checkmark}&={\left(a^2+2\cdot b^2\right)}^2-{\left(2\cdot a\cdot b\right)}^2& \cr \color{green}{\checkmark}&=\left(2\cdot b^2-2\cdot a\cdot b+a^2\right)\cdot \left(2\cdot b^2+2\cdot a\cdot b+a^2\right)& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK) | |||
| Equiv | [sum(k,k,1,n+1),stackeq(sum(k, k,1,n)+(n+1)),stackeq(n*(n+1)/ 2 +n+1),stackeq((n+1)*(n+1+1)/ 2),stackeq((n+1)*(n+2)/2)] |
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1 | \[\begin{array}{lll} &\sum_{k=1}^{n+1}{k}& \cr \color{green}{\checkmark}&=\sum_{k=1}^{n}{k}+\left(n+1\right)& \cr \color{green}{\checkmark}&=\frac{n\cdot \left(n+1\right)}{2}+n+1& \cr \color{green}{\checkmark}&=\frac{\left(n+1\right)\cdot \left(n+1+1\right)}{2}& \cr \color{green}{\checkmark}&=\frac{\left(n+1\right)\cdot \left(n+2\right)}{2}& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK) | |||
| Equiv | [log((a-1)^n*product(x_i^(-a), i,1,n)),stackeq(n*log(a-1)-a*s um(log(x_i),i,1,n))] |
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1 | \[\begin{array}{lll} &\ln \left( {\left(a-1\right)}^{n}\cdot \prod_{i=1}^{n}{\frac{1}{{{x}_{i}}^{a}}} \right)& \cr \color{green}{\checkmark}&=n\cdot \ln \left( a-1 \right)-a\cdot \sum_{i=1}^{n}{\ln \left( {x}_{i} \right)}& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK) | |||
| Equiv | [binomial(n,k)+binomial(n,k+1) ,stackeq(n!/(k!*(n-k)!)+n!/((k +1)!*(n-k-1)!)),stackeq(n!/(k! *(n-k)*(n-k-1)!)+n!/((k+1)!*(n -k-1)!)),stackeq(n!/(k!*(n-k-1 )!)*(1/(n-k)+1/(k+1))),stackeq (n!/(k!*(n-k-1)!)*((n+1)/((n-k )*(k+1)))),stackeq((n+1)*n!/(k !*(n-k-1)!)*(1/((k+1)*(n-k)))) ,stackeq((n+1)*n!/((k+1)*k!*(n -k)*(n-k-1)!)),stackeq(((n+1)! /((k+1)!)*(1/((n-k)*(n-k-1)!)) )),stackeq((n+1)!/((k+1)!*(n-k )!)),stackeq(binomial(n+1,k+1) )] |
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1 | \[\begin{array}{lll} &{{n}\choose{k}}+{{n}\choose{k+1}}& \cr \color{green}{\checkmark}&=\frac{n!}{k!\cdot \left(n-k\right)!}+\frac{n!}{\left(k+1\right)!\cdot \left(n-k-1\right)!}& \cr \color{green}{\checkmark}&=\frac{n!}{k!\cdot \left(n-k\right)\cdot \left(n-k-1\right)!}+\frac{n!}{\left(k+1\right)!\cdot \left(n-k-1\right)!}& \cr \color{green}{\checkmark}&=\frac{n!}{k!\cdot \left(n-k-1\right)!}\cdot \left(\frac{1}{n-k}+\frac{1}{k+1}\right)& \cr \color{green}{\checkmark}&=\frac{n!}{k!\cdot \left(n-k-1\right)!}\cdot \left(\frac{n+1}{\left(n-k\right)\cdot \left(k+1\right)}\right)& \cr \color{green}{\checkmark}&=\frac{\left(n+1\right)\cdot n!}{k!\cdot \left(n-k-1\right)!}\cdot \left(\frac{1}{\left(k+1\right)\cdot \left(n-k\right)}\right)& \cr \color{green}{\checkmark}&=\frac{\left(n+1\right)\cdot n!}{\left(k+1\right)\cdot k!\cdot \left(n-k\right)\cdot \left(n-k-1\right)!}& \cr \color{green}{\checkmark}&=\frac{\left(n+1\right)!}{\left(k+1\right)!}\cdot \left(\frac{1}{\left(n-k\right)\cdot \left(n-k-1\right)!}\right)& \cr \color{green}{\checkmark}&=\frac{\left(n+1\right)!}{\left(k+1\right)!\cdot \left(n-k\right)!}& \cr \color{green}{\checkmark}&={{n+1}\choose{k+1}}& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK) | |||
| Equiv | [(x-1)^2=(x-1)*(x-1), stackeq( x^2-2*x+1)] |
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1 | \[\begin{array}{lll}\color{green}{\checkmark}&{\left(x-1\right)}^2=\left(x-1\right)\cdot \left(x-1\right)& \cr \color{green}{\checkmark}&=x^2-2\cdot x+1& \cr \end{array}\] | (CHECKMARK, CHECKMARK) | |||
| Equiv | [(x-1)^2=(x-1)*(x-1), stackeq( x^2-2*x+2)] |
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0 | \[\begin{array}{lll}\color{green}{\checkmark}&{\left(x-1\right)}^2=\left(x-1\right)\cdot \left(x-1\right)& \cr \color{red}{?}&=x^2-2\cdot x+2& \cr \end{array}\] | (CHECKMARK,QMCHAR) | |||
| Equiv | [(x-2)^2=(x-1)*(x-1), stackeq( x^2-2*x+1)] |
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0 | \[\begin{array}{lll}\color{red}{?}&{\left(x-2\right)}^2=\left(x-1\right)\cdot \left(x-1\right)& \cr \color{green}{\checkmark}&=x^2-2\cdot x+1& \cr \end{array}\] | (QMCHAR, CHECKMARK) | |||
| Equiv | [4^((n+1)+1)-1= 4*4^(n+1)-1,st ackeq(4*(4^(n+1)-1)+3)] |
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1 | \[\begin{array}{lll}\color{green}{\checkmark}&4^{n+1+1}-1=4\cdot 4^{n+1}-1& \cr \color{green}{\checkmark}&=4\cdot \left(4^{n+1}-1\right)+3& \cr \end{array}\] | (CHECKMARK, CHECKMARK) | |||
| Equiv | [2*x+3*y=6 and 4*x+9*y=15,2*x+ 3*y=6 and -2*x=-3,3+3*y=6 and 2*x=3,y=1 and x=3/2] |
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1 | \[\begin{array}{lll} &\left\{\begin{array}{l}2\cdot x+3\cdot y=6\cr 4\cdot x+9\cdot y=15\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}2\cdot x+3\cdot y=6\cr -2\cdot x=-3\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}3+3\cdot y=6\cr 2\cdot x=3\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}y=1\cr x=\frac{3}{2}\cr \end{array}\right.& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [2*x+3*y=6 and 4*x+9*y=15,2*x+ 3*y=6 and -2*x=-3,3+3*y=6 and 2*x=3,y=1 and x=3] |
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0 | \[\begin{array}{lll} &\left\{\begin{array}{l}2\cdot x+3\cdot y=6\cr 4\cdot x+9\cdot y=15\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}2\cdot x+3\cdot y=6\cr -2\cdot x=-3\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}3+3\cdot y=6\cr 2\cdot x=3\cr \end{array}\right.& \cr \color{red}{?}&\left\{\begin{array}{l}y=1\cr x=3\cr \end{array}\right.& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR,QMCHAR) | |||
| Equiv | [x^2+y^2=8 and x=y, 2*x^2=8 an d y=x, x^2=4 and y=x, x= #pm#2 and y=x, (x= 2 and y=x) or (x =-2 and y=x), (x=2 and y=2) or (x=-2 and y=-2)] |
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1 | \[\begin{array}{lll} &\left\{\begin{array}{l}x^2+y^2=8\cr x=y\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}2\cdot x^2=8\cr y=x\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x^2=4\cr y=x\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x= \pm 2\cr y=x\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ and }}\, y=x\,{\mbox{ or }}\, x=-2\,{\mbox{ and }}\, y=x& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ and }}\, y=2\,{\mbox{ or }}\, x=-2\,{\mbox{ and }}\, y=-2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x^2+y^2=5 and x*y=2, x^2+y^2- 5=0 and x*y-2=0, x^2-2*x*y+y^2 -1=0 and x^2+2*x*y+y^2-9=0, (x -y)^2-1=0 and (x+y)^2-3^2=0, ( x-y=1 and x+y=3) or (x-y=-1 an d x+y=3) or (x-y=1 and x+y=-3) or (x-y=-1 and x+y=-3), (x=1 and y=2) or (x=2 and y=1) or ( x=-2 and y=-1) or (x=-1 and y= -2)] |
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1 | \[\begin{array}{lll} &\left\{\begin{array}{l}x^2+y^2=5\cr x\cdot y=2\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x^2+y^2-5=0\cr x\cdot y-2=0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x^2-2\cdot x\cdot y+y^2-1=0\cr x^2+2\cdot x\cdot y+y^2-9=0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}{\left(x-y\right)}^2-1=0\cr {\left(x+y\right)}^2-3^2=0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&x-y=1\,{\mbox{ and }}\, x+y=3\,{\mbox{ or }}\, x-y=-1\,{\mbox{ and }}\, x+y=3\,{\mbox{ or }}\, x-y=1\,{\mbox{ and }}\, x+y=-3\,{\mbox{ or }}\, x-y=-1\,{\mbox{ and }}\, x+y=-3& \cr \color{green}{\Leftrightarrow}&x=1\,{\mbox{ and }}\, y=2\,{\mbox{ or }}\, x=2\,{\mbox{ and }}\, y=1\,{\mbox{ or }}\, x=-2\,{\mbox{ and }}\, y=-1\,{\mbox{ or }}\, x=-1\,{\mbox{ and }}\, y=-2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [4*x^2+7*x*y+4*y^2=4 and y=x-4 , 4*x^2+7*x*(x-4)+4*(x-4)^2-4= 0 and y=x-4, 15*x^2-60*x+60=0 and y=x-4, (x-2)^2=0 and y=x-4 , x=2 and y=x-4, x=2 and y=-2] |
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1 | \[\begin{array}{lll} &\left\{\begin{array}{l}4\cdot x^2+7\cdot x\cdot y+4\cdot y^2=4\cr y=x-4\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}4\cdot x^2+7\cdot x\cdot \left(x-4\right)+4\cdot {\left(x-4\right)}^2-4=0\cr y=x-4\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}15\cdot x^2-60\cdot x+60=0\cr y=x-4\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}{\left(x-2\right)}^2=0\cr y=x-4\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x=2\cr y=x-4\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x=2\cr y=-2\cr \end{array}\right.& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [a^2=b and a^2=1, b=a^2 and (a =1 or a=-1), (b=1 and a=1) or (b=1 and a=-1)] |
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1 | \[\begin{array}{lll} &\left\{\begin{array}{l}a^2=b\cr a^2=1\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}b=a^2\cr a=1\,{\mbox{ or }}\, a=-1\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&b=1\,{\mbox{ and }}\, a=1\,{\mbox{ or }}\, b=1\,{\mbox{ and }}\, a=-1& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [a^2=b and x=1, b=a^2 and x=1] |
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1 | \[\begin{array}{lll} &\left\{\begin{array}{l}a^2=b\cr x=1\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}b=a^2\cr x=1\cr \end{array}\right.& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| Equiv | [a^2=b and b^2=a, b=a^2 and a^ 4=a, b=a^2 and a^4-a=0, b=a^2 and a*(a-1)*(a^2+a+1)=0, b=a^2 and (a=0 or a=1 or a^2+a+1=0) , (b=0 and a=0) or (b=1 and a= 1)] |
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[assumereal] |
1 | \[\begin{array}{lll}\color{blue}{(\mathbb{R})}&\left\{\begin{array}{l}a^2=b\cr b^2=a\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}b=a^2\cr a^4=a\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}b=a^2\cr a^4-a=0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}b=a^2\cr a\cdot \left(a-1\right)\cdot \left(a^2+a+1\right)=0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}b=a^2\cr a=0\,{\mbox{ or }}\, a=1\,{\mbox{ or }}\, a^2+a+1=0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&b=0\,{\mbox{ and }}\, a=0\,{\mbox{ or }}\, b=1\,{\mbox{ and }}\, a=1& \cr \end{array}\] | (ASSUMEREALVARS, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | ||
| Equiv | [2*x^3-9*x^2+10*x-3,stacklet(x ,1),2*1^3-9*1^2+10*1-3,stackeq (0),"So",2*x^3-9*x^2 +10*x-3,stackeq((x-1)*(2*x^2-7 *x+3)),stackeq((x-1)*(2*x-1)*( x-3))] |
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0 | \[\begin{array}{lll} &2\cdot x^3-9\cdot x^2+10\cdot x-3& \cr &\mbox{Let }x = 1& \cr \color{green}{\Leftrightarrow}&2\cdot 1^3-9\cdot 1^2+10\cdot 1-3& \cr \color{green}{\checkmark}&=0& \cr &\mbox{So}& \cr &2\cdot x^3-9\cdot x^2+10\cdot x-3& \cr \color{green}{\checkmark}&=\left(x-1\right)\cdot \left(2\cdot x^2-7\cdot x+3\right)& \cr \color{green}{\checkmark}&=\left(x-1\right)\cdot \left(2\cdot x-1\right)\cdot \left(x-3\right)& \cr \end{array}\] | (EMPTYCHAR, EMPTYCHAR, EQUIVCHAR, CHECKMARK, EMPTYCHAR, EMPTYCHAR, CHECKMARK, CHECKMARK) | |||
| Equiv | [2*x^2+x>=6, 2*x^2+x-6>= 0, (2*x-3)*(x+2)>= 0,((2*x- 3)>=0 and (x+2)>=0) or ( (2*x-3)<=0 and (x+2)<=0) , (x>=3/2 and x>=-2) or (x<=3/2 and x<=-2), x> ;=3/2 or x <=-2] |
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1 | \[\begin{array}{lll} &2\cdot x^2+x\geq 6& \cr \color{green}{\Leftrightarrow}&2\cdot x^2+x-6\geq 0& \cr \color{green}{\Leftrightarrow}&\left(2\cdot x-3\right)\cdot \left(x+2\right)\geq 0& \cr \color{green}{\Leftrightarrow}&2\cdot x-3\geq 0\,{\mbox{ and }}\, x+2\geq 0\,{\mbox{ or }}\, 2\cdot x-3\leq 0\,{\mbox{ and }}\, x+2\leq 0& \cr \color{green}{\Leftrightarrow}&x\geq \frac{3}{2}\,{\mbox{ and }}\, x\geq -2\,{\mbox{ or }}\, x\leq \frac{3}{2}\,{\mbox{ and }}\, x\leq -2& \cr \color{green}{\Leftrightarrow}&x\geq \frac{3}{2}\,{\mbox{ or }}\, x\leq -2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [2*x^2+x>=6, 2*x^2+x-6>= 0, (2*x-3)*(x+2)>= 0,((2*x- 3)>=0 and (x+2)>=0) or ( (2*x-3)<=0 and (x+2)<=0) , (x>=3/2 and x>=-2) or (x<=3/2 and x<=-2), x> ;=3/2 or x <=-2] |
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1 | \[\begin{array}{lll} &2\cdot x^2+x\geq 6& \cr \color{green}{\Leftrightarrow}&2\cdot x^2+x-6\geq 0& \cr \color{green}{\Leftrightarrow}&\left(2\cdot x-3\right)\cdot \left(x+2\right)\geq 0& \cr \color{green}{\Leftrightarrow}&2\cdot x-3\geq 0\,{\mbox{ and }}\, x+2\geq 0\,{\mbox{ or }}\, 2\cdot x-3\leq 0\,{\mbox{ and }}\, x+2\leq 0& \cr \color{green}{\Leftrightarrow}&x\geq \frac{3}{2}\,{\mbox{ and }}\, x\geq -2\,{\mbox{ or }}\, x\leq \frac{3}{2}\,{\mbox{ and }}\, x\leq -2& \cr \color{green}{\Leftrightarrow}&x\geq \frac{3}{2}\,{\mbox{ or }}\, x\leq -2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [2*x^2+x>=6, 2*x^2+x-6>= 0, (2*x-3)*(x+2)>= 0,((2*x- 3)>=0 and (x+2)>=0) or ( (2*x-3)<=0 and (x+2)<=0) , (x>=3/2 and x>=-2) or (x<=3/2 and x<=-2), x> ;=3/2 or x <=2] |
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0 | \[\begin{array}{lll} &2\cdot x^2+x\geq 6& \cr \color{green}{\Leftrightarrow}&2\cdot x^2+x-6\geq 0& \cr \color{green}{\Leftrightarrow}&\left(2\cdot x-3\right)\cdot \left(x+2\right)\geq 0& \cr \color{green}{\Leftrightarrow}&2\cdot x-3\geq 0\,{\mbox{ and }}\, x+2\geq 0\,{\mbox{ or }}\, 2\cdot x-3\leq 0\,{\mbox{ and }}\, x+2\leq 0& \cr \color{green}{\Leftrightarrow}&x\geq \frac{3}{2}\,{\mbox{ and }}\, x\geq -2\,{\mbox{ or }}\, x\leq \frac{3}{2}\,{\mbox{ and }}\, x\leq -2& \cr \color{red}{?}&x\geq \frac{3}{2}\,{\mbox{ or }}\, x\leq 2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR,QMCHAR) | |||
| Equiv | [x^2>=9 and x>3, x^2-9&g t;=0 and x>3, (x>=3 or x <=-3) and x>3, x>3] |
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1 | \[\begin{array}{lll} &\left\{\begin{array}{l}x^2\geq 9\cr x > 3\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x^2-9\geq 0\cr x > 3\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x\geq 3\,{\mbox{ or }}\, x\leq -3\cr x > 3\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&x > 3& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [-x^2+a*x+a-3<0, a-3<x^2 -a*x, a-3<(x-a/2)^2-a^2/4, a^2/4+a-3<(x-a/2)^2, a^2+4* a-12<4*(x-a/2)^2, (a-2)*(a+ 6)<4*(x-a/2)^2, "This inequality is required to be t rue for all x.", "So it must be true when the righ t hand side takes its minimum value.", "This happe ns for x=a/2.", (a-2)*(a+ 6)<0, ((a-2)<0 and (a+6) >0) or ((a-2)>0 and (a+6 )<0), (a<2 and a>-6) or (a>2 and a<-6), (-6&l t;a and a<2) or false, (-6& lt;a and a<2)] |
