Year 8 powers, roots and standard form test to download as PDF

This Year 8 powers, roots and standard form test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 12-13, and the full answers are on a separate page.

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

Mark/20

Question 1 – Indices and roots
Answer all parts. Show your working.
1. Work out \(\sqrt{196}\) and \(\sqrt[3]{125}\). (2 marks)
2. Write \(\dfrac{3^8\times3^2}{3^4}\) as a single power of 3. (1 mark)
3. Work out \(2^{-3}\). (1 mark)
Question 2 – Prime factors
Use prime factors.
1. Write 90 as a product of prime factors. (2 marks)
2. Find the HCF of 90 and 84. (1 mark)
3. Find the LCM of 90 and 84. (1 mark)
Question 3 – Standard form
Work out each answer and give it in standard form.
1. Write 0.000 072 in standard form. (1 mark)
2. \((4\times10^5)\times(3\times10^4)\) (1 mark)
3. \((9\times10^8)\div(3\times10^{-2})\) (1 mark)
4. \(6\times10^3+4\times10^2\) (1 mark)
Question 4 – Problem: the Earth and Mars
The Earth is \(1.5\times10^{8}\) km from the Sun. Mars is \(2.3\times10^{8}\) km from the Sun.
1. How much further from the Sun is Mars than Earth? Give your answer in standard form. (2 marks)
2. Light travels at \(3\times10^{5}\) km/s. How long does light take to travel from the Sun to Mars? Give your answer in seconds to 3 s.f. (2 marks)
Question 5 – Problem: the bacteria
A culture starts with 500 bacteria. The number doubles every hour.
1. How many bacteria are there after 6 hours? Give your answer in standard form. (2 marks)
2. After how many hours does the culture first exceed 1 million? (2 marks)

How to use this Year 8 powers, roots and standard form test

First, revise with the powers, roots 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 powers, roots 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 8 powers, roots 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.