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OCR GCSE Maths

Topic questions Number Standard form

Standard form

45 questions · 206 marks · about 3 hours

Standard form questions

TopicStandard form

OCR J560 Standard form 45 questions

Paper 1 June 2025 Foundation tier, Question 29, also on the Higher paper 5 marks

(a)

Write 0.0037 in standard form.

[1]
Reveal mark scheme Mark scheme for question 29(a)
(b)

A country consists of a south island and a north island. The table below shows the population and area of each island in June 2023.

PopulationArea (km2)
1.2× 1061.5× 105
4.0× 1061.1× 105

Work out the overall population density of the country in June 2023.

(b)........ people per km2

[4]
Reveal mark scheme Mark scheme for question 29(b)

Paper 4 June 2025 Higher tier, Question 9, also on the Foundation paper 5 marks

Also involves The four operations

(a)

Write 0.0037 in standard form.

[1]
Reveal mark scheme Mark scheme for question 9(a)
(b)

A country consists of a south island and a north island. The table below shows the population and area of each island in June 2023.

PopulationArea (km2)
1.2× 1061.5× 105
4.0× 1061.1× 105

Work out the overall population density of the country in June 2023.

(b)........ people per km2

[4]
Reveal mark scheme Mark scheme for question 9(b)

Paper 3 November 2024 Foundation tier, Question 13 5 marks

Also involves Converting between units

(a)

Write 0.001 025 in standard form.

[1]
Reveal mark scheme Mark scheme for question 13(a)
(b)

A weather blogger writes:

• 1.655 × 1012 raindrops fall in a storm

• the mass of each raindrop is 6 × 10-5 grams.

Calculate the total mass of all of the raindrops that fall in the storm. Give your answer in standard form in kilograms.

[4]
Reveal mark scheme Mark scheme for question 13(b)

Paper 1 June 2024 Foundation tier, Question 27, also on the Higher paper 3 marks

Write the following in order of size, smallest first.

0.2 2-2 2 × 10-2

Show how you decide.

smallest

[3]
Reveal mark scheme Mark scheme for question 27

Paper 3 June 2024 Foundation tier, Question 3 4 marks

Also involves Using a calculator

(a)

Use your calculator to work out.

(a)(i)

64

[1]
Reveal mark scheme Mark scheme for question 3(a)(i)
(a)(ii)
Question 3, shown as an image
[1]
Reveal mark scheme Mark scheme for question 3(a)(ii)
(b)

Complete this statement to make it correct. Give your answer as a number in ordinary form.

Question 3, shown as an image
[2]
Reveal mark scheme Mark scheme for question 3(b)

Paper 4 June 2024 Higher tier, Question 7, also on the Foundation paper 3 marks

Write the following in order of size, smallest first. 0.2 2-2 2 × 10-2

Show how you decide.

smallest

[3]
Reveal mark scheme Mark scheme for question 7

Paper 3 November 2023 Foundation tier, Question 25, also on the Higher paper 6 marks

A sheet of A4 card weighs 1.19 × 10-2 kg.

(a)

Work out the weight of 500 sheets of the A4 card.

[2]
(b)

Card is classified using W, the weight in grams per square metre (gsm).

Question 25, shown as an image

A sheet of A4 card is a rectangle that is 21 cm by 29.7 cm.

Calculate W for this A4 card.

[4]
Reveal mark scheme Mark scheme for question 25(b)

Paper 6 November 2023 Higher tier, Question 3 4 marks

Write these numbers in order of size, starting with the smallest.

Question 3, shown as an image

smallest

[4]
Reveal mark scheme Mark scheme for question 3

Paper 6 November 2023 Higher tier, Question 5, also on the Foundation paper 6 marks

Also involves Area and perimeter

A sheet of A4 card weighs 1.19 × 10-2 kg.

(a)

Work out the weight of 500 sheets of the A4 card.

[2]
Reveal mark scheme Mark scheme for question 5(a)
(b)

Card is classified using W, the weight in grams per square metre (gsm).

Question 5, shown as an image

A sheet of A4 card is a rectangle that is 21 cm by 29.7 cm.

Calculate W for this A4 card.

[4]
Reveal mark scheme Mark scheme for question 5(b)

Paper 4 June 2023 Higher tier, Question 5 6 marks

Also involves Forming and solving equations · Converting between units

(a)

Write 0.003 86 in standard form.

[1]
Reveal mark scheme Mark scheme for question 5(a)
(b)

The speed of sound is 3.43 × 10-1km/s. An object is travelling at the speed of sound.

Work out how far the object travels in one day.