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0 | \[\begin{array}{lll} &-x^2+a\cdot x+a-3 < 0& \cr \color{green}{\Leftrightarrow}&a-3 < x^2-a\cdot x& \cr \color{green}{\Leftrightarrow}&a-3 < {\left(x-\frac{a}{2}\right)}^2-\frac{a^2}{4}& \cr \color{green}{\Leftrightarrow}&\frac{a^2}{4}+a-3 < {\left(x-\frac{a}{2}\right)}^2& \cr \color{green}{\Leftrightarrow}&a^2+4\cdot a-12 < 4\cdot {\left(x-\frac{a}{2}\right)}^2& \cr \color{green}{\Leftrightarrow}&\left(a-2\right)\cdot \left(a+6\right) < 4\cdot {\left(x-\frac{a}{2}\right)}^2& \cr &\mbox{This inequality is required to be true for all x.}& \cr &\mbox{So it must be true when the right hand side takes its minimum value.}& \cr &\mbox{This happens for x=a/2.}& \cr &\left(a-2\right)\cdot \left(a+6\right) < 0& \cr \color{green}{\Leftrightarrow}&a-2 < 0\,{\mbox{ and }}\, a+6 > 0\,{\mbox{ or }}\, a-2 > 0\,{\mbox{ and }}\, a+6 < 0& \cr \color{green}{\Leftrightarrow}&a < 2\,{\mbox{ and }}\, a > -6\,{\mbox{ or }}\, a > 2\,{\mbox{ and }}\, a < -6& \cr \color{green}{\Leftrightarrow}&-6 < a\,{\mbox{ and }}\, a < 2\,{\mbox{ or }}\, \mathbf{False}& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}-6 < a\cr a < 2\cr \end{array}\right.& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EMPTYCHAR, EMPTYCHAR, EMPTYCHAR, EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x-2>0 and x*(x-2)<15,x& gt;2 and x^2-2*x-15<0,x> 2 and (x-5)*(x+3)<0,x>2 and ((x<5 and x>-3) or ( x>5 and x<-3)),x>2 an d (x<5 and x>-3),x>2 and x<5] |
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1 | \[\begin{array}{lll} &\left\{\begin{array}{l}x-2 > 0\cr x\cdot \left(x-2\right) < 15\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x > 2\cr x^2-2\cdot x-15 < 0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x > 2\cr \left(x-5\right)\cdot \left(x+3\right) < 0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x > 2\cr x < 5\,{\mbox{ and }}\, x > -3\,{\mbox{ or }}\, x > 5\,{\mbox{ and }}\, x < -3\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x > 2\cr x < 5\,{\mbox{ and }}\, x > -3\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x > 2\cr x < 5\cr \end{array}\right.& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [x-2>0 and x*(x-2)<15,x& gt;2 and x^2-2*x-15<0,x> 2 and (x-5)*(x+3)<0,x>2 and ((x<5 and x>-3) or ( x>5 and x<-3)),x>7 an d (x<5 and x>-3),x>2 and x<5] |
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0 | \[\begin{array}{lll} &\left\{\begin{array}{l}x-2 > 0\cr x\cdot \left(x-2\right) < 15\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x > 2\cr x^2-2\cdot x-15 < 0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x > 2\cr \left(x-5\right)\cdot \left(x+3\right) < 0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x > 2\cr x < 5\,{\mbox{ and }}\, x > -3\,{\mbox{ or }}\, x > 5\,{\mbox{ and }}\, x < -3\cr \end{array}\right.& \cr \color{red}{?}&\left\{\begin{array}{l}x > 7\cr x < 5\,{\mbox{ and }}\, x > -3\cr \end{array}\right.& \cr \color{red}{?}&\left\{\begin{array}{l}x > 2\cr x < 5\cr \end{array}\right.& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR,QMCHAR,QMCHAR) | |||
| Equiv | [x^2 + (a-2)*x + a = 0,(x + (a -2)/2)^2 -((a-2)/2)^2 + a = 0, (x + (a-2)/2)^2 =(a-2)^2/4 - a ,"This has real roots iff ",(a-2)^2/4-a >=0,a^2- 4*a+4-4*a >=0,a^2-8*a+4> =0,(a-4)^2-16+4>=0,(a-4)^2& gt;=12,a-4>=sqrt(12) or a-4 <= -sqrt(12),"Ignoring the negative solution.", a>=sqrt(12)+4,"Using e xternal domain information tha t a is an integer.",a> =8] |
[] |
0 | \[\begin{array}{lll} &x^2+\left(a-2\right)\cdot x+a=0& \cr \color{green}{\Leftrightarrow}&{\left(x+\frac{a-2}{2}\right)}^2-{\left(\frac{a-2}{2}\right)}^2+a=0& \cr \color{green}{\Leftrightarrow}&{\left(x+\frac{a-2}{2}\right)}^2=\frac{{\left(a-2\right)}^2}{4}-a& \cr &\mbox{This has real roots iff}& \cr &\frac{{\left(a-2\right)}^2}{4}-a\geq 0& \cr \color{green}{\Leftrightarrow}&a^2-4\cdot a+4-4\cdot a\geq 0& \cr \color{green}{\Leftrightarrow}&a^2-8\cdot a+4\geq 0& \cr \color{green}{\Leftrightarrow}&{\left(a-4\right)}^2-16+4\geq 0& \cr \color{green}{\Leftrightarrow}&{\left(a-4\right)}^2\geq 12& \cr \color{green}{\Leftrightarrow}&a-4\geq \sqrt{12}\,{\mbox{ or }}\, a-4\leq -\sqrt{12}& \cr &\mbox{Ignoring the negative solution.}& \cr &a\geq \sqrt{12}+4& \cr &\mbox{Using external domain information that a is an integer.}& \cr &a\geq 8& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EMPTYCHAR, EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EMPTYCHAR, EMPTYCHAR, EMPTYCHAR, EMPTYCHAR) | |||
| Equiv | [x^2#1,x^2-1#0,(x-1)*(x+1)#0,x <-1 nounor (-1<x nounand x<1) nounor x>1] |
[] |
1 | \[\begin{array}{lll} &x^2\neq 1& \cr \color{green}{\Leftrightarrow}&x^2-1\neq 0& \cr \color{green}{\Leftrightarrow}&\left(x-1\right)\cdot \left(x+1\right)\neq 0& \cr \color{green}{\Leftrightarrow}&x < -1\,{\mbox{ or }}\, -1 < x\,{\mbox{ and }}\, x < 1\,{\mbox{ or }}\, x > 1& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | ["Set P(n) be the stateme nt that",sum(k^2,k,1,n) = n*(n+1)*(2*n+1)/6, "Then P(1) is the statement", 1^2 = 1*(1+1)*(2*1+1)/6, 1 = 1 , "So P(1) holds. Now as sume P(n) is true.",sum(k ^2,k,1,n) = n*(n+1)*(2*n+1)/6, sum(k^2,k,1,n) +(n+1)^2= n*(n+ 1)*(2*n+1)/6 +(n+1)^2,sum(k^2, k,1,n+1)= (n+1)*(n*(2*n+1) +6* (n+1))/6,sum(k^2,k,1,n+1)= (n+ 1)*(2*n^2+7*n+6)/6,sum(k^2,k,1 ,n+1)= (n+1)*(n+1+1)*(2*(n+1)+ 1)/6] |
[] |
0 | \[\begin{array}{lll} &\mbox{Set P(n) be the statement that}& \cr &\sum_{k=1}^{n}{k^2}=\frac{n\cdot \left(n+1\right)\cdot \left(2\cdot n+1\right)}{6}& \cr &\mbox{Then P(1) is the statement}& \cr &1^2=\frac{1\cdot \left(1+1\right)\cdot \left(2\cdot 1+1\right)}{6}& \cr \color{green}{\Leftrightarrow}&1=1& \cr &\mbox{So P(1) holds. Now assume P(n) is true.}& \cr &\sum_{k=1}^{n}{k^2}=\frac{n\cdot \left(n+1\right)\cdot \left(2\cdot n+1\right)}{6}& \cr \color{green}{\Leftrightarrow}&\sum_{k=1}^{n}{k^2}+{\left(n+1\right)}^2=\frac{n\cdot \left(n+1\right)\cdot \left(2\cdot n+1\right)}{6}+{\left(n+1\right)}^2& \cr \color{green}{\Leftrightarrow}&\sum_{k=1}^{n+1}{k^2}=\frac{\left(n+1\right)\cdot \left(n\cdot \left(2\cdot n+1\right)+6\cdot \left(n+1\right)\right)}{6}& \cr \color{green}{\Leftrightarrow}&\sum_{k=1}^{n+1}{k^2}=\frac{\left(n+1\right)\cdot \left(2\cdot n^2+7\cdot n+6\right)}{6}& \cr \color{green}{\Leftrightarrow}&\sum_{k=1}^{n+1}{k^2}=\frac{\left(n+1\right)\cdot \left(n+1+1\right)\cdot \left(2\cdot \left(n+1\right)+1\right)}{6}& \cr \end{array}\] | (EMPTYCHAR, EMPTYCHAR, EMPTYCHAR, EMPTYCHAR, EQUIVCHAR, EMPTYCHAR, EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [(n+1)^2+sum(k^2,k,1,n) = (n+1 )^2+(n*(n+1)*(2*n+1))/6, sum(k ^2,k,1,n+1) = ((n+1)*(n*(2*n+1 )+6*(n+1)))/6, sum(k^2,k,1,n+1 ) = ((n+1)*(2*n^2+7*n+6))/6, s um(k^2,k,1,n+1) = ((n+1)*(n+2) *(2*(n+1)+1))/6] |
[] |
1 | \[\begin{array}{lll} &{\left(n+1\right)}^2+\sum_{k=1}^{n}{k^2}={\left(n+1\right)}^2+\frac{n\cdot \left(n+1\right)\cdot \left(2\cdot n+1\right)}{6}& \cr \color{green}{\Leftrightarrow}&\sum_{k=1}^{n+1}{k^2}=\frac{\left(n+1\right)\cdot \left(n\cdot \left(2\cdot n+1\right)+6\cdot \left(n+1\right)\right)}{6}& \cr \color{green}{\Leftrightarrow}&\sum_{k=1}^{n+1}{k^2}=\frac{\left(n+1\right)\cdot \left(2\cdot n^2+7\cdot n+6\right)}{6}& \cr \color{green}{\Leftrightarrow}&\sum_{k=1}^{n+1}{k^2}=\frac{\left(n+1\right)\cdot \left(n+2\right)\cdot \left(2\cdot \left(n+1\right)+1\right)}{6}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [conjugate(a)*conjugate(b),sta cklet(a,x+i*y),stacklet(b,r+i* s),stackeq(conjugate(x+i*y)*co njugate(r+i*s)),stackeq((x-i*y )*(r-i*s)),stackeq((x*r-y*s)-i *(y*r+x*s)),stackeq(conjugate( (x*r-y*s)+i*(y*r+x*s))),stacke q(conjugate((x+i*y)*(r+i*s))), stacklet(x+i*y,a),stacklet(r+i *s,b),stackeq(conjugate(a*b))] |
[] |
1 | \[\begin{array}{lll} &a^\star\cdot b^\star& \cr &\mbox{Let }a = x+\mathrm{i}\cdot y& \cr &\mbox{Let }b = r+\mathrm{i}\cdot s& \cr \color{green}{\checkmark}&=\left(x+\mathrm{i}\cdot y\right)^\star\cdot \left(r+\mathrm{i}\cdot s\right)^\star& \cr \color{green}{\checkmark}&=\left(x-\mathrm{i}\cdot y\right)\cdot \left(r-\mathrm{i}\cdot s\right)& \cr \color{green}{\checkmark}&=x\cdot r-y\cdot s-\mathrm{i}\cdot \left(y\cdot r+x\cdot s\right)& \cr \color{green}{\checkmark}&=\left(x\cdot r-y\cdot s+\mathrm{i}\cdot \left(y\cdot r+x\cdot s\right)\right)^\star& \cr \color{green}{\checkmark}&=\left(\left(x+\mathrm{i}\cdot y\right)\cdot \left(r+\mathrm{i}\cdot s\right)\right)^\star& \cr &\mbox{Let }x+\mathrm{i}\cdot y = a& \cr &\mbox{Let }r+\mathrm{i}\cdot s = b& \cr \color{green}{\checkmark}&=\left(a\cdot b\right)^\star& \cr \end{array}\] | (EMPTYCHAR, EMPTYCHAR, EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, EMPTYCHAR, EMPTYCHAR, CHECKMARK) | |||
| Equiv | [nounint(x*e^x,x,-inf,0),nounl imit(nounint(x*e^x,x,t,0),t,-i nf),nounlimit(e^t-t*e^t-1,t,-i nf),nounlimit(e^t,t,-inf)+noun limit(-t*e^t,t,-inf)+nounlimit (-1,t,-inf),-1] |
[] |
1 | \[\begin{array}{lll} &\int_{-\infty }^{0}{x\cdot e^{x}\;\mathrm{d}x}& \cr \color{green}{\Leftrightarrow}&\lim_{t\rightarrow -\infty }{\int_{t}^{0}{x\cdot e^{x}\;\mathrm{d}x}}& \cr \color{green}{\Leftrightarrow}&\lim_{t\rightarrow -\infty }{e^{t}-t\cdot e^{t}-1}& \cr \color{green}{\Leftrightarrow}&\lim_{t\rightarrow -\infty }{e^{t}}+\lim_{t\rightarrow -\infty }{\left(-t\right)\cdot e^{t}}+\lim_{t\rightarrow -\infty }{-1}& \cr \color{green}{\Leftrightarrow}&-1& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| Equiv | [noundiff(x^2,x),stackeq(nounl imit(((x+h)^2-x^2)/h,h,0)),sta ckeq(nounlimit(2*x+h,h,0)),sta ckeq(2*x)] |
[] |
1 | \[\begin{array}{lll} &\frac{\mathrm{d}}{\mathrm{d} x} x^2& \cr \color{green}{\checkmark}&=\lim_{h\rightarrow 0}{\frac{{\left(x+h\right)}^2-x^2}{h}}& \cr \color{green}{\checkmark}&=\lim_{h\rightarrow 0}{2\cdot x+h}& \cr \color{green}{\checkmark}&=2\cdot x& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK) | |||
| Equiv | [-12+3*noundiff(y(x),x)+8-8*no undiff(y(x),x)=0,-5*noundiff(y (x),x)=4,noundiff(y(x),x)=-4/5 ] |
[] |
[calculus] |
1 | \[\begin{array}{lll} &-12+3\cdot \left(\frac{\mathrm{d}}{\mathrm{d} x} y\left(x\right)\right)+8-8\cdot \left(\frac{\mathrm{d}}{\mathrm{d} x} y\left(x\right)\right)=0& \cr \color{green}{\Leftrightarrow}&-5\cdot \left(\frac{\mathrm{d}}{\mathrm{d} x} y\left(x\right)\right)=4& \cr \color{green}{\Leftrightarrow}&\left(\frac{\mathrm{d}}{\mathrm{d} x} y\left(x\right)\right)=\frac{-4}{5}& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR) | ||
| Equiv | [x^2+1,x^3/3+x,x^2+1,x^3/3+x+c ] |
[] |
[calculus] |
1 | \[\begin{array}{lll} &x^2+1& \cr \color{blue}{\int\ldots\mathrm{d}x}&\frac{x^3}{3}+x& \cr \color{blue}{\frac{\mathrm{d}}{\mathrm{d}x}\ldots}&x^2+1& \cr \color{blue}{\int\ldots\mathrm{d}x}&\frac{x^3}{3}+x+c& \cr \end{array}\] | (EMPTYCHAR,INTCHAR(x),DIFFCHAR(x),INTCHAR(x)) | ||
| Equiv | [3*x^(3/2)-2/x,(9*sqrt(x))/2+2 /x^2,3*x^(3/2)-2/x+c] |
[] |
[calculus] |
1 | \[\begin{array}{lll} &3\cdot x^{\frac{3}{2}}-\frac{2}{x}&{\color{blue}{{x \not\in {\left \{0 \right \}}}}}\cr \color{blue}{\frac{\mathrm{d}}{\mathrm{d}x}\ldots}&\frac{9\cdot \sqrt{x}}{2}+\frac{2}{x^2}&{\color{blue}{{x \in {\left( 0,\, \infty \right)}}}}\cr \color{blue}{\int\ldots\mathrm{d}x}&3\cdot x^{\frac{3}{2}}-\frac{2}{x}+c& \cr \end{array}\] | (EMPTYCHAR,DIFFCHAR(x),INTCHAR(x)) | ||
| Equiv | [x^2+1,stackeq(x^3/3+x),stacke q(x^2+1),stackeq(x^3/3+x+c)] |
[] |
[calculus] |
0 | \[\begin{array}{lll} &x^2+1& \cr \color{red}{?}&=\frac{x^3}{3}+x& \cr \color{red}{?}&=x^2+1& \cr \color{red}{?}&=\frac{x^3}{3}+x+c& \cr \end{array}\] | (EMPTYCHAR,QMCHAR,QMCHAR,QMCHAR) | ||
| Equiv | [diff(x^2*sin(x),x),stackeq(x^ 2*diff(sin(x),x)+diff(x^2,x)*s in(x)),stackeq(x^2*cos(x)+2*x* sin(x))] |
[] |
[calculus] |
1 | \[\begin{array}{lll} &\cos \left( x \right)\cdot x^2+2\cdot x\cdot \sin \left( x \right)& \cr \color{green}{\checkmark}&=x^2\cdot \cos \left( x \right)+2\cdot x\cdot \sin \left( x \right)& \cr \color{green}{\checkmark}&=x^2\cdot \cos \left( x \right)+2\cdot x\cdot \sin \left( x \right)& \cr \end{array}\] | (EMPTYCHAR, CHECKMARK, CHECKMARK) | ||
| Equiv | [y(x)*cos(x)+y(x)^2 = 6*x,cos( x)*diff(y(x),x)+2*y(x)*diff(y( x),x)-y(x)*sin(x) = 6,(cos(x)+ 2*y(x))*diff(y(x),x) = y(x)*si n(x)+6,diff(y(x),x) = (y(x)*si n(x)+6)/(cos(x)+2*y(x))] |
[] |
[calculus] |
1 | \[\begin{array}{lll} &y\left(x\right)\cdot \cos \left( x \right)+y^2\left(x\right)=6\cdot x& \cr \color{blue}{\frac{\mathrm{d}}{\mathrm{d}x}\ldots}&\cos \left( x \right)\cdot \left(\frac{\mathrm{d}}{\mathrm{d} x} y\left(x\right)\right)+2\cdot y\left(x\right)\cdot \left(\frac{\mathrm{d}}{\mathrm{d} x} y\left(x\right)\right)+\left(-y\left(x\right)\right)\cdot \sin \left( x \right)=6& \cr \color{green}{\Leftrightarrow}&\left(\cos \left( x \right)+2\cdot y\left(x\right)\right)\cdot \left(\frac{\mathrm{d}}{\mathrm{d} x} y\left(x\right)\right)=y\left(x\right)\cdot \sin \left( x \right)+6& \cr \color{green}{\Leftrightarrow}&\left(\frac{\mathrm{d}}{\mathrm{d} x} y\left(x\right)\right)=\frac{y\left(x\right)\cdot \sin \left( x \right)+6}{\cos \left( x \right)+2\cdot y\left(x\right)}& \cr \end{array}\] | (EMPTYCHAR,DIFFCHAR(x), EQUIVCHAR, EQUIVCHAR) | ||
| Equiv | [nounint(s^2+1,s),stackeq(s^3/ 3+s+c)] |
[] |
[calculus] |
1 | \[\begin{array}{lll} &\int {s^2+1}{\;\mathrm{d}s}& \cr \color{blue}{\int\ldots\mathrm{d}s}&=\frac{s^3}{3}+s+c& \cr \end{array}\] | (EMPTYCHAR,INTCHAR(s)) | ||
| Equiv | [nounint(x^3*log(x),x),x^4/4*l og(x)-1/4*nounint(x^3,x),x^4/4 *log(x)-x^4/16] |
[] |
[calculus] |
0 | \[\begin{array}{lll} &\int {x^3\cdot \ln \left( x \right)}{\;\mathrm{d}x}& \cr \color{green}{\Leftrightarrow}&\frac{x^4}{4}\cdot \ln \left( x \right)-\frac{1}{4}\cdot \int {x^3}{\;\mathrm{d}x}& \cr \color{red}{\cdots +c\quad ?}&\frac{x^4}{4}\cdot \ln \left( x \right)-\frac{x^4}{16}&{\color{blue}{{x \in {\left( 0,\, \infty \right)}}}}\cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR,PLUSC) | ||
| Equiv | [nounint(x^3*log(x),x),x^4/4*l og(x)-1/4*nounint(x^3,x),x^4/4 *log(x)-x^4/16+c] |
[] |
[calculus] |
1 | \[\begin{array}{lll} &\int {x^3\cdot \ln \left( x \right)}{\;\mathrm{d}x}& \cr \color{green}{\Leftrightarrow}&\frac{x^4}{4}\cdot \ln \left( x \right)-\frac{1}{4}\cdot \int {x^3}{\;\mathrm{d}x}& \cr \color{blue}{\int\ldots\mathrm{d}x}&\frac{x^4}{4}\cdot \ln \left( x \right)-\frac{x^4}{16}+c& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR,INTCHAR(x)) | ||
| Equiv | [noundiff(y,x)-2/x*y=x^3*sin(3 *x),1/x^2*noundiff(y,x)-2/x^3* y=x*sin(3*x),noundiff(y/x^2,x) =x*sin(3*x),y/x^2 = nounint(x* sin(3*x),x),y/x^2=(sin(3*x)-3* x*cos(3*x))/9+c] |
[] |
[calculus] |
1 | \[\begin{array}{lll} &\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2}{x}\cdot y=x^3\cdot \sin \left( 3\cdot x \right)& \cr \color{green}{\Leftrightarrow}&\frac{1}{x^2}\cdot \left(\frac{\mathrm{d} y}{\mathrm{d} x}\right)-\frac{2}{x^3}\cdot y=x\cdot \sin \left( 3\cdot x \right)& \cr \color{green}{\Leftrightarrow}&\left(\frac{\mathrm{d}}{\mathrm{d} x} \frac{y}{x^2}\right)=x\cdot \sin \left( 3\cdot x \right)& \cr \color{blue}{\int\ldots\mathrm{d}x}&\frac{y}{x^2}=\int {x\cdot \sin \left( 3\cdot x \right)}{\;\mathrm{d}x}& \cr \color{blue}{\int\ldots\mathrm{d}x}&\frac{y}{x^2}=\frac{\sin \left( 3\cdot x \right)-3\cdot x\cdot \cos \left( 3\cdot x \right)}{9}+c& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR,INTCHAR(x),INTCHAR(x)) |
EquivFirst
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| EquivFirst | x |
[x^2=4,x=2 or x=-2] |
-1 | The first argument to the Equiv answer test should be a list, but the test failed. Please contact your teacher. | ATEquivFirst_SA_not_list. | |||
