Vectors | Cambridge O Level Maths Calculator Questions 2025

1a

4 marks

The diagram shows triangle $O P T$ .

q22-paper4-spec-2025-cie-igcse-further-maths

In the diagram $\vec{O T} = t$ and $\vec{O P} = p$ .
$O K : K T = 2 : 1$ and $T L : L P = 2 : 1$ .

Find, in terms of t and p, in its simplest form

i) $\vec{P L}$

[2]

ii) $\vec{K L}$

[2]

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1b

2 marks

$K L$ is extended to the point $M$ .

$\vec{K M} = - \frac{2}{3} t + \frac{4}{3} p .$

Show that $M$ lies on $O P$ extended.

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1

2 marks

$\vec{V W} = (\begin{matrix} 10 \\ - 24 \end{matrix})$

Find $|\vec{V W}| .$

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1

6 marks

cie-igcse-2020-oct-nov-p4-tz3-q8b

In the diagram, $O A B$ and $O E D$ are straight lines.
$O$ is the origin, $A$ is the midpoint of $O B$ and $E$ is the midpoint of $A C$ .
$\vec{A C} = a$ and $\vec{C B} = b$ .

Find, in terms of $a$ and $b$ , in its simplest form

i)

\vec{A B}

,

\vec{A B} =

................................................ [1]

ii)

\vec{O E}

,

\vec{O E} =

................................................ [2]

iii)

the position vector of

D

.

[3]

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Vectors (Cambridge O Level Maths)

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