[2]
Reveal mark scheme Mark scheme for question 5(b)
(c)

In a science fiction story, a spacecraft travelling faster than the speed of light is said to be travelling at ‘warp n ’ where n is an integer.

Warp n is defined as n3 × the speed of light.

In the story, a spacecraft needs to travel from Earth to Neptune in less than 2 minutes.

• The speed of light is 3.00 × 105km/s.

• The distance from Earth to Neptune is 4.41 × 109km.

Find the smallest possible warp n at which the spacecraft can travel. You must show your working.

[3]
Reveal mark scheme Mark scheme for question 5(c)

Paper 1 November 2022 Foundation tier, Question 21 6 marks

The table below shows the approximate population of three countries in 2020.

CountryPopulation
China1.44 × 109
Kiribati1.19 × 105
Tuvalu1.18 × 104
(a)

Calculate the approximate total population of Kiribati and Tuvalu in 2020. Give your answer in standard form, correct to 3 significant figures.

[4]
Reveal mark scheme Mark scheme for question 21(a)
(b)

Show that in 2020 the population of China was approximately 120 000 times the population

of Tuvalu.

[2]
Reveal mark scheme Mark scheme for question 21(b)

Paper 3 November 2022 Foundation tier, Question 15 4 marks

(a)

102is written in words as ‘one hundred’.

Question 15, shown as an image
[2]
Reveal mark scheme Mark scheme for question 15(a)
(b)

Work out (3.5 × 10-1) × 100, giving your answer in standard form.

[2]
Reveal mark scheme Mark scheme for question 15(b)

Paper 4 November 2022 Higher tier, Question 1 2 marks

(a)

Write 65 400 in standard form.

[1]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Write 8.2 × 10-4 as an ordinary number.

[1]
Reveal mark scheme Mark scheme for question 1(b)

Paper 6 November 2022 Higher tier, Question 5 5 marks

Also involves Converting between units

In space, distances can be measured in Astronomical Units. In this question, use the conversion 1 Astronomical Unit = 1.5 × 108km.

(a)

On a particular day the distance from Earth to Neptune is 29.09 Astronomical Units.

Calculate the distance from Earth to Neptune in kilometres on that day. Give your answer in standard form.

[3]
Reveal mark scheme Mark scheme for question 5(a)
(b)

On a particular day the distance from Earth to Mars is 78 340 000 km.

Calculate the distance from Earth to Mars in Astronomical Units on that day.

(b)........ Astronomical Units

[2]
Reveal mark scheme Mark scheme for question 5(b)

Paper 1 June 2022 Foundation tier, Question 18, also on the Higher paper 2 marks

(a)

Write 6 050 000 in standard form.

[1]
Reveal mark scheme Mark scheme for question 18(a)
(b)

Write 4.58 × 10-3 as an ordinary number.

[1]
Reveal mark scheme Mark scheme for question 18(b)

Paper 2 June 2022 Foundation tier, Question 12, also on the Higher paper 4 marks

Dinosaurs first appeared on Earth 2.4 × 108 years ago. Dinosaurs became extinct on Earth 7 × 107 years ago.

(a)

Explain why it is appropriate to use standard form for these numbers.

[1]
Reveal mark scheme Mark scheme for question 12(a)
(b)

Use the given information to work out how long dinosaurs existed on Earth. Give your answer in standard form.

[3]
Reveal mark scheme Mark scheme for question 12(b)

Paper 3 June 2022 Foundation tier, Question 16 2 marks

For each statement, complete the box to show the power of 10.

(a)

One million = 10

[1]
Reveal mark scheme Mark scheme for question 16(a)
(b)

One thousandth = 10

[1]
Reveal mark scheme Mark scheme for question 16(b)

Paper 4 June 2022 Higher tier, Question 1, also on the Foundation paper 2 marks

(a)

Write 6 050 000 in standard form.

[1]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Write 4.58 × 10-3 as an ordinary number.

[1]
Reveal mark scheme Mark scheme for question 1(b)

Paper 5 June 2022 Higher tier, Question 3, also on the Foundation paper 4 marks

Dinosaurs first appeared on Earth 2.4 × 108 years ago. Dinosaurs became extinct on Earth 7 × 107 years ago.

(a)

Explain why it is appropriate to use standard form for these numbers.

[1]
Reveal mark scheme Mark scheme for question 3(a)
(b)

Use the given information to work out how long dinosaurs existed on Earth. Give your answer in standard form.

[3]
Reveal mark scheme Mark scheme for question 3(b)

Paper 6 June 2022 Higher tier, Question 3 4 marks

Also involves Using a calculator

Light from the Sun travels 1 kilometre in 3.3 × 10-6 seconds. The distance from the Sun to the Earth is 1.5 × 108kilometres.