| EquivFirst | [x^2=4,x=2 or x=-2] |
x |
-1 | The second argument to the Equiv answer test should be a list, but the test failed. Please contact your teacher. | ATEquivFirst_SB_not_list. | |||
| EquivFirst | [1/0] |
[x^2=4,x=2 or x=-2] |
-1 | ATEquivFirst_STACKERROR_SAns. | ||||
| EquivFirst | [x^2=4,x=2 or x=-2] |
[1/0] |
-1 | ATEquivFirst_STACKERROR_TAns. | ||||
| EquivFirst | [x^2=4,x=2 or x=-2] |
[x^2=4,x=2 or x=-2] |
1 | \[\begin{array}{lll} &x^2=4& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ or }}\, x=-2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR) | |||
| EquivFirst | [x^2=9,x=3 or x=-3] |
[x^2=4,x=2 or x=-2] |
0 | The first line in your argument must be "\(x^2=4\)". | ATEquivFirst_SA_wrong_start | |||
| EquivFirst | [x^2=4,x=2] |
[x^2=4,x=2 or x=-2] |
0 | \[\begin{array}{lll} &x^2=4& \cr \color{red}{\Leftarrow}&x=2& \cr \end{array}\] | (EMPTYCHAR,IMPLIEDCHAR) | |||
| EquivFirst | [x^2=4,x^2-4=0,(x-2)*(x+2)=0,x =2 or x=-2] |
[x^2=4,x=2 or x=-2] |
1 | \[\begin{array}{lll} &x^2=4& \cr \color{green}{\Leftrightarrow}&x^2-4=0& \cr \color{green}{\Leftrightarrow}&\left(x-2\right)\cdot \left(x+2\right)=0& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ or }}\, x=-2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| EquivFirst | [x^2=4,x= #pm#2, x=2 or x=-2] |
[x^2=4,x=2 or x=-2] |
1 | \[\begin{array}{lll} &x^2=4& \cr \color{green}{\Leftrightarrow}&x= \pm 2& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ or }}\, x=-2& \cr \end{array}\] | (EMPTYCHAR, EQUIVCHAR, EQUIVCHAR) | |||
| EquivFirst | [x^2-6*x+9=0,x=3] |
[x^2-6*x+9=0,x=3] |
1 | \[\begin{array}{lll} &x^2-6\cdot x+9=0& \cr \color{green}{\mbox{(Same roots)}}&x=3& \cr \end{array}\] | (EMPTYCHAR,SAMEROOTS) | |||
| EquivFirst | [x^2=4,x=2] |
[x^2=4,x=2] |
[assumepos] |
1 | \[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&x^2=4& \cr \color{green}{\Leftrightarrow}&x=2& \cr \end{array}\] | (ASSUMEPOSVARS, EQUIVCHAR) | ||
SingleFrac
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| SingleFrac | 1/0 |
1/n |
-1 | ATSingleFrac_STACKERROR_SAns. | ||||
| SingleFrac | 0 |
1/0 |
-1 | ATSingleFrac_STACKERROR_TAns. | ||||
| SingleFrac | x=3 |
2 |
0 | Your answer should be an expression, not an equation, inequality, list, set or matrix. | ATSingleFrac_SA_not_expression. | |||
| SingleFrac | 3 |
3 |
1 | |||||
| SingleFrac | 3 |
2 |
0 | Your answer is not algebraically equivalent to the correct answer. You must have done something wrong. | ATSingleFrac_ret_exp. | |||
| SingleFrac | 1/m |
1/n |
0 | Your answer is not algebraically equivalent to the correct answer. You must have done something wrong. | ATSingleFrac_true. ATSingleFrac_ret_exp. | |||
| SingleFrac | 1/n |
1/n |
1 | ATSingleFrac_true. | ||||
| SingleFrac | a+1/2 |
(2*a+1)/2 |
0 | Your answer needs to be a single fraction of the form \( {a}\over{b} \). | ATSingleFrac_part. | |||
| SingleFrac | a+1/2 |
(2*a+1)/2 |
0 | Your answer needs to be a single fraction of the form \( {a}\over{b} \). | ATSingleFrac_part. | |||
| SingleFrac | 4/(x^2+2*x-24)+2/(x^2+4*x-12) |
(6*x-16)/(x^3-28*x+48) |
0 | Your answer needs to be a single fraction of the form \( {a}\over{b} \). | ATSingleFrac_part. | |||
| 2 subtly different answers for the same question | ||||||||
| SingleFrac | 2*(1/n) |
2/n |
0 | Your answer needs to be a single fraction of the form \( {a}\over{b} \). | ATSingleFrac_part. | |||
| SingleFrac | 2/n |
2/n |
1 | ATSingleFrac_true. | ||||
| Simple Mistakes | ||||||||
| SingleFrac | 2/(n+1) |
1/(n+1) |
0 | Your answer is not algebraically equivalent to the correct answer. You must have done something wrong. | ATSingleFrac_true. ATSingleFrac_ret_exp. | |||
| SingleFrac | (2*n+1)/(n+2) |
1/n |
0 | Your answer is not algebraically equivalent to the correct answer. You must have done something wrong. | ATSingleFrac_true. ATSingleFrac_ret_exp. | |||
| SingleFrac | (2*n)/(n*(n+2)) |
(2*n)/(n*(n+3)) |
0 | Your answer is not algebraically equivalent to the correct answer. You must have done something wrong. | ATSingleFrac_true. ATSingleFrac_ret_exp. | |||
| SingleFrac | (x-1)/(x^2-1) |
1/(x+1) |
1 | ATSingleFrac_true. | ||||
| Fractions within fractions | ||||||||
| SingleFrac | (1/2)/(3/4) |
2/3 |
0 | Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction. | ATSingleFrac_div. | |||
| SingleFrac | (x-2)/4/(2/x^2) |
(x-2)*x^2/8 |
0 | Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction. | ATSingleFrac_div. | |||
| SingleFrac | 1/(1-1/x) |
x/(x-1) |
0 | Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction. | ATSingleFrac_div. | |||
| SingleFrac | (1+1/a)/a |
(1+a)/a^2 |
0 | Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction. | ATSingleFrac_div. | |||
| SingleFrac | a/(1+1/a) |
a^2/(1+a) |
0 | Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction. | ATSingleFrac_div. | |||
| SingleFrac | (1+2*b/a)/c |
(a+2*b)/(a*c) |
0 | Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction. | ATSingleFrac_div. | |||
| SingleFrac | c/(1+2*b/a) |
a*c/(a+2*b) |
0 | Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction. | ATSingleFrac_div. | |||
| SingleFrac | a*c/(a+2*b) |
a*c/(a+2*b) |
1 | ATSingleFrac_true. | ||||
| Negative cases | ||||||||
| SingleFrac | -1/2 |
-1/2 |
1 | ATSingleFrac_true. | ||||
| SingleFrac | -1/2 |
-1/3 |
0 | Your answer is not algebraically equivalent to the correct answer. You must have done something wrong. | ATSingleFrac_true. ATSingleFrac_ret_exp. | |||
| SingleFrac | -(1/2) |
-1/2 |
1 | ATSingleFrac_true. | ||||
| SingleFrac | -a/b |
-a/b |
1 | ATSingleFrac_true. | ||||
| SingleFrac | (-a)/b |
-a/b |
1 | ATSingleFrac_true. | ||||
| SingleFrac | a/(-b) |
-a/b |
1 | ATSingleFrac_true. | ||||
| SingleFrac | -(a/b) |
-a/b |
1 | ATSingleFrac_true. | ||||
| SingleFrac | -(1/(n-1)) |
1/(1-n) |
1 | ATSingleFrac_true. | ||||
| SingleFrac | a/(-1-1/a) |
-a^2/(1+a) |
0 | Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction. | ATSingleFrac_div. | |||
| Surds in answers | ||||||||
| SingleFrac | ((sqrt(5))^3 +6)/15 |
((sqrt(5))^3 +6)/15 |
1 | ATSingleFrac_true. | ||||
| SingleFrac | 1/(1-sqrt(2)) |
1/(1-sqrt(2)) |
1 | ATSingleFrac_true. | ||||
| SingleFrac | ((sqrt(5))^3+6)/15 |
((sqrt(5))^3+6)/15 |
1 | ATSingleFrac_true. | ||||
| SingleFrac | (5^(3/2)+6)/15 |
((sqrt(5))^3+6)/15 |
1 | ATSingleFrac_true. | ||||
PartFrac
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| PartFrac | 1/0 |
3*x^2 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test. | STACKERROR_OPTION. | ||
| PartFrac | 1/0 |
3*x^2 |
x |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATPartFrac_STACKERROR_SAns. | |
| PartFrac | 0 |
0 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATPartFrac_STACKERROR_Opt. | |
| PartFrac | 0 |
1/0 |
x |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATPartFrac_STACKERROR_TAns. | |
| PartFrac | 1/n=0 |
1/n |
n |
0 | Your answer should be an expression, not an equation, inequality, list, set or matrix. | ATPartFrac_SA_not_expression. | ||
| PartFrac | 1/n |
{1/n} |
n |
0 | The answer test failed. Please contact your systems administrator | ATPartFrac_TA_not_expression. | ||
| Basic tests | ||||||||
| PartFrac | 1/m |
1/n |
n |
0 | The variables in your answer are different to those of the question, please check them. | ATPartFrac_diff_variables. | ||
| PartFrac | 2/(x+1)-1/(x+2) |
s/((s+1)*(s+2)) |
s |
0 | The variables in your answer are different to those of the question, please check them. | ATPartFrac_diff_variables. | ||
| PartFrac | 1/n |
1/n |
n |
1 | ATPartFrac_true. | |||
| PartFrac | n^3/(n-1) |
n^3/(n-1) |
n |
0 | ATPartFrac_false_factor. | |||
| PartFrac | 1+n+n^2+1/(n-1) |
n^3/(n-1) |
n |
1 | ATPartFrac_true. | |||
| PartFrac | 1+n+n^2-1/(1-n) |
n^3/(n-1) |
n |
1 | ATPartFrac_true. | |||
| Distinct linear factors in denominator | ||||||||
| PartFrac | 1/(n+1)-1/n |
1/(n+1)-1/n |
n |
1 | ATPartFrac_true. | |||
| PartFrac | 1/(n+1)+1/(1-n) |
1/(n+1)-1/(n-1) |
n |
1 | ATPartFrac_true. | |||
| PartFrac | 1/(2*(n-1))-1/(2*(n+1)) |
1/((n-1)*(n+1)) |
n |
1 | ATPartFrac_true. | |||
| PartFrac | 1/(2*(n+1))-1/(2*(n-1)) |
1/((n-1)*(n+1)) |
n |
0 | Your answer as a single fraction is \(-\frac{1}{\left(n-1\right)\cdot \left(n+1\right)}\) | ATPartFrac_ret_expression. | ||
| PartFrac | -9/(x-2) + -9/(x+1) |
-9/(x-2) + -9/(x+1) |
x |
1 | ATPartFrac_true. | |||
| Addition and Subtraction errors | ||||||||
| PartFrac | 1/(x+1) + 1/(x+2) |
2/(x+1) + 1/(x+2) |
x |
0 | Your answer as a single fraction is \(\frac{2\cdot x+3}{\left(x+1\right)\cdot \left(x+2\right)}\) | ATPartFrac_ret_expression. | ||
| PartFrac | 1/(x+1) + 1/(x+2) |
1/(x+1) + 2/(x+2) |
x |
0 | Your answer as a single fraction is \(\frac{2\cdot x+3}{\left(x+1\right)\cdot \left(x+2\right)}\) | ATPartFrac_ret_expression. | ||
| Denominator Error | ||||||||
| PartFrac | 1/(x+1) + 1/(x+2) |
1/(x+3) + 1/(x+2) |
x |
0 | Your answer as a single fraction is \(\frac{2\cdot x+3}{\left(x+1\right)\cdot \left(x+2\right)}\) | ATPartFrac_ret_expression. | ||
| Repeated linear factors in denominator | ||||||||
| PartFrac | (9*y-8)/(y-4)^2 |
(9*y-8)/(y-4)^2 |
y |
0 | ATPartFrac_false_factor. | |||
| PartFrac | 9/(y-4)+28/(y-4)^2 |
(9*y-8)/(y-4)^2 |
y |
1 | ATPartFrac_true. | |||
| PartFrac | (-5/(x+3))+(16/(x+3)^2)-(2/(x+ 2))+4 |
(-5/(x+3))+(16/(x+3)^2)-(2/(x+ 2))+4 |
x |
1 | ATPartFrac_true. | |||
| PartFrac | (3*x^2-5)/((x-4)^2*x) |
(3*x^2-5)/((x-4)^2*x) |
x |
0 | ATPartFrac_false_factor. | |||
| PartFrac | -4/(16*x)+53/(16*(x-4))+43/(4* (x-4)^2) |
(3*x^2-5)/((x-4)^2*x) |
x |
0 | Your answer as a single fraction is \(\frac{49\cdot x^2-8\cdot x-64}{16\cdot {\left(x-4\right)}^2\cdot x}\) | ATPartFrac_ret_expression. | ||
| PartFrac | -5/(16*x)+53/(16*(x-4))+43/(4* (x-4)^2) |
(3*x^2-5)/((x-4)^2*x) |
x |
1 | ATPartFrac_true. | |||
| PartFrac | (5*x+6)/((x+1)*(x+5)^2) |
(5*x+6)/((x+1)*(x+5)^2) |
x |
0 | ATPartFrac_false_factor. | |||
| PartFrac | -1/(16*(x+5))+19/(4*(x+5)^2)+1 /(16*(x+1)) |
(5*x+6)/((x+1)*(x+5)^2) |
x |
1 | ATPartFrac_true. | |||
| PartFrac | 5/(x*(x+3)*(5*x-2)) |
5/(x*(x+3)*(5*x-2)) |
x |
0 | ATPartFrac_false_factor. | |||
| PartFrac | 125/(34*(5*x-2))+5/(51*(x+3))- 5/(6*x) |
5/(x*(x+3)*(5*x-2)) |
x |
1 | ATPartFrac_true. | |||
| PartFrac | -4/(16*x)+1/(2*(x-1))-1/(8*(x- 1)^2) |
(3*x^2-5)/((4*x-4)^2*x) |
x |
0 | Your answer as a single fraction is \(\frac{2\cdot x^2-x-2}{8\cdot {\left(x-1\right)}^2\cdot x}\) | ATPartFrac_ret_expression. | ||
| PartFrac | -5/(16*x)+1/(2*(x-1))-1/(8*(x- 1)^2) |
(3*x^2-5)/((4*x-4)^2*x) |
x |
1 | ATPartFrac_true. | |||
| Irreducible quadratic in denominator | ||||||||
| PartFrac | 1/(x-1)-(x+1)/(x^2+1) |
2/((x-1)*(x^2+1)) |
x |
1 | ATPartFrac_true. | |||
| PartFrac | 1/(2*x-2)-(x+1)/(2*(x^2+1)) |
1/((x-1)*(x^2+1)) |
x |
1 | ATPartFrac_true. | |||
| PartFrac | 1/(2*(x-1))+x/(2*(x^2+1)) |
1/((x-1)*(x^2+1)) |
x |
0 | Your answer as a single fraction is \(\frac{2\cdot x^2-x+1}{2\cdot \left(x-1\right)\cdot \left(x^2+1 \right)}\) | ATPartFrac_ret_expression. | ||
| PartFrac | (2*x+1)/(x^2+1)-2/(x-1) |
(2*x+1)/(x^2+1)-2/(x-1) |
x |
1 | ATPartFrac_true. | |||
| 2 answers to the same question | ||||||||
| PartFrac | 3/(x+1) + 3/(x+2) |
3*(2*x+3)/((x+1)*(x+2)) |
x |
1 | ATPartFrac_true. | |||
| PartFrac | 3*(1/(x+1) + 1/(x+2)) |
3*(2*x+3)/((x+1)*(x+2)) |
x |
1 | ATPartFrac_true. | |||
| Algebraically equivalent, but numerators of same order than denominator, i.e. not in partial fraction form. | ||||||||
| PartFrac | 3*x*(1/(x+1) + 2/(x+2)) |
-12/(x+2)-3/(x+1)+9 |
x |
0 | ATPartFrac_false_factor. | |||
| PartFrac | (3*x+3)*(1/(x+1) + 2/(x+2)) |
9-6/(x+2) |
x |
0 | ATPartFrac_false_factor. | |||
| PartFrac | n/(2*n-1)-(n+1)/(2*n+1) |
1/(4*n-2)-1/(4*n+2) |
n |
0 | ATPartFrac_false_factor. | |||
| Correct Answer, Numerator > Denominator | ||||||||
| PartFrac | 10/(x+3) - 2/(x+2) + x -2 |
(x^3 + 3*x^2 + 4*x +2)/((x+2)* (x+3)) |
x |
1 | ATPartFrac_true. | |||
| PartFrac | 2*x+1/(x+1)+1/(x-1) |
2*x^3/(x^2-1) |
x |
1 | ATPartFrac_true. | |||
| Simple mistakes | ||||||||
| PartFrac | 1/(n*(n-1)) |
1/(n*(n-1)) |
n |
0 | ATPartFrac_false_factor. | |||
| PartFrac | ((1-x)^4*x^4)/(x^2+1) |
((1-x)^4*x^4)/(x^2+1) |
x |
0 | ATPartFrac_false_factor. | |||
| PartFrac | 1/(n-1)-1/n^2 |
1/((n+1)*n) |
n |
0 | If your answer is written as a single fraction then the denominator would be \(\left(n-1\right)\cdot n^2\). In fact, it should be \(n\cdot \left(n+1\right)\). | ATPartFrac_denom_ret. | ||
| PartFrac | 1/(n-1)-1/n |
1/(n-1)+1/n |
n |
0 | Your answer as a single fraction is \(\frac{1}{\left(n-1\right)\cdot n}\) | ATPartFrac_ret_expression. | ||
| PartFrac | 1/(x+1)-1/x |
1/(x-1)+1/x |
x |
0 | Your answer as a single fraction is \(-\frac{1}{x\cdot \left(x+1\right)}\) | ATPartFrac_ret_expression. | ||
| PartFrac | 1/(n*(n+1))+1/n |
2/n-1/(n+1) |
n |
0 | ATPartFrac_false_factor. | |||
| Too many parts in the partial fraction | ||||||||
| PartFrac | s/((s+1)^2) + s/(s+2) - 1/(s+1 ) |
s/((s+1)*(s+2)) |
s |
0 | If your answer is written as a single fraction then the denominator would be \({\left(s+1\right)}^2\cdot \left(s+2\right)\). In fact, it should be \(\left(s+1\right)\cdot \left(s+2\right)\). | ATPartFrac_denom_ret. | ||
| Too few parts in the partial fraction | ||||||||
| PartFrac | s/(s+2) - 1/(s+1) |
s/((s+1)*(s+2)*(s+3)) |
s |
0 | If your answer is written as a single fraction then the denominator would be \(\left(s+1\right)\cdot \left(s+2\right)\). In fact, it should be \(\left(s+1\right)\cdot \left(s+2\right)\cdot \left(s+3\right)\). | ATPartFrac_denom_ret. | ||
| PartFrac | (3*x^2-5)/((4*x-4)^2*x) |
(3*x^2-5)/((4*x-4)^2*x) |
x |
0 | ATPartFrac_false_factor. | |||
Diff
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Diff | 1/0 |
3*x^2 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test. | STACKERROR_OPTION. | ||
| Diff | 0 |
1/0 |
(x |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Option field is invalid. You have a missing right bracket ) in the expression: (x. | STACKERROR_OPTION. | |
| Diff | 1/0 |
3*x^2 |
x |
-1 | ATDiff_STACKERROR_SAns. | |||
| Diff | 0 |
1/0 |
x |
-1 | ATDiff_STACKERROR_TAns. | |||
| Diff | 0 |
0 |
1/0 |
-1 | ATDiff_STACKERROR_Opt. | |||
| Basic tests | ||||||||
| Diff | 3*x^2 |
3*x^2 |
x |
1 | ATDiff_true. | |||
| Diff | 3*X^2 |
3*x^2 |
x |
0 | ATDiff_var_SB_notSA. | |||
| Diff | x^4/4 |
3*x^2 |
x |
0 | It looks like you have integrated instead! | ATDiff_int. | ||
| Diff | x^4/4+1 |
3*x^2 |
x |
0 | It looks like you have integrated instead! | ATDiff_int. | ||
| Diff | x^4/4+c |
3*x^2 |
x |
0 | It looks like you have integrated instead! | ATDiff_int. | ||
| Diff | y=x^4/4 |
x^4/4 |
x |
0 | Your answer should be an expression, not an equation, inequality, list, set or matrix. | ATDiff_SA_not_expression. | ||
| Diff | x^4/4 |
y=x^4/4 |
x |
0 | ||||
| Diff | y=x^4/4 |
