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O Level Elementary Mathematics Vectors Matrices Quiz

Free O Level E Maths Vectors Matrices quiz, Gemma31B Exam version, with questions, answers, and O Level-style practice for Singapore students.

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O Level Elementary Mathematics From Real Exams Generated by Gemma 4 31B Updated 2026-09-16

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Questions

O-Level Elementary Mathematics Quiz - Vectors Matrices

Name: ____________________
Class: ____________________
Date: ____________________
Score: ________ / 45

Duration: 60 Minutes
Total Marks: 45 Marks

Instructions:

Answer all questions.
Use a calculator where necessary.
Give your answers to 3 significant figures unless otherwise specified.
Show all necessary working.

Section A: Matrices (Questions 1–10)

Given matrix $A = \begin{pmatrix} 3 & -1 \\ 4 & 2 \end{pmatrix}$ and matrix $B = \begin{pmatrix} 0 & 5 \\ -2 & 1 \end{pmatrix}$ , find $A + B$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [2]
If $M = \begin{pmatrix} 2 & 7 \\ -3 & 0 \end{pmatrix}$ , find $3M$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [2]
Given $P = \begin{pmatrix} 1 & 4 \\ 2 & 3 \end{pmatrix}$ and $Q = \begin{pmatrix} 5 & -2 \\ 1 & 6 \end{pmatrix}$ , calculate $P - Q$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [2]
Find the value of $x$ and $y$ if $\begin{pmatrix} x & 4 \\ -1 & 2y \end{pmatrix} = \begin{pmatrix} 7 & 4 \\ -1 & 12 \end{pmatrix}$ .

$x = \underline{\hspace{2cm}}, y = \underline{\hspace{2cm}}$ [2]
Matrix $R = \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix}$ . Find $R^2$ (where $R^2 = R \times R$ ).

$\text{Answer: } \underline{\hspace{4cm}}$ [3]
Given $S = \begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix}$ and $T = \begin{pmatrix} 1 & 0 \\ 2 & 1 \end{pmatrix}$ , find $S \times T$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [3]
A matrix $K = \begin{pmatrix} a & 2 \\ 3 & b \end{pmatrix}$ is such that $2K = \begin{pmatrix} 8 & 4 \\ 6 & 10 \end{pmatrix}$ . Find the values of $a$ and $b$ .

$a = \underline{\hspace{2cm}}, b = \underline{\hspace{2cm}}$ [2]
Express the following information as a matrix: Store A sells 5 apples and 3 oranges. Store B sells 8 apples and 2 oranges.

$\text{Answer: } \underline{\hspace{4cm}}$ [2]
Given $A = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 0 & 2 \\ 1 & -1 \end{pmatrix}$ , find $2A - B$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [3]
If $\begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 13 \\ 11 \end{pmatrix}$ , find the values of $x$ and $y$ .

$x = \underline{\hspace{2cm}}, y = \underline{\hspace{2cm}}$ [3]

Section B: Vectors (Questions 11–20)

Given $\mathbf{a} = \begin{pmatrix} 3 \\ -4 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 2 \\ 1 \end{pmatrix}$ , find $2\mathbf{a} + \mathbf{b}$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [2]
Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} 6 \\ 8 \end{pmatrix}$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [2]
Given $\vec{AB} = \begin{pmatrix} 4 \\ 7 \end{pmatrix}$ and $\vec{BC} = \begin{pmatrix} -2 \\ 3 \end{pmatrix}$ , find $\vec{AC}$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [2]
If $\mathbf{p} = \begin{pmatrix} -1 \\ 5 \end{pmatrix}$ , find the vector $-\mathbf{p}$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [1]
Point $A$ is $(2, 3)$ and Point $B$ is $(5, 7)$ . Find the position vector $\vec{AB}$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [2]
Given $\mathbf{u} = \begin{pmatrix} 2 \\ k \end{pmatrix}$ and $\mathbf{v} = \begin{pmatrix} 3 \\ 6 \end{pmatrix}$ . If $\mathbf{u}$ is parallel to $\mathbf{v}$ , find the value of $k$ .

$k = \underline{\hspace{2cm}}$ [2]
In a triangle $OPQ$ , $\vec{OP} = \mathbf{p}$ and $\vec{OQ} = \mathbf{q}$ . Express $\vec{PQ}$ in terms of $\mathbf{p}$ and $\mathbf{q}$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [2]
Find the unit vector in the direction of $\mathbf{w} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [3]
Given $\vec{XY} = \begin{pmatrix} 2 \\ 3 \end{pmatrix}$ and $\vec{YZ} = \begin{pmatrix} 4 \\ -1 \end{pmatrix}$ . Find the magnitude of $\vec{XZ}$ .

