Edexcel IAL P2 Differentiation (stationary points) Questions
Increasing and decreasing functions; stationary points and their nature; optimisation problems.
- P2 · Pure Mathematics 2
- Calculator allowed
- 33 practice questions
What the questions test
The 33 P2 differentiation (stationary points) practice questions cover:
Worked example 1
Find the set of values of $x$ for which $f(x) = x^4 - 8x^2$ is an increasing function.
Mark scheme
- M1 for finding the derivative $f'(x) = 4x^3 - 16x$.
- M1 for setting $f'(x) > 0$ and factorising: $4x(x^2 - 4) > 0 \implies 4x(x-2)(x+2) > 0$.
- M1 for finding the critical values $x = -2, 0, 2$ and testing regions.
- A1 for stating the correct range: $-2 < x < 0$ or $x > 2$.
Worked example 2
Find the exact coordinates of the stationary point on the curve $y = \sqrt{x} - 2x$, for $x > 0$.
Mark scheme
- M1 for rewriting as $y = x^{0.5} - 2x$ and differentiating: $\frac{dy}{dx} = 0.5x^{-0.5} - 2$.
- M1 for setting to zero and rearranging: $\frac{1}{2\sqrt{x}} = 2 \implies \sqrt{x} = 0.25$.
- A1 for solving to get $x = 0.0625$ or $\frac{1}{16}$.
- A1 for finding the y-coordinate: $\sqrt{\frac{1}{16}} - 2(\frac{1}{16}) = \frac{1}{4} - \frac{1}{8} = \frac{1}{8}$, giving $(\frac{1}{16}, \frac{1}{8})$.
FAQ
What differentiation (stationary points) is in Edexcel IAL P2?
Increasing and decreasing functions; stationary points and their nature; optimisation problems.
Is P2 a calculator paper?
Yes, a calculator is allowed in P2, but method marks are only given for working you write down.
How are P2 differentiation (stationary points) 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.