(i)[4]
Show that $\frac{dy}{dx} = \frac{8\cos \theta}{1 - 4\cos \theta}$ by simplifying the parametric derivative.
(ii)[4]
Find the coordinates of the point on the curve where the gradient is $-4$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
A curve is defined parametrically by $x = \cos 2\theta - \cos \theta$, $y = 4\sin^2\theta$, with $0 \leq \theta \leq \pi$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write down $\frac{dx}{d\theta} = -2\sin 2\theta + \sin \theta$ or $\frac{dy}{d\theta} = 8\sin \theta \cos \theta$” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI