IGCSEMaths: ExtendedCIETopic QuestionsNumberPowers, Roots & Standard Form

Syllabus Edition

First teaching 2023

First exams 2025

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Powers, Roots & Standard Form (CIE IGCSE Maths: Extended)

Topic Questions

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1
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The Earth has a surface area of approximately 510 100 000 km2.

Write this surface area in standard form.
 

 .......................................... km2 

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2
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Write 15 060 in standard form.

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3
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Write each number in standard form.

i)
72 000
 
[1]
ii)

0.0018

[1]

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4
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Write 0.00527 in standard form.

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5
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Write 2 760 000 in standard form.

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6
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Write 23 000 in standard form.

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7
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Write 0.00813 in standard form.

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8
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Write 0.000 038 7 in standard form.

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9
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Here are some numbers written in standard form


3.4 cross times 10 to the power of negative 1 end exponent       1.36 cross times 10 to the power of 6       7.9 cross times 10 to the power of 0       2.4 cross times 10 to the power of 5       5.21 cross times 10 to the power of negative 3 end exponent       4.3 cross times 10 to the power of negative 2 end exponent


From these numbers, write down;

i)

the largest number,
 

[1]

ii)

the smallest number.

[1]

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10
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Write 4.82 cross times 10 to the power of negative 3 end exponent as an ordinary number.

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11
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Write 52 million in standard form.

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12
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Write 0.000 052 3 in standard form.

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1
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Find the value of 64 to the power of 2 over 3 end exponent.

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2
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Calculate  0.125 to the power of negative 2 over 3 end exponent .

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3
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Work out.

open parentheses 125 over 27 close parentheses to the power of negative 2 over 3 end exponent

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4
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Find the value of open parentheses 1 over 81 close parentheses to the power of negative 3 over 4 end exponent.

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5a
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Write 5400 000 as a number in standard form.

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5b
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Write 3.2 cross times 10-4 as an ordinary number.

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5c
Sme Calculator2 marks

The mass of the Sun is 2 cross times 1030 kg.
The mass of the largest known star is 315 times the mass of the Sun.

Work out the mass of this star.
Give your answer in kg in standard form.

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6
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Simplify  8 squared space cross times cube root of 4 to the power of 6 end root

Give your answer in the form 2a where a is an integer.

Show each stage of your working clearly.

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7
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Work out, giving your answer in standard form,

(7.1 × 10–15) × (2 × 103)

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1
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Work out, giving your answer in standard form,

(5.2 × 107) + (5.2 × 106) .

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2
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Work out open parentheses 3 space cross times space 10 to the power of 199 close parentheses space plus space open parentheses 2 space cross times space 10 to the power of 201 close parentheses.
Give your answer in standard form.

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3
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Work out  left parenthesis 6.4 cross times 10 to the power of 7 right parenthesis plus left parenthesis 9.6 cross times 10 to the power of 6 right parenthesis.
Give your answer in standard form.

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4
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Write the following numbers in order of size.
Start with the smallest number.

0.038 space cross times space 10 squared space space space space space space space 3800 space cross times space 10 to the power of negative 4 end exponent space space space space space space space space 380 space space space space space space space space space space 0.38 space cross times space 10 to the power of negative 1 end exponent

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5
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Work out the value of (9 cross times 10-4) cross times (3 cross times 107)
Give your answer in standard form.

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6
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Patrick has to work out the exact value of 64 to the power of 1 fourth end exponent

Patrick says,

″1 fourth of 64 is 16 so 64 to the power of 1 fourth end exponent = 16"

Explain what is wrong with what Patrick says.

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