Standard Form

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More questions on this topic: IGCSE Number: Standard Form (102)

From a Foundation paper

Edexcel

Edexcel · Old spec

AQA

OCR

Foundation June 2025 Paper 1 Q23

EdexcelFoundationCurrent spec3 marksStandard Form

23 Work out \(5.7 \times 10^2 + 9.8 \times 10^3\)
Give your answer in standard form. (3)

Higher June 2025 Paper 1 Q5

EdexcelHigherCurrent spec3 marksStandard Form

5 Work out \(5.7 \times 10^2 + 9.8 \times 10^3\)
Give your answer in standard form. (3)

Foundation November 2024 Paper 2 Q27

EdexcelFoundationCurrent spec2 marksStandard Form

27 \(1.25 \times 10^{-12} = k \times (4 \times 10^{-20})\)

Work out the value of \(k\).
Give your answer in standard form. (2)

Foundation November 2024 Paper 3 Q18

EdexcelFoundationCurrent spec2 marksStandard Form

18

(a) Write \(3.402 \times 10^5\) as an ordinary number. (1)
(b) Write 0.8026 in standard form. (1)

Higher November 2024 Paper 2 Q8

EdexcelHigherCurrent spec2 marksStandard Form

8 \(1.25 \times 10^{-12} = k \times (4 \times 10^{-20})\)

Work out the value of \(k\).
Give your answer in standard form. (2)

Higher November 2024 Paper 3 Q2

EdexcelHigherCurrent spec2 marksStandard Form

2

(a) Write \(3.402 \times 10^5\) as an ordinary number. (1)
(b) Write 0.8026 in standard form. (1)

Foundation June 2024 Paper 3 Q23

EdexcelFoundationCurrent spec4 marksStandard Form

23

(a)
(i) Write \(\ 5.3 \times 10^4\ \) as an ordinary number. (1)
(ii) Write \(\ 7.4 \times 10^{-5}\ \) as an ordinary number. (1)
(b) Calculate the value of \(\quad 9.7 \times 10^6 + 2.45 \times 10^7\)
Give your answer in standard form. (2)

Higher June 2024 Paper 3 Q2

EdexcelHigherCurrent spec4 marksStandard Form

2

(a)
(i) Write \(5.3 \times 10^4\) as an ordinary number. (1)
(ii) Write \(7.4 \times 10^{-5}\) as an ordinary number. (1)
(b) Calculate the value of \(9.7 \times 10^6 + 2.45 \times 10^7\)
Give your answer in standard form. (2)

Foundation November 2023 Paper 3 Q20

EdexcelFoundationCurrent spec2 marksStandard Form

20

(a) Write 468 000 in standard form. (1)
(b) Write \(5.037 \times 10^{-4}\) as an ordinary number. (1)

Higher November 2023 Paper 3 Q1

EdexcelHigherCurrent spec2 marksStandard Form

1

(a) Write 468 000 in standard form. (1)
(b) Write \(5.037 \times 10^{-4}\) as an ordinary number. (1)

Foundation June 2023 Paper 3 Q28

EdexcelFoundationCurrent spec4 marksStandard Form

28

(a) Write \(\quad (9 \times 10^4) : (4.5 \times 10^6) \quad\) in the form \(1 : n\) where \(n\) is an integer. (2)
(b) Write the following numbers in order of size.
Start with the smallest number.\[5.625 \times 10^4 \qquad 5625 \qquad 56\,250 \times 10^{-3} \qquad 0.005\,625 \times 10^5\] (2)

Foundation November 2022 Paper 3 Q29

EdexcelFoundationCurrent spec3 marksStandard Form

29

(a) Write \(\;6.75 \times 10^{-4}\;\) as an ordinary number. (1)
(b) Work out \(\quad \dfrac{2.56 \times 10^{6} \times 4.12 \times 10^{-3}}{1.6 \times 10^{-2}}\)
Give your answer in standard form. (2)

Foundation June 2022 Paper 1 Q26

EdexcelFoundationCurrent spec4 marksStandard Form

26

(a) Write \(1.63 \times 10^{-3}\) as an ordinary number. (1)
(b) Write 438 000 in standard form. (1)
(c) Work out \((4 \times 10^3) \times (6 \times 10^{-5})\)
Give your answer in standard form. (2)

Higher June 2022 Paper 1 Q4

EdexcelHigherCurrent spec4 marksStandard Form

4

(a) Write \(1.63 \times 10^{-3}\) as an ordinary number. (1)
(b) Write 438 000 in standard form. (1)
(c) Work out \((4 \times 10^3) \times (6 \times 10^{-5})\)
Give your answer in standard form. (2)

