Year 13 integration techniques and differential equations test to download as PDF

This Year 13 integration techniques and differential equations test lasts 40 minutes and is marked out of 20. It covers the whole chapter for pupils aged 17-18, and the full answers are on a separate page.

⏱️ Duration : 40 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Standard integrals
Evaluate \(\int_0^1\left(e^{2x}+\dfrac1{2x+1}\right)dx\), giving an exact answer.
Question 2 – Substitution
Use the substitution \(u=x^2+3\) to evaluate \(\int_0^1 2x\sqrt{x^2+3}\,dx\).
Question 3 – By parts
Find the exact value of \(\int_1^ex^2\ln x\,dx\).
Question 4 – Partial fractions
Express \(\dfrac{3x+5}{(x+1)(x+2)}\) in partial fractions and evaluate \(\int_2^3\dfrac{3x+5}{(x+1)(x+2)}dx\) in the form \(\ln k\).
Question 5 – A differential equation
Solve \(\dfrac{dy}{dx}=2xy^2\) given that \(y=1\) when \(x=0\), giving \(y\) in terms of \(x\), and state the values of \(x\) for which the solution is valid.

How to use this Year 13 integration techniques and differential equations test

First, revise with the integration techniques and differential equations lesson and the worksheet. Then sit the test in one go, with a timer set to 40 minutes. After that, mark your work with the integration techniques and differential equations test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 13 integration techniques and differential equations test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.

Integration techniques and differential equations – Year 13 A level maths test to download as PDF

Question 1 – Standard integrals

Question 2 – Substitution

Question 3 – By parts

Question 4 – Partial fractions

Question 5 – A differential equation

How to use this Year 13 integration techniques and differential equations test

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