Transformations and vectors: past paper questions

Real questions on transformations and vectors

The newest 20 of 86 written questions. Open one to see it on the real paper.

1. 0580/11 · May/June 2026 · Q19a[2]

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

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2. 0580/11 · May/June 2026 · Q19b[2]

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

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3. 0580/11 · May/June 2026 · Q19c[3]
   [Diagram: A coordinate grid with $x$ and $y$ axes from $-6$ to $6$. Triangle $T$ is shaded with vertices at $(1,1)$, $(2,1)$, and $(1,4)$. Triangle $A$ has vertices at $(-3,4)$, $(-3,-2)$, and $(-1,-2)$. Triangle $B$ has vertices at $(1,-2)$, $(4,-1)$, and $(1,-1)$.] (c) Describe fully the single transformation that ma...See it on the paper →
4. 0580/11 · May/June 2026 · Q19d[3]
   [Diagram: A coordinate grid with $x$ and $y$ axes from $-6$ to $6$. Triangle $T$ is shaded with vertices at $(1,1)$, $(2,1)$, and $(1,4)$. Triangle $A$ has vertices at $(-3,4)$, $(-3,-2)$, and $(-1,-2)$. Triangle $B$ has vertices at $(1,-2)$, $(4,-1)$, and $(1,-1)$.] (d) Describe fully the single transformation that ma...See it on the paper →
5. 0580/12 · May/June 2026 · Q29a(i)[2]
   29 The diagram shows three shapes, $A$, $B$ and $C$, on a grid. [Diagram: A coordinate grid with x-axis from -7 to 6 and y-axis from -3 to 5. Three shaded shapes are plotted. Shape A is a polygon on the left with vertices at (-6,1), (-4,1), (-4,3), (-5,4), (-6,4). Shape B is a polygon on the right with vertices at (3,1...See it on the paper →
6. 0580/12 · May/June 2026 · Q29a(ii)[3]
   29 The diagram shows three shapes, $A$, $B$ and $C$, on a grid. [Diagram: A coordinate grid with x-axis from -7 to 6 and y-axis from -3 to 5. Three shaded shapes are plotted. Shape A is a polygon on the left. Shape B is a polygon on the right. Shape C is a polygon in the middle-left.] (a) Describe fully the single tran...See it on the paper →
7. 0580/12 · May/June 2026 · Q29b[2]

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

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8. 0580/21 · May/June 2026 · Q8b[2]
   8 $P$ is the point $(0,4)$ and $Q$ is the point $(1,8)$. (b) Find the vector $\overrightarrow{QP}$.See it on the paper →
9. 0580/22 · May/June 2026 · Q5a(i)[2]

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

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10. 0580/22 · May/June 2026 · Q5a(ii)[2]