How long does it take light to travel from the Sun to the Earth? Give your answer in minutes and seconds.

........ minutes........ seconds

[4]
Reveal mark scheme Mark scheme for question 3

Paper 3 November 2021 Foundation tier, Question 14, also on the Higher paper 7 marks

This table shows the names and areas of five lakes.

Name of LakeArea in km2
Ladoga1.81 × 104
Mweru5.12 × 103
Tana3.20 × 103
Topozero9.86 × 102
Victoria6.89 × 104
(a)

Write the area of Lake Mweru as an ordinary number.

[1]
Reveal mark scheme Mark scheme for question 14(a)
(b)

Write the lakes in the order of their area, starting with the smallest.

smallest largest

[2]
Reveal mark scheme Mark scheme for question 14(b)
(c)

Calculate the difference between the areas of Lake Ladoga and Lake Tana. Give your answer in standard form, correct to 2 significant figures.

[4]
Reveal mark scheme Mark scheme for question 14(c)

Paper 6 November 2021 Higher tier, Question 1, also on the Foundation paper 7 marks

This table shows the names and areas of five lakes.

Name of LakeArea in km2
Ladoga1.81 × 104
Mweru5.12 × 103
Tana3.20 × 103
Topozero9.86 × 102
Victoria6.89 × 104
(a)

Write the area of Lake Mweru as an ordinary number.

[1]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Write the lakes in the order of their area, starting with the smallest.

smallest largest

[2]
Reveal mark scheme Mark scheme for question 1(b)
(c)

Calculate the difference between the areas of Lake Ladoga and Lake Tana. Give your answer in standard form, correct to 2 significant figures.

[4]
Reveal mark scheme Mark scheme for question 1(c)

Paper 1 November 2020 Foundation tier, Question 17 7 marks

The table below shows the number of barrels of oil produced per day by some countries.

CountryBarrels of oil produced per day
USA1.17× 107
China3.98× 106
UK9.39× 105
Cameroon9.32× 104
Japan3.92× 103
(a)

Write the number of barrels of oil produced per day by Cameroon as an ordinary number.

[1]
Reveal mark scheme Mark scheme for question 17(a)
(b)

How many more barrels of oil per day did China produce than the UK? Give your answer in standard form, correct to 3 significant figures.

[4]
Reveal mark scheme Mark scheme for question 17(b)
(c)

Jamal says the USA produced approximately three times more barrels of oil than Japan.

Is he correct? Show how you decide.

Jamal is........ because........

[2]
Reveal mark scheme Mark scheme for question 17(c)

Paper 4 November 2020 Higher tier, Question 1 3 marks

(a)

Write these numbers in standard form.

(a)(i)

6500

[1]
Reveal mark scheme Mark scheme for question 1(a)(i)
(a)(ii)

0.0584

[1]
Reveal mark scheme Mark scheme for question 1(a)(ii)
(b)

Work out (4.2 × 105) × (1.8 × 10-2), giving your answer in standard form.

[1]
Reveal mark scheme Mark scheme for question 1(b)

Paper 1 November 2019 Foundation tier, Question 17 8 marks

The table below shows the area, in square kilometres (km2), of some countries.

CountryArea (km2)
Australia7.69 × 106
Latvia6.46 × 104
Luxembourg2.59 × 103
Russia1.71 × 107
Singapore7.24 × 102
Sweden4.50 × 105
(a)

Write the area of Sweden as an ordinary number.

[1]
Reveal mark scheme Mark scheme for question 17(a)
(b)

Which of the above countries has the smallest area?

[1]
Reveal mark scheme Mark scheme for question 17(b)
(c)

Alexis says

The area of Australia is approximately three times larger than the area of Luxembourg

Is she correct? Show how you decide.

Alexis is........ because........

[2]
Reveal mark scheme Mark scheme for question 17(c)
(d)

Work out the total area of Russia and Australia. Give your answer in standard form, correct to 2 significant figures.

[4]
Reveal mark scheme Mark scheme for question 17(d)

Paper 4 November 2019 Higher tier, Question 2 4 marks

Also involves Rounding

Use the formula F = fraction to find the value of F when

Question 2, shown as an image

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

[4]
Reveal mark scheme Mark scheme for question 2

Paper 3 June 2019 Foundation tier, Question 17, also on the Higher paper 3 marks

Also involves Estimation and approximation

A grain of salt weighs 6.48 × 10-5kg on average. A packet contains 0.35 kg of salt.

