plumiPythagoras and trigonometry: Edexcel GCSE Maths questions
Every Edexcel GCSE Maths exam question on G20 Pythagoras and trigonometry, 2017–2025, with its mark scheme and examiner’s report.
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All 50 questions on Pythagoras and trigonometry, as a list
- June 2025, Paper 2H, Q7 (2 marks): ABC is a right-angled triangle. 7 cm A B 4 cm x C Calculate the value of x. Give your answer correct to 1 decimal place. x =
- June 2025, Paper 2H, Q19 (4 marks): ABCDEFGH is a cuboid. C B H 27 G D A 52 E 15 cm F Angle GEF = 52° Angle BHG = 27° EF = 15 cm Work out the size of angle GEB. Give your answer to the nearest deg
- June 2025, Paper 2H, Q23 (5 marks): ABCD is a quadrilateral. B A 125 6 cm 12 cm D 9 cm 60 C Find the size of angle ABC. Give your answer correct to the nearest degree. °
- June 2025, Paper 3H, Q8 (5 marks): The diagram shows trapezium ABCD. D C 8 cm A B 12 cm AB = 12 cm AD = 8 cm The trapezium has an area of 112 cm 2 Work out the perimeter of the trapezium. Give yo
- November 2024, Paper 2H, Q20 (3 marks): VABC is a solid pyramid. ABC is an equilateral triangle. V C F A M B M is the midpoint of AB. F is the point on MC such that MF : FC = 1 : 2 The vertex V is ver
- November 2024, Paper 3H, Q8 (2 marks): ABC is a right-angled triangle. A B 7.6 cm 62° C Calculate the length of AB. Give your answer correct to 1 decimal place. cm
- November 2024, Paper 3H, Q19 (4 marks): The diagram shows a cone. l Curved surface h area of cone = πrl r The radius of the base of the cone is 3 4 of the height of the cone. The total surface area of
- June 2024, Paper 2H, Q1 (2 marks): ABC is a right-angled triangle. A 19 cm 10 cm C B Work out the length of CB. Give your answer correct to 3 significant figures. cm
- June 2024, Paper 2H, Q10 (3 marks): The diagram shows two right-angled triangles. a 8 1 + x b 7 – 2x 4 All lengths are measured in centimetres. Given that sin a = tan b work out the value of x. x
- November 2023, Paper 3H, Q24 (4 marks): The diagram shows a triangular prism with a horizontal rectangular base ABCD. C T B D M A M is the midpoint of AD. The vertex T of the prism is vertically above
- June 2023, Paper 1H, Q22 (2 marks): ABCDEFGH is a cuboid. G H F E B C A D AF = 6.8 cm FC = 13.6 cm Work out the size of the angle between FC and the plane ABCD. °
- June 2023, Paper 2H, Q12 (4 marks): The points A, B, C and D lie on a circle, centre O. ABCD is a rectangle. 8 cm A B O 10 cm D C AB = 8 cm BC = 10 cm Work out the circumference of the circle. Giv
- June 2023, Paper 2H, Q19 (3 marks): ABC is a right-angled triangle. A 12.6 cm 9.3 cm x B C AB = 9.3 cm correct to the nearest mm. AC = 12.6 cm correct to the nearest mm. Calculate the lower bound
- June 2023, Paper 3H, Q10 (3 marks): ABD is a triangle. C is a point on BD. A 6.8 cm 41° 55° D B C Work out the length of DC. Give your answer correct to 1 decimal place. cm
- November 2022, Paper 2H, Q5 (2 marks): x cm 14.5 cm 53° Work out the value of x. Give your answer correct to 3 significant figures. x =
- November 2022, Paper 2H, Q13 (2 marks): A and B are points on a centimetre grid. A is the point with coordinates (−7, 6) B is the point with coordinates (8, −5) Work out the length of AB. Give your an
- November 2022, Paper 2H, Q20 (4 marks): ABCDEFGH is a cuboid. B C D A G H F E AD = 9 cm FD = 13 cm Angle GHF = 49° Work out the size of angle FAH. Give your answer correct to the nearest degree. °
- June 2022, Paper 1H, Q13 (3 marks): A right-angled triangle is formed by the diameters of three semicircular regions, A, B and C as shown in the diagram. A C B Show that area of region A = area of
- June 2022, Paper 3H, Q1 (2 marks): Here is a right-angled triangle. 8.5 cm 4 cm x cm Work out the value of x. x =
- June 2022, Paper 3H, Q12 (3 marks): ABC and ACD are right-angled triangles. A 20° 45° D 8 cm C B DC = 8 cm Angle ADC = 45° Angle ABC = 20° Work out the length of AB. Give your answer correct to 3
- June 2022, Paper 3H, Q18 (5 marks): Here is a prism ABCDSPQR. R S 12 cm Q P D C T 14 cm A B The base ABCD of the prism is a square of side 14 cm T is the point on BC such that BT : TC = 4 : 3 The
- November 2021, Paper 1H, Q18 (5 marks): Here is trapezium ABCD. A B 6 cm 30° D C The area of the trapezium is 66 cm2 the length of AB : the length of CD = 2 : 3 Find the length of AB. cm
- November 2021, Paper 2H, Q5 (4 marks): Here is a right‑angled triangle. 8 mm 10 mm The shaded shape below is made from two of these triangles. 8 mm 8 mm 10 mm Work out the perimeter of the shaded sha
- November 2021, Paper 2H, Q6 (4 marks): ABC is a right‑angled triangle. A 56° 12 cm C B (a) Work out the length of BC. Give your answer correct to 1 decimal place. cm PQR is a right‑angled triangle. P
- November 2020, Paper 2H, Q5 (2 marks): 178 mm x mm 34° Work out the value of x. Give your answer correct to 1 decimal place.