y=x^4/4 |
x |
0 | Your answer should be an expression, not an equation, inequality, list, set or matrix. | ATDiff_SA_not_expression. | ||
| Diff | 6000*(x-a)^5999 |
6000*(x-a)^5999 |
x |
1 | ATDiff_true. | |||
| Diff | 5999*(x-a)^5999 |
6000*(x-a)^5999 |
x |
0 | ||||
| Variable mismatch tests | ||||||||
| Diff | y^2-2*y+1 |
x^2-2*x+1 |
x |
0 | ATDiff_var_SB_notSA. | |||
| Diff | x^2-2*x+1 |
y^2-2*y+1 |
x |
0 | ATDiff_var_SA_notSB. | |||
| Diff | y^2+2*y+1 |
x^2-2*x+1 |
z |
0 | ATDiff_var_notSASB_SAnceSB. | |||
| Diff | x^4/4 |
3*x^2 |
y |
0 | ||||
| Edge cases | ||||||||
| Diff | e^x+c |
e^x |
x |
0 | It looks like you have integrated instead! | ATDiff_int. | ||
| Diff | e^x+2 |
e^x |
x |
0 | It looks like you have integrated instead! | ATDiff_int. | ||
| Diff | n*x^n |
n*x^(n-1) |
x |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. TIMEDOUT | ATDiff_STACKERROR_SAns. | |
| Diff | n*x^n |
(assume(n>0), n*x^(n-1)) |
x |
0 | ||||
Int
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Int | 1/0 |
1 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test. | STACKERROR_OPTION. | ||
| Int | 1/0 |
1 |
x |
-1 | ATInt_STACKERROR_SAns. | |||
| Int | 1 |
1/0 |
x |
-1 | ATInt_STACKERROR_TAns. | |||
| Int | 0 |
0 |
1/0 |
-1 | ATInt_STACKERROR_Opt. | |||
| Int | 0 |
0 |
[x,1/0] |
-1 | ATInt_STACKERROR_Opt. | |||
| Int | 0 |
0 |
[x,NOCONST,1/0] |
-1 | ATInt_STACKERROR_Opt. | |||
| Basic tests | ||||||||
| Int | x^3/3 |
x^3/3 |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | x^3/3+1 |
x^3/3 |
x |
0 | You need to add a constant of integration. This should be an arbitrary constant, not a number. | ATInt_const_int. | ||
| Int | x^3/3+c |
x^3/3 |
x |
1 | ATInt_true. | |||
| Int | x^3/3+c+1 |
x^3/3 |
x |
1 | ATInt_true. | |||
| Int | x^3/3+3*c |
x^3/3 |
x |
1 | ATInt_true. | |||
| Int | (x^3+c)/3 |
x^3/3 |
x |
1 | ATInt_true. | |||
| Int | x^3/3-c |
x^3/3 |
x |
1 | ATInt_true. | |||
| Int | x^3/3+c+k |
x^3/3 |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this. | ATInt_weirdconst. | ||
| Int | x^3/3+c^2 |
x^3/3 |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this. | ATInt_weirdconst. | ||
| Int | x^3/3*c |
x^3/3 |
x |
0 | The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[x^2\] In fact, the derivative of your answer, with respect to \(x\) is: \[c\cdot x^2\] so you must have done something wrong! | ATInt_generic. | ||
| Int | X^3/3+c |
x^3/3 |
x |
0 | The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[x^2\] In fact, the derivative of your answer, with respect to \(x\) is: \[0\] so you must have done something wrong! | ATInt_generic. ATInt_var_SB_notSA. | ||
| Int | sin(2*x) |
x^3/3 |
x |
0 | The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[x^2\] In fact, the derivative of your answer, with respect to \(x\) is: \[2\cdot \cos \left( 2\cdot x \right)\] so you must have done something wrong! | ATInt_generic. | ||
| Int | x^2/2-2*x+2+c |
(x-2)^2/2 |
x |
1 | ATInt_true. | |||
| Int | (t-1)^5/5+c |
(t-1)^5/5 |
t |
1 | ATInt_true. | |||
| Int | (v-1)^5/5+c |
(v-1)^5/5 |
v |
1 | ATInt_true. | |||
| Int | cos(2*x)/2+1+c |
cos(2*x)/2 |
x |
1 | ATInt_true. | |||
| Int | (x-a)^6001/6001+c |
(x-a)^6001/6001 |
x |
1 | ATInt_true. | |||
| Int | (x-a)^6001/6001 |
(x-a)^6001/6001 |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | 6000*(x-a)^5999 |
(x-a)^6001/6001 |
x |
0 | It looks like you have differentiated instead! | ATInt_diff. | ||
| Int | 4*%e^(4*x)/(%e^(4*x)+1) |
log(%e^(4*x)+1)+c |
x |
0 | The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\frac{4\cdot e^{4\cdot x}}{e^{4\cdot x}+1}\] In fact, the derivative of your answer, with respect to \(x\) is: \[\frac{16\cdot e^{4\cdot x}}{e^{4\cdot x}+1}-\frac{16\cdot e^{8 \cdot x}}{{\left(e^{4\cdot x}+1\right)}^2}\] so you must have done something wrong! | ATInt_generic. | ||
| The teacher adds a constant | ||||||||
| Int | x^3/3+c |
x^3/3+c |
x |
1 | ATInt_true. | |||
| Int | x^2/2-2*x+2+c |
(x-2)^2/2+k |
x |
1 | ATInt_true. | |||
| The teacher condones lack of constant, or numerical constant | ||||||||
| Int | x^3/3 |
x^3/3 |
[x,NOCONST] |
1 | ATInt_const_condone. | |||
| Int | x^3/3+c |
x^3/3 |
[x,NOCONST] |
1 | ATInt_true. | |||
| Int | x^2/2-2*x+2 |
(x-2)^2/2+k |
[x,NOCONST] |
1 | ATInt_const_condone. | |||
| Int | x^3/3+1 |
x^3/3 |
[x,NOCONST] |
1 | ATInt_const_int_condone. | |||
| Int | x^3/3+c^2 |
x^3/3 |
[x,NOCONST] |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this. | ATInt_weirdconst. | ||
| Int | n*x^n |
n*x^(n-1) |
x |
0 | The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\left(n-1\right)\cdot n\cdot x^{n-2}\] In fact, the derivative of your answer, with respect to \(x\) is: \[n^2\cdot x^{n-1}\] so you must have done something wrong! | ATInt_generic. | ||
| Int | n*x^n |
(assume(n>0), n*x^(n-1)) |
x |
0 | The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\left(n-1\right)\cdot n\cdot x^{n-2}\] In fact, the derivative of your answer, with respect to \(x\) is: \[n^2\cdot x^{n-1}\] so you must have done something wrong! | ATInt_generic. | ||
| Special case | ||||||||
| Int | exp(x)+c |
exp(x) |
x |
1 | ATInt_true. | |||
| Int | exp(x) |
exp(x) |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | exp(x) |
exp(x) |
[x,NOCONST] |
1 | ATInt_const_condone. | |||
| Student differentiates by mistake | ||||||||
| Int | 2*x |
x^3/3 |
x |
0 | It looks like you have differentiated instead! | ATInt_diff. | ||
| Int | 2*x+c |
x^3/3 |
x |
0 | It looks like you have differentiated instead! | ATInt_diff. | ||
| Sloppy logs (teacher ignores abs(x) ) | ||||||||
| Int | ln(x) |
ln(x) |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | ln(x) |
ln(x) |
[x,NOCONST] |
1 | ATInt_const_condone. | |||
| Int | ln(x)+c |
ln(x)+c |
x |
1 | ATInt_true_equiv. | |||
| Int | ln(k*x) |
ln(x)+c |
x |
1 | ATInt_true_equiv. | |||
| Fussy logs (teacher uses abs(x) ) | ||||||||
| Int | ln(x) |
ln(abs(x))+c |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this. | ATInt_EqFormalDiff. ATInt_logabs. | ||
| Int | ln(x)+c |
ln(abs(x))+c |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this. | ATInt_EqFormalDiff. ATInt_logabs. | ||
| Int | ln(x) |
ln(abs(x))+c |
[x, NOCONST] |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this. | ATInt_EqFormalDiff. ATInt_logabs. | ||
| Int | ln(abs(x)) |
ln(abs(x))+c |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | ln(abs(x))+c |
ln(abs(x))+c |
x |
1 | ATInt_true_equiv. | |||
| Int | ln(k*x) |
ln(abs(x))+c |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this. | ATInt_EqFormalDiff. ATInt_logabs. | ||
| Int | ln(k*abs(x)) |
ln(abs(x))+c |
x |
1 | ATInt_true_equiv. | |||
| Int | ln(abs(k*x)) |
ln(abs(x))+c |
x |
1 | ATInt_true_equiv. | |||
| Teacher uses ln(k*abs(x)) | ||||||||
| Int | ln(x) |
ln(k*abs(x)) |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this. | ATInt_EqFormalDiff. ATInt_logabs. | ||
| Int | ln(x)+c |
ln(k*abs(x)) |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this. | ATInt_EqFormalDiff. ATInt_logabs. | ||
| Int | ln(abs(x)) |
ln(k*abs(x)) |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | ln(abs(x))+c |
ln(k*abs(x)) |
x |
1 | ATInt_true_equiv. | |||
| Int | ln(k*x) |
ln(k*abs(x)) |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this. | ATInt_EqFormalDiff. ATInt_logabs. | ||
| Int | ln(k*abs(x)) |
ln(k*abs(x)) |
x |
1 | ATInt_true_equiv. | |||
| Other logs | ||||||||
| Int | ln(x)+ln(a) |
ln(k*abs(x+a)) |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this. | ATInt_generic. ATInt_logabs. | ||
| Int | log(x)^2-2*log(c)*log(x)+k |
ln(c/x)^2 |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. | ATInt_EqFormalDiff. | ||
| Int | log(x)^2-2*log(c)*log(x)+k |
ln(abs(c/x))^2 |
x |
0 | The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[-\frac{2\cdot \ln \left( \frac{\left| c\right| }{\left| x\right| } \right)}{x}\] In fact, the derivative of your answer, with respect to \(x\) is: \[\frac{2\cdot \ln \left( x \right)}{x}-\frac{2\cdot \ln \left( c \right)}{x}\] so you must have done something wrong! | ATInt_generic. | ||
| Int | c-(log(2)-log(x))^2/2 |
-1/2*log(2/x)^2 |
x |
1 | ATInt_true_equiv. | |||
| Int | ! | ln(abs(x+3))/2+c |
ln(abs(2*x+6))/2+c |
x |
-3 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. | ATInt_EqFormalDiff. | |
| Two logs | ||||||||
| Int | log(abs(x-3))+log(abs(x+3)) |
log(abs(x-3))+log(abs(x+3)) |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | log(abs(x-3))+log(abs(x+3))+c |
log(abs(x-3))+log(abs(x+3)) |
x |
1 | ATInt_true_equiv. | |||
| Int | log(abs(x-3))+log(abs(x+3)) |
log(x-3)+log(x+3) |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | log(abs(x-3))+log(abs(x+3))+c |
log(x-3)+log(x+3) |
x |
1 | ATInt_true_equiv. | |||
| Int | log(x-3)+log(x+3) |
log(x-3)+log(x+3) |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | log(x-3)+log(x+3)+c |
log(x-3)+log(x+3) |
x |
1 | ATInt_true_equiv. | |||
| Int | log(x-3)+log(x+3) |
log(abs(x-3))+log(abs(x+3)) |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this. | ATInt_EqFormalDiff. ATInt_logabs. | ||
| Int | log(x-3)+log(x+3)+c |
log(abs(x-3))+log(abs(x+3)) |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this. | ATInt_EqFormalDiff. ATInt_logabs. | ||
| Int | log(abs((x-3)*(x+3)))+c |
log(abs(x-3))+log(abs(x+3)) |
x |
1 | ATInt_true_equiv. | |||
| Int | log(abs((x^2-9)))+c |
log(abs(x-3))+log(abs(x+3)) |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. | ATInt_EqFormalDiff. | ||
| Int | 2*log(abs(x-2))-log(abs(x+2))+ (x^2+4*x)/2 |
-log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2+c |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | -log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2+c |
-log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2+c |
x |
1 | ATInt_true_equiv. | |||
| Int | -log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2+c |
-log((x+2))+2*log((x-2))+(x^2+ 4*x)/2 |
x |
1 | ATInt_true_equiv. | |||
| Inconsistent log(abs()) | ||||||||
| Int | log(abs(x-3))+log((x+3))+c |
log(x-3)+log(x+3) |
x |
0 | There appear to be strange inconsistencies between your use of \(\log(...)\) and \(\log(|...|)\). Please ask your teacher about this. | ATInt_true_equiv. ATInt_logabs_inconsistent. | ||
| Int | log((v-3))+log(abs(v+3))+c |
log(v-3)+log(v+3) |
v |
0 | There appear to be strange inconsistencies between your use of \(\log(...)\) and \(\log(|...|)\). Please ask your teacher about this. | ATInt_true_equiv. ATInt_logabs_inconsistent. | ||
| Int | log((x-3))+log(abs(x+3)) |
log(x-3)+log(x+3) |
x |
0 | There appear to be strange inconsistencies between your use of \(\log(...)\) and \(\log(|...|)\). Please ask your teacher about this. | ATInt_const. ATInt_logabs_inconsistent. | ||
| Int | 2*log((x-2))-log(abs(x+2))+(x^ 2+4*x)/2 |
-log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2 |
x |
0 | There appear to be strange inconsistencies between your use of \(\log(...)\) and \(\log(|...|)\). Please ask your teacher about this. | ATInt_EqFormalDiff. ATInt_logabs. ATInt_logabs_inconsistent. | ||
| Significant integration constant differences | ||||||||
| Int | 2*(sqrt(t)-5)-10*log((sqrt(t)- 5))+c |
2*(sqrt(t)-5)-10*log((sqrt(t)- 5))+c |
t |
1 | ATInt_true_equiv. | |||
| Int | 2*(sqrt(t))-10*log((sqrt(t)-5) )+c |
2*(sqrt(t)-5)-10*log((sqrt(t)- 5))+c |
t |
1 | ATInt_true_differentconst. | |||
| Int | 2*(sqrt(t)-5)-10*log((sqrt(t)- 5))+c |
2*(sqrt(t)-5)-10*log(abs(sqrt( t)-5))+c |
t |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this. | ATInt_EqFormalDiff. ATInt_logabs. | ||
| Int | 2*(sqrt(t))-10*log(abs(sqrt(t) -5))+c |
2*(sqrt(t)-5)-10*log(abs(sqrt( t)-5))+c |
t |
1 | ATInt_true_differentconst. | |||
| Trig | ||||||||
| Int | 2*sin(x)*cos(x) |
sin(2*x)+c |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | 2*sin(x)*cos(x)+k |
sin(2*x)+c |
x |
1 | ATInt_true. | |||
| Int | -2*cos(3*x)/3-3*cos(2*x)/2 |
-2*cos(3*x)/3-3*cos(2*x)/2+c |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | -2*cos(3*x)/3-3*cos(2*x)/2+1 |
-2*cos(3*x)/3-3*cos(2*x)/2+c |
x |
0 | You need to add a constant of integration. This should be an arbitrary constant, not a number. | ATInt_const_int. | ||
| Int | -2*cos(3*x)/3-3*cos(2*x)/2+c |
-2*cos(3*x)/3-3*cos(2*x)/2+c |
x |
1 | ATInt_true. | |||
| Int | (tan(2*t)-2*t)/2 |
-(t*sin(4*t)^2-sin(4*t)+t*cos( 4*t)^2+2*t*cos(4*t)+t)/(sin(4* t)^2+cos(4*t)^2+2*cos(4*t)+1) |
t |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | (tan(2*t)-2*t)/2+1 |
-(t*sin(4*t)^2-sin(4*t)+t*cos( 4*t)^2+2*t*cos(4*t)+t)/(sin(4* t)^2+cos(4*t)^2+2*cos(4*t)+1) |
t |
0 | You need to add a constant of integration. This should be an arbitrary constant, not a number. | ATInt_const_int. | ||
| Int | (tan(2*t)-2*t)/2+c |
-(t*sin(4*t)^2-sin(4*t)+t*cos( 4*t)^2+2*t*cos(4*t)+t)/(sin(4* t)^2+cos(4*t)^2+2*cos(4*t)+1) |
t |
1 | ATInt_true. | |||
| Int | tan(x)-x+c |
tan(x)-x |
x |
1 | ATInt_true. | |||
| Note the difference in feedback here, generated by the options. | ||||||||
| Int | ((5*%e^7*x-%e^7)*%e^(5*x)) |
((5*%e^7*x-%e^7)*%e^(5*x))/25+ c |
x |
0 | The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\frac{e^{5\cdot x+7}}{5}+\frac{\left(5\cdot e^7\cdot x-e^7\right) \cdot e^{5\cdot x}}{5}\] In fact, the derivative of your answer, with respect to \(x\) is: \[5\cdot e^{5\cdot x+7}+5\cdot \left(5\cdot e^7\cdot x-e^7\right) \cdot e^{5\cdot x}\] so you must have done something wrong! | ATInt_generic. | ||
| Int | ((5*%e^7*x-%e^7)*%e^(5*x)) |
((5*%e^7*x-%e^7)*%e^(5*x))/25+ c |
[x,x*%e^(5*x+7) ] |
0 | The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[x\cdot e^{5\cdot x+7}\] In fact, the derivative of your answer, with respect to \(x\) is: \[5\cdot e^{5\cdot x+7}+5\cdot \left(5\cdot e^7\cdot x-e^7\right) \cdot e^{5\cdot x}\] so you must have done something wrong! | ATInt_generic. | ||
| Inverse hyperbolic integrals | ||||||||
| Int | log(x-3)/6-log(x+3)/6+c |
log(x-3)/6-log(x+3)/6 |
x |
1 | ATInt_true_equiv. | |||
| Int | asinh(x) |
ln(x+sqrt(x^2+1)) |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | asinh(x)+c |
ln(x+sqrt(x^2+1)) |
x |
1 | ATInt_true. | |||
| Int | -acoth(x/3)/3 |
log(x-3)/6-log(x+3)/6 |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | -acoth(x/3)/3 |
log(x-3)/6-log(x+3)/6 |
[x, NOCONST] |
1 | ATInt_true. | |||
| Int | -acoth(x/3)/3+c |
log(x-3)/6-log(x+3)/6 |
x |
1 | ATInt_true. | |||
| Int | -acoth(x/3)/3+c |
log(abs(x-3))/6-log(abs(x+3))/ 6 |
x |
1 | ATInt_true. | |||
| Int | log(x-a)/(2*a)-log(x+a)/(2*a)+ c |
log(x-a)/(2*a)-log(x+a)/(2*a) |
x |
1 | ATInt_true_equiv. | |||
| Int | -acoth(x/a)/a+c |
log(x-a)/(2*a)-log(x+a)/(2*a) |
x |
1 | ATInt_true. | |||
| Int | -acoth(x/a)/a+c |
log(abs(x-a))/(2*a)-log(abs(x+ a))/(2*a) |
x |
1 | ATInt_true. | |||
| Int | log(x-a)/(2*a)-log(x+a)/(2*a)+ c |
log(abs(x-a))/(2*a)-log(abs(x+ a))/(2*a) |
x |
0 | The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this. | ATInt_EqFormalDiff. ATInt_logabs. | ||
| Int | log(x-3)/6-log(x+3)/6+c |
-acoth(x/3)/3 |
x |
1 | ATInt_true. | |||
| Int | log(abs(x-3))/6-log(abs(x+3))/ 6+c |
-acoth(x/3)/3 |
x |
1 | ATInt_true. | |||
| Int | log(x-3)/6-log(x+3)/6 |
-acoth(x/3)/3 |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | atan(2*x-3)+c |
atan(2*x-3) |
x |
1 | ATInt_true. | |||
| Int | atan((x-2)/(x-1))+c |
atan(2*x-3) |
x |
1 | ATInt_true. | |||
| Int | atan((x-2)/(x-1)) |
atan(2*x-3) |
x |
0 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | ||
| Int | atan((x-1)/(x-2)) |
atan(2*x-3) |
x |
0 | The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\frac{2}{{\left(2\cdot x-3\right)}^2+1}\] In fact, the derivative of your answer, with respect to \(x\) is: \[\frac{\frac{1}{x-2}-\frac{x-1}{{\left(x-2\right)}^2}}{\frac{{\left( x-1\right)}^2}{{\left(x-2\right)}^2}+1}\] so you must have done something wrong! | ATInt_generic. | ||
| Stoutemyer (currently fails) | ||||||||
| Int | ! | 2/3*sqrt(3)*(atan(sin(x)/(sqrt (3)*(cos(x)+1)))-(atan(sin(x)/ (cos(x)+1))))+x/sqrt(3) |
2*atan(sin(x)/(sqrt(3)*(cos(x) +1)))/sqrt(3) |
x |
-3 | You need to add a constant of integration, otherwise this appears to be correct. Well done. | ATInt_const. | |
GT
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| GT | 1/0 |
1 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATGT_STACKERROR_SAns. | ||
| GT | 1 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATGT_STACKERROR_TAns. | ||
| GT | 1 |
1 |
0 | ATGT_false. | ||||
| GT | 2 |
1 |
1 | ATGT_true. | ||||
| GT | 1 |
2.1 |
0 | ATGT_false. | ||||
| GT | pi |
3 |
1 | ATGT_true. | ||||
| GT | pi+2 |
5 |
1 | ATGT_true. | ||||
| Infinity | ||||||||
| GT | -inf |
0 |
0 | Not number | ||||
| GT | inf |
0 |
0 | Not number | ||||
GTE
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| GTE | 1/0 |
1 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATGTE_STACKERROR_SAns. | ||
| GTE | 1 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATGTE_STACKERROR_TAns. | ||
| GTE | 1 |
1 |
1 | ATGTE_true. | ||||
| GTE | 2 |
1 |
1 | ATGTE_true. | ||||
| GTE | 1 |
2.1 |
0 | ATGTE_false. | ||||
| GTE | pi |
3 |
1 | ATGTE_true. | ||||
| GTE | pi+2 |
5 |
1 | ATGTE_true. | ||||
NumRelative
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Basic tests | ||||||||
| NumRelative | 1/0 |
0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATNumRelative_STACKERROR_SAns. | ||
| NumRelative | 0 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATNumRelative_STACKERROR_TAns. | ||
| NumRelative | 0 |
0 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATNumRelative_STACKERROR_Opt. | |
| NumRelative | 0 |
(x |
-1 | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question. | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question. | ATNumRelativeTEST_FAILED-Empty TA. | ||
| NumRelative | 1.5 |
1.5 |
x |
-1 | The numerical tolerance for ATNumerical should be a floating point number, but is not. This is an internal error with the test. Please ask your teacher about this. | ATNumerical_STACKERROR_tol. | ||
| NumRelative | 1 |
0 |
(x |
0 | ||||
| NumRelative | x=1.5 |
1.5 |
0 | Your answer should be a floating point number, but is not. | ATNumerical_SA_not_number. | |||
| NumRelative | 1.5 |
x=1.5 |
0 | The value supplied for the teacher's answer should be a floating point number, but is not. This is an internal error with the test. Please ask your teacher about this. | ATNumerical_SB_not_number. | |||
| No option, so 5% | ||||||||
| NumRelative | 1.1 |
1 |
0 | |||||
| NumRelative | 1.05 |
1 |
1 | |||||
| NumRelative | 0.95 |
1 |
1 | |||||
| NumRelative | 0.949 |
1 |
0 | |||||
| NumRelative | 1.05e33 |
1e33 |
1 | |||||
| NumRelative | 1.06e33 |
1e33 |
0 | |||||
| NumRelative | 0.95e33 |
1e33 |
1 | |||||
| NumRelative | 0.949e33 |
1e33 |
0 | |||||
| NumRelative | 1.05e-33 |
1e-33 |
1 | |||||
| NumRelative | 1.06e-33 |
1e-33 |
0 | |||||
| NumRelative | 0.95e-33 |
1e-33 |
1 | |||||
| NumRelative | 0.949e-33 |
1e-33 |
0 | |||||
| Remove display dp etc. | ||||||||
| NumRelative | 1 |
displaydp(1.05,2) |
0.1 |
1 | ||||
| NumRelative | 1000 |
displaysci(1.05,2,3) |
0.1 |
1 | ||||
| Options passed | ||||||||
| NumRelative | 1.05 |
1 |
0.1 |
1 | ||||
| NumRelative | 1.05 |
3 |
0.1 |
0 | ||||
| NumRelative | 3.14 |
pi |
0.001 |
1 | ||||
| Infinity | ||||||||
| NumRelative | inf |
0 |
0 | Your answer should be a floating point number, but is not. | ATNumerical_SA_not_number. | |||
| Lists | ||||||||
| NumRelative | 1 |
[1,2] |
0 | Your answer should be a list, but is not. Note that the syntax to enter a list is to enclose the comma separated values with square brackets. | ATNumerical_SA_not_list. | |||
| NumRelative | [1,2] |
[1,2,3] |
0 | Your list should have \(3\) elements, but it actually has \(2\). | ATNumerical_wronglen. | |||
| NumRelative | [1,2] |
[1,2] |
1 | |||||
| NumRelative | [3.141,1.414] |
[pi,sqrt(2)] |
1 | |||||
| NumRelative | [3,1.414] |
[pi,sqrt(2)] |
0.01 |
0 | The entries underlined in red below are those that are incorrect. \[\left[ {\color{red}{\underline{3.0}}} , 1.414 \right] \] | ATNumerical_wrongentries SA/TA=[3.0]. | ||
| NumRelative | [3,1.414] |
{pi,sqrt(2)} |
0.01 |
0 | Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets. | ATNumerical_SA_not_set. | ||
| NumRelative | {1.414,3.1} |
{significantfigures(pi,6),sqrt
(2)} |
0.01 |
0 | The entries underlined in red below are those that are incorrect. \[\left \{{\color{red}{\underline{3.1}}} \right \}\] | ATNumerical_wrongentries: TA/SA=[3.14159], SA/TA=[3.1]. | ||
| NumRelative | {1.414,3.1} |
{pi,sqrt(2)} |
0.1 |
1 | ||||
NumAbsolute
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Basic tests | ||||||||
| NumAbsolute | 1/0 |
0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATNumAbsolute_STACKERROR_SAns. | ||
| NumAbsolute | 0 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATNumAbsolute_STACKERROR_TAns. | ||
| NumAbsolute | 0 |
0 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATNumAbsolute_STACKERROR_Opt. | |
| NumAbsolute | 0 |
(x |
-1 | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question. | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question. | ATNumAbsoluteTEST_FAILED-Empty TA. | ||
| NumAbsolute | 1 |
0 |
(x |
0 | ||||
| No option, so 5% | ||||||||
| NumAbsolute | 1.1 |
1 |
0 | |||||
| NumAbsolute | 1.05 |
1 |
1 | |||||
| Options passed | ||||||||
| NumAbsolute | 1.05 |
1 |
0.1 |
1 | ||||
| NumAbsolute | 1.05 |
3 |
0.1 |
0 | ||||
| NumAbsolute | 3.14 |
pi |
0.001 |
0 | ||||
| NumAbsolute | 1.41e-2 |
1.41e-2 |
0.0001 |
1 | ||||
| NumAbsolute | 0.0141 |
1.41e-2 |
0.0001 |
1 | ||||
| NumAbsolute | 0.00141 |
0.00141 |
0.0001 |
1 | ||||
| NumAbsolute | 0.00141 |
1.41*10^-3 |
0.0001 |
1 | ||||
| NumAbsolute | 1.41*10^-3 |
1.41*10^-3 |
0.0001 |
1 | ||||
| NumAbsolute | [3.141,1.414] |
[pi,sqrt(2)] |
0.01 |
1 | ||||
| NumAbsolute | [3,1.414] |
[pi,sqrt(2)] |
0.01 |
0 | The entries underlined in red below are those that are incorrect. \[\left[ {\color{red}{\underline{3.0}}} , 1.414 \right] \] | ATNumerical_wrongentries SA/TA=[3.0]. | ||
| NumAbsolute | [3,1.414] |
{pi,sqrt(2)} |
0.01 |
0 | Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets. | ATNumerical_SA_not_set. | ||
| NumAbsolute | {1.414,3.1} |
{significantfigures(pi,6),sqrt
(2)} |
0.01 |
0 | The entries underlined in red below are those that are incorrect. \[\left \{{\color{red}{\underline{3.1}}} \right \}\] | ATNumerical_wrongentries: TA/SA=[3.14159], SA/TA=[3.1]. | ||
| NumAbsolute | {1,1.414,3.1,2} |
{1,2,pi,sqrt(2)} |
0.1 |
1 | ||||
NumSigFigs
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Basic tests | ||||||||
| NumSigFigs | 3.141 |
3.1415927 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test. | STACKERROR_OPTION. | ||
| NumSigFigs | 1/0 |
3 |
3 |
-1 | ATNumSigFigs_STACKERROR_SAns. | |||
| NumSigFigs | 0 |
1/0 |
3 |
-1 | ATNumSigFigs_STACKERROR_TAns. | |||
| NumSigFigs | 0 |
0 |
1/0 |
-1 | ATNumSigFigs_STACKERROR_Opt. | |||
| NumSigFigs | 0 |
1 |
( |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Option field is invalid. You have a missing right bracket ) in the expression: (. | STACKERROR_OPTION. | |
| NumSigFigs | ( |
1 |
1 |
-1 | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | ATNumSigFigsTEST_FAILED-Empty SA. | |
| NumSigFigs | 1 |
3 |
pi |
-1 | The answer test failed to execute correctly: please alert your teacher. | ATNumSigFigs_STACKERROR_not_integer. | ||
| NumSigFigs | 1 |
3 |
[3,x] |
-1 | The answer test failed to execute correctly: please alert your teacher. | ATNumSigFigs_STACKERROR_not_integer. | ||
| NumSigFigs | 1 |
3 |
[1,2,3] |
-1 | The answer test failed to execute correctly: please alert your teacher. | ATNumSigFigs_STACKERROR_list_wrong_length. | ||
| NumSigFigs | 1 |
3 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test. | STACKERROR_OPTION. | ||
| NumSigFigs | pi |
pi |
4 |
0 | Your answer should be a decimal number, but is not! | ATNumSigFigs_NotDecimal. | ||
| Edge cases | ||||||||
| NumSigFigs | 0 |
0 |
2 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0 |
0 |
1 |
1 | ||||
| NumSigFigs | 0.0 |
0 |
1 |
1 | ||||
| NumSigFigs | 0.0 |
0 |
2 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0 |
0.0 |
2 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0.0 |
0.0 |
2 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0.00 |
0.00 |
2 |
1 | ||||
| Large numbers | ||||||||
| NumSigFigs | 5.4e21 |
5.3e21 |
2 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 5.3e21 |
5.3e21 |
2 |
1 | ||||
| NumSigFigs | 5.3e22 |
5.3e22 |
2 |
1 | ||||
| NumSigFigs | 5.3e20 |
5.3e22 |
2 |
0 | ATNumSigFigs_VeryInaccurate. | |||
| NumSigFigs | 6.02214086e23 |
6.02214086e23 |
9 |
1 | ||||
| NumSigFigs | 6.0221409e23 |
6.02214086e23 |
9 |
0 | Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 6.02214087e23 |
6.02214086e23 |
9 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 6.02214085e23 |
6.02214086e23 |
9 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 5.3910632e-44 |
5.3910632e-44 |
8 |
1 | ||||
| NumSigFigs | 5.391063e-44 |
5.3910632e-44 |
8 |
0 | Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 5.3910631e-44 |
5.3910632e-44 |
8 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 5.3910633e-44 |
5.3910632e-44 |
8 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 1.61622938e-35 |
1.61622938e-35 |
9 |
1 | ||||
| NumSigFigs | 1.6162294e-35 |
1.61622938e-35 |
9 |
0 | Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 1.61622939e-35 |
1.61622938e-35 |
9 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 1.61622937e-35 |
1.61622938e-35 |
9 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 1.2345e82 |
1.2345e82 |
5 |
1 | ||||
| NumSigFigs | 1.2346e82 |
1.2345e82 |
5 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 1.2344e82 |
1.2345e82 |
5 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| No trailing zeros. | ||||||||
| NumSigFigs | 1.234 |
4 |
1 |
0 | Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 3.141 |
3.1415927 |
3 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 3.141 |
3.1415927 |
4 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 3.146 |
3.1415927 |
4 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 3.147 |
3.1415927 |
4 |
0 | ATNumSigFigs_VeryInaccurate. | |||
| NumSigFigs | 3.142 |
3.1415927 |
4 |
1 | ||||
| NumSigFigs | 3.142 |
pi |
4 |
1 | ||||
| NumSigFigs | 3141 |
3.1415927 |
4 |
0 | ATNumSigFigs_VeryInaccurate. | |||
| NumSigFigs | 0.00123 |
0.001234567 |
3 |
1 | ||||
| NumSigFigs | 1.23e-3 |
0.001234567 |
3 |
1 | ||||
| NumSigFigs | 138*10^-3 |
138*10^-3 |
3 |
1 | ||||
| NumSigFigs | -138*10^-3 |
-138*10^-3 |
3 |
1 | ||||
| NumSigFigs | 138*10^-3 |
-138*10^-3 |
3 |
0 | Your answer has the wrong algebraic sign. | ATNumSigFigs_WrongSign. | ||
| NumSigFigs | 1.38*10^-1 |
138*10^-3 |
3 |
1 | ||||
| NumSigFigs | 1.24e-3 |
0.001234567 |
3 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 1.235e-3 |
0.001234567 |
4 |
1 | ||||
| NumSigFigs | 1000 |
999 |
2 |
1 | ATNumSigFigs_WithinRange. | |||
| NumSigFigs | 1E3 |
999 |
2 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | -100 |
-149 |
1 |
1 | ||||
| NumSigFigs | -0.05 |
-0.0499 |
1 |
1 | ||||
| NumSigFigs | -(0.05) |
-0.0499 |
1 |
1 | ||||
| NumSigFigs | 1170 |
1174.34 |
3 |
1 | ||||
| NumSigFigs | 61300 |
61250 |
3 |
1 | ||||
| Previous tricky case | ||||||||
| NumSigFigs | 0.1667 |
0.1667 |
4 |
1 | ||||
| NumSigFigs | 0.1666 |
0.1667 |
4 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 0.1663 |
0.1667 |
4 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 0.1662 |
0.1667 |
4 |
0 | ATNumSigFigs_VeryInaccurate. | |||
| NumSigFigs | 0.166 |
0.1667 |
4 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. ATNumSigFigs_VeryInaccurate. | ||
| NumSigFigs | 0.16667 |
0.1667 |
4 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| Negative numbers | ||||||||
| NumSigFigs | -3.141 |
-3.1415927 |
4 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | -3.141 |
-3.1415927 |
3 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | -3.141 |
-3.1415927 |
4 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | -3.142 |
-3.1415927 |
4 |
1 | ||||
| NumSigFigs | 3.142 |
-3.1415927 |
4 |
0 | Your answer has the wrong algebraic sign. | ATNumSigFigs_WrongSign. | ||
| NumSigFigs | -3.142 |
3.1415927 |
4 |
0 | Your answer has the wrong algebraic sign. | ATNumSigFigs_WrongSign. | ||
| NumSigFigs | -3.149 |
3.1415927 |
4 |
0 | Your answer has the wrong algebraic sign. | ATNumSigFigs_WrongSign. ATNumSigFigs_VeryInaccurate. | ||
| NumSigFigs | 2.15 |
75701719/35227192 |
3 |
1 | ||||
| Round teacher answer | ||||||||
| NumSigFigs | 0.0499 |
0.04985 |
3 |
1 | ||||
| NumSigFigs | 0.0498 |
0.04985 |
3 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 0.0498 |
0.04975 |
3 |
1 | ||||
| NumSigFigs | 0.0497 |
0.04975 |
3 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 0.0499 |
0.0498 |
3 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| Final zeros after the decimal are significant. | ||||||||
| NumSigFigs | 1.5 |
1.500 |
3 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 1.50 |
1.500 |
3 |
1 | ||||
| NumSigFigs | 1.500 |
1.500 |
3 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 245.0 |
245 |
3 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| Too few digits | ||||||||
| NumSigFigs | 180 |
178.35 |
3 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_WithinRange. ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 33 |
33.1558 |
3 |
0 | Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate. | ||
| Mixed options | ||||||||
| NumSigFigs | 3.142 |
3.1415927 |
[4,3] |
1 | ||||
| NumSigFigs | 3.143 |
3.1415927 |
[4,3] |