(a)

Use this information to calculate the number of grains of salt in the packet.

[2]
Reveal mark scheme Mark scheme for question 17(a)
(b)

Explain why your answer to part (a) is unlikely to be the actual number of grains of salt in the packet.

[1]
Reveal mark scheme Mark scheme for question 17(b)

Paper 3 June 2019 Foundation tier, Question 18, also on the Higher paper 4 marks

Also involves Using a calculator

Tom researches the weights of plant seeds.

• One poppy seed weighs 3 × 10-4grams.

• 250 pumpkin seeds weigh 21 grams.

• One sesame seed weighs 3.64 × 10-6 kilograms.

Write the three types of seed in order according to the weight of one seed. Write the lightest type of seed first. You must show how you decide.

lightest

[4]
Reveal mark scheme Mark scheme for question 18

Paper 5 June 2019 Higher tier, Question 1 2 marks

Work out (2 × 103) × (4 × 104), giving your answer in standard form.

[2]
Reveal mark scheme Mark scheme for question 1

Paper 6 June 2019 Higher tier, Question 1, also on the Foundation paper 3 marks

Also involves Estimation and approximation

A grain of salt weighs 6.48 × 10-5kg on average. A packet contains 0.35 kg of salt.

(a)

Use this information to calculate the number of grains of salt in the packet.

[2]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Explain why your answer to part (a) is unlikely to be the actual number of grains of salt in the packet.

[1]
Reveal mark scheme Mark scheme for question 1(b)

Paper 6 June 2019 Higher tier, Question 2, also on the Foundation paper 4 marks

Also involves Using a calculator

Tom researches the weights of plant seeds.

• One poppy seed weighs 3 × 10-4grams.

• 250 pumpkin seeds weigh 21 grams.

• One sesame seed weighs 3.64 × 10-6 kilograms.

Write the three types of seed in order according to the weight of one seed. Write the lightest type of seed first. You must show how you decide.

lightest

[4]
Reveal mark scheme Mark scheme for question 2

Paper 2 November 2018 Foundation tier, Question 13 3 marks

(a)

Write 0.003 16 in standard form.

[1]
Reveal mark scheme Mark scheme for question 13(a)
(b)

Work out.

Question 13, shown as an image

Give your answer in standard form.

[2]
Reveal mark scheme Mark scheme for question 13(b)

Paper 3 November 2018 Foundation tier, Question 22, also on the Higher paper 5 marks

A newborn baby has an approximate mass of 3.5 kilograms.

A human cell has an approximate mass of 2.7 × 10-11 grams.

Use these values to estimate the number of human cells in a newborn baby. Give your answer in standard form, correct to 2 significant figures.

[5]
Reveal mark scheme Mark scheme for question 22

Paper 5 November 2018 Higher tier, Question 1 5 marks

Work out.

(a)
Question 1, shown as an image
[2]
Reveal mark scheme Mark scheme for question 1(a)
(b)

4.3 × 105 + 3.8 × 104 Give your answer in standard form.

[3]
Reveal mark scheme Mark scheme for question 1(b)

Paper 6 November 2018 Higher tier, Question 3, also on the Foundation paper 5 marks

Also involves Converting between units

A newborn baby has an approximate mass of 3.5 kilograms.

A human cell has an approximate mass of 2.7 × 10–11 grams.

Use these values to estimate the number of human cells in a newborn baby. Give your answer in standard form, correct to 2 significant figures.

[5]
Reveal mark scheme Mark scheme for question 3

Paper 2 June 2018 Foundation tier, Question 13 6 marks

(a)

Calculate.

Question 13, shown as an image

Give your answer as a mixed number in its simplest form.

[3]
Reveal mark scheme Mark scheme for question 13(a)
(b)

Work out.

5 × 104 – 1.6 × 103

Give your answer in standard form.

[3]
Reveal mark scheme Mark scheme for question 13(b)

Paper 3 June 2018 Foundation tier, Question 22 3 marks

Also involves Ratio

Earth and Pluto go around the Sun. Their distance to the Sun varies.

Figure for question 22

The table shows the closest distance that Earth and Pluto get to the Sun.

Closest distance to the Sun (km)
Earth1.47 × 108
Pluto4.44 × 109
(a)

Show that the closest distance of Pluto to the Sun is roughly 30 times the closest distance of

Earth to the Sun.

[2]
Reveal mark scheme Mark scheme for question 22(a)
(b)

Give a reason why we cannot use this information to say

The distance of Pluto to the Sun is always 30 times the distance of Earth to the Sun.

[1]
Reveal mark scheme Mark scheme for question 22(b)

Paper 5 June 2018 Higher tier, Question 1 6 marks

(a)

Calculate.

