Transformations and vectors: past paper questions

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• Question 10May/June 2026, paper 12Structured2 marks

  The diagram shows triangle $A$. Reflect triangle $A$ in the line $y=x$. The diagram shows triangle $A$.

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• Question 8Oct/Nov 2025, paper 11Structured4 marksHas a diagram

  The diagram shows triangle $A$ and triangle $B$. Describe fully the single transformation that maps triangle $A$ onto triangle $B$.

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• Question 9Oct/Nov 2024, paper 11Structured5 marksHas a diagram

  The grid shows triangle $A$ and triangle $B$. Describe fully the single transformation that maps triangle $A$ onto triangle $B$.

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• 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 $AC$.

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• 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 $\overrightarrow{OR}=2\mathbf{b}$.

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• 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 $AT:TB=3:2$.

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• Question 7Oct/Nov 2023, paper 12Structured6 marksHas a diagram

  Shape A and triangles P and Q are drawn on a centimetre square grid. Describe fully the single transformation that maps triangle P onto triangle Q.

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• Question 11Oct/Nov 2025, paper 12Structured4 marks

  Shape $A$ and shape $B$ are drawn on the grid. Describe fully the single transformation that maps shape $A$ onto shape $B$.

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

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

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• 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 $QR$.

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• Question 7Oct/Nov 2024, paper 21Structured10 marks

  $ABCD$ is a parallelogram with sides $AB$, $BC$, $CD$ and $DA$. $A$ is the point $(-3,7)$ and $B$ is the point $(2,5)$. $\overrightarrow{AD}=\left(\begin{array}{c}-1\\ -6\end{array}\right)$ Find the coordinates of point $D$.

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• Question 2Oct/Nov 2023, paper 21Structured5 marksHas a diagram

  Triangle $A$, triangle $B$ and line $R$ are drawn on the grid. Write down the equation of line $R$.

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• 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 $\overrightarrow{AD}=2\mathbf{d}$.

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• Question 7Oct/Nov 2023, paper 22Structured10 marksHas a diagram

  Point $A$ and point $B$ are shown on a centimetre square grid. $ABC$ is a triangle. Here are five possible coordinates for point $C$.

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• 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 $BC$.

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• Question 9May/June 2023, paper 11Structured3 marksHas a diagram

  The diagram shows triangles $A$ and $B$. Describe fully the single transformation that maps triangle $A$ onto triangle $B$.

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• Question 12May/June 2025, paper 12Structured8 marksHas a diagram

  Triangle A and triangle B are drawn on the grid. Describe fully the single transformation that maps triangle A onto triangle B.

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• 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 $BC$.

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• Question 5May/June 2024, paper 22Structured11 marksHas a diagram

  Describe fully the single transformation that maps shape $A$ onto shape $B$.

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