1 | ||||
| NumSigFigs | 3.150 |
3.1415927 |
[4,3] |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 3.211 |
3.1415927 |
[4,3] |
0 | ATNumSigFigs_VeryInaccurate. | |||
| NumSigFigs | 3.1416 |
3.1415927 |
[4,3] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0.1666 |
0.1667 |
[4,3] |
1 | ||||
| NumSigFigs | 180 |
178.35 |
[3,1] |
1 | ATNumSigFigs_WithinRange. | |||
| NumSigFigs | 33 |
33.1558 |
[3,1] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 1.500 |
1.5 |
[3,1] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 245.0 |
245 |
[3,1] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 12345.7 |
12345.654321 |
[6,6] |
1 | ||||
| NumSigFigs | 12345.7 |
12345.654321 |
[6,3] |
1 | ||||
| NumSigFigs | 12300.0 |
12345.654321 |
[6,3] |
1 | ||||
| NumSigFigs | 12400.0 |
12345.654321 |
[6,3] |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 13500.0 |
12345.654321 |
[6,3] |
0 | ATNumSigFigs_VeryInaccurate. | |||
| NumSigFigs | 12000.0 |
12345.654321 |
[6,2] |
1 | ||||
| NumSigFigs | 13000.0 |
12345.654321 |
[6,2] |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 11000.0 |
12345.654321 |
[6,2] |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| Zero option and trailing zeros | ||||||||
| NumSigFigs | 0.0010 |
0 |
[1,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0.0010 |
0 |
[2,0] |
1 | ||||
| NumSigFigs | 0.0010 |
0 |
[3,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0.001 |
0 |
[1,0] |
1 | ||||
| NumSigFigs | 0.001 |
0 |
[2,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0.00100 |
null |
[2,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0.00100 |
null |
[3,0] |
1 | ||||
| NumSigFigs | 0.00100 |
null |
[4,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 5.00 |
null |
[2,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 5.00 |
null |
[3,0] |
1 | ||||
| NumSigFigs | 5.00 |
null |
[4,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 100 |
0 |
[1,0] |
1 | ||||
| NumSigFigs | 100 |
0 |
[2,0] |
1 | ATNumSigFigs_WithinRange. | |||
| NumSigFigs | 100 |
0 |
[3,0] |
1 | ATNumSigFigs_WithinRange. | |||
| NumSigFigs | 100 |
0 |
[4,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 10.0 |
0 |
[2,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 10.0 |
0 |
[3,0] |
1 | ||||
| NumSigFigs | 10.0 |
0 |
[4,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0 |
0 |
[1,0] |
1 | ||||
| NumSigFigs | 0 |
0 |
[2,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0.00 |
0 |
[1,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0.00 |
0 |
[2,0] |
1 | ||||
| NumSigFigs | 0.00 |
0 |
[3,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 0.00 |
0 |
[4,0] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| Condone too many sfs. | ||||||||
| NumSigFigs | 8.250 |
8.250 |
[4,-1] |
1 | ||||
| NumSigFigs | 8.25 |
8.250 |
[4,-1] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. | ||
| NumSigFigs | 8.250000 |
8.250 |
[4,-1] |
1 | ||||
| NumSigFigs | 8.250434 |
8.250 |
[4,-1] |
1 | ||||
| NumSigFigs | 82.4 |
82 |
[2,-1] |
1 | ||||
| NumSigFigs | 82.5 |
82 |
[2,-1] |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 83 |
82 |
[2,-1] |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| 1/7 = 0.142857142857... | ||||||||
| NumSigFigs | 0.1430 |
1/7 |
[4,-1] |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 0.1429 |
1/7 |
[4,-1] |
1 | ||||
| NumSigFigs | 0.1428 |
1/7 |
[4,-1] |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 0.143 |
1/7 |
[4,-1] |
0 | Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 0.14284 |
1/7 |
[4,-1] |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 0.14285 |
1/7 |
[4,-1] |
1 | ||||
| NumSigFigs | 0.14286 |
1/7 |
[4,-1] |
1 | ||||
| NumSigFigs | 0.14291 |
1/7 |
[4,-1] |
1 | ||||
| NumSigFigs | 0.14294 |
1/7 |
[4,-1] |
1 | ||||
| NumSigFigs | 0.14295 |
1/7 |
[4,-1] |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 0.142 |
1/7 |
[2,-1] |
1 | ||||
| NumSigFigs | 0.14290907676 |
1/7 |
[2,-1] |
1 | ||||
| NumSigFigs | 0.143 |
1/7 |
[2,-1] |
1 | ||||
| NumSigFigs | 0.1433333 |
1/7 |
[2,-1] |
1 | ||||
| NumSigFigs | 0.144 |
1/7 |
[2,-1] |
1 | ||||
| NumSigFigs | 0.145 |
1/7 |
[2,-1] |
1 | ||||
| NumSigFigs | 0.146 |
1/7 |
[2,-1] |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| Logarithms, numbers and surds | ||||||||
| NumSigFigs | 1.279 |
ev(lg(19),lg=logbasesimp) |
4 |
1 | ||||
| NumSigFigs | 3.14 |
pi |
3 |
1 | ||||
| NumSigFigs | 3.15 |
pi |
3 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. | ||
| NumSigFigs | 1.73205 |
sqrt(3) |
6 |
1 | ||||
| No support for matrices! | ||||||||
| NumSigFigs | matrix([0.33,1],[1,1]) |
matrix([0.333,1],[1,1]) |
2 |
-1 | Your answer should be a decimal number, but is not! | ATNumSigFigs_NotDecimal. | ||
| NumSigFigs | 3.1415 |
matrix([0.333,1],[1,1]) |
2 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. sigfigsfun(x,n,d) requires a real number, or a list of real numbers, as a first argument. Received: matrix([0.333,1],[1,1]) | TEST_FAILED | |
| Teacher uses dispsf | ||||||||
| NumSigFigs | 1.50 |
dispsf(1.500,3) |
3 |
1 | ||||
| NumSigFigs | 1.50 |
dispdp(1.500,3) |
3 |
1 | ||||
NumDecPlaces
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Basic tests | ||||||||
| NumDecPlaces | 1/0 |
3 |
2 |
-1 | ATNumDecPlaces_STACKERROR_SAns. | |||
| NumDecPlaces | 0.1 |
1/0 |
2 |
-1 | ATNumDecPlaces_STACKERROR_TAns. | |||
| NumDecPlaces | 0.1 |
0 |
1/0 |
-1 | ATNumDecPlaces_STACKERROR_Opt. | |||
| NumDecPlaces | 0.1 |
1 |
x |
-1 | For ATNumDecPlaces the test option must be a positive integer, in fact "\(x\)" was received. | ATNumDecPlaces_OptNotInt. | ||
| NumDecPlaces | 0.1 |
1 |
-1 |
-1 | For ATNumDecPlaces the test option must be a positive integer, in fact "\(-1\)" was received. | ATNumDecPlaces_OptNotInt. | ||
| NumDecPlaces | 0.1 |
1 |
0 |
-1 | For ATNumDecPlaces the test option must be a positive integer, in fact "\(0\)" was received. | ATNumDecPlaces_OptNotInt. | ||
| NumDecPlaces | 0.1 |
1 |
( |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Option field is invalid. You have a missing right bracket ) in the expression: (. | STACKERROR_OPTION. | |
| NumDecPlaces | ( |
1 |
1 |
-1 | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | ATNumDecPlacesTEST_FAILED-Empty SA. | |
| Student's answer not a floating point number | ||||||||
| NumDecPlaces | x |
3.143 |
2 |
0 | Your answer must be a floating point number, but is not. | ATNumDecPlaces_SA_Not_num. | ||
| NumDecPlaces | pi |
3.000 |
3 |
0 | Your answer must be a floating point number, but is not. | ATNumDecPlaces_SA_Not_num. | ||
| Right number of places | ||||||||
| NumDecPlaces | 3.14 |
3.143 |
2 |
1 | ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv. | |||
| NumDecPlaces | 3.14 |
3.14 |
2 |
1 | ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv. | |||
| NumDecPlaces | 3.140 |
3.140 |
3 |
1 | ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv. | |||
| NumDecPlaces | 3141.5972 |
3141.5972 |
4 |
1 | ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv. | |||
| NumDecPlaces | 4.14 |
3.14 |
2 |
0 | ATNumDecPlaces_Correct. ATNumDecPlaces_Not_equiv. | |||
| NumDecPlaces | 3.1416 |
pi |
4 |
1 | ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv. | |||
| NumDecPlaces | -7.3 |
-7.3 |
1 |
1 | ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv. | |||
| Wrong number of places | ||||||||
| NumDecPlaces | 3.14 |
3.143 |
1 |
0 | Your answer has been given to the wrong number of decimal places. | ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Equiv. | ||
| NumDecPlaces | 3.14 |
3.143 |
1 |
0 | Your answer has been given to the wrong number of decimal places. | ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Equiv. | ||
| NumDecPlaces | 3.14 |
3.140 |
3 |
0 | Your answer has been given to the wrong number of decimal places. | ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Equiv. | ||
| NumDecPlaces | 7.000 |
7 |
4 |
0 | Your answer has been given to the wrong number of decimal places. | ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Equiv. | ||
| NumDecPlaces | 7.0000 |
7 |
4 |
1 | ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv. | |||
| Both wrong DPs and inaccurate. | ||||||||
| NumDecPlaces | 8.0000 |
7 |
3 |
0 | Your answer has been given to the wrong number of decimal places. | ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Not_equiv. | ||
| Teacher needs to round their answer. | ||||||||
| NumDecPlaces | 4.000 |
3.99999 |
3 |
1 | ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv. | |||
| Teacher uses displaydp | ||||||||
| NumDecPlaces | 0.10 |
displaydp(0.1,2) |
2 |
1 | ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv. | |||
NumDecPlacesWrong
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Basic tests | ||||||||
| NumDecPlacesWrong | 1/0 |
3 |
2 |
-1 | ATNumDecPlacesWrong_STACKERROR_SAns. | |||
| NumDecPlacesWrong | 0.1 |
1/0 |
2 |
-1 | ATNumDecPlacesWrong_STACKERROR_TAns. | |||
| NumDecPlacesWrong | 0.1 |
0 |
1/0 |
-1 | ATNumDecPlacesWrong_STACKERROR_Opt. | |||
| NumDecPlacesWrong | 0.1 |
0 |
x |
-1 | For ATNumDecPlacesWrong the test option must be a positive integer, in fact "\(x\)" was received. | ATNumDecPlacesWrong_OptNotInt. | ||
| NumDecPlacesWrong | x^2 |
1234 |
4 |
0 | Your answer must be a floating point number, but is not. | ATNumDecPlacesWrong_SA_Not_num. | ||
| NumDecPlacesWrong | 1234.5 |
x^2 |
4 |
0 | ATNumDecPlacesWrong_Tans_Not_Num. | |||
| NumDecPlacesWrong | 3.141 |
31.41 |
4 |
1 | ATNumDecPlacesWrong_Correct. | |||
| NumDecPlacesWrong | 3.141 |
31.14 |
4 |
0 | ATNumDecPlacesWrong_Wrong. | |||
| NumDecPlacesWrong | pi |
31.14 |
4 |
0 | Your answer must be a floating point number, but is not. | ATNumDecPlacesWrong_SA_Not_num. | ||
| NumDecPlacesWrong | 0.1234 |
1234 |
4 |
1 | ATNumDecPlacesWrong_Correct. | |||
| NumDecPlacesWrong | 0.1235 |
1234 |
4 |
0 | ATNumDecPlacesWrong_Wrong. | |||
| NumDecPlacesWrong | 0.0001234 |
1234 |
4 |
1 | ATNumDecPlacesWrong_Correct. | |||
| NumDecPlacesWrong | 0.0001235 |
1234 |
4 |
0 | ATNumDecPlacesWrong_Wrong. | |||
| NumDecPlacesWrong | 0.1233 |
1234 |
3 |
1 | ATNumDecPlacesWrong_Correct. | |||
| NumDecPlacesWrong | 0.1243 |
1234 |
3 |
0 | ATNumDecPlacesWrong_Wrong. | |||
| NumDecPlacesWrong | 0.1230 |
1239 |
3 |
1 | ATNumDecPlacesWrong_Correct. | |||
| NumDecPlacesWrong | 0.1240 |
1239 |
3 |
0 | ATNumDecPlacesWrong_Wrong. | |||
| NumDecPlacesWrong | 1230 |
1239 |
3 |
1 | ATNumDecPlacesWrong_Correct. | |||
| NumDecPlacesWrong | 2230 |
1239 |
3 |
0 | ATNumDecPlacesWrong_Wrong. | |||
| NumDecPlacesWrong | 0.100 |
1.00 |
3 |
1 | ATNumDecPlacesWrong_Correct. | |||
| NumDecPlacesWrong | 0.1000 |
1.00 |
3 |
1 | ATNumDecPlacesWrong_Correct. | |||
| NumDecPlacesWrong | 0.1001 |
1.001 |
3 |
1 | ATNumDecPlacesWrong_Correct. | |||
| Condone lack of trailing zeros | ||||||||
| NumDecPlacesWrong | 0.100 |
1.0 |
4 |
1 | ATNumDecPlacesWrong_Correct. | |||
| NumDecPlacesWrong | 1 |
1.00 |
4 |
1 | ATNumDecPlacesWrong_Correct. | |||
| Teacher uses displaydp | ||||||||
| NumDecPlacesWrong | 0.101 |
displaydp(101,3) |
3 |
1 | ATNumDecPlacesWrong_Correct. | |||
SigFigsStrict
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Basic tests | ||||||||
| SigFigsStrict | 3.141 |
null |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test. | STACKERROR_OPTION. | ||
| SigFigsStrict | 3.141 |
null |
x^2 |
-1 | STACKERROR_OPTION. | |||
| SigFigsStrict | 3.141 |
null |
-2 |
-1 | STACKERROR_OPTION. | |||
| SigFigsStrict | 3.141 |
null |
0 |
-1 | STACKERROR_OPTION. | |||
| SigFigsStrict | 0.0010 |
null |
1 |
0 | ||||
| SigFigsStrict | 0.0010 |
null |
2 |
1 | ||||
| SigFigsStrict | 0.0010 |
null |
3 |
0 | ||||
| SigFigsStrict | 0.00100 |
null |
2 |
0 | ||||
| SigFigsStrict | 0.00100 |
null |
3 |
1 | ||||
| SigFigsStrict | 0.00100 |
null |
4 |
0 | ||||
| SigFigsStrict | 0.001 |
null |
1 |
1 | ||||
| SigFigsStrict | 0.001 |
null |
2 |
0 | ||||
| SigFigsStrict | 100 |
null |
1 |
1 | ||||
| SigFigsStrict | 100 |
null |
2 |
0 | ATSigFigsStrict_WithinRange. | |||
| SigFigsStrict | 100 |
null |
3 |
0 | ATSigFigsStrict_WithinRange. | |||
| SigFigsStrict | 100 |
null |
4 |
0 | ||||
| SigFigsStrict | 100. |
null |
1 |
0 | ||||
| SigFigsStrict | 100. |
null |
2 |
0 | ||||
| SigFigsStrict | 100. |
null |
3 |
1 | ||||
| SigFigsStrict | 100. |
null |
4 |
0 | ||||
| SigFigsStrict | 123. |
null |
1 |
0 | ||||
| SigFigsStrict | 123. |
null |
2 |
0 | ||||
| SigFigsStrict | 123. |
null |
3 |
1 | ||||
| SigFigsStrict | 123. |
null |
4 |
0 | ||||
| SigFigsStrict | 1.00e2 |
null |
1 |
0 | ||||
| SigFigsStrict | 1.00e2 |
null |
2 |
0 | ||||
| SigFigsStrict | 1.00e2 |
null |
3 |
1 | ||||
| SigFigsStrict | 1.00e2 |
null |
4 |
0 | ||||
| SigFigsStrict | 10.0 |
null |
2 |
0 | ||||
| SigFigsStrict | 10.0 |
null |
3 |
1 | ||||
| SigFigsStrict | 10.0 |
null |
4 |
0 | ||||
| SigFigsStrict | 0 |
null |
1 |
1 | ||||
| SigFigsStrict | 0 |
null |
2 |
0 | ||||
| SigFigsStrict | 0.0 |
null |
1 |
1 | ||||
| SigFigsStrict | 0.0 |
null |
2 |
0 | ||||
| SigFigsStrict | .0 |
null |
1 |
1 | ||||
| SigFigsStrict | .0 |
null |
2 |
0 | ||||
| SigFigsStrict | .001030 |
null |
4 |
1 | ||||
| SigFigsStrict | 0.00 |
null |
1 |
0 | ||||
| SigFigsStrict | 0.00 |
null |
2 |
1 | ||||
| SigFigsStrict | 0.00 |
null |
3 |
0 | ||||
| SigFigsStrict | 25.00e1 |
null |
1 |
0 | ||||
| SigFigsStrict | 25.00e1 |
null |
3 |
0 | ||||
| SigFigsStrict | 25.00e1 |
null |
4 |
1 | ||||
| SigFigsStrict | 25.00e1 |
null |
5 |
0 | ||||
| SigFigsStrict | 15.1 |
15.1 |
3 |
1 | ||||
| SigFigsStrict | 15.10 |
15.1 |
3 |
0 | ||||
| SigFigsStrict | 15.100 |
15.1 |
3 |
0 | ||||
| Units are ignored | ||||||||
| SigFigsStrict | 9.81*m/s^2 |
null |
3 |
1 | ||||
Units
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Units | 1/0 |
1 |
2 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATUnits_STACKERROR_SAns. | |
| Units | 1 |
1/0 |
2 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATUnits_STACKERROR_TAns. | |
| Units | 1 |
1 |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATUnits_STACKERROR_Opt. | |
| Units | x-1)^2 |
(x-1)^2 |
2 |
-1 | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question. | ATUnitsTEST_FAILED-Empty SA. | |
| Units | 12.3*m*s^(-1) |
3*m |
[3,x] |
-1 | The answer test failed to execute correctly: please alert your teacher. | ATNumSigFigs_STACKERROR_not_integer. | ||
| Units | 3*m*s^(-1) |
3*m |
[1,2,3] |
-1 | The answer test failed to execute correctly: please alert your teacher. | ATNumSigFigs_STACKERROR_list_wrong_length. | ||
| Units | 12.3*m*s^(-1) |
{12.3*m*s^(-1)} |
3 |
-1 | The answer test failed to execute correctly: please alert your teacher. | ATUnits_TA_not_expression. | ||
| Units | x=12.3*m*s^(-1) |
12.3*m*s^(-1) |
3 |
0 | Your answer needs to be a number together with units. Do not use sets, lists, equations or matrices. | ATUnits_SA_not_expression. | ||
