Year 12 integration test to download as PDF

This Year 12 integration test lasts 60 minutes and is marked out of 20. It covers the whole chapter for pupils aged 16-17, and the full answers are on a separate page.

⏱️ Duration : 60 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Indefinite integration
Find (a) \(\displaystyle\int\left(8x^3-\dfrac3{x^2}+\sqrt x\right)dx\) and (b) \(\displaystyle\int(x-3)^2\,dx\). (4 marks)
Question 2 – Finding a function
The curve with \(\dfrac{dy}{dx}=3x^2-8x+1\) passes through \((2,5)\). Find the equation of the curve.
Question 3 – Definite integral
Evaluate \(\displaystyle\int_1^4\left(\dfrac6{\sqrt x}+x\right)dx\).
Question 4 – Area
Find the area enclosed by the curve \(y=x^2-6x+8\) and the \(x\)-axis.
Question 5 – Problem: a skatepark ramp
The profile of a ramp is \(y=\tfrac14x^2\) for \(0\le x\le4\) (metres). The line \(y=x\) meets it at the origin and at \((4,4)\).
1. Show that the line is above the curve between 0 and 4. (1 mark)
2. Find the area between the line and the curve. (3 marks)

How to use this Year 12 integration test

First, revise with the integration lesson and the worksheet. Then sit the test in one go, with a timer set to 60 minutes. After that, mark your work with the integration test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 12 integration 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.