Transformations and vectors: past paper questions

Real questions on transformations and vectors

The newest 20 of 56 written questions. Open one to see it on the real paper.

1. 0980/11 · October/November 2025 · Q21a[3]
   21 Shapes $A$ and $B$ are shown on the grid. [Diagram: A Cartesian grid with $x$ and $y$ axes from $-5$ to $5$. A grey rectangle $A$ has vertices at $(1,1)$, $(3,1)$, $(3,2)$, and $(1,2)$. A white rectangle $B$ has vertices at $(-2,1)$, $(-1,1)$, $(-1,3)$, and $(-2,3)$.] (a) Describe fully the single transformation tha...See it on the paper →
2. 0980/11 · October/November 2025 · Q21b[2]

   2-mark question — its maths and diagrams are best seen on the paper.

   See it on the paper →
3. 0980/21 · October/November 2025 · Q5a[2]
   [Diagram: A Cartesian coordinate system with $x$ and $y$ axes. Triangle $T$ is a right-angled triangle with vertices at $(1,1)$, $(3,1)$, and $(3,2)$. Triangle $P$ is a right-angled triangle with vertices at $(-2,2)$, $(0,2)$, and $(0,3)$.] (a) Describe fully the single transformation that maps triangle $T$ onto triang...See it on the paper →
4. 0980/21 · October/November 2025 · Q5b[2]

   2-mark “Draw” question — its maths and diagrams are best seen on the paper.

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5. 0980/21 · October/November 2025 · Q24[4]
   24 [Diagram: A geometric figure with points $O,A,B,C,D,M$. $O,B,D$ are collinear on a horizontal line. $A,C,D$ are collinear on a slanted line. Vector $\mathbf{a}$ is shown from $O$ to $A$. Vector $\mathbf{b}$ is shown from $O$ to $B$. $M$ is a point on the segment $CD$. The text "NOT TO SCALE" is present.] In...See it on the paper →
6. 0980/22 · May/June 2025 · Q5a[1]
   [Diagram: A coordinate grid with $x$ and $y$ axes from $-4$ to $4$. Triangle $T$ is shaded with vertices at $(-2,1)$, $(-1,1)$, and $(-1,3)$. Triangle $U$ is unshaded with vertices at $(1,1)$, $(3,1)$, and $(3,2)$.] (a) Translate triangle $T$ by the vector $\left(\begin{array}{c}0\\ -2\end{array}\right)$.See it on the paper →
7. 0980/22 · May/June 2025 · Q5b[3]
   [Diagram: A Cartesian coordinate grid with $x$ and $y$ axes ranging from $-4$ to $4$. Triangle $T$ is shaded grey with vertices at $(-2,1)$, $(-1,1)$, and $(-1,3)$. Triangle $U$ is unshaded with vertices at $(1,1)$, $(3,1)$, and $(3,2)$.] (b) Describe fully the single transformation that maps triangle $T$ onto tr...See it on the paper →
8. 0980/22 · May/June 2025 · Q9c[2]
   9 $A$ is the point $(3,-1)$. $\overrightarrow{AB}=\left(\begin{array}{c}2\\ -4\end{array}\right)$ (c) $P$ is a point on $AB$. $AP:PB=1:3$ Find the position vector of $P$.See it on the paper →
9. 0980/11 · October/November 2024 · Q18b[2]
   18 The diagram shows a rectangle and two points, $P$ and $C$, on a $1{\text{ cm}}^2$ grid. [Diagram: A coordinate grid with x-axis from 0 to 8 and y-axis from 0 to 9. A shaded rectangle has vertices at (2,5), (7,5), (7,8), and (2,8). Point $C$ is marked at (1,5). Point $P$ is marked at (7,8).] (b) The rectangle is enlar...See it on the paper →
10. 0980/11 · October/November 2024 · Q18c[1]
    The diagram shows a rectangle and two points, $P$ and $C$, on a $1{\text{ cm}}^2$ grid. [Diagram: A coordinate grid with $x$ and $y$ axes. A shaded rectangle has vertices at $(2,5)$, $(7,5)$, $(7,8)$, and $(2,8)$. Point $C$ is at $(0,5)$. Point $P$ is at $(7,8)$.] (c) Find the area of the enlarged rectangle.See it on the paper →
11. 0980/41 · October/November 2024 · Q2a(i)[2]
    [Diagram: A Cartesian grid with axes $x$ and $y$ ranging from -6 to 6. Triangle $A$ is shaded with vertices at $(1,-1)$, $(1,-3)$, and $(5,-3)$. Triangle $B$ is unshaded with vertices at $(-5,1)$, $(-5,5)$, and $(-3,5)$.] (a) On the grid, draw (i) the image of triangle $A$ after a reflection in the line $x=1$See it on the paper →
12. 0980/41 · October/November 2024 · Q2a(ii)[2]
    [Diagram: A Cartesian grid with x-axis from -6 to 6 and y-axis from -5 to 6. Triangle A is shaded in the fourth quadrant with vertices at (1, -1), (1, -3), and (5, -3). Triangle B is in the second quadrant with vertices at (-5, 1), (-5, 5), and (-3, 5).] (a) On the grid, draw (ii) the image of triangle $A$ after an enl...See it on the paper →
13. 0980/41 · October/November 2024 · Q2b[3]
    [Diagram: A coordinate grid with $x$ and $y$ axes ranging from $-6$ to $6$. Triangle $A$ is shaded grey with vertices at $(1,-1)$, $(5,-1)$, and $(1,-3)$. Triangle $B$ is unshaded with vertices at $(-5,1)$, $(-5,5)$, and $(-3,5)$.] (b) Describe fully the single transformation that maps triangle $A$ onto triangle...See it on the paper →
14. 0980/41 · October/November 2024 · Q2c[2]
    [Diagram: A coordinate grid with x-axis from -6 to 6 and y-axis from -5 to 6. Triangle B is in the second quadrant with vertices at (-5, 1), (-5, 5), and (-3, 5). Triangle A is in the fourth quadrant with vertices at (1, -1), (1, -3), and (5, -3).] (c) The point $(a,b)$ is reflected in the line $y=k$ where $k$ is an...See it on the paper →
15. 0980/32 · May/June 2024 · Q3c(i)[2]
    The diagram shows four quadrilaterals, $A$, $B$, $C$ and $D$, on a $1{\text{ cm}}^2$ grid. [Diagram: A coordinate grid with four quadrilaterals labeled A, B, C, and D. Quadrilateral A is a shaded trapezium in the second quadrant with vertices at $(-5,1)$, $(-2,1)$, $(-3,4)$, and $(-5,4)$. Quadrilateral D is in the f...See it on the paper →
16. 0980/32 · May/June 2024 · Q3c(ii)[2]
    The diagram shows four quadrilaterals, $A$, $B$, $C$ and $D$, on a $1{\text{ cm}}^2$ grid. [Diagram: A coordinate grid with four quadrilaterals labeled A, B, C, and D. Quadrilateral A is a shaded trapezium in the second quadrant. Quadrilateral D is in the first quadrant. Quadrilateral B is in the fourth quadrant. Quadri...See it on the paper →
17. 0980/32 · May/June 2024 · Q3c(iii)[3]
    3 The diagram shows four quadrilaterals, $A$, $B$, $C$ and $D$, on a $1{\text{ cm}}^2$ grid. [Diagram: A coordinate grid with $x$ and $y$ axes. Four quadrilaterals are plotted. Quadrilateral $A$ is a shaded trapezium with vertices at $(-5,1)$, $(-2,1)$, $(-3,4)$ and $(-5,4)$. Quadrilateral $B$ is a trapezium with ve...See it on the paper →
18. 0980/32 · May/June 2024 · Q3d[2]