Foundation November 2021 Paper 3 Q23

EdexcelFoundationCurrent spec4 marksStandard Form

23

(a) Write \(4.5 \times 10^5\) as an ordinary number. (1)
(b) Write 0.007 in standard form. (1)
(c) Work out \(4.2 \times 10^3 + 5.3 \times 10^2\)
Give your answer in standard form. (2)

Higher November 2021 Paper 3 Q3

EdexcelHigherCurrent spec4 marksStandard Form

3

(a) Write \(4.5 \times 10^5\) as an ordinary number. (1)
(b) Write 0.007 in standard form. (1)
(c) Work out \(4.2 \times 10^3 + 5.3 \times 10^2\)
Give your answer in standard form. (2)

Foundation November 2019 Paper 3 Q28

EdexcelFoundationCurrent spec3 marksStandard Form

28

(a) Write 32 460 000 in standard form. (1)
(b) Write \(4.96 \times 10^{-3}\) as an ordinary number. (1)

Asma was asked to compare the following two numbers.

\(A = 6.212 \times 10^8\)     and     \(B = 4.73 \times 10^9\)

She says,

“6.212 is bigger than 4.73 so \(A\) is bigger than \(B\).”

(c) Is Asma correct?
You must give a reason for your answer. (1)

Foundation November 2019 Paper 2 Q27

EdexcelFoundationCurrent spec2 marksStandard Form

27 Work out \((3.42 \times 10^{-7}) \div (7.5 \times 10^{-6})\)
Give your answer in standard form. (2)

Higher November 2019 Paper 2 Q7

EdexcelHigherCurrent spec2 marksStandard Form

7 Work out \((3.42 \times 10^{-7}) \div (7.5 \times 10^{-6})\)
Give your answer in standard form. (2)

Higher November 2019 Paper 3 Q7

EdexcelHigherCurrent spec3 marksStandard Form

7

(a) Write 32 460 000 in standard form. (1)
(b) Write \(4.96 \times 10^{-3}\) as an ordinary number. (1)

Asma was asked to compare the following two numbers.

\(A = 6.212 \times 10^8\)   and   \(B = 4.73 \times 10^9\)

She says,

“6.212 is bigger than 4.73 so A is bigger than B.”

(c) Is Asma correct?
You must give a reason for your answer. (1)

Foundation June 2019 Paper 2 Q27

EdexcelFoundationCurrent spec2 marksStandard Form

27

(a) Write 0.00562 in standard form. (1)
(b) Write \(1.452 \times 10^3\) as an ordinary number. (1)

Higher June 2019 Paper 3 Q11

EdexcelHigherCurrent spec3 marksCompound MeasuresStandard Form

11 In May 2019, the distance between Earth and Mars was \(3.9 \times 10^7\) km.

In May 2019, a signal was sent from Earth to Mars.
Assuming that the signal sent from Earth to Mars travelled at a speed of \(3 \times 10^5\) km per second,

(a) how long did the signal take to get to Mars? (2)

The speed of the signal sent from Earth to Mars in May 2019 was actually less than \(3 \times 10^5\) km per second.

(b) How will this affect your answer to part (a)? (1)

Foundation November 2018 Paper 2 Q27

EdexcelFoundationCurrent spec4 marksStandard Form

27

(a) Write the number 0.000 075 47 in standard form. (1)
(b) Write \(3.42 \times 10^4\) as an ordinary number. (1)
(c) Work out  \(\dfrac{2.3 \times 10^4 \times 6.7 \times 10^3}{5 \times 10^{-8}}\) (2)

Higher November 2018 Paper 2 Q7

EdexcelHigherCurrent spec3 marksStandard Form

7

(a) Write the number  0.000 086 23  in standard form. (1)
(b) Work out   \(\dfrac{3.2 \times 10^3 + 5.1 \times 10^{-2}}{4.3 \times 10^{-4}}\)
Give your answer in standard form, correct to 3 significant figures. (2)

Foundation June 2018 Paper 3 Q18

EdexcelFoundationCurrent spec2 marksStandard Form

18 Work out the value of  \(\dfrac{2.645 \times 10^9}{1.15 \times 10^3}\)

Give your answer in standard form. (2)

Higher June 2018 Paper 3 Q9

EdexcelHigherCurrent spec4 marksStandard FormUsing a Calculator / BIDMAS

9 \(T = \sqrt{\dfrac{w}{d^3}}\)

\(w = 5.6 \times 10^{-5}\)
\(d = 1.4 \times 10^{-4}\)

(a) Work out the value of \(T\).
Give your answer in standard form correct to 3 significant figures. (2)

\(w\) is increased by 10%
\(d\) is increased by 5%

Lottie says,

“The value of \(T\) will increase because both \(w\) and \(d\) are increased.”

