plumiPythagoras and trigonometry: AQA GCSE Maths questions
Every AQA GCSE Maths exam question on G20 Pythagoras and trigonometry, 2017–2025, with its mark scheme and examiner’s report.
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All 44 questions on Pythagoras and trigonometry, as a list
- June 2025, Paper 2H, Q10 (3 marks): Use trigonometry to work out the value of x. You must show your working. Not drawn accurately x = cm
- November 2024, Paper 1H, Q13 (5 marks): (a) By rounding each number to one significant figure, estimate the value of + o 3 401 1.9 cos 58.7 You must show your working. Answer 13 (b) Here is a triangle
- November 2024, Paper 2H, Q6 (2 marks): Here is a right-angled triangle. Use Pythagoras’ theorem to show that x = 0.8 Not drawn accurately
- November 2024, Paper 2H, Q13 (4 marks): Two right-angled triangles are joined to make a larger triangle. Not drawn accurately Work out the size of angle x. x = °
- June 2024, Paper 2H, Q18 (3 marks): A diagonal of a rectangle is 23.7 cm long. The diagonal makes an angle of 52° with a side of length x cm Work out the value of x. x =
- June 2024, Paper 3H, Q2 (3 marks): Use Pythagoras’ theorem to work out the value of x. Give your answer as a decimal. Not drawn accurately Answer cm
- November 2023, Paper 2H, Q3 (3 marks): Use Pythagoras’ theorem to work out the value of x. Not drawn accurately x = cm
- November 2023, Paper 2H, Q28 (3 marks): VABCD is a pyramid with a horizontal square base. X is the centre of the base. V is vertically above X. BD = 18 cm Angle VBX = 72° Work out the length of VB. An
- November 2023, Paper 3H, Q9 (3 marks): Use trigonometry to work out the size of angle w. Not drawn accurately w = °
- November 2023, Paper 3H, Q16 (3 marks): PQ is a diameter of a circle. QR is a tangent to the circle. PQ = QR PR = 10 cm Work out the radius of the circle. Give your answer as a decimal. Not drawn accu
- June 2023, Paper 2H, Q17 (4 marks): Work out the size of angle x. Not drawn accurately x = °
- June 2023, Paper 3H, Q10 (3 marks): Use trigonometry to work out the value of x. Not drawn accurately x = cm
- June 2023, Paper 3H, Q16 (4 marks): Not drawn accurately In this right-angled triangle, a = 16 cm a : c = 4 : 5 Work out the area of the triangle. Answer cm2
- November 2022, Paper 2H, Q13 (5 marks): Trapezium DEFG is formed by joining triangle DEH to rectangle EFGH. ABC is similar to DEH. Work out the area of DEFG. Not drawn accurately Answer cm2
- June 2022, Paper 2H, Q11 (5 marks): A shape is made by joining a right-angled triangle to a rectangle. Work out the area of the shape. Not drawn accurately Answer cm2
- June 2022, Paper 3H, Q4 (3 marks): Use trigonometry to work out the size of angle x. Not drawn accurately x = °
- November 2021, Paper 1H, Q12 (3 marks): Here is a right-angled triangle. Use trigonometry to work out the value of x. Not drawn accurately Answer cm
- November 2021, Paper 2H, Q16 (2 marks): Here is a cube with edge length x cm One diagonal is shown. 16 (a) Circle the length, in centimetres, of the diagonal. 3 x 3 2 3x 3 x 3 3 x 16 (b) The total len
- November 2020, Paper 1H, Q5 (2 marks): Use trigonometry to work out the size of angle x. Not drawn accurately Answer degrees
- November 2020, Paper 2H, Q18 (4 marks): This shape is made from two right-angled triangles and a rectangle. Work out the size of angle x. Not drawn accurately Answer degrees
- November 2020, Paper 2H, Q23 (4 marks): Right-angled triangle ABC is the cross section of a prism. AB = 5 cm BC = 12 cm M is the midpoint of CF. AM = 16 cm Work out the volume of the prism. Answer cm3
- November 2020, Paper 3H, Q7 (3 marks): Use Pythagoras’ theorem to work out the value of x. Not drawn accurately Answer cm
