Maths with David

    9231. FP1. Polar Coordinates. Past Exam Questions

    1. November 2025 (9231/12). Question 5
      • The curve C has polar equation r^2 = tan 2 \theta , where 0 \leq \theta \leq \frac{1}{8} \pi
        • (a) Sketch C and state the greatest distance of a point on C from the pole. [2 marks]
        • (b) Find the exact value of the area of the region bounded by C and the half-line \theta = \frac{1}{8} \pi [4 marks]
        • (c) Show that C has Cartesian equation x^4 - 2xy - y^4 = 0 given that 0 \leq x \leq cos( \frac{1}{8} \pi ) and $latex 0 \leq y \leq sin ( \frac{1}{8} \pi ) [4 marks]
        • (d) Using your answer to (b), deduce the exact value of the area bounded by C, the x-axis and the line x = cos( \frac{1}{8} \pi) [2 marks]