Question 1, shown as an image

Give your answer as a mixed number in its simplest form.

[3]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Work out.

Question 1, shown as an image

Give your answer in standard form.

[3]
Reveal mark scheme Mark scheme for question 1(b)

Paper 2 November 2017 Foundation tier, Question 22 3 marks

(a)

Beth is given the following question.

Work out

Question 22, shown as an image

Give your answer in standard form.

This is Beth’s answer to the question.

Question 22, shown as an image

Explain why Beth’s answer is incorrect.

[1]
Reveal mark scheme Mark scheme for question 22(a)
(b)

Show that

Question 22, shown as an image
[2]
Reveal mark scheme Mark scheme for question 22(b)

Paper 3 November 2017 Foundation tier, Question 10 4 marks

(a)

Write 7 × 7 × 7 × 7 as a power of 7.

[1]
Reveal mark scheme Mark scheme for question 10(a)
(b)

Complete this working to write 43 as a power of 2.

43 = 4 × 4........

so 43 = 2 × 2 × 2 ×........

[2]
Reveal mark scheme Mark scheme for question 10(b)
(c)

Write these numbers in order, starting with the largest.

8.1 × 101 1.02 × 103 9.83 × 10–2 3 × 102

largest

[1]
Reveal mark scheme Mark scheme for question 10(c)

Paper 3 November 2017 Foundation tier, Question 13, also on the Higher paper 9 marks

Also involves The four operations

A company makes sweets. The sweets are put into packets.

Here are some facts.

Figure for question 13
(a)

Calculate the mean number of sweets in one packet.

[2]
Reveal mark scheme Mark scheme for question 13(a)
(b)

Sweets are made on 288 days each year.

Calculate the number of sweets made each year. Give your answer in standard form.

[3]
Reveal mark scheme Mark scheme for question 13(b)
(c)

The company has 152 machines making the sweets. Each machine operates for 15 hours each day.

(c)(i)

Calculate the number of sweets made by one machine each hour. Give your answer as an ordinary number correct to the nearest 10.

[3]
Reveal mark scheme Mark scheme for question 13(c)(i)
(c)(ii)

State one assumption you have made in part (c)(i).

[1]
Reveal mark scheme Mark scheme for question 13(c)(ii)

Paper 6 November 2017 Higher tier, Question 5, also on the Foundation paper 9 marks

Also involves Using a calculator

A company makes sweets. The sweets are put into packets.

Here are some facts.

Figure for question 5
(a)

Calculate the mean number of sweets in one packet.

[2]
Reveal mark scheme Mark scheme for question 5(a)
(b)

Sweets are made on 288 days each year.

Calculate the number of sweets made each year. Give your answer in standard form.

[3]
Reveal mark scheme Mark scheme for question 5(b)
(c)

The company has 152 machines making the sweets. Each machine operates for 15 hours each day.

(c)(i)

Calculate the number of sweets made by one machine each hour. Give your answer as an ordinary number correct to the nearest 10.

[3]
Reveal mark scheme Mark scheme for question 5(c)(i)
(c)(ii)

State one assumption you have made in part (c)(i).

[1]
Reveal mark scheme Mark scheme for question 5(c)(ii)

Paper 1 June 2017 Foundation tier, Question 14 3 marks

(a)

Write 543 000 in standard form.

[1]
Reveal mark scheme Mark scheme for question 14(a)
(b)

Write 6.3 × 10-2 as an ordinary number.

[1]
Reveal mark scheme Mark scheme for question 14(b)
(c)

Pierre is given this question.

Work out. 61 000 × 4000 Give your answer in standard form.

Pierre’s answer is 24.4 × 107.

Is Pierre correct? Explain your answer.

[1]
Reveal mark scheme Mark scheme for question 14(c)

Paper 6 June 2017 Higher tier, Question 1 7 marks

This table shows the populations of the four countries of the UK in 2012. All values are given correct to 3 significant figures.

CountryPopulation
England5.35 × 107
Wales3.07 × 106
Scotland5.31 × 106
Northern Ireland1.82 × 106
(a)

Write the population of England as an ordinary number.

[1]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Work out the total population of Wales, Scotland and Northern Ireland. Give your answer in standard form.

[2]
Reveal mark scheme Mark scheme for question 1(b)
(c)

The total population of the UK is predicted to reach 73.3 million in 2037.

Calculate the predicted percentage increase in the UK population from 2012 to 2037. Give your answer correct to 2 significant figures.

[4]
Reveal mark scheme Mark scheme for question 1(c)

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