plumiVectors: AQA GCSE Maths questions
Every AQA GCSE Maths exam question on G25 Vectors, 2017–2025, with its mark scheme and examiner’s report.
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All 22 questions on Vectors, as a list
- June 2025, Paper 2H, Q23 (5 marks): ABCD is a quadrilateral. AC and BD intersect at P. AB ሬሬሬሬሬ⃗ = 9b – 2a BC ሬሬሬሬሬሬ⃗ = 5a DC ሬሬሬሬሬሬ⃗ = 10b BP : PD = 3 : 2 AP : PC = 1 : k Work out the value of k.
- November 2024, Paper 1H, Q9 (3 marks): 2 a + 1 3b = 5 20 Work out the values of a and b. a = b =
- June 2024, Paper 2H, Q23 (4 marks): Prove that DEF is a straight line.
- November 2023, Paper 1H, Q28 (3 marks): PQRS is a quadrilateral. PQ is not parallel to SR. X is a point on QR. QX : XR = 2 : 3 QX ሬሬሬሬሬሬ⃗ = 2a + 4b Prove that PQRS is a trapezium. Not drawn accurately
- November 2023, Paper 3H, Q15 (4 marks): a = 3 m b = − 4 p The diagram shows the vector 2a + b Work out the values of m and p. m = p =
- November 2022, Paper 1H, Q7 (4 marks): The diagram shows the vectors a and b. As a column vector a = 2 3 7 (a) What is b as a column vector? Answer 7 (b) Work out 4a as a co
- November 2022, Paper 2H, Q25 (3 marks): Two congruent parallelograms, PQRV and VRST, are joined. QP ሬሬሬሬሬሬ⃗ = a PV ሬሬሬሬሬ⃗ = b X is the midpoint of VT. VW : WR = 1 : 2 Prove that Q, W and X lie on a st
- June 2022, Paper 1H, Q21 (4 marks): Five points are connected by vectors. FG ሬሬሬሬሬሬ⃗ = 2EH ሬሬሬሬሬሬ⃗ Work out FE ሬሬሬሬሬ⃗ in terms of a and b. Answer
- June 2022, Paper 3H, Q2 (1 mark): Work out − 8 4 – −2 3 Circle your answer. − 10 7 − 6 7 − 10 1 − 6 1
- November 2021, Paper 3H, Q27 (6 marks): In the diagram DE ሬሬሬሬሬሬ⃗ = a DH ሬሬሬሬሬሬ⃗ = b HG ሬሬሬሬሬሬ⃗ = 8b EX : XH = 3 : 1 EF : FG = 1 : 3 Not drawn accurately 27 (a) Show that DX ሬሬሬሬሬሬ⃗ = 4 1 a + 4 3 b 27
- November 2020, Paper 3H, Q23 (3 marks): In triangle JKL M is the midpoint of JK JN : NL = 3 : 2 KL ሬሬሬሬሬ⃗ = 7a NL ሬሬሬሬሬ⃗ = 4b Work out JM ሬሬሬሬሬ⃗ in terms of a and b. Give your answer in its simplest f
- November 2019, Paper 1H, Q17 (1 mark): a = − 2 3 and b = −5 1 Work out a – 3b Circle your answer. − 17 6 − − 13 6 17 0
- November 2019, Paper 3H, Q27 (3 marks): Here is quadrilateral PQRS. PS ሬሬሬሬሬ⃗ = a SR ሬሬሬሬሬሬ⃗ = b RQ ሬሬሬሬሬሬ⃗ = c X is a point on PS where PX : XS = 1 : 2 Y is a point on RQ where RY : YQ = 2 : 1 Not dr
- June 2019, Paper 1H, Q22 (4 marks): ABC and ACD are triangles. k is a constant. Not drawn accurately 22 (a) Show that CD ሬሬሬሬሬሬ⃗ = 6a + 4.5b 22 (b) BCD is a straight line. Work out the value of k.
- June 2019, Paper 3H, Q13 (3 marks): (a) Vectors a and b are drawn on a grid. Write b in terms of a. b = 13 (b) Vectors c and d are drawn on a grid. On the grid above, draw a vector representing c
- November 2018, Paper 2H, Q23 (1 mark): PQR is a straight line. PQ : QR = 3 : 1 PQ ሬሬሬሬሬሬ⃗ = a Not drawn accurately Circle the vector RQ ሬሬሬሬሬሬ⃗ 3 1 a 4 1 a – 3 1 a – 4 1 a
- June 2018, Paper 3H, Q11 (4 marks): a = 6 –10 b = –1 2 c = –4 7 11 (a) Work out a + b + c Answer 11 (b) Show that a + 2c is parallel to b
- November 2017, Paper 2H, Q26 (3 marks): ABCDE is a pentagon. Not drawn accurately Show that BCDE is a parallelogram.
- June 2017, Paper 2H, Q23 (3 marks): Not drawn accurately Is BCD a straight line? Show working to support your answer. Answer
- June 2017, Paper 3H, Q1 (1 mark): a = − − 1 4 and b = −1 3 Circle the vector 2a + b − − 3 5 − − 3 11 − − 1 5 −
- Specimen, Paper 3H, Q2 (1 mark): a = 5 2 and b = 2 3 Circle the vector a – b 3 5 1 7 3 1 7 5
- Specimen, Paper 3H, Q25 (4 marks): In triangle ABC M is the midpoint of AC N is the point on BC where BN : NC = 2 : 3 AC = 2a AB = 3b 25 (a) Work out MN in terms of a and b. Give your answe
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