Circles, arcs and sectors: past paper questions

Where the questions come from

• Question 23May/June 2026, paper 12Structured2 marks

  The circumference of a circle is $18\pi \text{ cm}$. Work out the radius of the circle.

  Try this question
• Question 27Oct/Nov 2025, paper 11Structured3 marksHas a diagram

  The diagram shows a semicircle. The radius of the semicircle is $8\text{ cm}$. Find the perimeter of the semicircle.

  Try this question
• Question 11Oct/Nov 2024, paper 11Structured3 marks

  The circumference of a wheel is $198.55\text{ cm}$. Calculate the diameter of the wheel.

  Try this question
• Question 17Oct/Nov 2023, paper 11Structured2 marks

  The circumference of a circle is $59\text{ cm}$. Calculate the radius of the circle.

  Try this question
• Question 16May/June 2026, paper 13Structured2 marks

  The area of a circle is $36\pi {\text{ cm}}^2$. Find the radius of the circle.

  Try this question
• Question 18Oct/Nov 2025, paper 13Structured2 marks

  The diameter of a circle is 16cm. Find the area of the circle.

  Try this question
• Question 20Oct/Nov 2024, paper 12Structured3 marksHas a diagram

  Points $A$ and $B$ lie on a circle, centre $O$ and radius $r$. The area of the circle is $120{\text{ cm}}^2$. Find the area of the right-angled triangle $AOB$.

  Try this question
• Question 25Oct/Nov 2023, paper 11Structured2 marks

  Calculate the area of a semicircle with radius $10\text{ cm}$.

  Try this question
• Question 17May/June 2026, paper 31Structured4 marksHas a diagram

  The diagram shows a circle inside a rectangle. The shaded area is $450{\text{ cm}}^2$. Find the radius of the circle.

  Try this question
• Question 22Oct/Nov 2025, paper 32Structured6 marksHas a diagram

  The diagram shows a garden. The garden has a circular pond and the shaded area is grass. The width of the grass area is equal to the diameter of the pond.

  Try this question
• Question 7Oct/Nov 2024, paper 33Structured12 marksHas a diagram

  Write down the mathematical name for this solid.

  Try this question
• Question 17Oct/Nov 2023, paper 12Structured4 marksHas a diagram

  $A$, $B$ and $C$ are points on a circle, centre $O$. Draw a tangent to the circle at point $A$.

  Try this question
• Question 20May/June 2026, paper 32Structured4 marksHas a diagram

  A metal rectangle is 25 cm by 60 cm. 12 circles, each with radius 5 cm, are cut out of the metal. Calculate the percentage of the metal remaining.

  Try this question
• Question 25May/June 2025, paper 12Structured3 marksHas a diagram

  The diagram shows a shape made from two different semicircles, with the same centre. The radius of the large semicircle is $7\text{ cm}$. The radius of the small semicircle is $4\text{ cm}$.

  Try this question
• Question 25May/June 2024, paper 11Structured7 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.

  Try this question
• Question 20Oct/Nov 2023, paper 13Structured2 marksHas a diagram

  The diagram shows a sector of a circle with radius $r\text{ cm}$ and sector angle ${72}^{\circ }$. The arc length is $9.35\text{ cm}$. Calculate the value of $r$.

  Try this question
• Question 19May/June 2025, paper 13Structured2 marksHas a diagram

  The diagram shows a sector of a circle with radius $3\text{ cm}$ and sector angle ${60}^{\circ }$. Calculate the area of the sector.

  Try this question
• Question 16May/June 2024, paper 12Structured5 marks

  A circle has an area of $36\pi {\text{ cm}}^2$. Find the circumference of the circle.

  Try this question
• Question 7Oct/Nov 2023, paper 32Structured16 marksHas a diagram

  Elize, Lily and Marco start a business. Elize invests $5000. Lily invests $8000.

  Try this question
• Question 29May/June 2025, paper 31Structured3 marksHas a diagram

  This shape is made from a rectangle and a semicircle. The diameter of the semicircle is $10\text{ cm}$. Calculate the perimeter of this shape.

  Try this question
• Question 8May/June 2024, paper 32Structured10 marksHas a diagram

  The diagram shows a plan, $ABCDE$, of the floor of a room in Jo's house. $F$ is a point inside the room. Show that $EF=1.9\text{ m}$.

  Try this question
• Question 9Oct/Nov 2023, paper 33Structured10 marksHas a diagram

  The diagram shows a semicircle with diameter $AB$. $O$ is the midpoint of $AB$ and $C$ is a point on the circumference. Calculate the area of triangle $ABC$.

  Try this question
• Question 8May/June 2024, paper 33Structured10 marksHas a diagram

  Find the area of this trapezium.

  Try this question
• Question 10May/June 2023, paper 31Structured7 marksHas a diagram

  The diagram shows a right-angled triangle, $ABC$, and a semicircle. The radius of the semicircle is $4.5\text{ cm}$. $AC=8.9\text{ cm}$ and $BC=13.2\text{ cm}$.

  Try this question
• Question 5May/June 2023, paper 32Structured11 marksHas a diagram

  This rectangle has an area of $12{\text{ cm}}^2$ and a perimeter of $16\text{ cm}$. This shape is made from six of these rectangles. Find the area and perimeter of this shape.

  Try this question