A-LevelMathematicsDifferentiation9709/32 · Feb/Mar 2018 · Q57 Marks
The parametric equations of a curve are x = 2t + sin 2t, y = 1 – 2 cos 2t, for −½π < t < ½π.
- (i)Show that dy/dx = 2 tan t.[5]
- (ii)Hence find the x-coordinate of the point on the curve at which the gradient of the normal is 2. Give your answer correct to 3 significant figures.[2]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.
- [B1] State correct derivative of x or y with respect to t
- [M1] Use dy/dx = dy/dt ÷ dx/dt
- [A1] Obtain dy/dx = 4 sin 2t / (2 + 2 cos 2t), or equivalent
- [M1] Use double angle formulae throughout
- [A1] Obtain the given answer correctly AG
- [B1] State or imply t = tan⁻¹(-¼)
- [B1] Obtain answer x = -0.961
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