Edexcel IAL P4 Differentiation Questions
Implicit and parametric differentiation; connected rates of change.
- P4 · Pure Mathematics 4
- Calculator allowed
- 30 practice questions
What the questions test
The 30 P4 differentiation practice questions cover:
Worked example 1
A curve has parametric equations $x = \ln t$ and $y = t^2$, $t > 0$. Find the equation of the normal to the curve at the point where $t = 1$. Give your answer in the form $ax + by + c = 0$.
Mark scheme
- M1 for finding the coordinates at $t = 1$: $x = 0$, $y = 1$.
- M1 for calculating $\frac{dx}{dt} = \frac{1}{t}$ and $\frac{dy}{dt} = 2t$, giving $\frac{dy}{dx} = 2t^2$.
- M1 for evaluating the tangent gradient at $t = 1$ to get $m_t = 2$.
- M1 for determining the normal gradient $m_n = -\frac{1}{2}$ and using $(0, 1)$ to form the equation $y - 1 = -\frac{1}{2}(x - 0)$.
- A1 for rearranging to the required integer format: $x + 2y - 2 = 0$.
Worked example 2
Find the equation of the tangent to the curve $2x^2 - xy + y^2 = 8$ at the point $(2, 2)$. Give your answer in the form $y = mx + c$.
Mark scheme
- M1 for differentiating $2x^2$ to $4x$ and $y^2$ to $2y\frac{dy}{dx}$.
- M1 for differentiating $-xy$ using the product rule to get $-y - x\frac{dy}{dx}$.
- M1 for setting the entire derivative to zero: $4x - y - x\frac{dy}{dx} + 2y\frac{dy}{dx} = 0$.
- M1 for substituting $x=2$ and $y=2$ to find the gradient $m$: $8 - 2 - 2\frac{dy}{dx} + 4\frac{dy}{dx} = 0 \implies 2\frac{dy}{dx} = -6 \implies m = -3$.
- A1 for using $y - 2 = -3(x - 2)$ to establish the final equation $y = -3x + 8$.
FAQ
What differentiation is in Edexcel IAL P4?
Implicit and parametric differentiation; connected rates of change.
Is P4 a calculator paper?
Yes, a calculator is allowed in P4, but method marks are only given for working you write down.
How are P4 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.