Robinson Tuition
Year 9 · Key Stage 3 · free KS3 maths worksheet

Index laws, standard form and surds

16 original questions, 48 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

  1. √144
  2. 3√125
  3. √0.49
  4. 3√−8
4 marks
Show answer
a) 12 b) 5 c) 0.7 d) -2
2

Here are five numbers.

6   9   16   27   40

Write down the two numbers that are powers of 3

1 mark
Show answer
9 and 27
3
  1. Work out the value of
    (i) 26   (ii) 34   (iii) 53
  2. Write 64 as a power of 4.
  3. Write 243 as a power of 3.
3 marks
Show answer
a) 64, 81, 125 b) 43 c) 35
4
  1. Write 105 as an ordinary number.
  2. Write one million as a power of 10.
  3. Write 10−2 as a decimal.
  4. Write 103 × 104 as a single power of 10.
4 marks
Show answer
a) 100000 b) 106 c) 0.01 d) 107
5

Write down the value of 1003

1 mark
Show answer
1000000
6

Work out

  1. 23 × 32
  2. 52 + 43
  3. (102 − 62) ÷ 23
3 marks
Show answer
a) 72 b) 89 c) 8
7
  1. Write 507,000 in standard form.
  2. Write 2.6 × 10−3 as an ordinary number.
2 marks
Show answer
a) 5.07 × 105 b) 0.0026
8

Ellie types √50 into her calculator. The calculator shows 5√2

  1. Explain what 5√2 means.
  2. Write √50 as a decimal. Give your answer correct to 2 decimal places.
  3. Ellie types √12 and the calculator shows 2√3. Write √12 as a decimal correct to 3 significant figures.
3 marks
Show answer
a) 5 × √2 b) 7.07 c) 3.46
9
  1. Write (53)4 as a single power of 5
  2. Write down the value of 80
2 marks
Show answer
a) 512 b) 1
10
  1. Write 82 as a power of 2.
  2. Write 43 × 25 as a single power of 2.
  3. Write 94 ÷ 27 as a single power of 3.
4 marks
Show answer
a) 26 b) 211 c) 35
11

Work out (9 × 108) ÷ (3 × 10−2)

Give your answer in standard form.

2 marks
Show answer
3 × 1010
12

The mass of the Earth is 5.97 × 1024 kg.
The mass of the Moon is 7.35 × 1022 kg.

  1. Work out how many times heavier the Earth is than the Moon. Give your answer to the nearest whole number.
  2. Work out the total mass of the Earth and the Moon. Give your answer in standard form, correct to 3 significant figures.
4 marks
Show answer
a) 81 b) 6.04 × 1024 kg

Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.

13
  1. Here are five numbers.
    √9   √10   √16   √20   ∛8
    Which of them are surds?
  2. Hamza types √48 into his calculator. The display shows 4√3. Show that √48 = 4√3
  3. Simplify √75
  4. Work out √2 × √8
4 marks
Show answer
a) √10 and √20 b) √48 = √16 × √3 = 4√3 c) 5√3 d) 4
14

Work out the value of

  1. 491/2
  2. 641/3
  3. 163/4
  4. 27−2/3
4 marks
Show answer
a) 7 b) 4 c) 8 d) 1/9
15

Rationalise the denominator of 12√3

Give your answer in its simplest form.

2 marks
Show answer
4√3

Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.

16

Rationalise the denominator of each of these. Give each answer in its simplest form.

  1. 10√5
  2. 32√6
  3. √3 + 1√3
5 marks
Show answer
a) 2√5 b) √6/4 c) (3 + √3)/3

Your score

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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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