Year 10 linear equations and inequalities test to download as PDF

This Year 10 linear equations and inequalities test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 14-15, and the full answers are on a separate page.

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

Mark/20

Question 1 – Solving equations
Non-calculator.
1. Solve \(5x+8=3x+20\). (2 marks)
2. Solve \(\dfrac{3x-2}{4}=5\). (2 marks)
Question 2 – Forming and solving
Calculator allowed. A plumber charges £45 call-out plus £28 per hour. Another plumber charges £20 call-out plus £33 per hour.
1. Show that the two plumbers charge the same for 5 hours. (2 marks)
2. Form an inequality and find when the first plumber is cheaper. (2 marks)
Question 3 – Inequalities
Non-calculator.
1. Solve \(4x-7\le13\). (2 marks)
2. Solve \(-5\lt 3x+1\lt 10\) and write down all the integer solutions. (2 marks)
Question 4 – Problem: inequality
A hall hire costs £80 plus £6 per guest. A party has a budget of £350.
1. Write an inequality for the number of guests \(g\). (1 mark)
2. Solve it. (2 marks)
3. What is the greatest number of guests? (1 mark)
Question 5 – Higher: quadratic inequality
Higher tier.
1. Solve \(x^2-3x-10\lt 0\). (3 marks)
2. Write down the integer values of \(x\) that satisfy it. (1 mark)

How to use this Year 10 linear equations and inequalities test

First, revise with the linear equations and inequalities 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 linear equations and inequalities test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 10 linear equations and inequalities 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.

Linear equations and inequalities – Year 10 GCSE maths test to download as PDF

Question 1 – Solving equations

Question 2 – Forming and solving

Question 3 – Inequalities

Question 4 – Problem: inequality

Question 5 – Higher: quadratic inequality

How to use this Year 10 linear equations and inequalities test

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