| Missing units | ||||||||
| Units | 12.3 |
12.3*m |
3 |
0 | Your answer must have units. | ATUnits_SA_no_units. | ||
| Units | 12 |
12.3*m |
3 |
0 | Your answer must have units. | ATUnits_SA_no_units. | ||
| Units | 1/2 |
12.3*m |
3 |
0 | Your answer must have units. | ATUnits_SA_no_units. | ||
| Units | e^(1/2) |
12.3*m |
3 |
0 | Your answer must have units. | ATUnits_SA_no_units. | ||
| Units | 9.81*m |
12.3 |
3 |
-1 | The answer test failed to execute correctly: please alert your teacher. | ATUnits_SB_no_units. | ||
| Only units | ||||||||
| Units | m/s |
12.3*m/s |
3 |
0 | Your answer needs to be a number together with units. Your answer only has units. | ATUnits_SA_only_units. | ||
| Units | m |
12.3*m/s |
3 |
0 | Your answer needs to be a number together with units. Your answer only has units. | ATUnits_SA_only_units. | ||
| Bad units | ||||||||
| Units | 9.81+m/s |
9.81*m/s |
3 |
0 | Your answer must have units, and you must use multiplication to attach the units to a value, e.g. 3.2*m/s. |
ATUnits_SA_bad_units. | ||
| Basic tests | ||||||||
| Units | 12.3*m/s |
12.3*m/s |
3 |
1 | ATUnits_units_match. | |||
| Units | 12.4*m/s |
12.3*m/s |
3 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. ATUnits_units_match. | ||
| Units | 12.4*m/s |
12.3*m/s |
[3,2] |
1 | ATUnits_units_match. | |||
| Units | 12.45*m/s |
12.3*m/s |
[3,2] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. ATUnits_units_match. | ||
| Units | 13.45*m/s |
12.3*m/s |
[3,2] |
0 | Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate. ATUnits_units_match. | ||
| Units | 7.54E-5*(s*M)^-1 |
5.625E-5*s^-1 |
[3,2] |
0 | Your units are incompatible with those used by the teacher. | ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units. | ||
| Units | 7.54E-5*(s*M)^-1 |
stackunits(5.625E-5,1/s) |
[3,2] |
0 | Your units are incompatible with those used by the teacher. | ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units. | ||
| Units | 12*m/s |
12.3*m/s |
3 |
0 | Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate. ATUnits_units_match. | ||
| Units | -9.81*m/s^2 |
-9.81*m/s^2 |
3 |
1 | ATUnits_units_match. | |||
| Units | -9.82*m/s^2 |
-9.815*m/s^2 |
3 |
1 | ATUnits_units_match. | |||
| Units | -9.81*m/s^2 |
-9.815*m/s^2 |
3 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. ATUnits_units_match. | ||
| Units | -9.81*m*s^(-2) |
-9.81*m/s^2 |
3 |
1 | ATUnits_units_match. | |||
| Units | -9.82*m/s^2 |
-9.81*m/s^2 |
3 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. ATUnits_units_match. | ||
| Units | -9.81*m*s^(-2) |
-9.81*m/s^2 |
3 |
1 | ATUnits_units_match. | |||
| Units | -9.81*m/s/s |
-9.81*m/s^2 |
3 |
1 | ATUnits_units_match. | |||
| Units | -9.81*m/s |
-9.81*m/s^2 |
3 |
0 | Your units are incompatible with those used by the teacher. Please check your units carefully. | ATUnits_incompatible_units. ATUnits_correct_numerical. | ||
| Units | -9.81*m/s |
-9.81*m/s^2 |
3 |
0 | Your units are incompatible with those used by the teacher. Please check your units carefully. | ATUnits_incompatible_units. ATUnits_correct_numerical. | ||
| Units | (-9.81)*m/s^2 |
-9.81*m/s^2 |
3 |
1 | ATUnits_units_match. | |||
| Units | 520*amu |
520*amu |
3 |
1 | ATNumSigFigs_WithinRange. ATUnits_units_match. | |||
| Units | 520*amu |
521*amu |
3 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_WithinRange. ATNumSigFigs_Inaccurate. ATUnits_units_match. | ||
| Missing units | ||||||||
| Units | (-9.81) |
-9.81*m/s^2 |
3 |
0 | Your answer must have units. | ATUnits_SA_no_units. | ||
| Units | 9.81*m/s |
-9.81*m/s^2 |
3 |
0 | Your answer has the wrong algebraic sign. Your units are incompatible with those used by the teacher. | ATNumSigFigs_WrongSign. ATUnits_incompatible_units. | ||
| Units | 8.81*m/s |
-9.81*m/s^2 |
3 |
0 | Your answer has the wrong algebraic sign. Your units are incompatible with those used by the teacher. | ATNumSigFigs_WrongSign. ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units. | ||
| Units | 8.1*m/s |
-9.81*m/s^2 |
3 |
0 | Your answer contains the wrong number of significant digits. Your answer has the wrong algebraic sign. Your units are incompatible with those used by the teacher. | ATNumSigFigs_WrongDigits. ATNumSigFigs_WrongSign. ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units. | ||
| Units | m/4 |
0.25*m |
3 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. ATUnits_units_match. | ||
| Student is too exact | ||||||||
| Units | pi*s |
3.14*s |
3 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. ATUnits_units_match. | ||
| Units | sqrt(2)*m |
1.41*m |
3 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. ATUnits_units_match. | ||
| Different units | ||||||||
| Units | 25*g |
0.025*kg |
2 |
1 | ATUnits_compatible_units kg. | |||
| Units | 26*g |
0.025*kg |
2 |
0 | The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error. | ATNumSigFigs_Inaccurate. ATUnits_compatible_units kg. | ||
| Units | 100*g |
10*kg |
2 |
0 | ATNumSigFigs_WithinRange. ATNumSigFigs_VeryInaccurate. ATUnits_compatible_units kg. | |||
| Units | 0.025*g |
0.025*kg |
2 |
0 | Please check your units carefully. | ATUnits_compatible_units kg. ATUnits_correct_numerical. | ||
| Units | 1000*m |
1*km |
2 |
1 | ATNumSigFigs_WithinRange. ATUnits_compatible_units m. | |||
| Units | 1*Mg/10^6 |
1*N*s^2/(km) |
1 |
1 | ATUnits_compatible_units kg. | |||
| Units | 1*Mg/10^6 |
1*kN*ns/(mm*Hz) |
1 |
1 | ATUnits_compatible_units kg. | |||
| Units | 3.14*Mg/10^6 |
%pi*kN*ns/(mm*Hz) |
3 |
1 | ATUnits_compatible_units kg. | |||
| Units | 3.141*Mg/10^6 |
%pi*kN*ns/(mm*Hz) |
3 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. ATUnits_compatible_units kg. | ||
| Units | 4.141*Mg/10^6 |
%pi*kN*ns/(mm*Hz) |
3 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. ATNumSigFigs_VeryInaccurate. ATUnits_compatible_units kg. | ||
| Units | 400*cc |
0.4*l |
2 |
1 | ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3. | |||
| Units | 400*cm^3 |
0.4*l |
2 |
1 | ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3. | |||
| Units | 400*ml |
0.4*l |
2 |
1 | ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3. | |||
| Units | 18*kJ |
18000.0*J |
2 |
1 | ATUnits_compatible_units (kg*m^2)/s^2. | |||
| Units | 18.1*kJ |
18000.0*J |
2 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. ATUnits_compatible_units (kg*m^2)/s^2. | ||
| Units | 120*kWh |
0.12*MWh |
2 |
1 | ATUnits_compatible_units (kg*m^2)/s^2. | |||
| Units | 2.0*hh |
720000*s |
2 |
1 | ATUnits_compatible_units s. | |||
| Units | 723*kVA |
0.723*MVA |
3 |
1 | ATUnits_compatible_units VA. | |||
| Edge case | ||||||||
| Units | 0*m/s |
0*m/s |
1 |
1 | ATUnits_units_match. | |||
| Units | 0.0*m/s |
0*m/s |
1 |
1 | ATUnits_units_match. | |||
| Units | 0*m/s |
0.0*m/s |
1 |
1 | ATUnits_units_match. | |||
| Units | 0.00*m/s |
0.0*m/s |
2 |
1 | ATUnits_units_match. | |||
| Units | 0.0*km/s |
0.0*m/s |
1 |
1 | ATUnits_compatible_units m/s. | |||
| Units | 0.0*m |
0.0*m/s |
1 |
0 | Your units are incompatible with those used by the teacher. Please check your units carefully. | ATUnits_incompatible_units. ATUnits_correct_numerical. | ||
| Units | 0.0 |
0.0*m/s |
1 |
0 | Your answer must have units. | ATUnits_SA_no_units. | ||
| Imperial | ||||||||
| Units | 7*in |
7*in |
1 |
1 | ATUnits_units_match. | |||
| Units | 6*in |
0.5*ft |
1 |
1 | ATUnits_compatible_units in. | |||
| Units | 2640*ft |
0.5*mi |
4 |
1 | ATNumSigFigs_WithinRange. ATUnits_compatible_units in. | |||
| Units | 2650*ft |
0.5*mi |
4 |
0 | ATNumSigFigs_WithinRange. ATNumSigFigs_VeryInaccurate. ATUnits_compatible_units in. | |||
| TODO | ||||||||
| Units | ! | 142.8*C |
415.9*K |
4 |
-3 | Your units are incompatible with those used by the teacher. | ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units. | |
| Units | ! | 520*mamu |
520*mamu |
3 |
-3 | The answer test failed to execute correctly: please alert your teacher. | ATUnits_SB_no_units. | |
UnitsStrict
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Differences from the Units test only | ||||||||
| UnitsStrict | 25*g |
0.025*kg |
2 |
0 | ATUnits_compatible_units kg. | |||
| UnitsStrict | 1*Mg/10^6 |
1*N*s^2/(km) |
1 |
0 | ATUnits_compatible_units kg. | |||
| UnitsStrict | 1*Mg/10^6 |
1*kN*ns/(mm*Hz) |
1 |
0 | ATUnits_compatible_units kg. | |||
| UnitsStrict | 3.14*Mg/10^6 |
%pi*kN*ns/(mm*Hz) |
3 |
0 | ATUnits_compatible_units kg. | |||
| UnitsStrict | 400*cc |
0.4*l |
2 |
0 | ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3. | |||
| UnitsStrict | 400*cm^3 |
0.4*l |
2 |
0 | ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3. | |||
| UnitsStrict | 400*ml |
0.4*l |
2 |
0 | ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3. | |||
| UnitsStrict | 400*mL |
0.4*l |
2 |
0 | ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3. | |||
| UnitsStrict | 142.8*C |
415.9*K |
4 |
0 | ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units. | |||
| We are not *that* strict! | ||||||||
| UnitsStrict | -9.81*m/s/s |
-9.81*m/s^2 |
3 |
1 | ATUnits_units_match. | |||
| Edge case | ||||||||
| UnitsStrict | 0*m/s |
0*m/s |
1 |
1 | ATUnits_units_match. | |||
| UnitsStrict | 0.0*m/s |
0*m/s |
1 |
1 | ATUnits_units_match. | |||
| UnitsStrict | 0*m/s |
0.0*m/s |
1 |
1 | ATUnits_units_match. | |||
| UnitsStrict | 0.0*m/s |
0.0*m/s |
1 |
1 | ATUnits_units_match. | |||
| UnitsStrict | 0.0*km/s |
0.0*m/s |
1 |
0 | ATUnits_compatible_units m/s. | |||
| UnitsStrict | 0.0*m |
0.0*m/s |
1 |
0 | ATUnits_incompatible_units. ATUnits_correct_numerical. | |||
| UnitsStrict | 0.0 |
0.0*m/s |
1 |
0 | Your answer must have units. | ATUnits_SA_no_units. | ||
| UnitsStrict | 2.33e-15*kg |
2.33e-15*kg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 7.03e-3*ng |
7.03e-3*ng |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 2.35e-6*ug |
2.35e-6*ug |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 9.83e-10*cg |
9.83e-10*cg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 9.73e-21*Gg |
9.73e-21*Gg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 7.19e-15*kg |
7.19e-15*kg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 8.12e-12*g |
8.12e-12*g |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 9.34e-12*g |
9.34e-12*g |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 1.07e-21*Gg |
1.07e-21*Gg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 1.91e-10*cg |
1.91e-10*cg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 5.67e-18*Mg |
5.67e-18*Mg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 2.04e-9*mg |
2.04e-9*mg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 6.75e-6*ug |
6.75e-6*ug |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 6.58e-6*ug |
6.58e-6*ug |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 3.58e-9*mg |
3.58e-9*mg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 9.99e-15*kg |
9.99e-15*kg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 9.8e-9*mg |
9.8e-9*mg |
[3,2] |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. ATUnits_units_match. | ||
| UnitsStrict | 9.80e-9*mg |
9.8e-9*mg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 9.83e-9*mg |
9.8e-9*mg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 9.78e-9*mg |
9.8e-9*mg |
[3,2] |
1 | ATUnits_units_match. | |||
| UnitsStrict | 36*Kj/mol |
36*Kj/mol |
2 |
1 | ATUnits_units_match. | |||
| UnitsStrict | -36*Kj/mol |
-36*Kj/mol |
2 |
1 | ATUnits_units_match. | |||
| UnitsStrict | (-36)*Kj/mol |
-36*Kj/mol |
2 |
1 | ATUnits_units_match. | |||
| UnitsStrict | (-36*Kj)/mol |
-36*Kj/mol |
2 |
1 | ATUnits_units_match. | |||
| UnitsStrict | -(36*Kj)/mol |
-36*Kj/mol |
2 |
1 | ATUnits_units_match. | |||
| UnitsStrict | -(36.2*Kj)/mol |
-36.3*Kj/mol |
2 |
0 | Your answer contains the wrong number of significant digits. | ATNumSigFigs_WrongDigits. ATUnits_units_match. | ||
UnitsRelative
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| UnitsRelative | 12.3*m/s |
12.3*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsRelative | 12*m/s |
12.3*m/s |
0.01 |
0 | ATUnits_units_match. | |||
| UnitsRelative | 1.1*Mg/10^6 |
1.2*kN*ns/(mm*Hz) |
0.15 |
1 | ATUnits_compatible_units kg. | |||
| UnitsRelative | 1.1*Mg/10^6 |
1.2*kN*ns/(mm*Hz) |
0.05 |
0 | ATUnits_compatible_units kg. | |||
| Edge case | ||||||||
| UnitsRelative | 0*m/s |
0*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsRelative | 0.0*m/s |
0*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsRelative | 0*m/s |
0.0*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsRelative | 0.0*m/s |
0.0*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsRelative | 0.0*km/s |
0.0*m/s |
0.01 |
1 | ATUnits_compatible_units m/s. | |||
| UnitsRelative | 0.0*m |
0.0*m/s |
0.01 |
0 | Your units are incompatible with those used by the teacher. Please check your units carefully. | ATUnits_incompatible_units. ATUnits_correct_numerical. | ||
| UnitsRelative | 0.0 |
0.0*m/s |
0.01 |
0 | Your answer must have units. | ATUnits_SA_no_units. | ||
| UnitsRelative | 0.0*kVA |
0.0*kVA |
0.002 |
1 | ATUnits_units_match. | |||
UnitsStrictRelative
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| UnitsStrictRelative | 12.3*m/s |
12.3*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsStrictRelative | 12*m/s |
12.3*m/s |
0.01 |
0 | ATUnits_units_match. | |||
| UnitsStrictRelative | 1.1*Mg/10^6 |
1.2*kN*ns/(mm*Hz) |
0.15 |
0 | ATUnits_compatible_units kg. | |||
| UnitsStrictRelative | 1.1*Mg/10^6 |
1.2*kN*ns/(mm*Hz) |
0.05 |
0 | ATUnits_compatible_units kg. | |||
| Edge case | ||||||||
| UnitsStrictRelative | 0*m/s |
0*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsStrictRelative | 0.0*m/s |
0*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsStrictRelative | 0*m/s |
0.0*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsStrictRelative | 0.0*m/s |
0.0*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsStrictRelative | 0.0*km/s |
0.0*m/s |
0.01 |
0 | ATUnits_compatible_units m/s. | |||
| UnitsStrictRelative | 0.0*m |
0.0*m/s |
0.01 |
0 | ATUnits_incompatible_units. ATUnits_correct_numerical. | |||
| UnitsStrictRelative | 0.0 |
0.0*m/s |
0.01 |
0 | Your answer must have units. | ATUnits_SA_no_units. | ||
| UnitsStrictRelative | 0*J |
0.0*J |
0.01 |
1 | ATUnits_units_match. | |||
UnitsAbsolute
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| UnitsAbsolute | -123000*J |
-123*kJ |
5*J |
0 | The units specified for the numerical tolerance must match the units used for the teacher's answer. This is an internal error with the test. Please ask your teacher about this. | ATUnits_SO_wrong_units. | ||
| UnitsAbsolute | 12.3*m/s |
12.3*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsAbsolute | 12*m/s |
12.3*m/s |
0.01 |
0 | ATUnits_units_match. | |||
