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.
What to expect: This mock test covers key concepts from the Matrices chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.
Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.
Sample questions
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1.Let $A = \begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix}$, $B = \begin{bmatrix} 2 & 3 \\ -1 & 0 \end{bmatrix}$. Find $A^2 + AB + B^2$. Which of the following matrices is the result?
- A.$\begin{bmatrix} 4 & 9 \\ 5 & 4 \end{bmatrix}$
- B.$\begin{bmatrix} 4 & 6 \\ 3 & 4 \end{bmatrix}$
- C.$\begin{bmatrix} 1 & 9 \\ 5 & 1 \end{bmatrix}$
- D.$\begin{bmatrix} 4 & 9 \\ -1 & 4 \end{bmatrix}$
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2.Given matrices $A = \begin{bmatrix} 1 & 3 \\ -2 & 0 \end{bmatrix}$, $B = \begin{bmatrix} 2 & 4 \\ 5 & 1 \end{bmatrix}$, and $C = \begin{bmatrix} -3 & 4 \\ 6 & 0 \end{bmatrix}$, which of the following verifies the associative property $(AB)C = A(BC)$?
- A.$$\begin{bmatrix} -9 & 68 \\ -36 & -16 \end{bmatrix}$$
- B.$$\begin{bmatrix} 9 & -68 \\ 36 & 16 \end{bmatrix}$$
- C.$$\begin{bmatrix} -9 & 50 \\ -20 & -16 \end{bmatrix}$$
- D.$$\begin{bmatrix} 0 & 68 \\ -36 & 0 \end{bmatrix}$$
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3.Find the matrix $ A $, if $ B = \begin{bmatrix} 2 & 1 \\ 0 & 1 \end{bmatrix} $ and $ B^2 = B + \frac{1}{2} A $.
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4.Evaluate the following matrix multiplication: $$\begin{bmatrix} \cos 45^\circ & \sin 30^\circ \\ \sqrt{2} \cos 0^\circ & \sin 0^\circ \end{bmatrix} \begin{bmatrix} \sin 45^\circ & \cos 90^\circ \\ \sin 90^\circ & \cot 45^\circ \end{bmatrix}$$
- A.$$\begin{bmatrix} 1 & \frac{1}{2} \\ 1 & 0 \end{bmatrix}$$
- B.$$\begin{bmatrix} \frac{1}{2} & 1 \\ 0 & 1 \end{bmatrix}$$
- C.$$\begin{bmatrix} 1 & 0 \\ \frac{1}{2} & 1 \end{bmatrix}$$
- D.$$\begin{bmatrix} 0 & 1 \\ 1 & \frac{1}{2} \end{bmatrix}$$
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5.Given matrices $A = \left[ \begin{array}{ll}2 & 3\\ 7 & 5 \end{array} \right]$ and $B = \left[ \begin{array}{cc}m - n & 6\\ 14 & m + n \end{array} \right]$, if $2A = B$, what are the values of $m$ and $n$?
- A.$m = 7$ and $n = 3$
- B.$m = 5$ and $n = 1$
- C.$m = 9$ and $n = 2$
- D.$m = 6$ and $n = 4$
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