plumiEquations of lines: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on F.1 Equations of lines, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
All papers
All years
Loading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDF
All 11 questions on Equations of lines, as a list
- June 2025, Paper 1, Q15 (9 marks): Three planes have equations 2 9 3 3 3 4 x y z x y z t x y z t + − = − + = + + = where t is a constant. The planes meet along a line of intersection. 15 (a) Find
- June 2025, AS Paper 1, Q10 (8 marks): The 3× 3 matrix M represents a reflection in the plane z = 0 The point A has position vector 2 5 4 The point A′ is the image of A under the reflection represent
- June 2024, AS Paper 1, Q4 (1 mark): The line L has vector equation r = [ 4 ] –7 0 + λ[ –9 ] 1 3 Give the equation of L in Cartesian form. Tick () one box. [1 mark] x + 4 –9 = y – 7 1 = z 3 x – 4
- June 2023, Paper 2, Q11 (9 marks): The line l1 passes through the points A(6, 2, 7) and B(4, −3, 7) 11 (a) Find a Cartesian equation of l1 [2 marks] 11 (b) The line l2 has vector equation r = 8 9
- June 2022, AS Paper 1, Q7 (9 marks): The lines l1 and l2 have equations l1 : r = 3 1 −2 2 664 3 775 + l 3 −4 1 2 664 3 775 l2 : r = −12 a −3 2 664 3 775 + m 3 2 −1 2 664 3 775 7 (a) Show that the p
- November 2021, Paper 2, Q11 (9 marks): The Cartesian equation of the line L1 is x + 1 3 = −y + 5 2 = 2z + 5 3 The Cartesian equation of the line L2 is 2x − 1 2 = y − 14 m = z + 12 p The non-singular
- November 2021, AS Paper 1, Q15 (8 marks): Two submarines are travelling on different straight lines. The two lines are described by the equations r = 2 −1 4 2 64 3 75 + l 5 3 −2 2 64 3 75 and x − 5 4 =
- November 2020, Paper 1, Q11 (11 marks): The lines l1, l2 and l3 are defined as follows. l1 : r − 1 5 −1 2 664 3 775 0 B B @ 1 C C A × −2 1 −3 2 664 3 775 = 0 l2 : r − −3 2 7 2 664 3 775 0 B B @ 1 C C
- November 2020, Paper 2, Q15 (16 marks): The points A(7, 2, 8), B(7, ×4, 0) and C(3, 3.2, 9.6) all lie in the plane P. 15 (a) Find a Cartesian equation of the plane P. [3 marks] 15 (b) The line L1 has
- November 2020, AS Paper 1, Q13 (9 marks): Line l1 has equation x − 2 3 = 1 − 2y 4 = −z and line l2 has equation r = −7 4 −2 2 64 3 75 + m 12 a + 3 2b 2 64 3 75 13 (a) In the case when l1 and l2 are para
- June 2019, AS Paper 1, Q13 (10 marks): Line l1 has Cartesian equation x − 3 = 2y + 2 3 = 2 − z 13 (a) Write the equation of line l1 in the form r = a + lb where l is a parameter and a and b are vecto
Questions, mark schemes and examiner’s reports are © AQA, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? AQA A-Level Further Maths past papers.
The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.