plumiPolar coordinates: AQA A‑Level Further Maths questions
Every AQA A-Level Further Maths exam question on G Polar coordinates, 2019–2025, with its mark scheme and examiner’s report.
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All 17 questions on Polar coordinates, as a list
- June 2025, Paper 2, Q14 (8 marks): A children’s play area in a park contains a paddling pool. The outline of the paddling pool is modelled by the polar curve ( ) = + 6 2cos 2 r θ where r is measu
- June 2025, AS Paper 1, Q15 (11 marks): The graph G1 has the polar equation r = 8 cos θ + √ 3 sin θ – π 6 < θ < 5π 6 The graph G2 has the polar equation θ = 2π 3 15 (a) Show that G1 is a straight line
- June 2024, Paper 1, Q16 (9 marks): The curve C has polar equation r = 2 + tan θ The curve C meets the line θ = π 4 at the point A The point B has polar coordinates (4, 0) The diagram shows part o
- 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, 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 1, Q9 (14 marks): Roberto is solving this mathematics problem: The curve C1 has polar equation r2 = 9 sin 2y for all possible values of y Find the area enclosed by C1 Roberto’s s
- June 2022, AS Paper 1, Q8 (7 marks): The curve C has the polar equation r = 4 − 2 cos y −p < y × p 8 (a) Verify that the point with polar coordinates 3, p 3 lies on C [1 mark] 8 (b) Find the exact
- November 2021, Paper 1, Q3 (1 mark): The curve C has polar equation r2 sin 2y = 4 Find a Cartesian equation for C. Circle your answer. [1 mark] y = 2x y = x 2 y = 2 x y = 4x for the next question
- November 2021, Paper 2, Q9 (14 marks): (a) The line L has polar equation r = 7 4 sec y − p 2 < y < p 2 Show that L is perpendicular to the initial line. [2 marks] 9 (b) The curve C has polar equation
- November 2021, AS Paper 1, Q17 (10 marks): The curve C1 has polar equation r = 2a(1 + sin y) for −p < y × p where a is a positive constant. Initial line M O C1 The point M lies on C1 and the initial line
- November 2020, Paper 2, Q14 (11 marks): The diagram shows the polar curve C1 with equation r = 2 siny The diagram also shows part of the polar curve C2 with equation r = 1 + cos 2y Initial line 2 O 14
- November 2020, AS Paper 1, Q11 (3 marks): Sketch the polar graph of r = sinhy + coshy for 0 × y × 2p [3 marks]
- November 2020, AS Paper 1, Q17 (4 marks): The polar equation of the circle C is r = a( cos y + sin y) Find, in terms of a, the radius of C. Fully justify your answer. [4 marks]
- June 2019, Paper 1, Q15 (11 marks): The diagram shows part of a spiral curve. The point P has polar coordinates (r, y) where 0 × y × p 2 The points T and S lie on the initial line and O is the pol
- June 2019, AS Paper 1, Q3 (1 mark): Point P has polar coordinates 2, 2p 3 . Which of the following are the Cartesian coordinates of P? Circle your answer. [1 mark] (1, − 3 p ) (− 3 p , 1) ( 3 p ,
- June 2019, AS Paper 1, Q4 (2 marks): The line L has polar equation r = k siny where k is a positive constant. 4 (a) Sketch L. [1 mark] Initial line O 4 (b) State the minimum distance between L and
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