Vectors in two dimensions: past paper questions

Where the questions come from

• Question 8May/June 2026, paper 21Structured8 marks

  $P$ is the point $(0,4)$ and $Q$ is the point $(1,8)$. Find the coordinates of the midpoint of $PQ$.

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• Question 10Oct/Nov 2025, paper 41Structured2 marks

  $A$ is the point $(2,1)$. $$\overrightarrow{AB}=\left(\begin{array}{c}2\\ 4\end{array}\right)$$ Find the coordinates of $B$.

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• Question 10Oct/Nov 2023, paper 41Structured13 marksHas a diagram

  $ABC$ is a triangle. $B$ is the point $(1,-10)$, $A$ is the point $(4,14)$ and $\overrightarrow{CA}=\left(\begin{array}{c}-11\\ 8\end{array}\right)$. Find the coordinates of $C$.

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• Question 9May/June 2025, paper 22Structured6 marks

  $A$ is the point $(3,-1)$. $$\overrightarrow{AB}=\left(\begin{array}{c}2\\ -4\end{array}\right)$$ $\overrightarrow{AC}=2\overrightarrow{AB}$ Find the coordinates of the point $C$.

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• Question 2Oct/Nov 2024, paper 43Structured12 marksHas a diagram

  $A$ is the point $(3,7)$ and $B$ is the point $(-1,5)$. Find the coordinates of the midpoint of the line $AB$.

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• Question 12Oct/Nov 2023, paper 42Structured11 marksHas a diagram

  $O$ is the origin $(0,0)$, $A$ is the point $(8,1)$ and $B$ is the point $(2,5)$. Write as column vectors.

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• Question 24May/June 2024, paper 22Structured5 marks

  $O$ is the origin and $OPQR$ is a parallelogram. $M$ is the midpoint of $PQ$ and $N$ divides $QR$ in the ratio $2:1$. $\overrightarrow{OP}=\mathbf{a}$ and $\overrightarrow{OR}=\mathbf{b}$.

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• Question 26May/June 2024, paper 23Structured4 marksHas a diagram

  In the diagram, $O$ is the origin. $\overrightarrow{OP}=\mathbf{p}$ and $\overrightarrow{OQ}=\mathbf{q}$. $R$ is the point of intersection of $PQ$ and $OS$, with $PR:RQ=1:2$ and $OR=RS$.

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