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

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11. 0580/22 · May/June 2026 · Q5b[3]
    [Diagram: A Cartesian grid with $x$ and $y$ axes. Shape $A$ is a shaded quadrilateral with vertices at $(-4,2)$, $(-2,2)$, $(-2,0)$, and $(-3,0)$. Shape $B$ is an unshaded quadrilateral with vertices at $(4,-2)$, $(6,-2)$, $(6,-3)$, and $(4,-4)$.] (b) Describe fully the single transformation that maps shape $A$...See it on the paper →
12. 0580/22 · May/June 2026 · Q22a(ii)[1]
    [Diagram: A parallelogram $OABC$ with vertices $O,A,B,C$ in counterclockwise order. Point $P$ is on the diagonal $AC$. Vector $\overrightarrow{OA}$ is labelled $\mathbf{a}$. Vector $\overrightarrow{OC}$ is labelled $\mathbf{c}$. The diagram is marked "NOT TO SCALE".] $OABC$ is a parallelogram. $\overrightarrow{OA} =...See it on the paper →
13. 0580/22 · May/June 2026 · Q22b[2]
    [Diagram: A parallelogram $OABC$ with vertices $O,A,B,C$ in counterclockwise order. Vector $\overrightarrow{OA}$ is labelled $\mathbf{a}$. Vector $\overrightarrow{OC}$ is labelled $\mathbf{c}$. Point $P$ is on diagonal $AC$. The diagram is marked "NOT TO SCALE".] $OABC$ is a parallelogram. $\overrightarrow{OA} = \ma...See it on the paper →
14. 0580/23 · May/June 2026 · Q10[1]
    10 The position vector of $A$ is $\left(\begin{array}{c}4\\ -1\end{array}\right)$ and $\overrightarrow{AB}=\left(\begin{array}{c}-7\\ 5\end{array}\right)$. Find the position vector of $B$.See it on the paper →
15. 0580/23 · May/June 2026 · Q12a(i)[3]
    [Diagram: A coordinate grid with x and y axes from -5 to 5. Triangle A is shaded with vertices at (2, -4), (4, -4), and (4, -2). Triangle B has vertices at (2, 2), (4, 2), and (4, 1). Triangle C has vertices at (-4, 2), (-2, 2), and (-4, -2).] (a) Describe fully the single transformation that maps (i) triangle $A$ onto...See it on the paper →
16. 0580/23 · May/June 2026 · Q12a(ii)[3]
    [Diagram: A Cartesian coordinate grid with $x$ and $y$ axes ranging from $-5$ to $5$. Three triangles are plotted: - Triangle $A$ (shaded grey) with vertices at $(1,-4)$, $(2,-4)$, and $(2,-2)$. - Triangle $B$ with vertices at $(2,2)$, $(4,2)$, and $(4,1)$. - Triangle $C$ with vertices at $(-4,2)$, $(-2,2)$, an...See it on the paper →
17. 0580/23 · May/June 2026 · Q12b(i)[1]
    [Diagram: A coordinate grid with $x$ and $y$ axes ranging from $-5$ to $5$. Three triangles are drawn: triangle $A$ is shaded grey with vertices at $(1,-4)$, $(2,-4)$ and $(2,-2)$; triangle $B$ has vertices at $(2,2)$, $(4,2)$ and $(4,1)$; triangle $C$ has vertices at $(-4,2)$, $(-2,2)$ and $(-4,-2)$] (b) On t...See it on the paper →
18. 0580/23 · May/June 2026 · Q12b(ii)[2]

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

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19. 0580/23 · May/June 2026 · Q28[3]
    28 [Diagram: A triangle with vertices $R$, $O$, $S$. Point $P$ is on the line segment $RS$. Vector $\overrightarrow{OR}$ is labelled $\mathbf{r}$. Vector $\overrightarrow{OS}$ is labeled $\mathbf{s}$. The text "NOT TO SCALE" is present.] In the diagram, $O$ is the origin, $\overrightarrow{OR}=\mathbf{r}$ and $\overri...See it on the paper →
20. 0580/12 · February/March 2026 · Q21a[3]
    21 The diagram shows two triangles, $A$ and $B$, on a $1{\text{ cm}}^2$ grid. [Diagram: A coordinate grid with x-axis from -6 to 8 and y-axis from 1 to 11. Triangle A has vertices at (0,4), (4,10), and (7,4). Triangle B has vertices at (-4,1), (-2,4), and (-1,2).] (a) Describe fully the single transformation that maps t...See it on the paper →

What examiners said

Comprehensive responses • Many candidates identified the transformation correctly and a considerable number of them found the centre correctly. Limited responses • It was extremely rare to see a correct scale factor with 3 or –3 often seen or no attempt made at all. • Some transposed the coordinates of the centre with (1, –5) seen. • Few candidates identified more than one transformation, and res...

— Examiner report, February/March 2026, 0580/12 Q21(a) (Cambridge)

Comprehensive responses • There were quite a number who managed to draw a correct image. Limited responses • Some rotated the triangle around the wrong centre of rotation or rotated the wrong triangle. • Some candidates drew more than one triangle in their response. • A few had the right idea although at least one of the vertices on their image was beyond reasonable accuracy.

— Examiner report, February/March 2026, 0580/12 Q21(b) (Cambridge)

Comprehensive responses • Some candidates found all 3 points correctly, while others had the right idea although made arithmetic slips, for example (11, 10) or (16, 1), which were often seen. Limited responses • Many did not make any attempt at this part of the question. • The point (7, 4), common to object and image, was often the only point of the three correct. • Some gave answers for, or show...

— Examiner report, February/March 2026, 0580/12 Q21(c) (Cambridge)