plumiSine and cosine rules: OCR GCSE Maths questions
Every OCR GCSE Maths exam question on G22 Sine and cosine rules, 2017–2025, with its mark scheme and examiner’s report.
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All 17 questions on Sine and cosine rules, as a list
- June 2025, Paper 4, Q20 (3 marks): The diagram shows triangle ABC. A Not to scale 40° 12 cm C 58° B AC 12 cm , angle CAB = 40 ° and angle ABC = 58 ° . = Calculate length BC. cm
- November 2024, Paper 4, Q16 (6 marks): AC is a diagonal of the quadrilateral ABCD. B Not to scale C 108° 38° 34° 65° 25° A D 72 m AD = 72 m . Angle ABC = 108 ° , angle BCA = 3 8 ° and angle BAC = 34
- November 2024, Paper 6, Q16 (4 marks): Work out the exact value of x in this triangle. Not to scale 7 cm x cm 30° 6 3 cm x =
- June 2024, Paper 6, Q18 (6 marks): The diagram shows two triangles ABC and ADC. Not to scale A D 8 cm 60° 6 cm B 55° 20° C Angle ABC 60 ° , angle ACB = 20 ° and angle ACD = 55 ° . = AB = 8 cm and
- November 2023, Paper 4, Q19 (5 marks): The diagram shows the positions of three towns A, B and C. N Not to scale N B N 61 km 35 km C A The bearing of town B from town A is 053°. The bearing of town C
- November 2023, Paper 6, Q18 (4 marks): A, B and C are points on the circumference of a circle. A 8cm B Not to scale D 58° 45° C Points C and D lie on a tangent to the circle at C. Angle BCD 45 ° . =
- June 2023, Paper 4, Q20 (5 marks): The diagram shows triangle ABC. B Not to scale 10.6 cm 8.2 cm A C 12.5 cm AB = 10.6 cm, BC = 8.2 cm and AC = 12.5 cm. (a) Show that angle BAC = 40.5°, correct t
- November 2022, Paper 6, Q19 (6 marks): PQS and QRS are triangles. R Not to scale 8 cm 13 cm Q 9 cm 30° 15° S P PQ = 9 cm, QR = 8 cm and RS = 13 cm. Angle QPS = 30° and angle PSQ = 15°. Calculate angl
- November 2021, Paper 4, Q17 (6 marks): The diagram shows triangle ABC. A Not to scale 53° 48 mm B 85 mm C AC = 48 mm, BC = 85 mm and angle BAC = 53°. Calculate length AB. You must show your working.
- November 2020, Paper 4, Q14 (6 marks): The diagram shows triangle ABC. A Not to scale 72° 15 cm B C 18 cm AC = 15 cm, BC = 18 cm and angle BAC = 72°. Calculate length AB, giving your answer correct t
- November 2019, Paper 4, Q15 (7 marks): (a) Calculate length DF in this triangle. F Not to scale 10 cm 30° D G 12 cm (a) cm (b) Calculate angle ACB in this triangle. B Not to scale 12.8 cm 63° C A 12.
- June 2019, Paper 6, Q17 (8 marks): T is a radar tower. A and B are two aircraft. At 3pm • aircraft A is 3250 km from T on a bearing of 015° • aircraft B is 4960 km from T on a bearing of 057°. A
- November 2018, Paper 4, Q3 (1 mark): Here is Mario’s answer to a question. Question 3 Answer 92 – 62 x = 9 mm x mm x = 45 x = 6.708( d.p.) 3 88° 43° 6 mm Work out the value of x. Explain the error
- November 2018, Paper 6, Q19 (6 marks): In this triangle: • AB = 9 cm • AC = 10 cm • BC 2 5 cm • angle BCA = 60° • angle ABC 1 90°. B Not to scale 9 cm 60° A C 10 cm Calculate the area of triangle ABC
- June 2018, Paper 4, Q18 (6 marks): Calculate the area of this triangle. Not to scale 5.8 cm 3.9 cm 6.4 cm cm2
- November 2017, Paper 4, Q17 (7 marks): ABC and ACD are triangles. Not to scale A 18 cm 78° D 46° 14 cm 81° C B (a) Show that AC = 13.0 cm, correct to 3 significant figures. (b) Calculate BC. (b) cm
- June 2017, Paper 4, Q14 (6 marks): The diagram shows triangle ABC with D on AC and E on AB. DE is a straight line. A 28 m Not to scale 41 m D 22 m E C 64 m 72° B AD = 28 m, AE = 41 m, DE = 22 m a
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