plumiTriple product, areas and volumes: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 11.2 Triple product, areas and volumes, 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 13 questions on Triple product, areas and volumes, as a list
- June 2025, Additional Pure Mathematics, Q2 (8 marks): The points P, Q, R and S have coordinates (1, 2, 4), (3, 1, 6), (4, 8, -2) and (5, 5, 5) respectively. (a) Find, in exact form, the area of triangle PQR. [3] (b
- June 2025, AS Additional Pure Mathematics, Q2 (6 marks): K O K O K O 2 The vectors p, q and r are such that p 3 , q 4 OO and r 1 OO. = KK OO = - KK = KK 7 9 2 - L P L P L P (a) (i) Determine the value of the integer k
- June 2024, AS Additional Pure Mathematics, Q2 (6 marks): The points A and B have position vectors a and b relative to the origin O. It is given that J N J N 2 m K O K O a 4 and b 4 OO , where m is a real parameter. =
- June 2023, Additional Pure Mathematics, Q3 (7 marks): The points A and B have position vectors a i p j q k and b 2 i 3 j 2 k respectively, = + + = + + relative to the origin O. (a) Determine the value of p and the
- June 2022, Additional Pure Mathematics, Q5 (8 marks): You are given the variable point A(3, −8, t), where t is a real parameter, and the fixed point B(1, 2, −2). (a) Using only the geometrical properties of the vec
- June 2022, AS Additional Pure Mathematics, Q1 (6 marks): K O K O K O 1 The points A, B and C have position vectors a 1 OO, b 3 OO and c 1 OO respectively, = KK = KK = KK 3 1 2 - L P L P L P relative to the origin O. (
- November 2021, Pure Core 1, Q4 (11 marks): Points A, B and C have coordinates (4, 2, 0), (1, 5, 3) and (1, 4, -2) respectively. The line l passes through A and B. (a) Find a cartesian equation for l. [3]
- November 2021, Additional Pure Mathematics, Q3 (6 marks): The points P, Q and R have position vectors p 2 i j 5 k , q = - + and i j k r 2 i j t k = + + = + + respectively, relative to the origin O. Determine the value(
- November 2021, AS Additional Pure Mathematics, Q1 (5 marks): K O K O K O 1 The points A, B and C have position vectors a 0 OO , b 4 OO and c 0 OO respectively, relative to = KK = KK = KK 0 0 1 L P L P L P the origin O. (a
- November 2020, Additional Pure Mathematics, Q4 (7 marks): Points A, B and C have position vectors a, b and c respectively, relative to origin O. It is given that b c a and that a = . 3 = # (a) Determine each of the fol
- November 2020, AS Additional Pure Mathematics, Q6 (9 marks): The points A and B have position vectors a i 2 j + and b k i3 4 j 5 k respectively. = + =- + - (a) Determine the area of triangle OAB, giving your answer in an
- June 2019, Additional Pure Mathematics, Q6 (12 marks): K O K O K O 6 (a) For the vectors p 2 OO , q 1 OO and r 4 OO , calculate = = = - KK KK KK 3 1 5 - L P L P L P • p • q # r , • p # (q # r) , • (p # q) # r . [6]
- June 2019, AS Additional Pure Mathematics, Q5 (8 marks): The tetrahedron T, shown below, has vertices at O(0, 0, 0), A(1, 2, 2), B(2, 1, 2) and C(2, 2, 1). C Diagram not drawn to scale B O A ^ h 1 Show that the surfac
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