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
Opt
Mark
SubstEquiv
1/0
x^2-2*x+1
-1 ATSubstEquiv_STACKERROR_SAns.
TEST_FAILED
SubstEquiv
x^2
x^2-2*x+1
[1/0]
-1 ATSubstEquiv_STACKERROR_Opt.
TEST_FAILED
SubstEquiv
x^2
x^2-2*x+1
x
-1 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 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. $\left[ C_{1}=C_{2} , C_{2}=C_{1} , C_{3}=C_{3} , C_{4}=C_{4} \right]$