Polar coordinates — AS & A Level Further Mathematics (9231) questions by topic
Sketching and converting polar curves defines this topic: sketching r = theta * e^((1/8) theta) over a full revolution, sketching r^2 = 1/(theta^2 + 1) and stating the polar coordinates of its furthest point from the pole, and showing that x^2 - y^2 = a converts to r^2 = a sec 2theta.
Find, sketch and show lead the command words across 14 questions from 2023 to 2025 papers, worth from 10 to 16 marks, the highest mark floor in this syllabus set, so each response is a sustained sketch-and-justify task rather than a quick calculation. With no examiner-report extracts logged for this topic, submitting each conversion and sketch for instant marking is the way to confirm the Cartesian-to-polar substitution and the curve's key features are both correct before finishing the sketch.
May–June 2025, Paper 11
The curve C has polar equation r = theta e^((1/8) theta), for 0 <= theta <= 2pi. Sketch C.
Answer this question and get it marked →May–June 2025, Paper 12
The curve C has polar equation r = thetae^{(1/8)theta}, for 0 <= theta <= 2pi. Sketch C.
Answer this question and get it marked →May–June 2025, Paper 13
The curve C has polar equation r^2 = e^(sin(theta)) cos(theta), for -(1/2)pi <= theta <= (1/2)pi. Find the polar coordinates of the point on C that is furthest from the pole,…
Answer this question and get it marked →May–June 2024, Paper 12
The curve C has polar equation r^2 = (pi - theta)arctan(pi - theta), for 0 <= theta <= pi. Sketch C and state the polar coordinates of the point of C furthest from the pole.
Answer this question and get it marked →May–June 2024, Paper 13
The curve C has polar equation r^2 = sin(2theta) cos(theta), for 0 <= theta <= pi. Sketch C and state the equation of the line of symmetry. (Answer on the grid provided in the…
Answer this question and get it marked →October–November 2024, Paper 11
Show that the curve with Cartesian equation (x^2 + y^2)^2 = 6xy has polar equation r^2 = 3 sin 2theta.
Answer this question and get it marked →October–November 2024, Paper 12
The curve C1 has polar equation r = a(cos(theta) + sin(theta)) for -(1/4)pi <= theta <= (3/4)pi, where a is a positive constant. Find a Cartesian equation for C1 and show that it…
Answer this question and get it marked →October–November 2024, Paper 13
Show that the curve with Cartesian equation (x^2 + y^2)^2 = 6xy has polar equation r^2 = 3 sin 2theta.
Answer this question and get it marked →May–June 2023, Paper 11
The curve C has polar equation r^2 = 1/(theta^2 + 1), for 0 <= theta <= pi. Sketch C and state the polar coordinates of the point of C furthest from the pole.
Answer this question and get it marked →May–June 2023, Paper 12
The curve C has polar equation r^2 = 1/(theta^2 + 1), for 0 <= theta <= pi. Sketch C and state the polar coordinates of the point of C furthest from the pole.
Answer this question and get it marked →May–June 2023, Paper 13
Show that the curve with Cartesian equation x^2 - y^2 = a, where a is a positive constant, has polar equation r^2 = asec 2theta.
Answer this question and get it marked →October–November 2023, Paper 11
Show that the curve with Cartesian equation (x - 1/2)^2 + y^2 = 1/4 has polar equation r = cos theta.
Answer this question and get it marked →October–November 2023, Paper 12
The curve C has polar equation r = e^(-theta) - e^(-(1/2)pi), where 0 <= theta <= (1/2)pi. Sketch C and state, in exact form, the greatest distance of a point on C from the pole.
Answer this question and get it marked →October–November 2023, Paper 13
Show that the curve with Cartesian equation (x - 1/2)^2 + y^2 = 1/4 has polar equation r = cos theta.
Answer this question and get it marked →Other AS & A Level Further Mathematics topics
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