O Level Elementary Mathematics Vectors Matrices Quiz

O-Level Elementary Mathematics Quiz - Vectors Matrices

Name: ________________________
Class: ________________________
Date: ________________________
Score: _______ / 40

Duration: 50 minutes
Total Marks: 40

Instructions:

• Answer all 20 questions.
• Show your working clearly where required.
• Section A: Vectors (1–10). Section B: Matrices (11–20).
• Use the answer space provided.

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Section A: Vectors (Questions 1–10)

1. Given $\mathbf{a} = \begin{pmatrix} 3 \\ -2 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 1 \\ 4 \end{pmatrix}$, write down the vector $\mathbf{a} + \mathbf{b}$. [2]

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2. A vector $\mathbf{v}$ has magnitude 5 units and is directed due east. Write $\mathbf{v}$ as a column vector using $\mathbf{i}$ as unit east and $\mathbf{j}$ as unit north. [1]

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3. Points $A(1,2)$ and $B(4,6)$ are given. Find the vector $\overrightarrow{AB}$ as a column vector. [2]

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4. Given $\mathbf{p} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}$, find $3\mathbf{p}$. [1]

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5. $\overrightarrow{PQ} = \begin{pmatrix} -3 \\ 2 \end{pmatrix}$ and $\overrightarrow{QR} = \begin{pmatrix} 4 \\ -1 \end{pmatrix}$. Find $\overrightarrow{PR}$. [2]

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6. In the diagram below, $OABC$ is a parallelogram with $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OC} = \mathbf{c}$. Express $\overrightarrow{OB}$ in terms of $\mathbf{a}$ and $\mathbf{c}$. [2]

Generated diagram for Q6.

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7. Given $\mathbf{u} = \begin{pmatrix} 6 \\ 8 \end{pmatrix}$, find the magnitude $|\mathbf{u}|$. [2]

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8. $\mathbf{m} = \begin{pmatrix} x \\ 3 \end{pmatrix}$ and $\mathbf{n} = \begin{pmatrix} 2 \\ -1 \end{pmatrix}$. If $\mathbf{m} + \mathbf{n} = \begin{pmatrix} 5 \\ 2 \end{pmatrix}$, find $x$. [2]

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9. A translation maps point $P(2, -1)$ to $P'(5, 3)$. Write the translation vector as a column vector. [2]

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10. Points $X(0,0)$, $Y(3,1)$, $Z(6,2)$ are collinear. State the vector $\overrightarrow{XY}$ and $\overrightarrow{YZ}$, and explain if they are parallel. [3]

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Section B: Matrices (Questions 11–20)

11. Write the following information as a $2 \times 3$ matrix:
Apples: 4 red, 2 green, 1 yellow; Oranges: 3 red, 0 green, 5 yellow. [2]

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

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13. Given $M = \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix}$, find $2M$. [1]

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14. A matrix $C = \begin{pmatrix} 5 & -2 \\ 4 & 1 \end{pmatrix}$. Find $-C$. [1]

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15. The table shows the number of books read by two students in three months:

Month	Ali	Bala
Jan	3	5
Feb	2	1
Mar	4	2

Write this as a $3 \times 2$ matrix. [2]

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16. Given $P = \begin{pmatrix} 1 & 3 \\ 2 & 0 \end{pmatrix}$ and $Q = \begin{pmatrix} 4 & 1 \\ 2 & 2 \end{pmatrix}$, find $P - Q$. [2]

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17. Given $X = \begin{pmatrix} 2 & 1 \end{pmatrix}$ and $Y = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$, find the product $XY$. [2]

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18. A shop sells pens at \2$and notebooks at$$5$. Matrix$S = \begin{pmatrix} 10 & 4 \end{pmatrix}$shows quantity sold (pens, notebooks) on Monday. Find the total sales using matrix multiplication with price matrix$P = \begin{pmatrix} 2 \ 5 \end{pmatrix}$. [3]

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19. Given $R = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ and $T = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$, find $RT$. [3]

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20. The matrix below shows the scores of 2 players in 2 games: $G = \begin{pmatrix} 7 & 5 \\ 3 & 8 \end{pmatrix}$ If each score is doubled next week, write the new matrix. [2]

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