plumiTriple product, areas and volumes: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 10.2 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 11 questions on Triple product, areas and volumes, as a list
- June 2025, Further Pure 1, Q9 (10 marks): The parallelogram P has vertices E, F, G and H, with coordinates E F G H 10 1 6 7 2 7 10 2 9 13 3 4 , , , , , , , , (a) Determine the exact area of P, giving yo
- June 2025, AS Further Pure 1, Q3 (9 marks): A B C D E F G H Figure 1 Figure 1 shows the parallelepiped ABCDHEFG. Relative to a fixed origin O, the points A, B, D and E have coordinates (3, 2, 7), (4, 4, 3
- June 2023, Further Pure 1, Q7 (15 marks): With respect to a fixed origin O the point A has coordinates (3, 6, 5) and the line l has equation (r – (12i + 30j + 39k)) × (7i + 13j + 24k) = 0 The points B a
- June 2023, AS Further Pure 1, Q5 (9 marks): The points A, B and C are the vertices of a triangle. Given that • AB → = p 4 6 and AC → = q 4 5 where p and q are constants • AB → × AC → is para
- June 2022, Further Pure 1, Q3 (9 marks): With respect to a fixed origin O, the points A and B have coordinates (2, 2, –1) and (4, 2p, 1) respectively, where p is a constant. For each of the following,
- June 2022, AS Further Pure 1, Q5 (11 marks): z = 0 M P N D C B A Figure 1 The points A(3, 2, −4) , B(9, −4, 2) , C(−6, −10, 8) and D(−4, −5, 10) are the vertices of a tetrahedron. The plane with equation z
- November 2020, Further Pure 1, Q3 (9 marks): The points A, B and C, with position vectors a = 3i − 2j + k , b = i + 4j + 5k and c = −2i + 3j + 3k respectively, lie on the plane Π (a) Find AB → × AC → (3) (
- November 2020, AS Further Pure 1, Q5 (10 marks): A B C D E F Figure 3 Figure 3 shows a solid display stand with parallel triangular faces ABC and DEF. Triangle DEF is similar to triangle ABC. With respect to a
- June 2019, Further Pure 1, Q7 (10 marks): With respect to a fixed origin O, the points A, B and C have coordinates (3, 4, 5), (10, –1, 5) and (4, 7, –9) respectively. The plane Ȇ has equation 4x – 8y +
- June 2019, AS Further Pure 1, Q4 (8 marks): A C D B Figure 1 Figure 1 shows a sketch of a solid doorstop made of wood. The doorstop is modelled as a tetrahedron. Relative to a fixed origin O, the vertices
- June 2018, AS Further Pure 1, Q4 (9 marks): A scientist is investigating the properties of a crystal. The crystal is modelled as a tetrahedron whose vertices are A (12, 4, −1), B (10, 15, −3), C (5, 8, 5)
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