Secondary 4 Elementary Mathematics Vectors Matrices Quiz

Secondary 4 Elementary Mathematics Quiz - Vectors Matrices

Name: ___________________________
Class: ____________
Date: ____________
Score: ____________

Duration: 60 minutes
Total Marks: 40

Instructions:

• Answer all 20 questions.
• Show your working clearly where required.
• Use the spaces provided to write your answers.
• Calculators may be used.

---

Section A: Matrices – Display, Interpretation, and Scalar Multiplication (Questions 1–7)

1. [2 marks]
The table below shows the number of books sold by a shop on Monday and Tuesday.

	Fiction	Non-Fiction
Monday	12	8
Tuesday	15	10

Write this information as a $2 \times 2$ matrix $M$, with rows for Monday and Tuesday.

Answer:
$M = \begin{pmatrix} \quad & \quad \\ \quad & \quad \end{pmatrix}$

2. [1 mark]
Given the matrix $A = \begin{pmatrix} 3 & 5 \\ 2 & 7 \end{pmatrix}$, what does the element in the second row and first column represent if $A$ shows test scores of 2 students in English and Maths?

Answer: ________________________________________

3. [2 marks]
A matrix $B = \begin{pmatrix} 4 & 6 \\ 1 & 3 \end{pmatrix}$ shows the cost ($) of two items at two stalls. Find$2B$.

Answer:
$2B = \begin{pmatrix} \quad & \quad \\ \quad & \quad \end{pmatrix}$

4. [2 marks]
The matrix $C = \begin{pmatrix} -2 & 0 \\ 5 & -3 \end{pmatrix}$. Calculate $-3C$.

Answer:
$-3C = \begin{pmatrix} \quad & \quad \\ \quad & \quad \end{pmatrix}$

5. [1 mark]
A class has a matrix $D = \begin{pmatrix} 9 & 4 & 7 \end{pmatrix}$ showing the number of red, blue, and green files. How many columns does $D$ have?

Answer: ____________

6. [2 marks]
The weekly savings (in $) of three students are shown by$S = \begin{pmatrix} 10 & 15 & 20 \end{pmatrix}$. If each student saves triple the amount next week, write the new matrix.

Answer: ________________________________________

7. [2 marks]
Matrix $P = \begin{pmatrix} 2 & 1 \\ 0 & 4 \end{pmatrix}$ shows points earned by two players in two rounds. State the value of the element $p_{12}$ and explain what it means.

Answer: ________________________________________

---

Section B: Matrix Addition, Subtraction, and Multiplication (Questions 8–14)

8. [2 marks]
$A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$, $B = \begin{pmatrix} 5 & 0 \\ 1 & 2 \end{pmatrix}$. Find $A + B$.

Answer:
$A + B = \begin{pmatrix} \quad & \quad \\ \quad & \quad \end{pmatrix}$

9. [2 marks]
Using the same $A$ and $B$ above, find $B - A$.

Answer:
$B - A = \begin{pmatrix} \quad & \quad \\ \quad & \quad \end{pmatrix}$

10. [3 marks]
$X = \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix}$, $Y = \begin{pmatrix} 4 & 2 \\ 1 & 5 \end{pmatrix}$. Calculate $XY$.

Answer:
$XY = \begin{pmatrix} \quad & \quad \\ \quad & \quad \end{pmatrix}$

11. [2 marks]
$A = \begin{pmatrix} 3 & 2 \end{pmatrix}$, $B = \begin{pmatrix} 1 \\ 4 \end{pmatrix}$. Find $AB$.

Answer:
$AB = \begin{pmatrix} \quad \end{pmatrix}$

12. [2 marks]
With the same $A$ and $B$ from Q11, explain why $BA$ cannot be found, or if it can, state its order.

Answer: ________________________________________

13. [3 marks]
$M = \begin{pmatrix} 1 & 0 & 2 \\ 3 & 1 & 1 \end{pmatrix}$, $N = \begin{pmatrix} 2 & 1 \\ 0 & 3 \\ 1 & 2 \end{pmatrix}$. Find $MN$.

Answer:
$MN = \begin{pmatrix} \quad & \quad \\ \quad & \quad \end{pmatrix}$

14. [2 marks]
Two classes recorded the number of students who brought umbrellas on two days: Class 4A: $\begin{pmatrix} 10 & 12 \end{pmatrix}$, Class 4B: $\begin{pmatrix} 8 & 9 \end{pmatrix}$. Find the total as a single matrix.

Answer: ________________________________________

---

Section C: Vectors – Basics, Operations, and Geometry (Questions 15–20)

15. [1 mark]
Write the vector $\vec{AB}$ as a column vector if $A$ is at $(1,2)$ and $B$ is at $(4,6)$.

Answer: $\begin{pmatrix} \quad \\ \quad \end{pmatrix}$

16. [2 marks]
Given $\vec{u} = \begin{pmatrix} 3 \\ -2 \end{pmatrix}$ and $\vec{v} = \begin{pmatrix} 1 \\ 4 \end{pmatrix}$, find $\vec{u} + \vec{v}$.

Answer: $\begin{pmatrix} \quad \\ \quad \end{pmatrix}$

17. [2 marks]
Given $\vec{p} = \begin{pmatrix} 5 \\ 1 \end{pmatrix}$, find $3\vec{p}$.

Answer: $\begin{pmatrix} \quad \\ \quad \end{pmatrix}$

18. [2 marks]
$\vec{a} = \begin{pmatrix} 2 \\ 3 \end{pmatrix}$, $\vec{b} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}$. Find $2\vec{a} - \vec{b}$.

Answer: $\begin{pmatrix} \quad \\ \quad \end{pmatrix}$

19. [3 marks]
In the diagram below, $O$ is the origin, $\vec{OA} = \begin{pmatrix} 2 \\ 1 \end{pmatrix}$ and $\vec{OB} = \begin{pmatrix} 4 \\ 3 \end{pmatrix}$. Find $\vec{AB}$ and the magnitude $|\vec{AB}|$.

Generated diagram for Q19.

Answer:
$\vec{AB} = \begin{pmatrix} \quad \\ \quad \end{pmatrix}$, $|\vec{AB}| =$ ____________

20. [3 marks]
$\vec{m} = \begin{pmatrix} 3 \\ 2 \end{pmatrix}$, $\vec{n} = \begin{pmatrix} -1 \\ 4 \end{pmatrix}$. Given that $\vec{r} = 2\vec{m} + \vec{n}$, find $\vec{r}$ and the unit vector in the direction of $\vec{r}$.

Answer:
$\vec{r} = \begin{pmatrix} \quad \\ \quad \end{pmatrix}$, unit vector = $\begin{pmatrix} \quad \\ \quad \end{pmatrix}$