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.Given matrices $A = \begin{bmatrix} 2 & -1 \\ 2 & 0 \end{bmatrix}$, $B = \begin{bmatrix} -3 & 2 \\ 4 & 0 \end{bmatrix}$ and $C = \begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$, find the matrix $X$ such that $A + X = 2B + C$.
2. 2.If $ \begin{bmatrix} 1 & 2 \\ 2 & 9 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 9 \end{bmatrix} $, then the values of $ x $ and $ y $ are:
   • A.$ x = 10, y = 0 $
   • B.$ x = 5, y = 4 $
   • C.$ x = 0, y = 1 $
   • D.$ x = 4, y = 5 $
3. 3.Determine which of the following confirms that $\mathbf{X} = \begin{bmatrix} 2  3 \\ 3  2 \end{bmatrix}$ is the solution of the matrix equation $\mathbf{X}^2 - 4\mathbf{X} - 5\mathbf{I} = 0$.
   • A.$\mathbf{X}^2 - 4\mathbf{X} - 5\mathbf{I} = \begin{bmatrix} 0  0 \\ 0  0 \end{bmatrix}$
   • B.$\mathbf{X}^2 - 4\mathbf{X} - 5\mathbf{I} = \begin{bmatrix} 5  0 \\ 0  5 \end{bmatrix}$
   • C.$\mathbf{X}^2 - 4\mathbf{X} - 5\mathbf{I} = \begin{bmatrix} 13  12 \\ 12  13 \end{bmatrix}$
   • D.$\mathbf{X}^2 - 4\mathbf{X} - 5\mathbf{I} = \begin{bmatrix} 0  12 \\ 12  0 \end{bmatrix}$
4. 4.If $ M = \begin{bmatrix} 4 & 1 \\ -1 & 2 \end{bmatrix} $, show that: $6M - M^2 = 9I$; where $I$ is a $2 \times 2$ unit matrix.
5. 5.If $ A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix} $ and $ I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $, then the value of $ A^2 - 5A + 7I $ is:
   • A.$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$
   • B.$\begin{bmatrix} 8 & 5 \\ -5 & 3 \end{bmatrix}$
   • C.$\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$
   • D.$\begin{bmatrix} 7 & 0 \\ 0 & 7 \end{bmatrix}$