Implicit and parametric differentiationAQA A-Level Maths: Flashcards

What these 12 flashcards ask

Differentiate y^2 with respect to x.
Differentiate xy with respect to x.
Differentiate y^3 with respect to x.
What does implicit differentiation produce?
Formula for \frac{dy}{dx} for a parametric curve?
Where is the tangent to a parametric curve horizontal?
Where is the tangent to a parametric curve vertical?
Gradient of the normal if the tangent has gradient m?
For x=4\cos t, y=3\sin t, find \frac{dy}{dx}.
How do you eliminate t from x=4\cos t, y=3\sin t?
For x^2+y^2=25, find \frac{dy}{dx}.
When can you cancel a factor in \frac{dy}{dt}\div\frac{dx}{dt}?

Exam questions on Implicit and parametric differentiation

A curve has equation $x^2+y^2-6x+4y=12$ .
Find the coordinates of the points on the curve where the tangent is parallel to the $y$ -axis.2 marks
A curve has equation $xy^2+x^2=6$ and passes through the point $(2,1)$ .
Find the equation of the tangent to the curve at $(2,1)$ , in the form $ax+by=c$ with integer coefficients.2 marks
A curve is defined by the parametric equations $x=t^2+2t$ and $y=t^3-3t$ , where $t$ is a real parameter.
Show that $\frac{dy}{dx}=\frac{3(t-1)}{2}$ for $t\ne-1$ .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).