IGCSEMaths: CoreCIETopic QuestionsNumberPowers, Roots & Standard Form

Syllabus Edition

First teaching 2023

First exams 2025

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

Topic Questions

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1
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Write down the value of 19 to the power of 0.

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2
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The cost of building a ship was $153000000.

Write 153000000 in standard form.

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3
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Write the number 40 in standard form.

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4
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Write 2020 in standard form.

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5
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Write 15060 in standard form.

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6a
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Write 72000 in standard form.

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6b
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Write 0.0018 in standard form.

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7
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Write down the value of 250.

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8a
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Write 640000 in standard form.

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8b
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Write 0.0006 in standard form.

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9
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Write 0.00527 in standard form.

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10
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Write 2760000 in standard form.

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11
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Write 0.0000523 in standard form.

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1
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i)
Write 4.81 cross times 10 to the power of negative 3 end exponent as an ordinary number.
[1]
ii)
Write 75000 in standard form.
[1]
iii)
Calculate  fraction numerator 6.3 cross times 10 squared over denominator 7 cross times 10 to the power of negative 3 end exponent end fraction
Write your answer in standard form.
[2]

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2
Sme Calculator1 mark

Find the value of x when 5 to the power of x cross times 5 cubed equals 5 to the power of 12

x equals...........................

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3
Sme Calculator2 marks

The average distance from Earth to Mars is 2.25 cross times 10 to the power of 8 km.
A space ship travels from Earth to Mars at an average speed of 5.8 cross times 10 to the power of 4 km/h.

Find how long, in hours, the journey takes.

.............................. hours

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4
Sme Calculator1 mark

Find the value of  p when  5 to the power of p divided by space 5 to the power of 8 space equals space 5 to the power of 13.

p space equals....................... 

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5
Sme Calculator3 marks

Mercury is 58 000 000 km from the sun.

Jupiter is 7.22×108 km further from the sun than Mercury.

Earth is 1.5×108 km from the sun. 

Find how many times further from the sun Jupiter is, than Earth.

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1
Sme Calculator3 marks
i)
Write 9.314 cross times 10 to the power of 5 as an ordinary number.

[1]

ii)
Calculate open parentheses 4.1 cross times 10 to the power of negative 3 end exponent close parentheses cross times open parentheses 8.9 cross times 10 to the power of 7 close parentheses
Give your answer in standard form.

[2]

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2
Sme Calculator2 marks

Find the value of

i)
3 to the power of 0 comma
[1]
ii)
5 to the power of negative 2 end exponent.
[1]

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3a
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Write the number 0.0605 in standard form.

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3b
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Calculate open parentheses 1.63 cross times 10 to the power of 12 close parentheses cross times open parentheses 2.47 cross times 10 to the power of negative 1 end exponent close parentheses

Give your answer in standard form.

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4a
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Write 45000 in standard form.

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4b
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Write 2.06 cross times 10 to the power of negative 2 end exponent as an ordinary number.

[1]

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5
Sme Calculator3 marks
i)
Write down the reciprocal of 15.
[1]
ii)
Write down the value of 15 to the power of 0.
[1]
iii)
Write 0.015 in standard form.

[1]

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6a
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Find the value of

6 to the power of 0 plus 6 squared

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6b
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Find the value of

5-4

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7
Sme Calculator3 marks
i)
Write 4.2 cross times 10 to the power of negative 3 end exponent as an ordinary number.
[1]
ii)
Calculate open parentheses 8.1 cross times 10 cubed close parentheses plus open parentheses 7.9 cross times 10 to the power of 4 close parentheses
Give your answer in standard form.
[2]

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8
Sme Calculator3 marks

Find the value of

i)
cube root of 512
[1]
ii)
6 to the power of 8 over 2 to the power of 6
[1]
iii)
70
[1]

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9
Sme Calculator1 mark

Find the value of open parentheses square root of 25 close parentheses squared.

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