0580.C4.7.01 — angle in a semicircle = 90°.: past paper questions

Real questions on 0580.c4.7.01 — angle in a semicircle = 90°.

The newest 20 of 28 written questions. Open one to see it on the real paper.

1. 0580/11 · May/June 2026 · Q10[2]
   10 The diagram shows two straight lines intersecting two parallel lines. [Diagram: Two horizontal parallel lines with arrows pointing right. A straight line on the left intersects both, with an angle $x^{\circ }$ at the top intersection (bottom-left) and an angle $67^{\circ }$ at the bottom intersection (top-right). A straig...See it on the paper →
2. 0580/33 · May/June 2026 · Q3a[1]

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

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3. 0580/33 · May/June 2026 · Q3b[1]
   3 The diagram shows shapes drawn on a $1{\text{ cm}}^2$ grid. [Diagram: A grid with shapes A, B, C, D, E drawn on it. Shape B is a polygon with vertices at grid intersections.] (b) Find the area of shape $B$.See it on the paper →
4. 0580/33 · May/June 2026 · Q4[2]
   4 Calculate. $\frac{32.7}{8.54-2.6}$ Give your answer correct to 2 decimal places.See it on the paper →
5. 0580/33 · May/June 2026 · Q5a[1]

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

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6. 0580/33 · May/June 2026 · Q5b[1]

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

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7. 0580/33 · May/June 2026 · Q6[2]
   6 Write these numbers in order, starting with the smallest. $0.581$ $\sqrt[3]{0.2}$ $\frac{32}{55}$ $\frac{\pi }{5}$ $58\%$See it on the paper →
8. 0580/33 · May/June 2026 · Q7[2]
   [Diagram: A square labeled 'diagram A' is divided by a vertical dashed line into a left rectangle of width 5 cm and a right rectangle of width 10 cm. To the right, a T-shaped polygon labeled 'diagram B' is shown with a bottom width of 10 cm. The text 'NOT TO SCALE' is present.] Diagram $A$ shows a square of side $15$ c...See it on the paper →
9. 0580/33 · May/June 2026 · Q8a[2]
   (a) In this sequence the first term and the sixth term are missing. $\dots ,17,13,8,2,\dots$ Fill in the first term and the sixth term.See it on the paper →
10. 0580/33 · May/June 2026 · Q25a[1]
    [Diagram: A circle with centre $O$ and diameter $AC$. Point $B$ is on the circumference. Line segment $AB$ is labelled $14\text{ cm}$. Line segment $BC$ is labelled $8\text{ cm}$. The diagram is marked NOT TO SCALE.] The diagram shows a circle, centre $O$ and diameter $AC$. $B$ is a point on the circumference of the ci...See it on the paper →
11. 0580/33 · May/June 2026 · Q25b[2]
    [Diagram: A circle with centre $O$ and diameter $AC$. Point $B$ is on the circumference. Line segment $AB$ is labelled $14\text{ cm}$. Line segment $BC$ is labelled $8\text{ cm}$. The text "NOT TO SCALE" is present.] The diagram shows a circle, centre $O$ and diameter $AC$. $B$ is a point on the circumference of the ci...See it on the paper →
12. 0580/33 · May/June 2026 · Q25c[2]
    [Diagram: A circle with centre $O$. $AC$ is a horizontal diameter. $B$ is a point on the upper circumference. Triangle $ABC$ is inscribed in the circle. The length of side $AB$ is labelled $14\text{ cm}$. The length of side $BC$ is labelled $8\text{ cm}$. The text "NOT TO SCALE" is to the right of the circle.] The diag...See it on the paper →
13. 0580/33 · May/June 2026 · Q26[4]
    26 The diagram shows a sphere and a cone. [Diagram: A sphere with radius labelled $3.6\text{ cm}$. A cone with slant height labelled $8\text{ cm}$ and base radius labelled $r\text{ cm}$. Text "NOT TO SCALE".] The radius of the sphere is $3.6\text{ cm}$. The radius of the cone is $r\text{ cm}$ and the slant height is $8...See it on the paper →
14. 0580/42 · May/June 2026 · Q6[3]
    6 A semicircle has a diameter of $15.8\text{ cm}$. Calculate the perimeter of the semicircle.See it on the paper →
15. 0580/03 · Specimen 2025 · Q21a[1]

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

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16. 0580/12 · October/November 2025 · Q24[1]
    [Diagram: A circle with centre $O$. A line segment $OA$ connects the centre to an external point $A$. A line segment $OB$ connects the centre to a point $B$ on the circle. A line $ABC$ is tangent to the circle at $B$. The angle $\angle OAB$ is marked as $36^{\circ }$. The diagram is labelled "NOT TO SCALE".] $B$ is a poin...See it on the paper →
17. 0580/22 · October/November 2025 · Q23a[1]
    [Diagram: A major sector AOB of a circle with centre O. The radius OB is labelled 12 cm. The reflex angle AOB is labelled 240°. The text "NOT TO SCALE" is present.] The diagram shows a major sector, $AOB$, of a circle. The sector angle is $240^{\circ }$ and the radius is $12$ cm. (a) Show that the length of the major arc...See it on the paper →
18. 0580/23 · October/November 2025 · Q19a[2]
    The diagram shows a circle, centre $O$, radius $12$ cm. [Diagram: A circle with centre $O$. Two radii $OA$ and $OB$ are drawn. The angle $\angle AOB$ is marked as $60^{\circ }$. The text "NOT TO SCALE" is present.] (a) Work out the area of the **minor** sector $AOB$. Give your answer in terms of $\pi$ in its simplest form...See it on the paper →
19. 0580/23 · October/November 2025 · Q19b[3]
    [Diagram: A circle with centre $O$. Points $A$ and $B$ are on the circumference. The angle $\angle AOB$ is marked as $60^{\circ }$. The text "NOT TO SCALE" is present.] The diagram shows a circle, centre $O$, radius $12$ cm. (b) Calculate the length of the major arc $AB$. Give your answer in terms of $\pi$ in its simplest...See it on the paper →
20. 0580/22 · February/March 2025 · Q14a[2]
    [Diagram: A circle with points $A,B,C,D,E$ on its circumference. A line $FG$ is tangent to the circle at $C$. The angle $\angle BAD$ is marked as $110^{\circ }$. The angle $\angle ADB$ is marked as $20^{\circ }$. The angle $\angle BEC$ is marked as $45^{\circ }$. The text "NOT TO SCALE" is present.] $A,B,C,D$ and $E$ lie...See it on the paper →

What examiners said

Most candidates found angle BCD correctly and many provided a correct geometrical explanation for this answer. The most common incorrect values stated were 110, 45 and 90. The most common errors were in the explanation: • Some candidates described opposite sides, rather than opposite angles, as summing to 180°. • Other candidates stated that the opposite angles were equal to 180°, without referri...

— Examiner report, February/March 2025, 0580/22 Q14(a) (Cambridge)

58° was seen often, but very few candidates were able to give the correct geometrical reason. Most knew ACB was a right-angle, but not the wording of the circle theorem. Many just showed the calculation to arrive at 58, showing that they knew the angles in a triangle add up to 180°.

— Examiner report, May/June 2023, 0580/13 Q20(b) (Cambridge)

Most candidates knew the triangle was right-angled and so gained the credit for angle x. However, quite a number assumed the two parts of the question were connected by parallel line properties and gave the answer 46, the answer for y. The reason was often not expressed accurately and often a triangle, rather than an angle, in a semicircle was given. The explanation also needed reference to the an...

— Examiner report, February/March 2023, 0580/12 Q15(a) (Cambridge)