| UnitsAbsolute | 1.1*Mg/10^6 |
1.2*kN*ns/(mm*Hz) |
0.15 |
1 | ATUnits_compatible_units kg. | |||
| The following illustrates that we convert to base units to compare. | ||||||||
| UnitsAbsolute | 1.1*Mg/10^6 |
1.2*kN*ns/(mm*Hz) |
0.1 |
1 | ATUnits_compatible_units kg. | |||
| UnitsAbsolute | 1.1*Mg/10^6 |
1.2*kN*ns/(mm*Hz) |
0.09 |
0 | ATUnits_compatible_units kg. | |||
| Units in the options | ||||||||
| UnitsAbsolute | -123000*J |
-123*kJ |
5*kJ |
1 | ATUnits_compatible_units (kg*m^2)/s^2. | |||
| UnitsAbsolute | -123006*J |
-123*kJ |
5*kJ |
1 | ATUnits_compatible_units (kg*m^2)/s^2. | |||
| UnitsAbsolute | -129006*J |
-123*kJ |
5*kJ |
0 | ATUnits_compatible_units (kg*m^2)/s^2. | |||
| UnitsAbsolute | 1.1*Mg/10^6 |
1.2*kN*ns/(mm*Hz) |
0.1*kN*ns/(mm*H z) |
1 | ATUnits_compatible_units kg. | |||
| UnitsAbsolute | 1.1*Mg/10^6 |
1.2*kN*ns/(mm*Hz) |
0.09*kN*ns/(mm* Hz) |
0 | ATUnits_compatible_units kg. | |||
| Edge case | ||||||||
| UnitsAbsolute | 0*m/s |
0*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsAbsolute | 0.0*m/s |
0*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsAbsolute | 0*m/s |
0.0*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsAbsolute | 0.0*m/s |
0.0*m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsAbsolute | 0.0*km/s |
0.0*m/s |
0.01 |
1 | ATUnits_compatible_units m/s. | |||
| UnitsAbsolute | 0.0*m |
0.0*m/s |
0.01 |
0 | Your units are incompatible with those used by the teacher. Please check your units carefully. | ATUnits_incompatible_units. ATUnits_correct_numerical. | ||
| UnitsAbsolute | 0.0 |
0.0*m/s |
0.01 |
0 | Your answer must have units. | ATUnits_SA_no_units. | ||
| UnitsAbsolute | 1.0*m/s |
m/s |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsAbsolute | 15/pi*kN/mm^2 |
15/pi*kN/mm^2 |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsAbsolute | (15*kN)/(pi*mm^2) |
(15*kN)/(pi*mm^2) |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsAbsolute | (15/pi)*(kN/mm^2) |
(15/pi)*(kN/mm^2) |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsAbsolute | (600*N)/(%pi*mm^2) |
(600*N)/(%pi*mm^2) |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsAbsolute | (600/pi)*kN/m^2 |
(600/pi)*kN/m^2 |
0.01 |
1 | ATUnits_units_match. | |||
| UnitsAbsolute | (600/pi)*kN/mm^2 |
(600/pi)*kN/mm^2 |
0.01 |
1 | ATUnits_units_match. | |||
String
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| String | Hello |
hello |
0 | |||||
| String | hello |
hello |
1 | |||||
| String | hello |
heloo |
0 | |||||
StringSloppy
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| StringSloppy | hello |
Hello |
1 | |||||
| StringSloppy | hel lo |
Hello |
0 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Illegal spaces found in expression hel_lo. | ATStringSloppy_STACKERROR_SAns. | ||
| StringSloppy | hel lo |
Hel*lo |
0 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Illegal spaces found in expression hel_lo. | ATStringSloppy_STACKERROR_SAns. | ||
| StringSloppy | hello |
heloo |
0 | |||||
Levenshtein
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| Levenshtein | "Hello" |
"Hello" |
0 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test. | STACKERROR_OPTION. | ||
| Levenshtein | 1/0 |
"Hello" |
0.9 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATLevenshtein_STACKERROR_SAns. | |
| Levenshtein | x^2 |
"Hello" |
0.9 |
0 | The first argument to the Levenshtein answer test must be a string. The test failed. Please contact your teacher. | ATLevenshtein_SA_not_string. | ||
| Levenshtein | "Hello" |
"Hello" |
0.9 |
0 | The second argument to the Levenshtein answer test must be in the form [allow, deny] where each item is a list of strings. This argument is malformed and so the test failed. Please contact your teacher. | ATLevenshtein_SB_malformed. | ||
| Levenshtein | "Hello" |
["Hello"] |
0.9 |
0 | The second argument to the Levenshtein answer test must be in the form [allow, deny] where each item is a list of strings. This argument is malformed and so the test failed. Please contact your teacher. | ATLevenshtein_SB_malformed. | ||
| Levenshtein | "Hello" |
[["Hello"]] |
0.9 |
0 | The second argument to the Levenshtein answer test must be in the form [allow, deny] where each item is a list of strings. This argument is malformed and so the test failed. Please contact your teacher. | ATLevenshtein_SB_malformed. | ||
| Levenshtein | "Hello" |
[["Hello"], x^2] |
0.9 |
0 | The second argument to the Levenshtein answer test must be in the form [allow, deny] where each item is a list of strings. This argument is malformed and so the test failed. Please contact your teacher. | ATLevenshtein_SB_malformed. | ||
| Levenshtein | "Hello" |
[["Hello"], [x^2]] |
0.9 |
0 | The second argument to the Levenshtein answer test must be in the form [allow, deny] where each item is a list of strings. This argument is malformed and so the test failed. Please contact your teacher. | ATLevenshtein_SB_malformed. | ||
| Levenshtein | "Hello" |
[["Hello"], ["G oodbye"], ["Excess&q uot;]] |
0.9 |
0 | The second argument to the Levenshtein answer test must be in the form [allow, deny] where each item is a list of strings. This argument is malformed and so the test failed. Please contact your teacher. | ATLevenshtein_SB_malformed. | ||
| Levenshtein | "Hello" |
[[], ["Goodbye"]] |
0.9 |
0 | The second argument to the Levenshtein answer test must be in the form [allow, deny] where each item is a list of strings. This argument is malformed and so the test failed. Please contact your teacher. | ATLevenshtein_SB_malformed. | ||
| Levenshtein | "Hello" |
[["Hello"], ["G oodbye"]] |
z |
0 | The tolerance in the Levenshtein answer test must be a number, but is not. The test failed. Please contact your teacher. | ATLevenshtein_tol_not_number. | ||
| Levenshtein | "Hello" |
[["Hello"], ["G oodbye"]] |
[z] |
0 | The tolerance in the Levenshtein answer test must be a number, but is not. The test failed. Please contact your teacher. | ATLevenshtein_tol_not_number. | ||
| Usage tests | ||||||||
| Levenshtein | "Hello" |
[["Hello"], ["G oodbye"]] |
0.9 |
1 | ATLevenshtein_true: [[1.0,"Hello"],[0.0,"Goodbye"]]. | |||
| Levenshtein | "hello" |
[["Hello"], ["G oodbye"]] |
[0.9] |
1 | ATLevenshtein_true: [[1.0,"Hello"],[0.0,"Goodbye"]]. | |||
| Levenshtein | "hello" |
[["Hello", "Goo d day", "Hi"], ["Goodbye", "By e", "Fairwell"] ] |
[0.8, CASE] |
1 | The closest match was "\(\mbox{Hello}\)". | ATLevenshtein_match: [[0.8,"Hello"],[0.25,"Fairwell"]]. | ||
| Levenshtein | "goodday" |
[["Hello", "Goo d day", "Hi"], ["Goodbye", "By e", "Fairwell"] ] |
0.8 |
1 | The closest match was "\(\mbox{Good day}\)". | ATLevenshtein_match: [[0.875,"Good day"],[0.57143,"Goodbye"]]. | ||
| Levenshtein | "goodday" |
[["Hello", "Goo d day", "Hi"], ["Goodbye", "By e", "Fairwell"] ] |
[0.8, CASE] |
0 | ATLevenshtein_far: [[0.75,"Good day"],[0.42857,"Goodbye"]]. | |||
| Levenshtein | "Jello" |
[["Hello", "Goo d day", "Hi"], ["Goodbye", "By e", "Fairwell"] ] |
0.9 |
0 | ATLevenshtein_far: [[0.8,"Hello"],[0.25,"Fairwell"]]. | |||
| Levenshtein | "Jello" |
[["Hello", "Goo d day", "Hi"], ["Goodbye", "By e", "Fairwell"] ] |
0.75 |
1 | The closest match was "\(\mbox{Hello}\)". | ATLevenshtein_match: [[0.8,"Hello"],[0.25,"Fairwell"]]. | ||
| Levenshtein | "Jello" |
[["Hello", "Goo d day", "Hi"], []] |
0.75 |
1 | The closest match was "\(\mbox{Hello}\)". | ATLevenshtein_match: [[0.8,"Hello"],[0,[]]]. | ||
| Levenshtein | "Good bye" |
[["Hello", "Goo d day", "Hi"], ["Goodbye", "By e", "Fairwell"] ] |
0.75 |
0 | ATLevenshtein_deny: [[0.625,"Good day"],[0.875,"Goodbye"]]. | |||
| Levenshtein | "Good, day!" |
[["Hello", "Goo d day", "Hi"], ["Goodbye", "By e", "Fairwell"] ] |
0.75 |
1 | The closest match was "\(\mbox{Good day}\)". | ATLevenshtein_match: [[0.8,"Good day"],[0.5,"Goodbye"]]. | ||
| Levenshtein | sremove_chars(".,!?"
, "Good, day!") |
[["Hello", "Goo d day", "Hi"], ["Goodbye", "By e", "Fairwell"] ] |
0.75 |
1 | ATLevenshtein_true: [[1.0,"Good day"],[0.5,"Goodbye"]]. | |||
| Levenshtein | " good day " |
[["Hello", "Goo d day", "Hi"], ["Goodbye", "By e", "Fairwell"] ] |
0.75 |
1 | ATLevenshtein_true: [[1.0,"Good day"],[0.5,"Goodbye"]]. | |||
| Levenshtein | " good day " |
[["Hello", "Goo d day", "Hi"], ["Goodbye", "By e", "Fairwell"] ] |
[0.75, WHITESPA CE] |
0 | ATLevenshtein_far: [[0.47059,"Good day"],[0.29412,"Goodbye"]]. | |||
SRegExp
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| SRegExp | 1/0 |
"hello" |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATSRegExp_STACKERROR_SAns. | ||
| SRegExp | "1/0" |
1/0 |
-1 | TEST_FAILED | The answer test failed to execute correctly: please alert your teacher. Division by zero. | ATSRegExp_STACKERROR_TAns. | ||
| SRegExp | Hello |
hello |
-1 | The second argument to the SRegExp answer test must be a string. The test failed. Please contact your teacher. | ATSRegExp_SB_not_string. | |||
| SRegExp | Hello |
"hello" |
-1 | The first argument to the SRegExp answer test must be a string. The test failed. Please contact your teacher. | ATSRegExp_SA_not_string. | |||
| SRegExp | "aaaaabbb" |
"(aaa)*b" |
1 | ATSRegExp: ["aaab","aaa"]. | ||||
| SRegExp | "aab" |
"(aaa)*b" |
1 | ATSRegExp: ["b",false]. | ||||
| SRegExp | "aaac" |
"(aaa)*b" |
0 | |||||
| Anchor pattern to the start and the end of the string | ||||||||
| SRegExp | "aab" |
"^[aA]*b$" |
1 | ATSRegExp: ["aab"]. | ||||
| SRegExp | "aab" |
"^(aaa)*b$" |
0 | |||||
| SRegExp | "aAb" |
"^[aA]*b$" |
1 | ATSRegExp: ["aAb"]. | ||||
| SRegExp | " aAb" |
"^[aA]*b$" |
0 | |||||
| Case insensitive | ||||||||
| SRegExp | "caAb" |
"(?i:a*b)" |
1 | ATSRegExp: ["aAb"]. | ||||
| Options | ||||||||
| SRegExp | "Alice went to the market " |
"(Alice|Bob) went to the (bank|market)" |
1 | ATSRegExp: ["Alice went to the market","Alice","market"]. | ||||
| SRegExp | "Malice went to the shop& quot; |
"(Alice|Bob) went to the (bank|market)" |
0 | |||||
| Whitespace, note test rendering issue, the test string has additional spaces and tabs as does the result | ||||||||
| SRegExp | "Alice went to th e market" |
"(Alice|Bob)\\s+went\\s+t o\\s+the\\s+(bank|market)" ; |
1 | ATSRegExp: ["Alice went to the market","Alice","market"]. | ||||
| SRegExp | "Alice went to th emarket" |
"(Alice|Bob)\\s+went\\s+t o\\s+the\\s+(bank|market)" ; |
0 | |||||
| Escaping patterns, note the function that does it | ||||||||
| SRegExp | "x^2.2" |
"x\\^2\\.2" |
1 | ATSRegExp: ["x^2.2"]. | ||||
| SRegExp | "x^2+sin(x)" |
sconcat(string_to_regex("
sin(x)"),"$") |
1 | ATSRegExp: ["sin(x)"]. | ||||
| SRegExp | "sin(x)+x^2" |
sconcat(string_to_regex("
sin(x)"),"$") |
0 | |||||
LowestTerms
| Test | ? | Student response | Teacher answer | Opt | Mark | CAS errors | Feedback | Answer note |
|---|---|---|---|---|---|---|---|---|
| LowestTerms | 1/0 |
0 |
-1 | ATLowestTerms_STACKERROR_SAns. | ||||
| Mix of floats and rational numbers | ||||||||
| LowestTerms | 0.5 |
0 |
1 | |||||
| LowestTerms | 0.33 |
0 |
1 | |||||
| LowestTerms | 2/4 |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{2}{4} \right] \] Please try again. | ATLowestTerms_entries. | |||
| Negative numbers | ||||||||
| LowestTerms | -1/3 |
0 |
1 | |||||
| LowestTerms | 1/-3 |
0 |
1 | |||||
| LowestTerms | -2/4 |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{-2}{4} \right] \] Please try again. | ATLowestTerms_entries. | |||
| LowestTerms | 2/-4 |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{2}{-4} \right] \] Please try again. | ATLowestTerms_entries. | |||
| LowestTerms | -1/-3 |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{-1}{-3} \right] \] Please try again. | ATLowestTerms_entries. | |||
| LowestTerms | -2/-4 |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{-2}{-4} \right] \] Please try again. | ATLowestTerms_entries. | |||
| Polynomials | ||||||||
| LowestTerms | x+1/3 |
0 |
1 | |||||
| LowestTerms | x+2/6 |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{2}{6} \right] \] Please try again. | ATLowestTerms_entries. | |||
| LowestTerms | 2*x/4+2/6 |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{2}{6} \right] \] Please try again. | ATLowestTerms_entries. | |||
| LowestTerms | 2/4*x+2/6 |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{2}{4} , \frac{2}{6} \right] \] Please try again. | ATLowestTerms_entries. | |||
| LowestTerms | x-1/-4 |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{-1}{-4} \right] \] Please try again. | ATLowestTerms_entries. | |||
| Trig functions | ||||||||
| LowestTerms | cos(x) |
0 |
1 | |||||
| LowestTerms | cos(3/6*x) |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{3}{6} \right] \] Please try again. | ATLowestTerms_entries. | |||
| Matrices | ||||||||
| LowestTerms | matrix([1,2/4],[2,3]) |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{2}{4} \right] \] Please try again. | ATLowestTerms_entries. | |||
| Equations | ||||||||
| LowestTerms | x=1/2 |
0 |
1 | |||||
| LowestTerms | 3/9=x |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{3}{9} \right] \] Please try again. | ATLowestTerms_entries. | |||
| Use predicate lowesttermsp | ||||||||
| LowestTerms | x^2/x |
0 |
1 | |||||
| LowestTerms | (2*x)/(4*t) |
0 |
1 | |||||
| LowestTerms | (2/4)*(x^2/t) |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{2}{4} \right] \] Please try again. | ATLowestTerms_entries. | |||
| LowestTerms | x^(2/4) |
0 |
0 | The following terms in your answer are not in lowest terms. \[\left[ \frac{2}{4} \right] \] Please try again. | ATLowestTerms_entries. | |||
| Need to rationalize demoninator | ||||||||
| LowestTerms | sqrt(3)/3 |
sqrt(3)/3 |
1 | |||||
| LowestTerms | 1/sqrt(3) |
sqrt(3)/3 |
0 | You must clear the following from the denominator of your fraction: \[\left[ \sqrt{3} \right] \] | ATLowestTerms_not_rat. | |||
| LowestTerms | 1/(1-sqrt(2)) |
1/(1-sqrt(2)) |
0 | You must clear the following from the denominator of your fraction: \[\left[ \sqrt{2} \right] \] | ATLowestTerms_not_rat. | |||
| LowestTerms | 1/(1+i) |
(1-i)/2 |
0 | You must clear the following from the denominator of your fraction: \[\left[ \mathrm{i} \right] \] | ATLowestTerms_not_rat. | |||
| LowestTerms | 1+2/sqrt(3) |
(2*sqrt(3)+3)/3 |
0 | You must clear the following from the denominator of your fraction: \[\left[ \sqrt{3} \right] \] | ATLowestTerms_not_rat. | |||
| LowestTerms | 1/(1+1/root(3,2)) |
sqrt(3)/(sqrt(3)+1) |
0 | You must clear the following from the denominator of your fraction: \[\left[ 3^{\frac{1}{2}} \right] \] | ATLowestTerms_not_rat. | |||
| LowestTerms | 1/(1+1/root(2,3)) |
1/(1+1/root(2,3)) |
0 | You must clear the following from the denominator of your fraction: \[\left[ 2^{\frac{1}{3}} \right] \] | ATLowestTerms_not_rat. | |||
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