    2-mark question — its maths and diagrams are best seen on the paper.

    See it on the paper →
19. 0980/31 · October/November 2023 · Q6a[2]
    [Diagram: A Cartesian coordinate grid with $x$ and $y$ axes. Triangle $A$ is shaded grey with vertices at $(1,3)$, $(1,5)$, and $(5,3)$. Triangle $B$ is unshaded with vertices at $(3,0)$, $(3,2)$, and $(7,0)$. Triangle $C$ is unshaded with vertices at $(-5,-3)$, $(-5,3)$, and $(0,-3)$.] (a) Describe fully the...See it on the paper →
20. 0980/31 · October/November 2023 · Q6b[3]
    [Diagram: A coordinate grid with x-axis from -8 to 8 and y-axis from -6 to 10. Three triangles are plotted: Triangle A is shaded grey with vertices at (2,3), (2,5), and (5,3). Triangle B has vertices at (3,0), (3,2), and (7,0). Triangle C has vertices at (-5,-3), (-5,3), and (1,-3).] (b) Describe fully the single trans...See it on the paper →

What examiners said

This part was generally well attempted, with many candidates correctly applying the translation. However, a small number of responses revealed a misunderstanding of the direction, as some candidates incorrectly translated the triangle along the direction of the x-axis instead of the y-axis. Another error was to count 2 squares down from a bottom corner and start to draw the top of the triangle fro...

— Examiner report, May/June 2025, 0980/22 Q5(a) (Cambridge)

Many candidates showed clear understanding of what was needed and scored all 3 marks. Those candidates who scored 2 marks normally did so for rotation with an accurate direction and angle. There were some who were confused about direction, with clockwise 90 being a common error. The centre of rotation proved the most difficult part for candidates to get right, with (0, 0), (0, 1) or (1, 0) being c...

— Examiner report, May/June 2025, 0980/22 Q5(b) (Cambridge)

This transformation part of the paper was answered very well by some candidates. However, it was a topic where a significant number found difficulty in scoring high marks. Many identified this part as a translation though translocation, transition and transformation were common incorrect attempts along with those who chose an incorrect type of transformation. Vectors were commonly seen, often corr...

— Examiner report, May/June 2024, 0980/32 Q3(c)(i) (Cambridge)