plumiVectors: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP3.5 Vectors, 2019–2025, with its mark scheme and examiner’s report.
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All 14 questions on Vectors, as a list
- June 2025, Further Pure 3 (FP3), Q8 (10 marks): The plane Π1 has equation 4 7 3 2 5 1 1 6 2 λ μ r where λ and μ are scalar parameters. (a) Determine 7 5 6 3 2 i j k i j k
- January 2025, Further Pure 3 (FP3), Q6 (10 marks): The plane Π has equation 1 2 3 5 0 2 2 7 3 λ μ r where λ and μ are scalar parameters. (a) Determine a vector perpendicular to Π Th
- June 2024, Further Pure 3 (FP3), Q9 (10 marks): The plane Π1 has vector equation r 5 3 0 3 0 1 1 2 2 s t where s and t are scalar parameters. (a) Determine a Cartesian equatio
- January 2024, Further Pure 3 (FP3), Q6 (12 marks): The points A, B and C have coordinates (3, 2, 2), (–1, 1, 3) and (–2, 4, 2) respectively. The plane Π1 contains the points A, B and C (a) Determine a Cartesian
- June 2023, Further Pure 3 (FP3), Q4 (12 marks): The plane Π1 contains the point A(2, 4, –5) and is normal to the vector 1 3 3 The plane Π2 contains the point B(3, 6, –2) and is normal to the vector 2
- January 2023, Further Pure 3 (FP3), Q7 (10 marks): The plane ∏has equation r = 1 2 3 0 3 2 1 1 2 λ μ where λ and μ are scalar parameters. (a) Determine a vector perpendicular to Π The line l meets Π at the point
- June 2022, Further Pure 3 (FP3), Q8 (12 marks): The plane Π has equation 3x + 4y – z = 17 The line l1 is perpendicular to Π and passes through the point P(–4, –5, 3) The line l1 intersects Π at the point Q (a
- January 2022, Further Pure 3 (FP3), Q7 (11 marks): The line l1 has equation x y z − = − − = − 3 4 5 2 4 7 The plane Π has equation 2x + 4y – z = 1 The line l1 intersects the plane Π at the point P (a) Determine
- October 2021, Further Pure 3 (FP3), Q4 (11 marks): The matrix M is given by 2 0 1 3 2 2 1 − − k k (a) Show that det M = 5k − 10 Given that k ≠ 2 (b) find M−1 in terms of k. The points O (0, 0, 0)
- October 2021, Further Pure 3 (FP3), Q5 (10 marks): The skew lines l1 and l2 have equations l1 : r = (i + 2j − 5k) + λ (5i + j) and l2 : r = (2i − 4j + 4k) + μ (8i − 2j + 3k) where λ and μ are scalar parameters.
- June 2021, Further Pure 3 (FP3), Q6 (13 marks): The line l1 has equation r = i + j + k + λ(i + 3k) and the line l2 has equation r = 2i + sj + μ(i − 2j + k) where s is a constant and λ and μ are scalar paramet
- January 2021, Further Pure 3 (FP3), Q1 (6 marks): Relative to a fixed origin O, the points A, B, C and D have coordinates (0, 4, 1), (4, 0, 0), (3, 5, 2) and (2, 2, k) respectively, where k is a constant. (a) D
- January 2021, Further Pure 3 (FP3), Q7 (11 marks): The point P has coordinates (1, 2, 1) The line l has Cartesian equation x y z − = + = + − 3 5 1 3 5 8 The plane Π1 contains the point P and the line l. (a) Show
- October 2020, Further Pure 3 (FP3), Q8 (10 marks): The plane P1 has equation x – 5y + 3z = 11 The plane P2 has equation 3x – 2y + 2z = 7 The planes P1 and P2 intersect in the line l. (a) Find a vector equation f
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