# SubstEquiv: 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.

## SubstEquiv

Test | ? | Student response | Teacher answer | Opt | Mark | Answer note | |
---|---|---|---|---|---|---|---|

SubstEquiv | 1/0 |
x^2-2*x+1 |
-1 | ATSubstEquiv_STACKERROR_SAns. | |||

TEST_FAILED | |||||||

The answer test failed to execute correctly: please alert your teacher. Division by zero. | |||||||

SubstEquiv | x^2 |
x^2-2*x+1 |
[1/0] |
-1 | ATSubstEquiv_STACKERROR_Opt. | ||

TEST_FAILED | |||||||

The answer test failed to execute correctly: please alert your teacher. Division by zero. | |||||||

SubstEquiv | x^2 |
x^2-2*x+1 |
x |
-1 | ATSubstEquiv_Opt_List. | ||

The option to this answer test must be a list. This is an error. Please contact your teacher. | |||||||

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 | ATSubstEquiv_Subst [X = x]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ X=x \right] \] | |||||||

SubstEquiv | x^2+y |
a^2+b |
1 | ATSubstEquiv_Subst [x = a,y = b]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ x=a , y=b \right] \] | |||||||

SubstEquiv | x^2+y/z |
a^2+c/b |
1 | ATSubstEquiv_Subst [x = a,y = c,z = b]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ x=a , y=c , z=b \right] \] | |||||||

SubstEquiv | y=x^2 |
a^2=b |
1 | ATSubstEquiv_Subst [x = a,y = b]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ x=a , y=b \right] \] | |||||||

SubstEquiv | {x=1,y=2} |
{x=2,y=1} |
1 | ATSubstEquiv_Subst [x = y,y = x]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ x=y , y=x \right] \] | |||||||

Where a variable is also a function name. | |||||||

SubstEquiv | cos(a*x)/(x*(ln(x))) |
cos(a*y)/(y*(ln(y))) |
1 | ATSubstEquiv_Subst [a = a,x = y]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ a=a , x=y \right] \] | |||||||

SubstEquiv | cos(a*x)/(x*(ln(x))) |
cos(x*a)/(a*(ln(a))) |
1 | ATSubstEquiv_Subst [a = x,x = a]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ a=x , x=a \right] \] | |||||||

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 | ATSubstEquiv_Subst [x = y,y = x]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ x=y , y=x \right] \] | |||||||

SubstEquiv | x+1>y |
x<y+1 |
1 | ATSubstEquiv_Subst [x = y,y = x]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ x=y , y=x \right] \] | |||||||

Matrices | |||||||

SubstEquiv | matrix([1,A^2+A+1],[2,0]) |
matrix([1,x^2+x+1],[2,0]) |
1 | ATSubstEquiv_Subst [A = x]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ A=x \right] \] | |||||||

SubstEquiv | matrix([B,A^2+A+1],[2,C]) |
matrix([y,x^2+x+1],[2,z]) |
1 | ATSubstEquiv_Subst [A = x,B = y,C = z]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ A=x , B=y , C=z \right] \] | |||||||

SubstEquiv | matrix([B,A^2+A+1],[2,C]) |
matrix([y,x^2+x+1],[2,x]) |
0 | ATMatrix_wrongentries. | |||

The entries underlined in red below are those that are incorrect. \[ \left[\begin{array}{cc} {\color{red}{\underline{B}}} & {\color{red}{\underline{A^2+A+1}}} \\ 2 & {\color{red}{\underline{C}}} \end{array}\right]\] | |||||||

Lists | |||||||

SubstEquiv | [x^2+1,x^2] |
[A^2+1,A^2] |
1 | ATSubstEquiv_Subst [x = A]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ x=A \right] \] | |||||||

SubstEquiv | [x^2-1,x^2] |
[A^2+1,A^2] |
0 | (ATList_wrongentries 1, 2). | |||

The entries underlined in red below are those that are incorrect. \[\left[ {\color{red}{\underline{x^2-1}}} , {\color{red}{\underline{x ^2}}} \right] \] | |||||||

SubstEquiv | [A,B,C] |
[B,C,A] |
1 | ATSubstEquiv_Subst [A = B,B = C,C = A]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ A=B , B=C , C=A \right] \] | |||||||

SubstEquiv | [A,B,C] |
[B,B,A] |
0 | (ATList_wrongentries 1, 3). | |||

The entries underlined in red below are those that are incorrect. \[\left[ {\color{red}{\underline{A}}} , B , {\color{red}{\underline{C }}} \right] \] | |||||||

SubstEquiv | [1,[A,B],C] |
[1,[a,b],C] |
1 | ATSubstEquiv_Subst [A = a,B = b,C = C]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ A=a , B=b , C=C \right] \] | |||||||

Sets | |||||||

SubstEquiv | {x^2+1,x^2} |
{A^2+1,A^2} |
1 | ATSubstEquiv_Subst [x = A]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ x=A \right] \] | |||||||

SubstEquiv | {x^2-1,x^2} |
{A^2+1,A^2} |
0 | ATSet_wrongentries. | |||

The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{x^2-1 , x^2 \right \}\] | |||||||

