A-LevelMathematicsDifferentiation9709/31 · Oct/Nov 2018 · Q47 Marks
The parametric equations of a curve are x = 2 sin θ + sin 2θ, y = 2 cos θ + cos 2θ, where 0 < θ < π.
- (i)Obtain an expression for dy/dx in terms of θ.[3]
- (ii)Hence find the exact coordinates of the point on the curve at which the tangent is parallel to the y-axis.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] (i) Obtain dx/dθ = 2cosθ + 2cos2θ or dy/dθ = -2sinθ - 2sin2θ
- [M1] (i) Use dy/dx = dy/dθ ÷ dx/dθ
- [A1] (i) Obtain correct dy/dx in any form, e.g. -(2sinθ + 2sin2θ) / (2cosθ + 2cos2θ)
- [M1*] (ii) Equate denominator to zero and use any correct double angle formula
- [A1] (ii) Obtain correct 3-term quadratic in cosθ in any form
- [depM1*] (ii) Solve for θ
- [A1] (ii) Obtain x = 3√3/2 and y = 1/2, or exact equivalents
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