Implicit and parametric differentiationEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

\frac{d}{dx}\left(y^{3}\right)
\frac{d}{dx}(xy)
Parametric gradient?
Normal gradient from tangent gradient m?
Equation of a line through (x1,y1) with gradient m?
When is the tangent of a parametric curve horizontal?
When is the tangent of a parametric curve vertical?
\frac{dy}{dx} for x^{2}+y^{2}=25?
Gradient of x^{2}+y^{2}-4x+6y=12 at (5,1)?
\frac{dy}{dx} for x=t^{2}+1, y=t^{3}-3t?
For x=2\sin t, y=3\cos2t, what is \frac{dy}{dx}?
First step before finding a tangent to a parametric curve?

Exam questions on Implicit and parametric differentiation

A curve has equation $x^{2}+y^{2}-4x+6y=12$ .
The point $(5,1)$ lies on the curve. Find an equation of the normal to the curve at $(5,1)$ , in the form $ax+by+c=0$ where $a$ , $b$ and $c$ are integers.2 marks
A curve $C$ has equation $x^{2}+xy+y^{2}=7$ .
Find the coordinates of the points on $C$ where $\frac{dy}{dx}=0$ .2 marks
A curve is given by the parametric equations $x=t^{2}+1$ , $y=t^{3}-3t$ , where $t$ is a real parameter.
Find $\frac{dy}{dx}$ in terms of $t$ , and hence find the gradient of the curve at the point where $t=2$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).