Edexcel IAL P3 Further Integration Questions
Integrating eˣ, 1/x, sin x and cos x, including f(ax + b) forms (substitution and parts are P4).
- P3 · Pure Mathematics 3
- Calculator allowed
- 35 practice questions
What the questions test
The 35 P3 further integration practice questions cover:
Worked example 1
Find $\int (\sin x + \cos x)^2 \, dx$.
Mark scheme
- M1 for expanding the bracket to $\sin^2 x + 2\sin x \cos x + \cos^2 x$.
- M1 for simplifying using $\sin^2 x + \cos^2 x \equiv 1$ and $2\sin x \cos x \equiv \sin 2x$.
- M1 for integrating $1 + \sin 2x$.
- A1 for $x - \frac{1}{2}\cos 2x + c$.
Worked example 2
Find $\int (\cos x - \sin x)^2 \, dx$.
Mark scheme
- M1 for expanding the bracket to $\cos^2 x - 2\sin x \cos x + \sin^2 x$.
- M1 for simplifying to $1 - \sin 2x$.
- M1 for integrating the expression term by term.
- A1 for $x + \frac{1}{2}\cos 2x + c$.
FAQ
What further integration is in Edexcel IAL P3?
Integrating eˣ, 1/x, sin x and cos x, including f(ax + b) forms (substitution and parts are P4).
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 integration 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.