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O Level Elementary Mathematics Vectors Matrices Quiz

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O Level Elementary Mathematics AI Generated Generated by Gemma 4 31B Updated 2026-06-03
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Questions

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O-Level Elementary Mathematics Quiz - Vectors Matrices

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

Duration: 60 Minutes
Total Marks: 45

Instructions:

  1. Answer all questions in the spaces provided.
  2. Show all essential working. Marks may be awarded for correct method even if the final answer is incorrect.
  3. Use a calculator where necessary.
  4. Give non-exact numerical answers to 3 significant figures.

Section A: Matrices (Questions 1–10)

  1. Given matrix A=(3−125)A = \begin{pmatrix} 3 & -1 \\ 2 & 5 \end{pmatrix} and matrix B=(04−32)B = \begin{pmatrix} 0 & 4 \\ -3 & 2 \end{pmatrix}, find A+BA + B.
    [2 marks]


    Answer: ____________________

  2. If M=(47−21)M = \begin{pmatrix} 4 & 7 \\ -2 & 1 \end{pmatrix}, find 3M3M.
    [2 marks]


    Answer: ____________________

  3. Given P=(2314)P = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} and Q=(5−102)Q = \begin{pmatrix} 5 & -1 \\ 0 & 2 \end{pmatrix}, calculate P−QP - Q.
    [2 marks]


    Answer: ____________________

  4. A matrix R=(x83y)R = \begin{pmatrix} x & 8 \\ 3 & y \end{pmatrix} is equal to (583−2)\begin{pmatrix} 5 & 8 \\ 3 & -2 \end{pmatrix}. State the values of xx and yy.
    [2 marks]


    Answer: x=x = ______, y=y = ______

  5. Find the product of (21)(34)\begin{pmatrix} 2 & 1 \end{pmatrix} \begin{pmatrix} 3 \\ 4 \end{pmatrix}.
    [2 marks]


    Answer: ____________________

  6. Calculate (1234)(56)\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} 5 \\ 6 \end{pmatrix}.
    [2 marks]


    Answer: ____________________

  7. Given C=(2013)C = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}, find C2C^2 (where C2=C×CC^2 = C \times C).
    [3 marks]


    Answer: ____________________

  8. Matrix D=(a24b)D = \begin{pmatrix} a & 2 \\ 4 & b \end{pmatrix}. If 2D=(648−10)2D = \begin{pmatrix} 6 & 4 \\ 8 & -10 \end{pmatrix}, find the values of aa and bb.
    [2 marks]


    Answer: a=a = ______, b=b = ______

  9. The prices of two items, A and B, are given by matrix P=(5.003.50)P = \begin{pmatrix} 5.00 & 3.50 \end{pmatrix}. The quantities bought by two customers are given by matrix Q=(2413)Q = \begin{pmatrix} 2 & 4 \\ 1 & 3 \end{pmatrix}. Find the matrix PQPQ representing the total cost for each customer.
    [3 marks]


    Answer: ____________________

  10. If (2301)(xy)=(134)\begin{pmatrix} 2 & 3 \\ 0 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 13 \\ 4 \end{pmatrix}, solve for xx and yy.
    [3 marks]


    Answer: x=x = ______, y=y = ______

Section B: Vectors (Questions 11–20)

  1. Given a⃗=(4−3)\vec{a} = \begin{pmatrix} 4 \\ -3 \end{pmatrix} and b⃗=(25)\vec{b} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}, find 2a⃗+b⃗2\vec{a} + \vec{b}.
    [2 marks]


    Answer: ____________________

  2. Find the magnitude of the vector v⃗=(68)\vec{v} = \begin{pmatrix} 6 \\ 8 \end{pmatrix}.
    [2 marks]


    Answer: ____________________

  3. Given OA⃗=(37)\vec{OA} = \begin{pmatrix} 3 \\ 7 \end{pmatrix} and OB⃗=(−14)\vec{OB} = \begin{pmatrix} -1 \\ 4 \end{pmatrix}, find the vector AB⃗\vec{AB}.
    [2 marks]