$\text{Answer: } \underline{\hspace{4cm}}$ [3]
A quadrilateral $ABCD$ has $\vec{AB} = \begin{pmatrix} 2 \\ 3 \end{pmatrix}$ and $\vec{DC} = \begin{pmatrix} 2 \\ 3 \end{pmatrix}$ . What type of quadrilateral is $ABCD$ ? Explain your answer.

$\text{Answer: } \underline{\hspace{4cm}}$ [3]

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Answers

Answer Key - O-Level Elementary Mathematics Quiz (Vectors Matrices)

Section A: Matrices

$\begin{pmatrix} 3+0 & -1+5 \\ 4-2 & 2+1 \end{pmatrix} = \begin{pmatrix} 3 & 4 \\ 2 & 3 \end{pmatrix}$ [2]
$\begin{pmatrix} 2(2) & 7(3) \\ -3(3) & 0(3) \end{pmatrix} = \begin{pmatrix} 6 & 21 \\ -9 & 0 \end{pmatrix}$ [2]
$\begin{pmatrix} 1-5 & 4-(-2) \\ 2-1 & 3-6 \end{pmatrix} = \begin{pmatrix} -4 & 6 \\ 1 & -3 \end{pmatrix}$ [2]
$x = 7, 2y = 12 \implies y = 6$ [2]
$\begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix} \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix} = \begin{pmatrix} (4+0) & (2+3) \\ (0+0) & (0+9) \end{pmatrix} = \begin{pmatrix} 4 & 5 \\ 0 & 9 \end{pmatrix}$ [3]
$\begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix} \begin{pmatrix} 1 & 0 \\ 2 & 1 \end{pmatrix} = \begin{pmatrix} (4+4) & (0+2) \\ (1+6) & (0+3) \end{pmatrix} = \begin{pmatrix} 8 & 2 \\ 7 & 3 \end{pmatrix}$ [3]
$2a = 8 \implies a = 4; 2b = 10 \implies b = 5$ [2]
$\begin{pmatrix} 5 & 3 \\ 8 & 2 \end{pmatrix}$ (Accept transposed version if labeled) [2]
$\begin{pmatrix} 4 & 2 \\ 6 & 8 \end{pmatrix} - \begin{pmatrix} 0 & 2 \\ 1 & -1 \end{pmatrix} = \begin{pmatrix} 4 & 0 \\ 5 & 9 \end{pmatrix}$ [3]
$2x + 3y = 13$ and $x + 4y = 11$ . From eq 2, $x = 11 - 4y$ . Sub into eq 1: $2(11-4y) + 3y = 13 \implies 22 - 8y + 3y = 13 \implies -5y = -9 \implies y = 1.8$ . $x = 11 - 4(1.8) = 3.8$ . [3]

Section B: Vectors

$\begin{pmatrix} 6 \\ -8 \end{pmatrix} + \begin{pmatrix} 2 \\ 1 \end{pmatrix} = \begin{pmatrix} 8 \\ -7 \end{pmatrix}$ [2]
$\sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$ [2]
$\vec{AC} = \vec{AB} + \vec{BC} = \begin{pmatrix} 4 \\ 7 \end{pmatrix} + \begin{pmatrix} -2 \\ 3 \end{pmatrix} = \begin{pmatrix} 2 \\ 10 \end{pmatrix}$ [2]
$\begin{pmatrix} 1 \\ -5 \end{pmatrix}$ [1]
$\vec{AB} = \begin{pmatrix} 5-2 \\ 7-3 \end{pmatrix} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$ [2]
$\frac{2}{3} = \frac{k}{6} \implies 3k = 12 \implies k = 4$ [2]
$\vec{PQ} = \vec{PO} + \vec{OQ} = -\mathbf{p} + \mathbf{q}$ or $\mathbf{q} - \mathbf{p}$ [2]
Magnitude $= 5$ . Unit vector $= \frac{1}{5} \begin{pmatrix} 3 \\ 4 \end{pmatrix} = \begin{pmatrix} 0.6 \\ 0.8 \end{pmatrix}$ [3]
$\vec{XZ} = \begin{pmatrix} 2+4 \\ 3-1 \end{pmatrix} = \begin{pmatrix} 6 \\ 2 \end{pmatrix}$ . Magnitude $= \sqrt{6^2 + 2^2} = \sqrt{40} \approx 6.32$ [3]
Parallelogram. Because $\vec{AB} = \vec{DC}$ , the opposite sides are equal in length and parallel. [3]