- November 2020, Paper 2H, Q7 (4 marks): The diagram shows a right-angled triangle and a quarter circle. C D 9 m A 6 m B The right-angled triangle ABC has angle ABC = 90° The quarter circle has centre
- November 2020, Paper 3H, Q9 (5 marks): The diagram shows a prism. 40° 12 cm 20 cm 10 cm The cross section of the prism has exactly one line of symmetry. Work out the volume of the prism. Give your an
- November 2020, Paper 3H, Q18 (4 marks): The diagram shows a cube. A B D C F G E H AH = 11.3 cm correct to the nearest mm. Calculate the lower bound for the length of an edge of the cube. You must show
- November 2019, Paper 2H, Q12 (4 marks): The diagram shows triangle ABC. B 8.6 cm E 40° A C 4.4 cm D ADC and DEB are straight lines. AD = 4.4 cm BC = 8.6 cm E is the midpoint of DB. Angle CDB = 90° Ang
- June 2019, Paper 2H, Q5 (2 marks): ABC is a right-angled triangle. A 16 cm 38° B C Calculate the length of AB. Give your answer correct to 2 decimal places. cm
- June 2019, Paper 2H, Q19 (4 marks): The diagram shows a triangular prism. F E C B 35° 15 cm D 15 cm A The base, ABCD, of the prism is a square of side length 15 cm. Angle ABE and angle CBE are rig
- June 2019, Paper 3H, Q8 (2 marks): ABC is a right-angled triangle. B 6 cm A 8 cm C Here is Sarah’s method to find the length of BC. BC2 = AB2 + AC2 = 62 + 82 = 100 BC = 10 (a) What mistake has
- June 2019, Paper 3H, Q22 (4 marks): The diagram shows a circle, centre O. y P (3p, p) B (16, 0) O x 30° A AB is the tangent to the circle at the point A. Angle OBA 30° Point B has coordinates (16,
- November 2018, Paper 1H, Q8 (3 marks): (a) Write down the exact value of tan 45° Here is a right-angled triangle. 60° x cm 4 cm cos 60° = 0.5 (b) Work out the value of x.
- November 2018, Paper 2H, Q13 (3 marks): The diagram shows a circle and an equilateral triangle. One side of the equilateral triangle is a diameter of the circle. The circle has a circumference of 44 c
- November 2018, Paper 3H, Q6 (4 marks): ABC is a right-angled triangle. B A C 14 cm AC = 14 cm. Angle C = 90q size of angle B : size of angle A = 3 : 2 Work out the length of AB. Give your answer corr
- November 2018, Paper 3H, Q12 (4 marks): Here is a pyramid with a square base ABCD. T B C A D AB = 5 m The vertex T is 12 m vertically above the midpoint of AC. Calculate the size of angle TAC. °
- November 2018, Paper 3H, Q16 (5 marks): Here is a shaded shape ABCD. B D C O A The shape is made from a triangle and a sector of a circle, centre O and radius 6 cm. OCD is a straight line. AD = 14 cm
- June 2018, Paper 1H, Q8 (4 marks): The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5 Work out the area of the triangle. cm2
- June 2018, Paper 2H, Q18 (4 marks): ABCDEFGH is a cuboid. F G H E B A D C AB = 7.3 cm CH = 8.1 cm Angle BCA = 48q Find the size of the angle between AH and the plane ABCD. Give your answer correct
- June 2018, Paper 3H, Q5 (3 marks): ABC is a right-angled triangle. A 11 cm C 7 cm B (a) Work out the size of angle ABC. Give your answer correct to 1 decimal place. q The length of the side AB is
- June 2018, Paper 3H, Q17 (5 marks): A 11.4 cm B 86q 109q 34q C 12.5 cm D Work out the length of AD. Give your answer correct to 3 significant figures. cm
- June 2018, Paper 3H, Q19 (5 marks): Here are two right-angled triangles. 6x + 5 x f e 4x – 1 12x + 31 Given that tan e = tan f find the value of x. You must show all your working.
- November 2017, Paper 2H, Q7 (5 marks): ABCDLVDWUDSH]LXP FP B C FP FP A D FP :RUNRXWWKHVL]HRIDQJOHCDA. *LYH\RXUDQVZHUFRUUHFWWRGHFLPDOSODFH
- November 2017, Paper 2H, Q20 (5 marks): B A C P O OACLVDVHFWRURIDFLUFOHFHQWUHOUDGLXV P BALVWKHWDQJHQWWRWKHFLUFOHDWSRLQWA. BCLVWKHWDQJHQWWRWKHFLUFOHDWSRLQWC.
- June 2017, Paper 1H, Q5 (5 marks): This rectangular frame is made from 5 straight pieces of metal. 5 m 12 m The weight of the metal is 1.5 kg per metre. Work out the total weight of the metal in
- June 2017, Paper 2H, Q21 (4 marks): The diagram shows 3 identical circles inside a rectangle. Each circle touches the other two circles and the sides of the rectangle, as shown in the diagram. The
- June 2017, Paper 3H, Q7 (2 marks): ABC is a right-angled triangle. B C 23q 15 cm A Calculate the length of AB. Give your answer correct to 3 significant figures. cm
- June 2017, Paper 3H, Q8 (4 marks): A square, with sides of length x cm, is inside a circle. Each vertex of the square is on the circumference of the circle. The area of the circle is 49 cm2. Work
- June 2017, Paper 3H, Q18 (5 marks): A 5 cm B O D 5 cm C A, B and C are points on a circle of radius 5 cm, centre O. DA and DC are tangents to the circle. DO = 9 cm Work out the length of arc ABC.
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