(b) Lottie is wrong.
Explain why. (2)

Foundation November 2017 Paper 1 Q21

EdexcelFoundationCurrent spec3 marksStandard Form

21 Work out \(\dfrac{0.06 \times 0.0003}{0.01}\)

Give your answer in standard form. (3)

Foundation June 2017 Paper 2 Q15

EdexcelFoundationCurrent spec3 marksStandard Form

15

(a) Write \(4.7 \times 10^{-1}\) as an ordinary number. (1)
(b) Work out the value of \((2.4 \times 10^3) \times (9.5 \times 10^5)\)
Give your answer in standard form. (2)

Higher June 2017 Paper 2 Q10

EdexcelHigherCurrent spec4 marksStandard Form

10 The table shows some information about eight planets.

PlanetDistance from Earth (km)Mass (kg)
Earth0\(5.97 \times 10^{24}\)
Jupiter\(6.29 \times 10^{8}\)\(1.898 \times 10^{27}\)
Mars\(7.83 \times 10^{7}\)\(6.42 \times 10^{23}\)
Mercury\(9.17 \times 10^{7}\)\(3.302 \times 10^{23}\)
Neptune\(4.35 \times 10^{9}\)\(1.024 \times 10^{26}\)
Saturn\(1.28 \times 10^{9}\)\(5.68 \times 10^{26}\)
Uranus\(2.72 \times 10^{9}\)\(8.683 \times 10^{25}\)
Venus\(4.14 \times 10^{7}\)\(4.869 \times 10^{24}\)
(a) Write down the name of the planet with the greatest mass. (1)
(b) Find the difference between the mass of Venus and the mass of Mercury. (1)

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

(c) Is Nishat right?
You must show how you get your answer. (2)

Higher June 2017 Paper 1 Q8

EdexcelHigherCurrent spec3 marksStandard Form

8

(a) Write \(7.97 \times 10^{-6}\) as an ordinary number. (1)
(b) Work out the value of \((2.52 \times 10^{5}) \div (4 \times 10^{-3})\)
Give your answer in standard form. (2)

1MA0 Higher June 2017 Paper 1 Q18

EdexcelHigherOld spec4 marksStandard Form

18

(a) Write 5 400 000 as a number in standard form. (1)
(b) Write \(3.2 \times 10^{-4}\) as an ordinary number. (1)

The mass of the Sun is \(2 \times 10^{30}\) kg.
The mass of the largest known star is 315 times the mass of the Sun.

(c) Work out the mass of this star.
Give your answer in kg in standard form. (2)

1MA0 Higher November 2016 Paper 1 Q20

EdexcelHigherOld spec5 marksRatio & Basic ProportionStandard Form

20 William is building a planetary path for people to walk along.
The planetary path will have a model of the Sun and models of the planets.

William uses two different scales.
He uses

  1 cm to 1000 km for the diameter of each planet
  1 m to 1 000 000 km for the distance from the Sun to each planet

William makes a model of the planet Venus.
The model has a diameter of 12.1 cm.

(a) Work out the real diameter of the planet Venus.
Give your answer in standard form. (2)

William works out the distance from the model of the Sun to the model of the planet Neptune.

The real distance from the Sun to the planet Neptune is \(4.503 \times 10^9\) km.

(b) Work out the distance from the model of the Sun to the model of the planet Neptune.
Give your answer in km, correct to 1 decimal place. (3)

1MA0 Higher June 2016 Paper 1 Q16

EdexcelHigherOld spec2 marksStandard Form

16 Work out the value of \((3.5 \times 10^6) \div (5 \times 10^{-3})\)
Give your answer in standard form. (2)

1MA0 Higher November 2015 Paper 2 Q16

EdexcelHigherOld spec3 marksStandard Form

16

(a) Write 640 000 000 in standard form. (1)
(b) Work out \((3 \times 10^7) \div (6 \times 10^4)\)
Give your answer in standard form. (2)

1MA0 Higher June 2015 Paper 2 Q15

EdexcelHigherOld spec3 marksStandard Form

15

(a) Work out the value of \(25^{-3}\) (1)
(b) Work out the value of \(350^3\)
Give your answer in standard form. (2)

1MA0 Higher June 2014 Paper 1 Q17

EdexcelHigherOld spec4 marksStandard Form

17

(a) Write down the value of \(10^0\) (1)
(b) Write down the value of \(10^{-2}\) (1)
(c) Write these numbers in order of size.
Start with the smallest number.
\(2.73 \times 10^3\)\(27.3 \times 10^{-3}\)\(273 \times 10^2\)0.00273
(2)

1MA0 Higher November 2013 Paper 2 Q19

EdexcelHigherOld spec2 marksStandard Form

19

(a) Write \(7.8 \times 10^{-4}\) as an ordinary number. (1)
(b) Write 95 600 000 as a number in standard form. (1)

1MA0 Higher November 2013 Paper 1 Q14

EdexcelHigherOld spec4 marksStandard Form

14

(a) Write down the reciprocal of 5 (1)
(b) Evaluate \(3^{-2}\) (1)
(c) Calculate \(9 \times 10^4 \times 3 \times 10^3\)
Give your answer in standard form. (2)

1MA0 Higher June 2013 Paper 1 Q15

EdexcelHigherOld spec3 marksStandard Form

*15 One sheet of paper is \(9 \times 10^{-3}\) cm thick.

