plumiSine and cosine rules, area of a triangle: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.05.1 Sine and cosine rules, area of a triangle, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 14 questions on Sine and cosine rules, area of a triangle, as a list
- June 2025, Paper 1, Q6 (8 marks): B NOT TO SCALE 6cm A C D The diagram shows a triangle ABC. The arc BD is part of a circle with centre A and radius 6 cm. 2. The area of the sector ABD is 14 4 .
- June 2025, AS Paper 2, Q3 (6 marks): In a triangle ABC, AB = 9 cm, BC = 7 cm and AC = 4 cm. 2 (a) Show that cos CAB . [2] = 3 (b) Hence find the exact value of sin CAB. [2] (c) Find the exact area
- June 2024, AS Paper 1, Q3 (5 marks): In the triangle ABC, AB = 3, AC = 5 and angle BAC = a. 5. The area of the triangle is 2 Determine the two possible values of cos a. Give your answers in exact f
- June 2024, AS Paper 2, Q2 (5 marks): D C 5 cm A B 14cm The diagram shows a parallelogram ABCD where AB 14 cm , AD 5 cm and angle DAB is = = 2. obtuse. The area of ABCD is 50 cm (a) Determine, in de
- June 2023, Paper 1, Q1 (5 marks): In the triangle ABC, the length AB = 6 cm, the length AC = 15 cm and the angle BAC = 30°. (a) Calculate the length BC. [2] D is the point on AC such that the le
- June 2023, Paper 2, Q4 (9 marks): x2 4 The diagram shows part of the graph of y . The normal to the curve at the point A(1, 1) meets = the curve again at B. Angle AOB is denoted by a. y B 2 A 1
- June 2022, AS Paper 2, Q7 (9 marks): A 2i + 4j C O 4i – 3j B The diagram shows the parallelogram OACB where OA 2 i 4 j and OB 4 i 3 j . = + = - 2 5 (a) Show that cos AOB . [5] = - 25 (b) Hence find
- November 2021, Paper 3, Q2 (6 marks): B A 60° C The diagram shows triangle ABC in which angle A is 60° and the lengths of AB and AC are ( 4 h ) cm and ( 4 h ) cm respectively. + - (a) Show that the
- November 2021, AS Paper 1, Q1 (7 marks): In the triangle ABC, AB = 3, BC = 4 and angle ABC = 30°. Find the following. (a) The area of the triangle. [2] (b) The length AC. [2] (c) The angle ACB. [3]
- November 2020, Paper 3, Q1 (2 marks): Triangle ABC has AB = 8.5 cm, BC = 6.2 cm and angle B = 35°. Calculate the area of the triangle. [2]
- November 2020, AS Paper 2, Q1 (5 marks): B 25° O A 9.5 cm The diagram shows a sector AOB of a circle with centre O and radius 9.5 cm. The angle AOB is 25°. (a) Calculate the length of the straight line
- June 2019, Paper 3, Q1 (2 marks): C 13.5cm 8.3cm 32° A B The diagram shows triangle ABC, with AC 13 5cm . , BC 8 3cm . and angle ABC 32° . = = = Find angle CAB. [2]
- June 2019, AS Paper 1, Q6 (6 marks): B xcm 60° A ycm C The diagram shows triangle ABC, with AB = x cm, AC = y cm and angle BAC = 60°. It is given that ^ h 3cm2 the area of the triangle is x y . + (
- June 2018, AS Paper 2, Q1 (6 marks): In triangle ABC, AB = 20 cm and angle B = 45°. (i) Given that AC = 16 cm, find the two possible values for angle C, correct to 1 decimal place. [4] (ii) Given i
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