A-LevelFurther MathematicsPolar coordinates9231/12 · May/June 2018 · Q38 Marks
The curve C has polar equation r = cos 2θ, for -¼π ≤ θ ≤ ¼π.
- (i)Sketch C.[2]
- (ii)Find the area of the region enclosed by C, showing full working.[3]
- (iii)Find a cartesian equation of C.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- B1 (i) Correct position including label of 1 on initial line, and symmetric about initial
- B1 (i) Single correct loop.
- M1 (ii) Correct integral. ½∫cos²2θdθ
- M1 (ii) Correct use of double angle formula. ½∫(½(1+cos4θ))dθ
- A1 (ii) ¼[θ + ¼sin4θ] from -¼π to ¼π = π/8 ≈ 0.393
- B1 (iii) Uses trig identity r = cos²θ - sin²θ OE
- M1 (iii) Uses x=rcosθ or y=rsinθ or both, AEF
- A1 (iii) (x²+y²)^(3/2) = x²-y²
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