Trigonometry: past paper questions

Where the questions come from

• Question 17May/June 2026, paper 12Structured9 marks

  In a right-angled triangle • the base is $x\text{ cm}$ • the height is $7\text{ cm}$ shorter than the base • the hypotenuse (longest side) is $2\text{ cm}$ longer than the base. Use this information to form an equation and show that it simplifies to $x^2-18x+45=0$.

  Try this question
• Question 23Oct/Nov 2025, paper 12Structured4 marksHas a diagram

  The diagram shows a square-based pyramid. $X$ is the centre of the square base. Vertex $E$ is vertically above $X$ and $EX=7\text{ cm}$.

  Try this question
• Question 25Oct/Nov 2024, paper 11Structured3 marksHas a diagram

  The diagram shows a cuboid. $EH=6\mathrm{c}\mathrm{m}$, $HG=2\mathrm{c}\mathrm{m}$ and $EC=7\mathrm{c}\mathrm{m}$. Calculate $CG$.

  Try this question
• Question 9Oct/Nov 2023, paper 21Structured14 marksHas a diagram

  The diagram shows a triangular prism. $AB=6\text{ cm}$, angle $BAC={55}^{\circ }$ and the length of the prism is $20\text{ cm}$. The area of triangle $ABC$ is $34.4{\text{ cm}}^2$.

  Try this question
• Question 22May/June 2026, paper 22Structured8 marksHas a diagram

  The diagram shows a triangular garden $ABD$. A path from $A$ meets $BD$ at point $C$. $CD=8\text{ m}$, angle $ADC={18}^{\circ }$, angle $ACB={34}^{\circ }$ and angle $ABC={90}^{\circ }$.

  Try this question
• Question 20Oct/Nov 2025, paper 21Structured9 marksHas a diagram

  The diagram shows a triangular field, ABC.

  Try this question
• Question 8Oct/Nov 2024, paper 21Structured8 marksHas a diagram

  $ABCD$ is a field. $AB=320\text{ m}$, $BC=250\text{ m}$, $CD=132\text{ m}$ and $AD=365\text{ m}$. Angle $BCD={90}^{\circ }$.

  Try this question
• Question 9Oct/Nov 2023, paper 22Structured11 marksHas a diagram

  $ABCD$ is a rectangular field. $C$ is due south of $A$. $AB=450\text{ m}$ and $BC=210\text{ m}$.

  Try this question
• Question 25Oct/Nov 2025, paper 21Structured6 marks

  The diagram shows a cuboid.

  Try this question
• Question 9Oct/Nov 2024, paper 21Structured10 marksHas a diagram

  $ABD$ is a triangle. $C$ is a point on $BD$ and $E$ is a point on $AD$. $AB$ is parallel to $EC$ and $CD=DE$.

  Try this question
• Question 22Oct/Nov 2025, paper 22Structured10 marksHas a diagram

  $ABCD$ is a field. A straight path crosses the field from $B$ to $D$. Calculate $AB$.

  Try this question
• Question 8Oct/Nov 2024, paper 22Structured12 marksHas a diagram

  $ADB$ and $AEC$ are straight lines. $BC$ is parallel to $DE$. $BC=9.8\text{ cm}$, $BD=2.7\text{ cm}$, $DE=5.6\text{ cm}$ and $CE=3.9\text{ cm}$.

  Try this question
• Question 11May/June 2023, paper 21Structured9 marksHas a diagram

  The diagram shows an open container on a horizontal surface. The container is a prism with trapezium $ABCD$ as its cross-section. $AB=28\text{ cm}$, $DC=24\text{ cm}$, $AD=16\text{ cm}$ and $BF=29\text{ cm}$.

  Try this question
• Question 22May/June 2025, paper 22Structured9 marksHas a diagram

  The diagram shows a triangular field $ABC$. $AB=150\text{ m}$, $BC=187\text{ m}$ and angle $ABC={112}^{\circ }$. Fencing is needed for the perimeter of the field.

  Try this question
• 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 $D$.

  Try this question
• Question 9May/June 2023, paper 22Structured12 marksHas a diagram

  $A$, $B$ and $C$ are points on horizontal ground. The bearing of $B$ from $A$ is ${072}^{\circ }$. The bearing of $C$ from $A$ is ${205}^{\circ }$.

  Try this question
• Question 7May/June 2024, paper 21Structured10 marksHas a diagram

  A cuboid has dimensions 5 cm by 12 cm by $h$ cm. The volume of the cuboid is $480{\text{ cm}}^3$. Calculate the value of $h$.

  Try this question
• Question 9May/June 2024, paper 21Structured10 marksHas a diagram

  The diagram shows the positions of three ports $A$, $B$ and $C$. The bearing of port $B$ from port $A$ is ${107}^{\circ }$. The bearing of port $C$ from port $A$ is ${192}^{\circ }$.

  Try this question
• Question 10May/June 2024, paper 22Structured7 marksHas a diagram

  The diagram shows a pentagon. Calculate the interior angle $B$.

  Try this question