plumiConic sections: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on D.6 Conic sections, 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.
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All 13 questions on Conic sections, as a list
- June 2025, Paper 1, Q8 (3 marks): The curve 1 C has equation + = 2 2 1 4 25 x y The curve 1 C is translated by the vector 1 3 to give the curve 2 C Find the coordinates of the points wh
- June 2024, Paper 1, Q8 (4 marks): The ellipse E has equation _ x2 + y2 9 = 1 The line with equation y = mx + 4 is a tangent to E Without using differentiation show that m = ±√ 7 [4 marks]
- June 2024, AS Paper 1, Q16 (6 marks): The curve C has the polar equation r = 2 √cos2 θ + 4 sin2 θ –π < θ ≤ π 16 (a) Show that the Cartesian equation of C can be written as x2 a2 + y2 b2 = 1 where a
- June 2023, Paper 1, Q14 (10 marks): The curve C has polar equation r = 4 5 + 3 cosy ( − < y × ) 14 (a) Show that r takes values in the range 1 k × r × k , where k is an integer. [2 marks] 14 (b) F
- June 2023, Paper 2, Q5 (5 marks): Josh and Zoe are solving the following mathematics problem: The curve C1 has equation x2 16 − y2 9 = 1 The matrix M = 0 1 1 0 " # maps C1 onto C2 Find the equat
- June 2023, AS Paper 1, Q11 (8 marks): A point has Cartesian coordinates (x, y) and polar coordinates (r, θ) where r ≥ 0 and – π < θ ≤ π 11 (a) Express r in terms of x and y [1 mark] 11 (b) Express x
- June 2022, Paper 2, Q10 (7 marks): The curve C1 has equation x2 25 − y2 4 = 1 The curve C2 has equation x2 − 25y2 − 6x − 200y − 416 = 0 10 (a) Find a sequence of transformations that maps the gra
- June 2022, AS Paper 1, Q10 (6 marks): The diagram below shows an ellipse E The coordinate axes are the lines of symmetry of E O x y 2 – 2 – 3 3 10 (a) Write down an equation of E [2 marks] 10 (b) Th
- November 2021, Paper 2, Q6 (8 marks): The ellipse E1 has equation x2 + y2 4 = 1 E1 is translated by the vector 3 0 to give the ellipse E2 6 (a) Write down the equation of E2 [1 mark] 6 (b) The ellip
- November 2021, AS Paper 1, Q14 (9 marks): Curve C1 has equation x2 16 + y2 4 = 1 14 (a) Curve C2 is a reflection of C1 in the line y = x Write down an equation of C2 [1 mark] 14 (b) Curve C3 is a circle
- November 2020, Paper 1, Q5 (9 marks): H1 is the locus of points such that the distance from the point (5, 0) is twice the distance from the line x = 2 5 (a) Show that the equation of H1 can be writt
- June 2019, Paper 2, Q8 (9 marks): A parabola P1 has equation y2 = 4ax where a > 0 P1 is translated by the vector b 0 , where b > 0 , to give the parabola P2 8 (a) The line y = mx is a tangent to
- June 2019, AS Paper 1, Q5 (8 marks): A hyperbola H has the equation x2 a2 − y2 4a2 = 1 where a is a positive constant. 5 (a) Write down the equations of the asymptotes of H. [1 mark] 5 (b) Sketch t
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