IGCSEMaths: ExtendedCIEExam QuestionsNumberPowers, Roots & Standard Form

Syllabus Edition

First teaching 2023

First exams 2025

|

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

Exam Questions

1 hour40 questions

Select a question set to download for
Powers, Roots & Standard Form

Select an answer set to view for
Powers, Roots & Standard Form

Easy
Medium
Hard
1
Sme Calculator1 mark

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

How did you do?

Did this page help you?

2
Sme Calculator1 mark

Work out.

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

How did you do?

Did this page help you?

3
Sme Calculator1 mark

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

How did you do?

Did this page help you?

1
Sme Calculator1 mark

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

How did you do?

Did this page help you?

2
Sme Calculator1 mark

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

How did you do?

Did this page help you?

3
Sme Calculator1 mark

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.

How did you do?

Did this page help you?

4
Sme Calculator3 marks

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

How did you do?

Did this page help you?

5a
Sme Calculator1 mark

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.

How did you do?

5b
Sme Calculator1 mark

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

How did you do?

5c
Sme Calculator2 marks

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.

How did you do?

Did this page help you?

6
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.

How did you do?

Did this page help you?

7a
Sme Calculator1 mark

Write 640 000 000 in standard form.

How did you do?

7b
Sme Calculator2 marks

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

How did you do?

Did this page help you?

8a
Sme Calculator1 mark

Work out the value of 25-3

How did you do?

8b
Sme Calculator2 marks

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

How did you do?

Did this page help you?

1a
Sme Calculator1 mark

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 

How did you do?

1b
Sme Calculator2 marks

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 ................................................

How did you do?

1c
Sme Calculator2 marks

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


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

How did you do?

1d
Sme Calculator2 marks

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


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

How did you do?

Did this page help you?

2
Sme Calculator2 marks

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.

How did you do?

Did this page help you?

3
Sme Calculator3 marks

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.

How did you do?

Did this page help you?

4a
Sme Calculator2 marks

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.

How did you do?

4b
Sme Calculator2 marks

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.

How did you do?

Did this page help you?