Year 10 formulae and identities test to download as PDF

This Year 10 formulae and identities 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 – Substitution and rearranging
Calculator allowed.
1. Use \(s=ut+\tfrac12at^2\) to work out \(s\) when \(u=6\), \(a=-2\) and \(t=4\). (2 marks)
2. Make \(x\) the subject of \(y=5x-3\). (2 marks)
Question 2 – Changing the subject
Non-calculator.
1. Make \(r\) the subject of \(A=\pi r^2\) where \(r>0\). (2 marks)
2. Make \(m\) the subject of \(E=\tfrac12mv^2\). (2 marks)
Question 3 – Identity and proof
Calculator allowed.
1. Show that \((x+4)(x-4)+16\equiv x^2\). (2 marks)
2. Prove that the sum of three consecutive even numbers is a multiple of 6. Let the numbers be \(2n\), \(2n+2\), \(2n+4\). (2 marks)
Question 4 – Problem: the taxi
A taxi company charges £\(C\) for a journey of \(d\) miles using the formula \(C=2.50+1.70d\).
1. Work out the cost of a 12-mile journey. (1 mark)
2. A journey costs £29.40. Work out the distance. (2 marks)
3. Make \(d\) the subject of the formula. (1 mark)
Question 5 – Higher: the subject appears twice
Higher tier.
1. Make \(x\) the subject of \(y=\dfrac{x+4}{x-1}\). (3 marks)
2. Make \(t\) the subject of \(v=u+at\) and then find \(t\) when \(v=20\), \(u=5\), \(a=2.5\). (1 mark)

How to use this Year 10 formulae and identities test

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

Finally, you can download this Year 10 formulae and identities 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.