- November 2019, Paper 2H, Q12 (4 marks): An isosceles triangle has base 16 cm and perpendicular height 15 cm Some of these triangles are used to make a large triangle. Work out the perimeter of the lar
- November 2019, Paper 3H, Q19 (3 marks): Here is a cuboid. DH = 8 cm DB = 13 cm 19 (a) Work out the size of angle DBH. Answer degrees 19 (b) Using your answer to part (a), work out the size of angle EC
- June 2019, Paper 2H, Q7 (4 marks): The diagram shows rectangle ABDE and right-angled triangle ABC. AC = 17 cm BC = 8 cm BC : CD = 1 : 2 Work out the area of rectangle ABDE. Not drawn accurately A
- June 2019, Paper 2H, Q19 (4 marks): Work out the area of the trapezium. Not drawn accurately Answer cm2
- June 2019, Paper 3H, Q24 (3 marks): The length of a diagonal of a cuboid is 20 cm The diagonal makes an angle of 24° with the base. The area of the base is 150 cm2 Work out the volume of the cuboi
- November 2018, Paper 2H, Q25 (5 marks): ABC and ACD are triangles. Work out the size of angle x. Not drawn accurately Answer degrees
- November 2018, Paper 3H, Q11 (2 marks): Use trigonometry to work out the size of angle x. Not drawn accurately Answer degrees
- November 2018, Paper 3H, Q23 (5 marks): The diagram shows the side view of a step ladder with a horizontal strut of length 48 cm The strut is one third of the way up the ladder. The symmetrical cross
- June 2018, Paper 2H, Q19 (4 marks): A pentagon is made from a square and an isosceles triangle. Work out the perimeter of the pentagon. Not drawn accurately Answer cm
- June 2018, Paper 2H, Q21 (4 marks): Liz and Tia are walking towards a shop along different straight paths. The diagram shows their positions at 2 pm Not drawn accurately 21 (a) Assume they walk at
- June 2018, Paper 3H, Q20 (3 marks): All dimensions are in centimetres. Use Pythagoras’ theorem to work out the exact value of y x Not drawn accurately Answer
- June 2018, Paper 3H, Q25 (6 marks): ABCDEF is a triangular prism which represents part of a hill. ABCF is the horizontal rectangular base. D is vertically above C. 25 (a) Work out the height CD. A
- November 2017, Paper 2H, Q9 (2 marks): Work out the size of angle x. Not drawn accurately Answer degrees
- November 2017, Paper 2H, Q17 (3 marks): Work out the area of the parallelogram. Not drawn accurately Answer cm2
- November 2017, Paper 3H, Q27 (6 marks): VABCD is a square-based pyramid. The horizontal base ABCD has side length 10 cm and centre M. Angle VMA is 90° Angle VAM is 68° Volume of pyramid = 3 1 × area o
- June 2017, Paper 2H, Q7 (2 marks): Use trigonometry to work out the length x. Not drawn accurately Answer cm
- June 2017, Paper 2H, Q15 (2 marks): Sami is trying to work out the exact value of y using Pythagoras’ theorem. Here is her working. (2y)2 = 62 + 82 2y2 = 36 + 64 2y2 = 100 y2 = 100 ÷ 2 y2 = 50 y =
- June 2017, Paper 3H, Q25 (6 marks): Rectangle ABCD is the horizontal base of a triangular prism ABCDEF. AE = BE E is vertically above M, the midpoint of AB. AB = 16 cm AE = 17 cm BC = 30 cm 25 (a)
- Specimen, Paper 1H, Q13 (3 marks): Here are sketches of four triangles. 1 cm 0.53 cm 50° 0.77 cm 1 cm 50° Not drawn accurately 1 cm 1 cm 0.64 cm 50° 0.86 cm 50° In each triangle the longest side
- Specimen, Paper 2H, Q24 (6 marks): A Big Wheel is modelled as a circle with centre O and radius 15 metres. The wheel turns in an anticlockwise direction. The lowest point on the wheel is always 2
- Specimen, Paper 3H, Q15 (4 marks): The diagram shows a design for a zipwire. The zipwire will run between the top of two vertical posts, AB and CD. Work out the distance AD. 2.3 m B C A Not drawn
- Specimen, Paper 3H, Q28 (4 marks): The diagram shows a line joining O to P. The gradient of the line is 2 The length of the line is 2645 Work out the coordinates of P. O P x Not drawn accurately
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