    Answer: ____________________

  4. Vector p⃗=(x12)\vec{p} = \begin{pmatrix} x \\ 12 \end{pmatrix} is parallel to vector q⃗=(34)\vec{q} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}. Find the value of xx.
    [2 marks]


    Answer: ____________________

  5. Find the unit vector in the direction of w⃗=(34)\vec{w} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}.
    [3 marks]


    Answer: ____________________

  6. Given u⃗=3i−2j\vec{u} = 3\mathbf{i} - 2\mathbf{j} and v⃗=i+4j\vec{v} = \mathbf{i} + 4\mathbf{j}, express u⃗−2v⃗\vec{u} - 2\vec{v} in terms of i\mathbf{i} and j\mathbf{j}.
    [2 marks]


    Answer: ____________________

  7. A point P(2,3)P(2, 3) is translated by the vector (−41)\begin{pmatrix} -4 \\ 1 \end{pmatrix} to point P′P'. Find the coordinates of P′P'.
    [2 marks]


    Answer: ____________________

  8. In △ABC\triangle ABC, AB⃗=(23)\vec{AB} = \begin{pmatrix} 2 \\ 3 \end{pmatrix} and BC⃗=(4−1)\vec{BC} = \begin{pmatrix} 4 \\ -1 \end{pmatrix}. Find the vector AC⃗\vec{AC}.
    [2 marks]


    Answer: ____________________

  9. Given OA⃗=(52)\vec{OA} = \begin{pmatrix} 5 \\ 2 \end{pmatrix} and OB⃗=(16)\vec{OB} = \begin{pmatrix} 1 \\ 6 \end{pmatrix}, find the magnitude of AB⃗\vec{AB}.
    [3 marks]


    Answer: ____________________

  10. Point MM divides the line segment ABAB in the ratio 1:21:2. Given OA⃗=(24)\vec{OA} = \begin{pmatrix} 2 \\ 4 \end{pmatrix} and OB⃗=(810)\vec{OB} = \begin{pmatrix} 8 \\ 10 \end{pmatrix}, find the position vector OM⃗\vec{OM}.
    [4 marks]


    Answer: ____________________

Answers

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

Section A: Matrices

  1. (3+0−1+42−35+2)=(33−17)\begin{pmatrix} 3+0 & -1+4 \\ 2-3 & 5+2 \end{pmatrix} = \begin{pmatrix} 3 & 3 \\ -1 & 7 \end{pmatrix} [2 marks]
  2. (1221−63)\begin{pmatrix} 12 & 21 \\ -6 & 3 \end{pmatrix} [2 marks]
  3. (2−53−(−1)1−04−2)=(−3412)\begin{pmatrix} 2-5 & 3-(-1) \\ 1-0 & 4-2 \end{pmatrix} = \begin{pmatrix} -3 & 4 \\ 1 & 2 \end{pmatrix} [2 marks]
  4. x=5,y=−2x = 5, y = -2 [2 marks]
  5. (2×3)+(1×4)=6+4=10(2 \times 3) + (1 \times 4) = 6 + 4 = 10 [2 marks]
  6. ((1×5)+(2×6)(3×5)+(4×6))=(1739)\begin{pmatrix} (1 \times 5) + (2 \times 6) \\ (3 \times 5) + (4 \times 6) \end{pmatrix} = \begin{pmatrix} 17 \\ 39 \end{pmatrix} [2 marks]
  7. (2013)(2013)=((4+0)(0+0)(2+3)(0+9))=(4059)\begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix} \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix} = \begin{pmatrix} (4+0) & (0+0) \\ (2+3) & (0+9) \end{pmatrix} = \begin{pmatrix} 4 & 0 \\ 5 & 9 \end{pmatrix} [3 marks]
  8. 2a=6→a=32a = 6 \rightarrow a = 3; 2b=−10→b=−52b = -10 \rightarrow b = -5 [2 marks]
  9. (5.003.50)(2413)=((10+3.5)(20+10.5))=(13.5030.50)\begin{pmatrix} 5.00 & 3.50 \end{pmatrix} \begin{pmatrix} 2 & 4 \\ 1 & 3 \end{pmatrix} = \begin{pmatrix} (10+3.5) & (20+10.5) \end{pmatrix} = \begin{pmatrix} 13.50 & 30.50 \end{pmatrix} [3 marks]
  10. y=4y = 4 (from 2nd row 0x+1y=40x + 1y = 4). Substitute into 1st row: 2x+3(4)=13→2x=1→x=0.52x + 3(4) = 13 \rightarrow 2x = 1 \rightarrow x = 0.5 [3 marks]

