Circles, arcs and sectors: past paper questions

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• Question 15May/June 2026, paper 21Structured4 marksHas a diagram

  Shape $A$ is one quarter of a circle with radius $t\text{ cm}$. Shape $B$ is a sector of a circle with radius $2t\text{ cm}$ and sector angle ${135}^{\circ }$. The area of shape $B$ is $k$ times the area of shape $A$.

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• Question 12Oct/Nov 2025, paper 21Structured4 marksHas a diagram

  The diagram shows a sector of a circle with centre $O$ and radius $9\text{ cm}$. The perimeter of the sector is $(18+2\pi )\text{ cm}$. Find the area of the sector.

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• Question 9Oct/Nov 2024, paper 22Structured3 marks

  Points $A$, $B$, $C$ and $D$ lie on a circle. $ABCD$ is a square with area $72{\text{ cm}}^2$. Calculate the area of the circle.

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• Question 22Oct/Nov 2023, paper 21Structured4 marksHas a diagram

  $ABCD$ is a rhombus with side length $13.6\text{ cm}$. Angle $ABC={41}^{\circ }$. $BAC$ is a sector of a circle with centre $B$.

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• Question 13May/June 2026, paper 22Structured2 marks

  A sector of a circle has sector angle ${90}^{\circ }$ and radius $12\text{ cm}$. Calculate the arc length of the sector.

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• Question 23Oct/Nov 2025, paper 22Structured7 marksHas a diagram

  The diagram shows a major sector, $AOB$, of a circle. The sector angle is ${240}^{\circ }$ and the radius is $12\text{ cm}$. Show that the length of the major arc $AB$ is $16\pi \text{ cm}$.

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• Question 10Oct/Nov 2024, paper 41Structured14 marksHas a diagram

  This rectangle has area $190{\text{ cm}}^2$. By forming and solving an equation, show that $x=8.5$.

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• Question 8Oct/Nov 2023, paper 41Structured14 marksHas a diagram

  The diagram shows a solid formed by joining two hemispheres and a cylinder. The radius of the large hemisphere is $5.4\text{ cm}$. The radius of the small hemisphere and the radius of the cylinder are both $3.6\text{ cm}$.

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• Question 23May/June 2026, paper 23Structured3 marksHas a diagram

  A minor sector of a circle of radius $6\text{ cm}$ has sector angle ${50}^{\circ }$. Find the area of the major sector.

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• Question 19Oct/Nov 2025, paper 23Structured5 marksHas a diagram

  The diagram shows a circle, centre $O$, radius $12\text{ cm}$. Work out the area of the minor sector $AOB$.

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• Question 4Oct/Nov 2024, paper 42Structured15 marksHas a diagram

  The angles of a quadrilateral are $w^{\circ }$, $x^{\circ }$, $y^{\circ }$ and $z^{\circ }$. The ratio $w:(x+y+z)=3:5$. Find the value of $w$.

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• Question 4Oct/Nov 2023, paper 42Structured12 marksHas a diagram

  The diagram shows a sector of a circle that is made into a cone by joining $OA$ to $OB$. The sector angle is $x^{\circ }$ and the radius of the sector is $7.5\mathrm{c}\mathrm{m}$. The base radius of the cone is $1.5\mathrm{c}\mathrm{m}$.

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• Question 6May/June 2026, paper 42Structured3 marks

  A semicircle has a diameter of $15.8\text{ cm}$. Calculate the perimeter of the semicircle.

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• Question 7Oct/Nov 2025, paper 42Structured8 marksHas a diagram

  The diagram shows a parallelogram. The parallelogram has the same perimeter as a circle with radius 4 m. Show that $x=6.06\text{ m}$, correct to 2 decimal places.

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• Question 7Oct/Nov 2024, paper 43Structured15 marksHas a diagram

  Calculate the area of the trapezium.

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• Question 8Oct/Nov 2023, paper 43Structured17 marksHas a diagram

  The diagram shows a shape made from a major sector $AOB$ and triangles $OBC$ and $AOD$. $OB=6\text{ cm}$, $BC=2\text{ cm}$, obtuse angle $AOC={135}^{\circ }$ and angle $BCO={90}^{\circ }$. Show that angle $BOC={19.5}^{\circ }$, correct to 1 decimal place.

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• Question 10May/June 2025, paper 22Structured2 marksHas a diagram

  The diagram shows a sector of a circle, centre $O$. The length of the arc is $n\pi \text{ cm}$. Find the value of $n$.

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• Question 7May/June 2024, paper 21Structured7 marksHas a diagram

  The diagram shows a shape made from a triangle $JKL$ and a semicircle with diameter $JL$. $JKL$ is an isosceles right-angled triangle with $JK=JL=12.8\text{ cm}$. Calculate the area of this shape.

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• Question 11May/June 2023, paper 22Structured3 marks

  The diagram shows a shape, $ABCD$, formed by the sectors of two circles with the same centre $O$. Both sector angles are ${140}^{\circ }$, $OC=3.2\mathrm{c}\mathrm{m}$ and $CB=2.6\mathrm{c}\mathrm{m}$. The area of the shape is $k\pi {\mathrm{c}\mathrm{m}}^2$.

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• Question 20May/June 2025, paper 23Structured3 marks

  The diagram shows a sector of a circle, centre $O$. The radius of the circle is $6\text{ cm}$. Calculate the length of the major arc $AB$.

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• Question 14May/June 2024, paper 21Structured3 marksHas a diagram

  The diagram shows a circle with radius $9\text{ cm}$. Calculate the area of the shaded major sector.

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• Question 4May/June 2023, paper 41Structured14 marksHas a diagram

  Calculate the area of triangle $PQR$.

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• Question 19May/June 2025, paper 41Structured4 marksHas a diagram

  The diagram shows a major sector of a circle with radius $7.5\text{ cm}$. Calculate the perimeter of the major sector.

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• Question 9May/June 2024, paper 42Structured10 marksHas a diagram

  $OAB$ is a sector of a circle, centre $O$, radius 17 cm. $OCD$ is a sector of a circle, centre $O$, radius 10 cm. $OCA$ and $ODB$ are straight lines and angle $AOB={60}^{\circ }$.

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• Question 1May/June 2023, paper 42Structured18 marksHas a diagram

  The diagram shows an isosceles triangle with the base extended. Find the value of $x$.

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• Question 21May/June 2025, paper 43Structured4 marks

  The diagram shows an equilateral triangle $ABC$ with all sides of length $12\text{ cm}$. $ANP$ is a sector of a circle, centre $A$. $N$ lies on $AC$ such that $AN:NC=2:1$.

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• Question 11May/June 2024, paper 43Structured9 marksHas a diagram

  In the circle, centre $O$, the length of the minor arc $PQ$ is $\frac{3}{7}$ of the length of the major arc $PQ$. Show that $x=108$.

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• Question 9May/June 2023, paper 43Structured10 marksHas a diagram

  The diagram shows a shape made from a square $ABCD$ and two equal sectors of a circle. The square has side $11\text{ cm}$. $MAB$ and $DCN$ are straight lines.

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