Secondary 4 Elementary Mathematics Vectors Matrices Quiz

Secondary 4 Elementary Mathematics Quiz - Vectors Matrices

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

Duration: 60 Minutes
Total Marks: 45

Instructions:

• Answer all questions.
• Show all necessary working.
• Use a calculator where necessary.
• Give your answers in the spaces provided.

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Section A: Matrices (Questions 1–10)

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

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2. If $M = \begin{pmatrix} 4 & 7 \\ -2 & 0 \end{pmatrix}$, calculate $3M$. [2]

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3. Given $P = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}$ and $Q = \begin{pmatrix} 5 & 0 \\ -1 & 2 \end{pmatrix}$, find $P - Q$. [2]

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4. Find the product of $\begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix}$ and $\begin{pmatrix} 5 \\ 2 \end{pmatrix}$. [2]

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5. Given $R = \begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}$ and $S = \begin{pmatrix} 4 & 1 \\ 2 & 1 \end{pmatrix}$, calculate $RS$. [3]

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6. Given $R = \begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}$ and $S = \begin{pmatrix} 4 & 1 \\ 2 & 1 \end{pmatrix}$, calculate $SR$. [3]

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7. State whether $RS = SR$ for the matrices in questions 5 and 6. Justify your answer. [1]

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8. A matrix $T = \begin{pmatrix} x & 4 \\ 2 & 3 \end{pmatrix}$ is equal to $\begin{pmatrix} 7 & 4 \\ 2 & 3 \end{pmatrix}$. Find the value of $x$. [1]

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9. Given $A = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}$, find a matrix $B$ such that $A + B = \begin{pmatrix} 5 & 2 \\ 4 & 8 \end{pmatrix}$. [2]

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10. A shop sells two types of fruit, Apples and Oranges. The quantities sold on Monday and Tuesday are represented by matrix $Q = \begin{pmatrix} 15 & 20 \\ 10 & 25 \end{pmatrix}$ (rows are days, columns are fruits). The prices per unit are $\begin{pmatrix} 1.20 \\ 0.80 \end{pmatrix}$. Find the total revenue for Monday. [3]

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Section B: Vectors (Questions 11–20)

11. Given $\mathbf{a} = \begin{pmatrix} 3 \\ -4 \end{pmatrix}$, find the magnitude $|\mathbf{a}|$. [2]

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12. If $\vec{AB} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}$ and $\vec{BC} = \begin{pmatrix} 4 \\ -1 \end{pmatrix}$, find $\vec{AC}$. [2]

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13. Given $\vec{OA} = \begin{pmatrix} 6 \\ 2 \end{pmatrix}$ and $\vec{OB} = \begin{pmatrix} -1 \\ 5 \end{pmatrix}$, find $\vec{AB}$. [2]

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14. Find the vector $\vec{XY}$ if $X$ is $(2, 3)$ and $Y$ is $(5, -1)$. [2]

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15. Given $\mathbf{u} = \begin{pmatrix} 2 \\ 3 \end{pmatrix}$, find the vector $3\mathbf{u}$. [2]

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16. If $\vec{PQ} = \begin{pmatrix} 4 \\ 6 \end{pmatrix}$, find the vector $\vec{QP}$. [1]

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17. Given $\mathbf{a} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 3 \\ -1 \end{pmatrix}$, express $\mathbf{c} = 2\mathbf{a} + 3\mathbf{b}$ as a column vector. [3]

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18. Point $M$ is the midpoint of line segment $AB$. If $\vec{OA} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}$ and $\vec{OB} = \begin{pmatrix} 8 \\ 10 \end{pmatrix}$, find $\vec{OM}$. [3]

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19. Given $\vec{AB} = \mathbf{a}$ and $\vec{BC} = 2\mathbf{a}$, find $\vec{AC}$ in terms of $\mathbf{a}$. [2]

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20. A vector $\mathbf{v} = \begin{pmatrix} k \\ 12 \end{pmatrix}$ has a magnitude of 13. Find the two possible values of $k$. [3]

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