plumiPolar curves: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on G.1 Polar curves, 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 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 15 questions on Polar curves, 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, 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, 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
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.