Year 10 simultaneous equations test to download as PDF

This Year 10 simultaneous equations 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 – Elimination
Solve the simultaneous equations \(3x+2y=12\) and \(5x-3y=1\). (4 marks)
Question 2 – Forming simultaneous equations
2 adult tickets and 3 child tickets cost £34. 3 adult tickets and 1 child ticket cost £30. Work out the cost of one adult ticket and one child ticket. (4 marks)
Question 3 – Substitution
Solve \(y=3x-4\) and \(2x+y=11\). (3 marks) Then show that \((3,5)\) is on the line \(y=3x-4\) but not on \(x+y=7\). (1 mark)
Question 4 – Graphs and problem
The lines \(y=2x+1\) and \(x+y=10\) are drawn on a grid.
1. Find the coordinates of the point where the lines cross. (2 marks)
2. A taxi firm charges £2 plus £1.50 per mile. Another charges £5 plus £1 per mile. Find the distance where the charges are the same. (2 marks)
Question 5 – Higher: linear and quadratic
Higher tier. Solve \(y=x+2\) and \(x^2+y^2=34\). (4 marks)

How to use this Year 10 simultaneous equations test

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

Finally, you can download this Year 10 simultaneous 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.