0580.C4.1.13 — triangles.: past paper questions

Real questions on 0580.c4.1.13 — triangles.

The newest 20 of 54 written questions. Open one to see it on the real paper.

1. 0580/22 · May/June 2026 · Q11[2]
   11 Find the number of sides of a regular polygon with interior angle $140^{\circ }$.See it on the paper →
2. 0580/23 · May/June 2026 · Q13a[2]
   [Diagram: A circle with centre $O$. Points $A$, $B$ and $C$ are on the circumference. $AOC$ is a straight line (a diameter). $M$ is a point on the chord $AB$. Lines are drawn for $AC$, $AB$, $BC$, and $OM$. The diagram is labelled NOT TO SCALE.] $A$, $B$ and $C$ are points on a circle with centre $O$. $AOC$ is a strai...See it on the paper →
3. 0580/23 · May/June 2026 · Q15a[1]
   The diagram shows a cyclic quadrilateral $ABCD$. [Diagram: A circle with points $A,B,C,D$ on the circumference in counterclockwise order. Lines connect $A$ to $B$, $B$ to $C$, $C$ to $D$, $D$ to $A$, $A$ to $C$, and $B$ to $D$. Angle $ADB$ is marked as $41^{\circ }$. Angle $DBC$ is marked as $86^{\circ }$. The text "NOT T...See it on the paper →
4. 0580/23 · May/June 2026 · Q15b[2]
   The diagram shows a cyclic quadrilateral $ABCD$. [Diagram: A circle with points $A,B,C,D$ on the circumference forming a cyclic quadrilateral. Diagonals $AC$ and $BD$ are drawn. Angle $ADB$ is marked as $41^{\circ }$. Angle $ABC$ is marked as $86^{\circ }$. The text "NOT TO SCALE" is present.] Find (b) angle $BDC$.See it on the paper →
5. 0580/43 · May/June 2026 · Q13a[8]
   [Diagram: Triangle $ABC$ with angle $ABC=120^{\circ }$, side $BC=15$ cm, side $AC=15\sqrt{3}$ cm. Labelled "NOT TO SCALE".] The diagram shows triangle $ABC$. $BC=15$ cm, $AC=15\sqrt{3}$ cm and angle $ABC=120^{\circ }$. (a) Show that triangle $ABC$ is an isosceles triangle.See it on the paper →
6. 0580/43 · May/June 2026 · Q13b[3]
   [Diagram: Triangle $ABC$ with angle $ABC=120^{\circ }$, side $BC=15$ cm, side $AC=15\sqrt{3}$ cm. Labelled NOT TO SCALE.] The diagram shows triangle $ABC$. $BC=15$ cm, $AC=15\sqrt{3}$ cm and angle $ABC=120^{\circ }$. (b) Calculate the shortest distance from $B$ to $AC$.See it on the paper →
7. 0580/43 · May/June 2026 · Q15[3]

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

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8. 0580/12 · February/March 2026 · Q6[6]

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

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9. 0580/32 · February/March 2026 · Q3[2]

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

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10. 0580/32 · February/March 2026 · Q6a[1]
    6 (a) Measure the reflex sector angle.See it on the paper →
11. 0580/32 · February/March 2026 · Q6b[3]

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

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12. 0580/32 · February/March 2026 · Q7a[1]
    [Diagram: A line segment with endpoints $A$ and $B$. A point $P$ is marked on the line segment between $A$ and $B$.] (a) Measure the length of line $AB$.See it on the paper →
13. 0580/32 · February/March 2026 · Q7b[3]

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

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14. 0580/32 · February/March 2026 · Q9a(i)[1]
    9 (a) [Diagram: A clock face with numbers 1 to 12 arranged in a circle, with a dot at the center. No hands are drawn.] (i) Complete the clock diagram to show the time 13 22.See it on the paper →
15. 0580/32 · February/March 2026 · Q9a(ii)[2]
    [Diagram: A clock face with numbers 1 to 12 arranged in a circle, with a dot at the center.] (ii) A train leaves a station at 13 22. It takes 170 minutes to reach the first stop. Work out the time it reaches the first stop.See it on the paper →
16. 0580/32 · February/March 2026 · Q9b[2]
    (b) A bus takes 1 hour 15 minutes to travel 45 km between two towns. Work out the average speed of the bus in kilometres per hour. ................................................ km/h [2]See it on the paper →
17. 0580/32 · February/March 2026 · Q16b[5]
    16 These are the first four diagrams in a sequence. The diagrams are made using grey squares and white squares. [Diagram: A sequence of four diagrams on a grid. Diagram 1 is a 1x2 rectangle of grey squares. Diagram 2 is a 2x3 rectangle with the top-left 2x1 block white and the rest grey. Diagram 3 is a 3x4 rectangle wi...See it on the paper →
18. 0580/32 · February/March 2026 · Q16c[1]
    16 These are the first four diagrams in a sequence. The diagrams are made using grey squares and white squares. [Diagram: A sequence of four diagrams on a grid. Diagram 1 is a 1x2 rectangle of grey squares. Diagram 2 is a 2x3 rectangle with the top-left 2x1 block white and the rest grey. Diagram 3 is a 3x4 rectangle wi...See it on the paper →
19. 0580/32 · February/March 2026 · Q16d[2]
    16 These are the first four diagrams in a sequence. The diagrams are made using grey squares and white squares. [Diagram: A sequence of four diagrams on a grid. Diagram 1 is a 1x2 rectangle of grey squares. Diagram 2 is a 2x3 rectangle with the top-left 2x1 block white and the rest grey. Diagram 3 is a 3x4 rectangle wi...See it on the paper →
20. 0580/32 · February/March 2026 · Q25[3]
    25 [Diagram: A right-angled triangle with the right angle at the bottom left. The horizontal base is labelled $21\text{ cm}$. The text "NOT TO SCALE" is present.] The area of this triangle is $147{\text{ cm}}^2$. Calculate the length of the longest side.See it on the paper →

What examiners said

Comprehensive responses • Many candidates made some progress on at least one of the constructions, even though construction arcs were often not seen. Limited responses • It was quite rare to see both isosceles triangles since many simply repeated the first one on the second 4 cm line. • An equilateral triangle with sides of 4 cm was often seen.

— Examiner report, February/March 2026, 0580/12 Q6 (Cambridge)

Comprehensive responses • Some candidates drew an accurate and complete diagram. Limited responses • Some drew an incomplete diagram, often with 1 or 4 correct lines. • A few added incorrect lines.

— Examiner report, February/March 2026, 0580/32 Q3 (Cambridge)

Comprehensive responses • Few candidates gave the correct reflex angle. • Many measured the acute angle. Limited responses • Many gave the incorrect angle of 30°. • Some gave angles such as 60°, 150°, 180°, 45° and 360°. • A significant number made no attempt at a response.

— Examiner report, February/March 2026, 0580/32 Q6(a) (Cambridge)