plumiFurther vectors: Edexcel A‑Level Further Maths questions
Every Edexcel A-Level Further Maths exam question on CP.6 Further vectors, 2018–2025, with its mark scheme and examiner’s report.
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All 30 questions on Further vectors, as a list
- June 2025, Core Pure 2, Q2 (8 marks): An archer shoots an arrow towards a target. In a model • the arrow is a particle • the flight path of the arrow is a straight line • the target is part of a pla
- 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 Core Pure, Q9 (7 marks): An engineer detects a source of water below the surface of the ground. The engineer models the situation relative to a fixed origin O. In the model • the surfac
- June 2025, AS Core Pure, Q10 (8 marks): The plane Π1 has equation x + y – z = 3 The plane Π2 has equation ax + 3y + 5z = 4 where a is an integer. Given that Π1 is perpendicular to Π2 (a) determine the
- 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 2024, Core Pure 1, Q7 (10 marks): The line l1 has equation r = i – 2j + 3k + λ(2i + j – 4k) and the line l2 has equation r = 5i + pj – 7k + μ(6i + j + 8k) where λ and μ are scalar parameters and
- June 2024, Further Pure 1, Q9 (10 marks): (i) The line l1 has equation 2 3 3 4 1 1 r λ The line l2 has equation 13 1 5 2 8 5 r μ where λ and μ are scalar parameters. The li
- June 2024, AS Core Pure, Q6 (12 marks): The drainage system for a sports field consists of underground pipes. This situation is modelled with respect to a fixed origin O. According to the model, • the
- June 2024, AS Further Pure 1, Q3 (6 marks): Vectors u and v are given by u i j k v i j k 5 4 3 6 2 and a where a is a constant. (a) Determine, in terms of a, the vector product u × v (2) Given that • AB →
- June 2023, Core Pure 1, Q5 (12 marks): The line l1 has equation x y z 5 1 4 3 3 5 The plane Π1 has equation 2x + 3y – 2z = 6 (a) Find the point of intersection of l1 and Π1 (2) The line l2 is the ref
- 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 Core Pure, Q6 (11 marks): The line l1 has equation 2 3 2 0 0 1 λ r where λ is a scalar parameter. The line l2 is parallel to 1 2 3 (a) Show that l1 and l
- 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, Core Pure 2, Q8 (13 marks): Two birds are flying towards their nest, which is in a tree. Relative to a fixed origin, the flight path of each bird is modelled by a straight line. In the mod
- 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, Further Pure 1, Q6 (6 marks): The points P, Q and R have position vectors 1 2 4 , 3 1 5 and 2 0 3 respectively. (a) Determine a vector equation of the plane that pas
- June 2022, AS Core Pure, Q6 (13 marks): The surface of a horizontal tennis court is modelled as part of a horizontal plane, with the origin on the ground at the centre of the court, and • i and j are
- 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 2021, Core Pure 1, Q7 (8 marks): The plane Π has equation 3 1 2 3 2 0 2 1 1 λ μ − = + + r where λ and μ are scalar parameters. (a) Show that vector 2i +
- November 2021, Further Pure 1, Q4 (7 marks): n vA vL Figure 2 A small aircraft is landing in a field. In a model for the landing the aircraft travels in different straight lines before and after it lands,
- November 2021, Further Pure 1, Q7 (7 marks): With respect to a fixed origin O, the line l has equation (r – (12i + 16j – 8k)) × (9i + 6j + 2k) = 0 The point A lies on l such that the direction cosines of O
- November 2020, Core Pure 1, Q4 (9 marks): The plane Π1 has equation r = 2i + 4j – k + λ (i + 2j – 3k) + μ(–i + 2j + k) where λ and μ are scalar parameters. (a) Find a Cartesian equation for Π1 (4) The l
- 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 Core Pure, Q4 (13 marks): All units in this question are in metres. A lawn is modelled as a plane that contains the points L (–2, –3, –1), M (6, –2, 0) and N (2, 0, 0), relative to a fix
- 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, Core Pure 1, Q7 (7 marks): The line lKDVHTXDWLRQ x y z − = + − = − 1 2 1 1 4 3 The line l2KDVHTXDWLRQ r = i + 3k + t(i − j + 2k where tLVDVFDODUSDUDPHWHU D 6KRZWKDWl an
- 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 Core Pure, Q4 (11 marks): Part of the mains water system for a housing estate consists of water pipes buried beneath the ground surface. The water pipes are modelled as straight line seg
- 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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