ICSE Class 10 Matrices — Mock Test (2027)

Free online mock test for Matrices (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.

Sample questions

1. 1.If $A = \begin{bmatrix} 4 & -4 \\ -3 & 3 \end{bmatrix}$, $B = \begin{bmatrix} 6 & 5 \\ 3 & 0 \end{bmatrix}$, and $C = \begin{bmatrix} 2 & 3 \\ -1 & -2 \end{bmatrix}$, it is found that $AB = AC$. Which of the following conclusions can be drawn from this result?
   • A.Matrix multiplication follows the cancellation law, so $B = C$.
   • B.The cancellation law does not apply to matrix multiplication, so $B$ and $C$ may differ.
   • C.Matrix $A$ must be singular because $AB = AC$ but $B \neq C$.
   • D.The result $AB = AC$ implies that $B$ and $C$ are inverses of each other.
2. 2.Find $x$ and $y$, if $\begin{bmatrix} -3 & 2 \\ 0 & -5 \end{bmatrix} \begin{bmatrix} x \\ 2 \end{bmatrix} = \begin{bmatrix} -5 \\ y \end{bmatrix}$.
3. 3.Find the matrix $ A $ if $ A + B = \begin{bmatrix} 5 & 4 \\ 7 & 3 \end{bmatrix} $ and $ A - B = \begin{bmatrix} 11 & 2 \\ -1 & 7 \end{bmatrix} $. What is the value of $ A $?
   • A.$ \begin{bmatrix} 8 & 3 \\ 3 & 5 \end{bmatrix} $
   • B.$ \begin{bmatrix} 3 & 8 \\ 5 & 3 \end{bmatrix} $
   • C.$ \begin{bmatrix} 16 & 6 \\ 6 & 10 \end{bmatrix} $
   • D.$ \begin{bmatrix} 4 & 6 \\ 8 & -4 \end{bmatrix} $
4. 4.Find the matrix $M$, such that $M \times \begin{bmatrix} 3 & 6 \\ -2 & -8 \end{bmatrix} = [-2 \quad 16]$. What is the matrix $M$?
   • A.[-4 -5]
   • B.[4 5]
   • C.[-4 5]
   • D.[2 -4]
5. 5.Given matrix $B = \begin{bmatrix} 1 & 1 \\ 8 & 3 \end{bmatrix}$, find the matrix $X$ if $X = B^2 - 4B$. Using $X$, determine which values of $a$ and $b$ satisfy $$X \begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} 5 \\ 50 \end{bmatrix}$$
   • A.$a = 1, b = 10$
   • B.$a = 10, b = 1$
   • C.$a = 5, b = 5$
   • D.$a = 2, b = 8$