CIE IGCSE Maths: Extended

Topic Questions

IGCSEMaths: ExtendedCIETopic Questions1. Number1.4 Powers, Roots & Standard Form

Syllabus Edition

First teaching 2021

Last exams 2024

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1.4 Powers, Roots & Standard Form

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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 0.000 052 3 in standard form.

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11
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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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12
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Write 52 million in standard form.

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1a
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The table shows the surface area of some countries and their estimated population in 2017.

Country Surface area (km2) Estimated population in 2017
Brunei 5.77 × 103 433 100
China 9.60 × 106 1 388 000 000
France 6.41 × 105 67 000 000
Maldives 3.00 × 102 374 600

Find the total surface area of Brunei and the Maldives.
 

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

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1b
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The ratio       surface space area space of space the space Maldives space colon space surface space area space of space China
can be written in the form   1 : n.

Find the value of n.


n space equals ................................................

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1c
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Find the surface area of France as a percentage of the surface area of China.


 ............................................. %

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1d
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Find the population density of the Maldives.
[Population density = population ÷ surface area]


 ...............................people/km2 

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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 exact value of 8 to the power of 2 over 3 end exponent cross times 49 to the power of negative 1 half end exponent.

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5
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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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6a
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Write 640 000 000 in standard form.

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6b
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Work out (3 cross times 107) ÷ (6 cross times 104)
Give your answer in standard form.

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7a
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Write 5400 000 as a number in standard form.

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7b
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Write 3.2 cross times 10-4 as an ordinary number.

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7c
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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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8
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p squared space equals space fraction numerator x space minus space y over denominator x y end fraction

x space equals space 8.5 space cross times space 10 to the power of 9 space space y space equals space 4 space cross times space 10 to the power of 8

Find the value of p.

Give your answer in standard form correct to 2 significant figures.

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9a
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T space equals space square root of w over d cubed end root w space equals space 5.6 space cross times space 10 to the power of negative 5 end exponent d space equals space 1.4 space cross times space 10 to the power of negative 4 end exponent

Work out the value of T.
Give your answer in standard form correct to 3 significant figures.

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9b
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w is increased by 10%
d is increased by 5%

Lottie says,

"The value of T will increase because both w and d are increased."

Lottie is wrong.
Explain why.

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10
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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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1
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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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2
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Write 2 to the power of negative 4 end exponent as a decimal.

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3
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Calculate open parentheses 3 cross times 10 to the power of negative 3 end exponent close parentheses cubed.
Give your answer in standard form.

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4
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Calculate the value of open parentheses 2.3 cross times 10 to the power of negative 3 end exponent close parentheses plus open parentheses 6.8 cross times 10 to the power of negative 4 end exponent close parentheses.
Give your answer in standard form.

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5
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Mohsin has 720 apple trees on his farm.

Each apple tree produces 16 boxes of apples each year.
One box contains 18 kg of apples.
 
Calculate the total mass of apples produced by the 720 trees in one year.
Give your answer in standard form.

 

............................................... kg

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6
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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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7
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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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8a
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The table shows some information about eight planets.

Planet Distance from Earth (km) Mass (kg)
Earth

0

5.97 cross times1024
Jupiter

6.29 cross times 108

 1.898 cross times 1027
Mars 7.83 cross times 107 6.42 cross times 1023
Mercury 9.17 cross times 107

3.302 cross times 1023
Neptune 4.35 cross times 109

1.024 cross times 1026
Saturn 1.28 cross times 109

5.68 cross times 1026
Uranus 2.72  cross times 109

8.683 cross times 1025
Venus 4.14  cross times 107

4.869 cross times 1024


Write down the name of the planet with the greatest mass.

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8b
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Find the difference between the mass of Venus and the mass of Mercury.

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8c
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Nishat says that Neptune is over a hundred times further away from Earth than Venus is.

Is Nishat right?
You must show how you get your answer.

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9
Sme Calculator2 marks

Work out (13.8 cross times 107) cross times (5.4 cross times 10−12)
Give your answer as an ordinary number.

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10
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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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11a
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Work out the value of 25-3

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11b
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Work out the value of 3503
Give your answer in standard form.

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12
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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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