Geometrical constructions Notes and examples: past paper questions

Real questions on geometrical constructions notes and examples

The newest 20 of 59 written questions. Open one to see it on the real paper.

1. 4024/12 · May/June 2026 · Q5a[3]

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

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2. 4024/12 · May/June 2026 · Q7[3]

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

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3. 4024/22 · October/November 2025 · Q4a[2]

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

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4. 4024/12 · May/June 2025 · Q3[3]

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

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5. 4024/22 · May/June 2025 · Q20a(i)[1]
   20 $ABCD$ and $EFGD$ are rectangles. [Diagram: Two rectangles, $ABCD$ and $EFGD$, sharing side $AD$ and $DG$. $ABCD$ is the lower rectangle, $EFGD$ is the larger rectangle containing $ABCD$. Points are labeled $A,B,C,D,E,F,G$. Lengths are labeled: $EF=2x-3$, $AE=x$, $FG=x+3$, $CG=x-2$. The region $EABF$ i...See it on the paper →
6. 4024/11 · October/November 2024 · Q25[3]
   The diagram shows a cuboid. $EH=6\text{ cm}$, $HG=2\text{ cm}$ and $EC=7\text{ cm}$. Calculate $CG$. [Diagram: A cuboid with vertices labelled $A,B,C,D$ on the top face and $E,F,G,H$ on the bottom face. $E$ is below $A$, $F$ below $B$, $G$ below $C$, $H$ below $D$. The length $EH$ is labelled 6. The lengt...See it on the paper →
7. 4024/12 · October/November 2024 · Q10b(i)[2]

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

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8. 4024/12 · October/November 2024 · Q10b(ii)[1]

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

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9. 4024/12 · October/November 2024 · Q17b[2]
   [Diagram: A shaded triangle $ABC$ on a 1 cm square grid. Point $A$ is at $(0,1)$. Point $B$ is at $(4,5)$. Point $C$ is at $(4,-5)$. The y-axis is labeled $y$ and the x-axis is labeled $x$. Grid lines are shown at integer intervals from -6 to 6 on both axes.] The diagram shows a shaded triangle, $ABC$, drawn on a 1...See it on the paper →
10. 4024/11 · May/June 2024 · Q4a[2]

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

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11. 4024/12 · May/June 2024 · Q15[2]
    [Diagram: A quadrilateral $ABCD$ with diagonal $BC$. Triangle $ABC$ has sides $AB=5$, $AC=7$, $BC=8$. Triangle $CBD$ shares side $BC$. Angles are marked at $A$, $C$ (in $ABC$), and $B$ (in $ABC$ and $CBD$). The diagram is marked "NOT TO SCALE".] Triangle $ABC$ is mathematically similar to triangle $CBD$. $AB = 5 \text{...See it on the paper →
12. 4024/12 · May/June 2024 · Q17a[2]
    [Diagram: A circle with centre $O$. Points $A,B,C,D$ are on the circumference. Chords $AB,BC,CD,DA$ form a quadrilateral. Lines $OB$ and $OC$ are radii. Angle $BAD=120^{\circ }$. Angle $OBC=20^{\circ }$. Angle $BCD=x^{\circ }$. Angle $ADC=y^{\circ }$. Label "NOT TO SCALE".] $A,B,C$ and $D$ are points on a circle, c...See it on the paper →
13. 4024/12 · May/June 2024 · Q17b[2]
    [Diagram: A circle with centre $O$. Points $A,B,C,D$ are on the circumference. Angle $BAD=120^{\circ }$. Angle $OBC=20^{\circ }$. Angle $BDC=y^{\circ }$. Angle $OCD=x^{\circ }$.] $A,B,C$ and $D$ are points on a circle, centre $O$. Angle $BAD=120^{\circ }$ and angle $OBC=20^{\circ }$. (b) Find the value of $y$.See it on the paper →
14. 4024/22 · May/June 2024 · Q5c(i)[2]

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

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15. 4024/12 · October/November 2023 · Q2[1]

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

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16. 4024/11 · May/June 2023 · Q6b[1]

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

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17. 4024/21 · May/June 2023 · Q7a(ii)[2]
    (a) $ABC$ is a triangle with $AC=8.3\text{ cm}$ and $\angle BAC=105^{\circ }$. (ii) By taking suitable measurements from your triangle, calculate the perimeter of triangle $ABC$.See it on the paper →
18. 4024/22 · May/June 2023 · Q8a(i)[2]
    [Diagram: A rectangle labelled $R$ with the text "NOT TO SCALE" to its right] The length of the rectangle $R$ is twice its width. Rectangle $R$ has a perimeter of $20.4\text{ cm}$. (i) Find the length and width of the rectangle $R$.See it on the paper →
19. 4024/22 · May/June 2023 · Q8a(ii)[2]
    [Diagram: A rectangle labelled $R$, with text "NOT TO SCALE" to its right] The length of the rectangle $R$ is twice its width. Rectangle $R$ has a perimeter of $20.4\text{cm}$. (ii) Rectangle $S$ is mathematically similar to rectangle $R$. Rectangle $S$ has a perimeter of $30.6\text{cm}$. Calculate the length of rect...See it on the paper →
20. 4024/12 · October/November 2022 · Q14a[2]

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

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What examiners said

The best responses showed sketches of the hexagons with the lengths of the sides shown clearly. Some responses showed accurate hexagons but a sketch of a hexagon was sufficient here. A few did not include labels of the lengths of the sides while others had incorrect labels, for example all sides labelled 30 cm or all labelled 6 cm or some 3 cm and some 6 cm.

— Examiner report, May/June 2023, 4024/11 Q6(b) (Cambridge)

Few candidates could accurately measure the sides of the triangle. Not all correctly find the perimeter of the triangle. The best responses listed all measurements and then found the sum of these, showing each step in the working.

— Examiner report, May/June 2023, 4024/21 Q7(a)(ii) (Cambridge)

Over half of the candidates were able to calculate the correct length and width, however some transposed their answers. Some expressed the length and width correctly using algebra but others didn’t succeed in formulating the correct expression for the perimeter, as a result leading to the incorrect length. Common wrong methods led to a length of 13.6 and a width of 6.8 or a length of 10.2 and a wi...

— Examiner report, May/June 2023, 4024/22 Q8(a)(i) (Cambridge)