Edexcel IAL P3 Further Differentiation Questions
Chain, product and quotient rules; differentiating eˣ, ln x, sin x, cos x, tan x (and sec, cosec, cot); dy/dx = 1/(dx/dy).
- P3 · Pure Mathematics 3
- Calculator allowed
- 35 practice questions
What the questions test
The 35 P3 further differentiation practice questions cover:
Worked example 1
A curve has the equation $y = e^{-x}\sin x$. Find the exact x-coordinate of the first positive turning point of the curve.
Mark scheme
- M1 for using the product rule to differentiate: $\frac{dy}{dx} = -e^{-x}\sin x + e^{-x}\cos x$.
- M1 for setting the derivative equal to 0 to find turning points: $e^{-x}(\cos x - \sin x) = 0$.
- M1 for dividing by $e^{-x}$ (since $e^{-x} \ne 0$) to get $\cos x = \sin x$.
- M1 for dividing by $\cos x$ to obtain $\tan x = 1$.
- A1 for identifying the first positive solution as $x = \frac{\pi}{4}$.
Worked example 2
Find the equation of the normal to the curve $y = x^2 e^{-x}$ at the point where $x = 1$. Give your answer in the form $y = mx + c$.
Mark scheme
- M1 for finding the y-coordinate at $x=1$: $y = e^{-1}$.
- M1 for applying the product rule to find $\frac{dy}{dx} = 2x e^{-x} - x^2 e^{-x}$.
- M1 for evaluating the gradient at $x=1$: $m_t = 2e^{-1} - e^{-1} = e^{-1}$.
- M1 for finding the perpendicular gradient of the normal: $m_n = -e$.
- A1 for forming the equation $y - e^{-1} = -e(x - 1)$ and rearranging to $y = -ex + e + e^{-1}$.
FAQ
What further differentiation is in Edexcel IAL P3?
Chain, product and quotient rules; differentiating eˣ, ln x, sin x, cos x, tan x (and sec, cosec, cot); dy/dx = 1/(dx/dy).
Is P3 a calculator paper?
Yes, a calculator is allowed in P3, but method marks are only given for working you write down.
How are P3 further differentiation questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.