Trigonometry: past paper questions

Where the questions come from

• Question 7May/June 2026, paper 21Structured2 marks

  The diagram shows the positions of three ships $P$, $Q$ and $R$. Ship $Q$ is $40\text{ km}$ due east of ship $R$. Ship $P$ is $40\text{ km}$ due north of ship $Q$.

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• Question 20Oct/Nov 2024, paper 21Structured5 marksHas a diagram

  The diagram shows two right-angled triangles $PQS$ and $RQT$. $PQR$ and $QTS$ are straight lines. Calculate angle $QTR$.

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• Question 18Oct/Nov 2023, paper 21Structured3 marksHas a diagram

  Calculate the value of $y$.

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• Question 18May/June 2026, paper 21Structured2 marks

  $y=\sin {60}^{\circ }\times \tan {30}^{\circ }$. Find the value of $y$.

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• Question 19Oct/Nov 2025, paper 22Structured3 marksHas a diagram

  The diagram shows a box in the shape of a cuboid. Mala has a straight rod of length $10\text{ cm}$. Show that this rod does not fit completely inside the box.

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• Question 21May/June 2026, paper 21Structured9 marksHas a diagram

  The diagram shows a solid cuboid $ABCDEFGH$. $BF=2\text{ cm}$, $BC=6\text{ cm}$ and $CD=9\text{ cm}$. Calculate the volume of the cuboid.

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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 21Oct/Nov 2023, paper 21Structured4 marksHas a diagram

  The diagram shows a cuboid $ABCDEFGH$. $AB=15.1\text{ cm}$, $BC=4.5\text{ cm}$ and $CG=9.2\text{ cm}$. Calculate the angle that the diagonal $BH$ makes with the face $ADHE$.

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• Question 10Oct/Nov 2025, paper 23Structured4 marksHas a diagram

  The diagram shows a right-angled triangle $ABC$. Work out the exact length of $AC$.

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• Question 16Oct/Nov 2024, paper 23Structured3 marks

  Calculate the shortest distance from $C$ to $AB$.

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• Question 19Oct/Nov 2023, paper 23Structured4 marksHas a diagram

  Calculate the obtuse angle $PRQ$.

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• Question 13May/June 2026, paper 23Structured3 marksHas a diagram

  $A$, $B$ and $C$ are points on a circle with centre $O$. $AOC$ is a straight line and $M$ is the midpoint of $AB$. $AB=6\text{ cm}$ and $OM=4\text{ cm}$.

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• Question 21Oct/Nov 2023, paper 23Structured6 marks

  The diagram shows a cuboid $ABCDEFGH$. $AB=14\text{ cm}$, $BC=5\text{ cm}$ and $CG=8\text{ cm}$. $M$ is the midpoint of $HG$.

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• Question 19May/June 2026, paper 23Structured4 marks

  Find the exact value of $x$.

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• Question 23Oct/Nov 2025, paper 23Structured3 marks

  Work out the area of triangle $ABC$.

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• Question 22Oct/Nov 2024, paper 23Structured4 marksHas a diagram

  The diagram shows a cuboid with a diagonal $PB$. Calculate the angle between the diagonal $PB$ and the base $ABCD$.

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• Question 5Oct/Nov 2023, paper 41Structured14 marksHas a diagram

  $ACD$ is a right-angled triangle. $B$ is on $AC$ and $BC=54.5\text{ m}$. $AD=83.2\text{ m}$ and angle $ABD={38}^{\circ }$.

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• Question 11May/June 2026, paper 42Structured2 marks

  Calculate $XY$.

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• Question 13Oct/Nov 2025, paper 41Structured3 marksHas a diagram

  The diagram shows two vertical poles, $AE$ and $PT$, standing on horizontal ground, $AP$. Calculate the angle of elevation of the point $T$ from the point $E$.

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• Question 6Oct/Nov 2024, paper 41Structured11 marksHas a diagram

  The diagram shows a field $ABCD$. A straight path $AC$ goes across the field. Show that $AC=1028\text{ m}$, correct to the nearest metre.

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• Question 6Oct/Nov 2023, paper 42Structured7 marks

  The diagram shows a right-angled triangle. Find the value of $w$.

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• Question 14May/June 2026, paper 42Structured2 marks

  $\cos x=0.41$ Find the reflex angle $x$.

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• Question 21Oct/Nov 2025, paper 41Structured2 marks

  In triangle $STU$, $ST=8\text{ cm}$, $SU=9\text{ cm}$ and angle $TSU={50}^{\circ }$. Calculate the area of triangle $STU$.

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• Question 9Oct/Nov 2024, paper 41Structured12 marksHas a diagram

  $ABCDEFGH$ is a solid cuboid. $AB=10\text{ cm}$, $BC=8\text{ cm}$ and $CG=17\text{ cm}$. Work out the volume of the cuboid.

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• Question 7Oct/Nov 2023, paper 42Structured16 marksHas a diagram

  The diagram shows a right-angled triangle $PQR$ on horizontal ground. $X$ is vertically above $R$ and the angle of elevation of $X$ from $P$ is ${21}^{\circ }$. $XR=2.8\mathrm{m}$ and $RQ=7.1\mathrm{m}$.

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• Question 16May/June 2026, paper 42Structured9 marksHas a diagram

  $ABCDE$ is a square-based pyramid. $EC$ and $BD$ intersect at $F$. $AF$ is perpendicular to the base $BCDE$.

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• Question 27Oct/Nov 2025, paper 41Structured4 marksHas a diagram

  The diagram shows a prism of length $15\text{ cm}$. The cross-section of the prism is a trapezium. Angle $DAB={90}^{\circ }$ and angle $ADC={90}^{\circ }$.

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• Question 7Oct/Nov 2024, paper 42Structured20 marksHas a diagram

  The diagram shows a field, $ABCD$ with $B$ north of $A$. $BD$ is a path across the field. $AB=85\text{ m}$, $AD=72\text{ m}$, $BD=129\text{ m}$, angle $BDC={39}^{\circ }$ and angle $BCD={60}^{\circ }$.

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• Question 7Oct/Nov 2023, paper 43Structured11 marks

  Complete the table of values for $y=3\cos 2x^{\circ }$.

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• Question 20May/June 2026, paper 42Structured10 marksHas a diagram

  The diagram shows a field $ABCD$ with a straight footpath from $A$ to $C$. Find the bearing of $A$ from $B$.

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