Vectors practice questions

Secondary 4 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise vectors free

What this topic covers

Addition and Subtraction of Vectors
Expressing Vectors in Terms of Two Basis Vectors
Position Vectors
Scalar Multiples of a Vector
Vectors in Two Dimensions

Worked examples

Example 1

Given

\mathbf{a} = \begin{pmatrix} 3 \\ 5 \end{pmatrix}

and

\mathbf{b} = \begin{pmatrix} 6 \\ 10 \end{pmatrix}

, state whether

\mathbf{a}

and

\mathbf{b}

are parallel.

Show the worked solution

$Two vectors are parallel when one is a scalar multiple of the other: $\mathbf{b} = k\mathbf{a}$, $k \neq 0$.$
$Check if $\mathbf{b} = k\mathbf{a}$ for some scalar $k$:$
$\dfrac{6}{3} = 2$ and $\dfrac{10}{5} = 2$
$Since both ratios are equal ($= 2$), the vectors are parallel.$
$Answer: yes.$

Answer: $yes$

Example 2

Simplify

\overrightarrow{OS} - \overrightarrow{OP}

Show the worked solution

$\overrightarrow{OS} - \overrightarrow{OP}$
$= \overrightarrow{OS} + \overrightarrow{PO} \quad \scriptsize\textit{reverse direction to negate}$
$= \overrightarrow{PO} + \overrightarrow{OS} \quad \scriptsize\textit{vector addition is commutative}$
$= \overrightarrow{PS} \quad \scriptsize\textit{triangle law: }O\textit{ cancels}$

Answer: $PS$

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.