Year 9 direct and inverse proportion test to download as PDF

This Year 9 direct and inverse proportion test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 13-14, and the full answers are on a separate page.

⏱️ Duration : 45 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Direct proportion
\(y\) is directly proportional to \(x\). When \(x=7\), \(y=35\).
1. Find the constant of proportionality. (1 mark)
2. Write an equation for \(y\) in terms of \(x\). (1 mark)
3. Find \(y\) when \(x=12\). (1 mark)
4. Find \(x\) when \(y=95\). (1 mark)
Question 2 – Inverse proportion
\(y\) is inversely proportional to \(x\). When \(x=15\), \(y=4\).
1. Find \(k\) in \(y=\dfrac{k}{x}\). (1 mark)
2. Find \(y\) when \(x=20\). (1 mark)
3. Find \(x\) when \(y=12\). (1 mark)
4. Describe what happens to \(y\) when \(x\) is multiplied by 3. (1 mark)
Question 3 – Shopping for the art club
6 pencils cost £2.28.
1. Find the cost of one pencil. (1 mark)
2. Find the cost of 15 pencils. (1 mark)
3. The club has £9.50. How many pencils can it buy? (2 marks)
Question 4 – Problem: painting the hall
Five decorators can paint the village hall in 6 days, all working at the same rate.
1. How many decorator-days of work are needed? (1 mark)
2. How long would 3 decorators take? (1 mark)
3. The hall must be ready in 4 days. How many decorators are needed? Explain your answer. (2 marks)
Question 5 – Is it proportional?
The table shows pairs of values of \(x\) and \(y\).
\(x\) 2 4 5 10
\(y\) 20 10 8 4
1. Show that \(y\) is inversely proportional to \(x\). (2 marks)
2. Write a formula for \(y\). (1 mark)
3. Find \(y\) when \(x=16\). (1 mark)

\(x\)	2	4	5	10
\(y\)	20	10	8	4

How to use this Year 9 direct and inverse proportion test

First, revise with the direct and inverse proportion lesson and the worksheet. Then sit the test in one go, with a timer set to 45 minutes. After that, mark your work with the direct and inverse proportion test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 9 direct and inverse proportion 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.