O Level Elementary Mathematics Vectors Matrices Quiz

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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]

Image pending generation: 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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O-Level Elementary Mathematics Quiz - Vectors Matrices (Answer Key)

Total Marks: 40
Topic: Vectors and Matrices (Syllabus 4052 N9, Vectors as applied in O-Level EMath)

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Section A: Vectors

Q1. [2 marks]
$\mathbf{a} + \mathbf{b} = \begin{pmatrix} 3 \\ -2 \end{pmatrix} + \begin{pmatrix} 1 \\ 4 \end{pmatrix} = \begin{pmatrix} 3+1 \\ -2+4 \end{pmatrix} = \begin{pmatrix} 4 \\ 2 \end{pmatrix}$
Teaching note: Add corresponding components. Mark: 1 for each correct component.

Q2. [1 mark]
$\mathbf{v} = \begin{pmatrix} 5 \\ 0 \end{pmatrix}$ (or $5\mathbf{i}$)
Teaching note: Due east means positive x-direction, no north component.

Q3. [2 marks]
$\overrightarrow{AB} = \begin{pmatrix} 4-1 \\ 6-2 \end{pmatrix} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$
Teaching note: Subtract coordinates of start from end: $(x_B-x_A, y_B-y_A)$.

Q4. [1 mark]
$3\mathbf{p} = 3 \begin{pmatrix} 2 \\ 5 \end{pmatrix} = \begin{pmatrix} 6 \\ 15 \end{pmatrix}$

Q5. [2 marks]
$\overrightarrow{PR} = \overrightarrow{PQ} + \overrightarrow{QR} = \begin{pmatrix} -3 \\ 2 \end{pmatrix} + \begin{pmatrix} 4 \\ -1 \end{pmatrix} = \begin{pmatrix} 1 \\ 1 \end{pmatrix}$

Q6. [2 marks]
$\overrightarrow{OB} = \mathbf{a} + \mathbf{c}$
Teaching note: In a parallelogram, diagonal from O = OA + OC. Image must show OABC with a and c as adjacent sides.

Q7. [2 marks]
$|\mathbf{u}| = \sqrt{6^2 + 8^2} = \sqrt{36+64} = \sqrt{100} = 10$
Teaching note: Magnitude = sqrt(x²+y²).

Q8. [2 marks]
$\begin{pmatrix} x+2 \\ 3+(-1) \end{pmatrix} = \begin{pmatrix} 5 \\ 2 \end{pmatrix} \Rightarrow x+2=5 \Rightarrow x=3$

Q9. [2 marks]
Translation = $\begin{pmatrix} 5-2 \\ 3-(-1) \end{pmatrix} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$

Q10. [3 marks]
$\overrightarrow{XY} = \begin{pmatrix} 3 \\ 1 \end{pmatrix}$, $\overrightarrow{YZ} = \begin{pmatrix} 3 \\ 1 \end{pmatrix}$. They are equal so parallel (and same direction). [1+1+1]

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Section B: Matrices

Q11. [2 marks]
$\begin{pmatrix} 4 & 2 & 1 \\ 3 & 0 & 5 \end{pmatrix}$ (rows: apples, oranges; cols: red, green, yellow)

Q12. [2 marks]
$A+B = \begin{pmatrix} 1+2 & 2+0 \\ 3+1 & 4+5 \end{pmatrix} = \begin{pmatrix} 3 & 2 \\ 4 & 9 \end{pmatrix}$

Q13. [1 mark]
$2M = \begin{pmatrix} 4 & 2 \\ 0 & 6 \end{pmatrix}$

Q14. [1 mark]
$-C = \begin{pmatrix} -5 & 2 \\ -4 & -1 \end{pmatrix}$

Q15. [2 marks]
$\begin{pmatrix} 3 & 5 \\ 2 & 1 \\ 4 & 2 \end{pmatrix}$ (rows: Jan, Feb, Mar; cols: Ali, Bala)

Q16. [2 marks]
$P-Q = \begin{pmatrix} 1-4 & 3-1 \\ 2-2 & 0-2 \end{pmatrix} = \begin{pmatrix} -3 & 2 \\ 0 & -2 \end{pmatrix}$

Q17. [2 marks]
$XY = \begin{pmatrix} 2 & 1 \end{pmatrix} \begin{pmatrix} 3 \\ 4 \end{pmatrix} = (2\times3 + 1\times4) = (10)$
Teaching note: 1x2 times 2x1 gives 1x1 scalar-like matrix.

Q18. [3 marks]
Sales = $S P = \begin{pmatrix} 10 & 4 \end{pmatrix} \begin{pmatrix} 2 \\ 5 \end{pmatrix} = 10\times2 + 4\times5 = 20+20 = 40$
Total = \40$. [1 for setup, 2 for calc]

Q19. [3 marks]
$RT = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} = \begin{pmatrix} 1\times0+2\times1 & 1\times1+2\times0 \\ 3\times0+4\times1 & 3\times1+4\times0 \end{pmatrix} = \begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}$

Q20. [2 marks]
$2G = \begin{pmatrix} 14 & 10 \\ 6 & 16 \end{pmatrix}$