SubstEquiv | {A+1,B^2,C} |
{B,C+1,A^2} |
1 | ATSubstEquiv_Subst [A = C,B = A,C = B]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ A=C , B=A , C=B \right] \] | |||||||

SubstEquiv | {1,{A,B},C} |
{1,{a,b},C} |
1 | ATSubstEquiv_Subst [A = a,B = b,C = C]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ A=a , B=b , C=C \right] \] | |||||||

SubstEquiv | y=A+B |
x=a+b |
[x] |
0 | ATEquation_default | ||

SubstEquiv | y=A+B |
x=a+b |
[z] |
1 | ATSubstEquiv_Subst [A = a,B = b,y = x]. | ||

Your answer would be correct if you used the following substitution of variables. \[\left[ A=a , B=b , y=x \right] \] | |||||||

SubstEquiv | A*cos(t)+B*sin(t) |
P*cos(t)+Q*sin(t) |
1 | ATSubstEquiv_Subst [A = P,B = Q,t = t]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ A=P , B=Q , t=t \right] \] | |||||||

SubstEquiv | A*cos(t)+B*sin(t) |
P*cos(x)+Q*sin(x) |
1 | ATSubstEquiv_Subst [A = P,B = Q,t = x]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ A=P , B=Q , t=x \right] \] | |||||||

Fix some variables. | |||||||

SubstEquiv | A*cos(x)+B*sin(x) |
P*cos(x)+Q*sin(x) |
[x] |
1 | ATSubstEquiv_Subst [A = P,B = Q]. | ||

Your answer would be correct if you used the following substitution of variables. \[\left[ A=P , B=Q \right] \] | |||||||

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] |
0 | |||

SubstEquiv | A*cos(t)+B*sin(t) |
P*cos(x)+Q*sin(x) |
[z] |
1 | ATSubstEquiv_Subst [A = P,B = Q,t = x]. | ||

Your answer would be correct if you used the following substitution of variables. \[\left[ A=P , B=Q , t=x \right] \] | |||||||

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 | ATSubstEquiv_Subst [A = P,B = Q,C = R,D = S]. | ||

Your answer would be correct if you used the following substitution of variables. \[\left[ A=P , B=Q , C=R , D=S \right] \] | |||||||

SubstEquiv | sqrt(2*g*y) |
sqrt(2*g*x) |
1 | ATSubstEquiv_Subst [g = g,y = x]. | |||

Your answer would be correct if you used the following substitution of variables. \[\left[ g=g , y=x \right] \] | |||||||

SubstEquiv | sqrt(2*g*y) |
sqrt(2*g*x) |
[g] |
1 | ATSubstEquiv_Subst [y = x]. | ||

Your answer would be correct if you used the following substitution of variables. \[\left[ y=x \right] \] | |||||||

SubstEquiv | C1*%e^x*sin(4*x)+C2*%e^x*cos(4 *x)+C4*x*%e^-x+C3*%e^-x |
e^(x)*A*cos(4*x)+B*e^(x)*sin(4 *x)+C*e^(-x)+D*x*e^(-x) |
[x] |
1 | ATSubstEquiv_Subst [C1 = B,C2 = A,C3 = C,C4 = D]. | ||

Your answer would be correct if you used the following substitution of variables. \[\left[ C_{1}=B , C_{2}=A , C_{3}=C , C_{4}=D \right] \] | |||||||

SubstEquiv | C1*%e^x*sin(4*x)+C2*%e^x*cos(4 *x)+C4*x*%e^-x+C3*%e^-x |
C4*x*e^(-x)+e^(x)*C1*cos(4*x)+ C2*e^(x)*sin(4*x)+C3*e^(-x) |
[x] |
1 | ATSubstEquiv_Subst [C1 = C2,C2 = C1,C3 = C3,C4 = C4]. | ||

Your answer would be correct if you used the following substitution of variables. \[\left[ C_{1}=C_{2} , C_{2}=C_{1} , C_{3}=C_{3} , C_{4}=C_{4} \right] \] | |||||||

SubstEquiv | C1*%e^x*sin(4*x)+C2*%e^x*cos(4 *x)+C4*x*%e^-x+C3*%e^-x |
A*x*e^(-x)+e^(x)*B*cos(4*x)+C* e^(x)*sin(4*x)+D*e^(-x) |
[x] |
1 | ATSubstEquiv_Subst [C1 = C,C2 = B,C3 = D,C4 = A]. | ||

Your answer would be correct if you used the following substitution of variables. \[\left[ C_{1}=C , C_{2}=B , C_{3}=D , C_{4}=A \right] \] | |||||||

SubstEquiv | C1*%e^x*sin(4*x)+C2*%e^x*cos(4 *x)+C4*x*%e^-x+C3*%e^-x |
e^(x)*C1*cos(4*x)+C2*e^(x)*sin (4*x)+C3*e^(-x)+C4*x*e^(-x) |
[x] |
1 | ATSubstEquiv_Subst [C1 = C2,C2 = C1,C3 = C3,C4 = C4]. | ||

Your answer would be correct if you used the following substitution of variables. \[\left[ C_{1}=C_{2} , C_{2}=C_{1} , C_{3}=C_{3} , C_{4}=C_{4} \right] \] |