Year 10 indices and standard form test to download as PDF

This Year 10 indices and standard form 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 – Index laws
Non-calculator.
1. Simplify \((4x^3)^2\times3x\). (2 marks)
2. Work out the value of \(\left(\dfrac25\right)^{-2}\) and of \(9^{\frac12}\). (2 marks)
Question 2 – Standard form
Non-calculator.
1. Write \(0.000\,086\) in standard form. (1 mark)
2. Work out \((3\times10^5)\times(4\times10^{-2})\). Give your answer in standard form. (2 marks)
3. Work out \((7.2\times10^6)\div(9\times10^2)\) in standard form. (1 mark)
Question 3 – Problem: the speed of sound
Calculator allowed. The speed of light is \(3\times10^8\) m/s and the speed of sound in air is \(3.4\times10^2\) m/s.
1. How many times faster is light than sound? Give your answer in standard form to 3 s.f. (2 marks)
2. Lightning strikes \(5.1\times10^3\) m away. How many seconds after the flash is the thunder heard? (2 marks)
Question 4 – Estimating
Calculator allowed.
1. Estimate \(\dfrac{58.7\times0.41}{0.19}\) by rounding each number to 1 significant figure. (2 marks)
2. Is your estimate bigger or smaller than the accurate answer? Explain. (2 marks)
Question 5 – Higher: indices
Higher tier.
1. Work out \(64^{-\frac23}\), giving your answer as a fraction. (2 marks)
2. Solve \(2^{x+3}=\dfrac1{16}\). (2 marks)

How to use this Year 10 indices and standard form test

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

Finally, you can download this Year 10 indices and standard form 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.