Circles, arcs and sectors: past paper questions

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• Question 23May/June 2026, paper 22Structured12 marksHas a diagram

  The diagram shows a sector of a circle with centre $O$ and radius $9.1\text{ cm}$. The length of the major arc $AB$ is $44\text{ cm}$. Find the angle of the major sector $AOB$.

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• Question 10Oct/Nov 2025, paper 11Structured2 marks

  A circle has diameter $12\text{ cm}$. Find the area of the circle.

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• Question 15Oct/Nov 2024, paper 11Structured4 marks

  A sector of a circle with angle ${60}^{\circ }$ has arc length $4\pi \mathrm{c}\mathrm{m}$. Find the area of the sector.

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• Question 21Oct/Nov 2023, paper 12Structured5 marksHas a diagram

  Diagram A shows a sector of a circle, centre D and radius 3/4y cm. The obtuse angle EDF = 6x°. Diagram B shows a sector of a circle, centre P and radius y cm.

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• Question 23Oct/Nov 2025, paper 22Structured5 marksHas a diagram

  The diagram shows a shaded area in a large circle, centre $O$. The radius of the large circle is $10\text{ cm}$. $OAB$ is a sector of a small circle, centre $O$.

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• Question 9Oct/Nov 2024, paper 22Structured10 marksHas a diagram

  $A$, $B$, $C$ and $D$ are points on a circle, centre $O$. $AOD$ and $OCE$ are straight lines. $DE$ is a tangent to the circle at $D$.

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• Question 10Oct/Nov 2023, paper 21Structured8 marksHas a diagram

  The diagram shows a circle, centre $O$, with diameters $AC$ and $BD$. Show that triangle $OAB$ is congruent to triangle $ODC$.

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• Question 23May/June 2025, paper 12Structured5 marksHas a diagram

  $OAB$ is a minor sector of a circle, centre $O$. $OCD$ is a major sector of a different circle, centre $O$. $OCA$ and $ODB$ are straight lines.

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• Question 8May/June 2024, paper 22Structured15 marksHas a diagram

  [Volume of a cone $=\frac{1}{3}\pi r^{2}h$] [Volume of a sphere $=\frac{4}{3}\pi r^3$] [Curved surface area of cone $=\pi rl$] [Surface area of a sphere $=4\pi r^2$] A solid is formed by placing a cone on top of a hemisphere.

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• Question 16May/June 2023, paper 11Structured3 marksHas a diagram

  $OMN$ is a sector of a circle, centre $O$. $ON=20\text{ cm}$ and the area of the sector is $30\pi {\text{ cm}}^2$. Find the value of $x$.

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• Question 8May/June 2023, paper 22Structured11 marksHas a diagram

  The length of the rectangle $R$ is twice its width. Rectangle $R$ has a perimeter of $20.4\text{ cm}$. Find the length and width of the rectangle $R$.

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