IGCSE Mathematics 0580 · Geometry · 5

0580.C4.1.05 — perpendicular.: past paper questions

20 real questionsasked in 5 of the last 10 exam series2019–2026usually: Find, Calculate, Draw, Write, Measure

Real questions on 0580.c4.1.05 — perpendicular.

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

0580/42 · May/June 2026 · Q3[2]
2-mark question — its maths and diagrams are best seen on the paper.
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0580/42 · May/June 2026 · Q20a[1]
The diagram shows a field $A B C D$ with a straight footpath from $A$ to $C$ . [Diagram: A quadrilateral $A B C D$ with a diagonal $A C$ . A North arrow points up from vertex $B$ . The angle between the North line and $B A$ is $10 3^{\circ}$ . The angle $A B C$ is $11 2^{\circ}$ . The angle $D A C$ is $7 9^{\circ}$ . The length $A B$ is $50.3\tex...See it on the paper →
0580/42 · May/June 2026 · Q20b[3]
The diagram shows a field $A B C D$ with a straight footpath from $A$ to $C$ . [Diagram: A quadrilateral $A B C D$ with a diagonal $A C$ . Side $A B = 50.3 m$ , side $A D = 38.2 m$ , diagonal $A C = 86.8 m$ . Angle $∠ D A C = 7 9^{\circ}$ . At vertex $B$ , a North arrow is shown. The angle between the North directi...See it on the paper →
0580/42 · May/June 2026 · Q20c[6]
[Diagram: A quadrilateral $A B C D$ with a diagonal $A C$ . $A B = 50.3 m$ , $A D = 38.2 m$ , $A C = 86.8 m$ . Angle $∠ D A B = 7 9^{\circ}$ . At vertex $B$ , a North arrow is shown. The angle between the North arrow and $B A$ is $10 3^{\circ}$ . The angle between $B A$ and $B C$ is $11 2^{\circ}$ . Label "NOT TO SCALE".]...See it on the paper →
0580/03 · Specimen 2025 · Q11a[1]
1-mark “Write” question — its maths and diagrams are best seen on the paper.
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0580/03 · Specimen 2025 · Q11c[2]
2-mark “Calculate” question — its maths and diagrams are best seen on the paper.
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0580/03 · Specimen 2025 · Q11d[3]
3-mark “Calculate” question — its maths and diagrams are best seen on the paper.
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0580/11 · October/November 2025 · Q13b[1]
13 The scale drawing shows the positions of town $A$ and town $B$ . The scale is 1 centimetre represents 10 kilometres. [Diagram: A scale drawing with two points, $A$ and $B$ . Each point has a vertical arrow pointing up labelled "North". Point $B$ is in the upper right area. Point $A$ is in the lower left area. Text "Sc...See it on the paper →
0580/11 · October/November 2025 · Q27[3]
[Diagram: A semicircle with a vertical radius line labelled 8 cm. NOT TO SCALE] The diagram shows a semicircle. The radius of the semicircle is 8 cm. Find the perimeter of the semicircle. Give your answer in terms of $π$ in its simplest form.See it on the paper →
0580/13 · October/November 2025 · Q24b[2]
(b) The bearing of $B$ from $A$ is $07 0^{\circ}$ . Find the bearing of $A$ from $B$ .See it on the paper →
0580/23 · October/November 2025 · Q13[4]
[Diagram: A circle with centre $O$ . Points $A, B, C, D$ are on the circumferenc. $E D$ and $E B$ are tangents to the circle at $D$ and $B$ respectively. $A C$ is a chord parallel to $E B$ . Angle $A O D = 4 4^{\circ}$ . Angle $D E B = x^{\circ}$ . The diagram is marked NOT TO SCALE.] $A, B, C$ and $D$ are points on the circumferenc of...See it on the paper →
0580/13 · May/June 2025 · Q10a[1]
1-mark “Draw” question — its maths and diagrams are best seen on the paper.
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0580/22 · February/March 2024 · Q26[5]
26 $A$ is the point $(6, 1)$ and $B$ is the point $(2, 7)$ . Find the equation of the perpendicular bisector of $A B$ . Give your answer in the form $y = m x + c$ .See it on the paper →
0580/12 · May/June 2023 · Q2a[1]
1-mark “Draw” question — its maths and diagrams are best seen on the paper.
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0580/12 · May/June 2023 · Q2b[1]
[Diagram: A line segment with endpoints labelled $A$ and $B$ ] (b) Measure the line $A B$ in centimetres.See it on the paper →
0580/11 · October/November 2022 · Q3b[1]
1-mark “Draw” question — its maths and diagrams are best seen on the paper.
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0580/13 · May/June 2022 · Q2c[1]
1-mark “Draw” question — its maths and diagrams are best seen on the paper.
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0580/12 · October/November 2020 · Q10[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
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0580/41 · October/November 2019 · Q1a[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
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0580/21 · May/June 2019 · Q8[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
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What examiners said

Generally, candidates were able to identify only one description (although for some their choice was spoilt by a second or third description indicated). Many candidates had worked through the list of descriptions, crossing out those that were not suitable in order to help them identify the one that was.
— Examiner report, May/June 2025, 0580/13 Q10(a) (Cambridge)

Most responses showed a line perpendicular to AB, drawn to an appropriate degree of accuracy. Some responses showed a construction with arcs, which was not essential for this question. A common mistake seen was to draw a parallel line, rather than a perpendicular one.
— Examiner report, May/June 2023, 0580/12 Q2(a) (Cambridge)

Most candidates successfully measured the length of the line, giving the answer in centimetres as requested. This required a decimal point, which was not always immediately clear in some responses. Some responses suggested that candidates measured from the end of the ruler rather than the start of the scale since 7.9 cm was a common error.
— Examiner report, May/June 2023, 0580/12 Q2(b) (Cambridge)

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