Vector geometry: past paper questions

Where the questions come from

• Question 20May/June 2026, paper 12Structured5 marksHas a diagram

  $OPQ$ is a triangle and $O$ is the origin. $R$ is a point on $OQ$ and $OQ=3OR$. $\overrightarrow{OP}=3\mathbf{a}$ and $\overrightarrow{OR}=2\mathbf{b}$.

  Try this question
• Question 26Oct/Nov 2025, paper 11Structured7 marksHas a diagram

  The diagram shows triangle $OAB$. $\overrightarrow{OA}=\mathbf{a}$ and $\overrightarrow{OB}=4\mathbf{b}$. $T$ is a point on $AB$ such that $AT:TB=3:2$.

  Try this question
• Question 23Oct/Nov 2023, paper 11Structured5 marks

  In the diagram, $OABC$ is a parallelogram. $\overrightarrow{OA}=\mathbf{a}$ and $\overrightarrow{OC}=\mathbf{c}$. $X$ is the midpoint of $AC$.

  Try this question
• Question 21Oct/Nov 2025, paper 12Structured5 marksHas a diagram

  $OPQR$ is a parallelogram. $\overrightarrow{OP}=\mathbf{a}$ and $\overrightarrow{OR}=2\mathbf{b}$. $M$ is the midpoint of $QR$.

  Try this question
• Question 24May/June 2024, paper 11Structured4 marksHas a diagram

  $ABCD$ is a quadrilateral. $H$, $K$, $L$ and $M$ are the midpoints of $AB$, $BC$, $CD$ and $AD$ respectively. $\overrightarrow{AB}=2\mathbf{a}$, $\overrightarrow{BC}=2\mathbf{b}$ and $\overrightarrow{AD}=2\mathbf{d}$.

  Try this question
• Question 24Oct/Nov 2023, paper 12Structured5 marks

  OAB is a triangle. P lies on AB and AP : PB = 2 : 3.

  Try this question
• Question 25May/June 2024, paper 12Structured3 marksHas a diagram

  $OCB$ is a triangle. $A$ is a point on $OC$ such that $OA:AC=1:3$. $X$ is the midpoint of $BC$.

  Try this question
• Question 27May/June 2023, paper 11Structured6 marksHas a diagram

  $OABC$ is a parallelogram. $\overrightarrow{OA}=2\mathbf{a}$ and $\overrightarrow{OC}=3\mathbf{c}$. $M$ is the midpoint of $BC$.

  Try this question