Section B: Vectors

  1. 2(4−3)+(25)=(8−6)+(25)=(10−1)2\begin{pmatrix} 4 \\ -3 \end{pmatrix} + \begin{pmatrix} 2 \\ 5 \end{pmatrix} = \begin{pmatrix} 8 \\ -6 \end{pmatrix} + \begin{pmatrix} 2 \\ 5 \end{pmatrix} = \begin{pmatrix} 10 \\ -1 \end{pmatrix} [2 marks]
  2. 62+82=36+64=100=10\sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 [2 marks]
  3. AB⃗=OB⃗−OA⃗=(−14)−(37)=(−4−3)\vec{AB} = \vec{OB} - \vec{OA} = \begin{pmatrix} -1 \\ 4 \end{pmatrix} - \begin{pmatrix} 3 \\ 7 \end{pmatrix} = \begin{pmatrix} -4 \\ -3 \end{pmatrix} [2 marks]
  4. x3=124→x3=3→x=9\frac{x}{3} = \frac{12}{4} \rightarrow \frac{x}{3} = 3 \rightarrow x = 9 [2 marks]
  5. Magnitude =32+42=5= \sqrt{3^2 + 4^2} = 5. Unit vector =15(34)=(0.60.8)= \frac{1}{5} \begin{pmatrix} 3 \\ 4 \end{pmatrix} = \begin{pmatrix} 0.6 \\ 0.8 \end{pmatrix} [3 marks]
  6. (3i−2j)−2(i+4j)=3i−2j−2i−8j=i−10j(3\mathbf{i} - 2\mathbf{j}) - 2(\mathbf{i} + 4\mathbf{j}) = 3\mathbf{i} - 2\mathbf{j} - 2\mathbf{i} - 8\mathbf{j} = \mathbf{i} - 10\mathbf{j} [2 marks]
  7. (23)+(−41)=(−24)→P′(−2,4)\begin{pmatrix} 2 \\ 3 \end{pmatrix} + \begin{pmatrix} -4 \\ 1 \end{pmatrix} = \begin{pmatrix} -2 \\ 4 \end{pmatrix} \rightarrow P'(-2, 4) [2 marks]
  8. AC⃗=AB⃗+BC⃗=(23)+(4−1)=(62)\vec{AC} = \vec{AB} + \vec{BC} = \begin{pmatrix} 2 \\ 3 \end{pmatrix} + \begin{pmatrix} 4 \\ -1 \end{pmatrix} = \begin{pmatrix} 6 \\ 2 \end{pmatrix} [2 marks]
  9. AB⃗=(1−56−2)=(−44)\vec{AB} = \begin{pmatrix} 1-5 \\ 6-2 \end{pmatrix} = \begin{pmatrix} -4 \\ 4 \end{pmatrix}. ∣AB⃗∣=(−4)2+42=32≈5.66|\vec{AB}| = \sqrt{(-4)^2 + 4^2} = \sqrt{32} \approx 5.66 [3 marks]
  10. OM⃗=2OA⃗+1OB⃗1+2=13[2(24)+(810)]=13(1218)=(46)\vec{OM} = \frac{2\vec{OA} + 1\vec{OB}}{1+2} = \frac{1}{3} \left[ 2\begin{pmatrix} 2 \\ 4 \end{pmatrix} + \begin{pmatrix} 8 \\ 10 \end{pmatrix} \right] = \frac{1}{3} \begin{pmatrix} 12 \\ 18 \end{pmatrix} = \begin{pmatrix} 4 \\ 6 \end{pmatrix} [4 marks]