IGCSEMaths: CoreCIEExam QuestionsNumberPowers, Roots & Standard Form

Syllabus Edition

First teaching 2021

Last exams 2024

|

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

Exam Questions

1 hour34 questions
Easy
Medium
Hard
1
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Write down the value of 190.

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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 15 060

in standard form.

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6
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Write down the value of 250.

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7a
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Write the following numbers in standard form.

640000

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7b
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0.0006

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8
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Write 23000 in standard form.

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9a
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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 space space space space space space space space space space space 1.36 cross times 10 to the power of 6 space space space space space space space space space space space space space space space 7.9 cross times 10 to the power of 0 space space space space space space space space space space space space space space space space space 2.4 cross times 10 to the power of 5 space space space space space space space space space space 5.21 cross times 10 to the power of negative 3 end exponent space space space space space space space space space space space space 4.3 cross times 10 to the power of negative 2 end exponent

From these numbers, write down

the largest number,

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9b
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the smallest number.

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10
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Find the value of

i)
the square root of 19044,

[1]

ii)
2 to the power of 7.
[1]

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11
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Write 0.000052 3 in standard form.

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12a
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Write in standard form.

72000

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12b
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Write in standard form.

0.0018

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13
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Write 0.00527 in standard form.

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14
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Write 2760000 in standard form.

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15
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Write 0.00813 in standard form.

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1
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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
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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.

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5
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i)
Write down the reciprocal of 15.
[1]
ii)
Write down the value of 15°.
[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
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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 to the power of 5 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
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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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9a
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In 2016, the population of Nigeria was 187000000.

Write 187000 000 in standard form.

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9b
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In 2016, the population of South Africa was 5.50 space cross times space 10 to the power of 7.
In 2016, the population of Kenya was 4.72 space cross times space 10 to the power of 7

Calculate the difference between the population of South Africa and the population of Kenya.
Give your answer in standard form.

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10
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Find the value of

i)
square root of 2.89 end root

[1]

ii)
14 cubed
[1]
iii)
4 to the power of negative 2 end exponent
[1]

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11
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Write 0.000038 7 in standard form.

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12
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Find the value of open parentheses square root of 25 close parentheses squared.

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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
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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
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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
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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
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Work out the value of 4 to the power of negative 2 end exponent.

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6a
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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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6b
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Write 52 million in standard form.

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7
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The door to the museum has an 8-digit code to unlock it.

  • The next odd number after 35 gives digits 1 and 2.
  • The next prime number after 23 gives digits 3 and 4.
  • The square root of 225 gives digits 5 and 6.
  • The value of 26 gives digits 7 and 8.

Use this information to complete the door code.
Digits 1 and 2 have been completed for you.

Digit 1 2 3 4 5 6 7 8
Code 3 7            

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