Robinson Tuition
Year 7 · Key Stage 3 · free KS3 maths worksheet

Powers, roots and BIDMAS

12 original questions, 28 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

Write down the value of 62

1 mark
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36
2

Write down the value of √81

1 mark
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9
3

Here is a list of numbers.

21   34   37   45   51   58   59

  1. Write down the even numbers in the list.
  2. Write down the prime numbers in the list.
2 marks
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a) 34 and 58 b) 37 and 59
4

Here is a list of numbers.

15   21   27   36   49   55   64   100   125

From the list, write down

  1. all the triangular numbers
  2. all the square numbers
  3. all the cube numbers.

Some numbers belong in more than one answer.

3 marks
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a) 15, 21, 36, 55 b) 36, 49, 64, 100 c) 27, 64, 125
5

Work out 3 + 4 × 5

1 mark
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23
6
  1. 132 = 169. Write down the value of √169
  2. Write down the value of 3√125
  3. √50 lies between two consecutive whole numbers. Write down the two whole numbers.
3 marks
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a) 13 b) 5 c) 7 and 8
7

Use your calculator to work out

  1. 2.33
  2. √17.64
  3. 37
3 marks
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a) 12.167 b) 4.2 c) 2187
8

Work out 32 + 4 × (7 − 2)

2 marks
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29
9

Here are the first five triangular numbers.

1    3    6    10    15

  1. Describe how the sequence continues from one term to the next.
  2. Work out the next two terms of the sequence.
3 marks
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a) open: the amount added increases by 1 each time (add 2, add 3, add 4, ...) b) 21 and 28
10

Square tables are pushed together in a row for a class party.

1 table seats 6 pupils, 2 tables seat 10 pupils and 3 tables seat 14 pupils.

  1. How many pupils can sit at 5 tables?
  2. A Year 7 class has 30 pupils. How many tables are needed so that every pupil has a seat?
3 marks
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a) 22 b) 7
11

Sophie adds up odd numbers, starting from 1.

1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16

  1. Write down the next line of the pattern.
  2. What type of numbers are the answers?
  3. Use the pattern to work out 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 without adding the numbers one by one.
3 marks
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a) 1 + 3 + 5 + 7 + 9 = 25 b) square numbers c) 100
12

Work out

  1. √(36 + 64)
  2. √36 + √64
  3. 40 − (3 + 2)2 ÷ 5
3 marks
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a) 10 b) 14 c) 35

Your score

Answer the questions above and your score appears here.

Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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