Year 7 expanding brackets and substitution test to download as PDF

This Year 7 expanding brackets and substitution test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 11-12, and the full answers are on a separate page.

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

Mark/20

Question 1 – Substitution
Work out the value of each expression when x = 5 and y = -3.
1. \(4x-2y\) (1 mark)
2. \(x^{2}-y^{2}\) (1 mark)
3. \(3(x+y)\) (1 mark)
4. \(\dfrac{xy}{3}\) (1 mark)
Question 2 – Expanding and factorising
(a) Expand \(4(3x-2)\). (1 mark)
(b) Expand and simplify \(2(x+5)+3(x-1)\). (2 marks)
(c) Factorise \(12y-18\). (1 mark)
Question 3 – Using a formula
The cost, £C, of hiring a bicycle is given by C = 5 + 3h, where h is the number of hours.
1. Work out the cost of hiring a bicycle for 4 hours. (1 mark)
2. Work out the number of hours when the cost is £29. (2 marks)
3. Explain what the number 5 means in this formula. (1 mark)
Question 4 – Problem: the garden border
A rectangular flowerbed is (x + 4) metres long and x metres wide.
1. Write an expression for the area of the flowerbed and expand it. (2 marks)
2. Write an expression for the perimeter in simplest form. (1 mark)
3. The area is 45 m². Show that x = 5 works. (1 mark)
Question 5 – Problem: the concert tickets
The school music concert sells adult tickets at £a and child tickets at £c. A family buys 2 adult tickets and 3 child tickets and pays 2a + 3c. The school sells 40 family packs altogether.
1. Write an expression for the money from the family packs, in the form 40(2a + 3c), then expand it. (2 marks)
2. Adult tickets cost £8 and child tickets cost £5. Work out the money raised. (1 mark)
3. The school wants to raise £1 500 from family packs. By how much does it miss its target? (1 mark)

How to use this Year 7 expanding brackets and substitution test

First, revise with the expanding brackets and substitution 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 expanding brackets and substitution test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 7 expanding brackets and substitution 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.