Mark wants to put 500 sheets of paper into the paper tray of his printer.
The paper tray is 4 cm deep.

Is the paper tray deep enough for 500 sheets of paper?
You must explain your answer. (3)

1MA0 Higher March 2013 Paper 1 Q16

EdexcelHigherOld spec4 marksStandard Form

16

(a) Write \(8.2 \times 10^5\) as an ordinary number. (1)
(b) Write 0.000 376 in standard form. (1)
(c) Work out the value of \((2.3 \times 10^{12}) \div (4.6 \times 10^3)\)
Give your answer in standard form. (2)

1MA0 Higher November 2012 Paper 1 Q20

EdexcelHigherOld spec2 marksStandard Form

20 Write the following numbers in order of size.
Start with the smallest number.

\(0.038 \times 10^2\)     \(3800 \times 10^{-4}\)     380     \(0.38 \times 10^{-1}\) (2)

1MA0 Higher November 2012 Paper 2 Q19

EdexcelHigherOld spec3 marksRatio & Basic ProportionStandard Form

19 Rob is learning about the planets.

Rob makes a model of the Sun.
He also makes a model of the planet Jupiter.

Rob is going to hang the two models in the school hall.
Rob wants a distance of 16 m between the two models.

The real distance between the planet Jupiter and the Sun is \(8 \times 10^8\) km.

Work out the scale Rob should use.
Give your answer in the form \(1 : n\) (3)

1MA0 Higher June 2012 Paper 2 Q19

EdexcelHigherOld spec3 marksStandard Form

19

\[p^2 = \frac{x - y}{xy}\]

\(x = 8.5 \times 10^9\)
\(y = 4 \times 10^8\)

Find the value of \(p\).
Give your answer in standard form correct to 2 significant figures. (3)

1MA0 Higher June 2012 Paper 1 Q17

EdexcelHigherOld spec4 marksStandard Form

17

(a) Write down the value of \(10^0\) (1)
(b) Write \(6.7 \times 10^{-5}\) as an ordinary number. (1)
(c) Work out the value of \((3 \times 10^7) \times (9 \times 10^6)\)
Give your answer in standard form. (2)

Foundation June 2025 Paper 1 Q20

AQAFoundationCurrent spec4 marksStandard Form

20

(a) Work out \(\quad 0.6 \div 100\)

Give your answer in standard form. [2 marks]

(b) Work out \(\quad 40 \times 30 \times 10^5\)

Give your answer in standard form. [2 marks]

Higher June 2025 Paper 1 Q6

AQAHigherCurrent spec4 marksStandard Form

6

(a) Work out \(\quad 0.6 \div 100\)

Give your answer in standard form. [2 marks]

(b) Work out \(\quad 40 \times 30 \times 10^5\)

Give your answer in standard form. [2 marks]

Foundation June 2024 Paper 2 Q20

AQAFoundationCurrent spec3 marksPercentagesStandard Form

20 The mass of an iceberg is 2 200 000 kg

This value is a 12% reduction from the original mass of the iceberg.

Work out the original mass of the iceberg.

Give your answer in standard form. [3 marks]

Higher June 2024 Paper 2 Q2

AQAHigherCurrent spec3 marksPercentagesStandard Form

2 The mass of an iceberg is 2 200 000 kg

This value is a 12% reduction from the original mass of the iceberg.

Work out the original mass of the iceberg.

Give your answer in standard form. [3 marks]

Foundation November 2023 Paper 1 Q29

AQAFoundationCurrent spec3 marksRatio & Basic ProportionStandard Form

29

(a) Write \(\quad 2 \times 10^3 \quad\) as an ordinary number. [1 mark]
(b) Simplify \(\quad (2 \times 10^3) : (5 \times 10^{-1})\)

Give your answer in the form \(\quad n : 1\) [2 marks]

Higher November 2023 Paper 1 Q12

AQAHigherCurrent spec3 marksRatio & Basic ProportionStandard Form

12

(a) Write \(\quad 2 \times 10^3 \quad\) as an ordinary number. [1 mark]
(b) Simplify \(\quad (2 \times 10^3) : (5 \times 10^{-1})\)

Give your answer in the form \(\quad n : 1\) [2 marks]

Higher June 2023 Paper 1 Q12

AQAHigherCurrent spec3 marksStandard Form

12

(a) \(a \times 10^n\) is a number in standard form.

Complete the inequality for the value of \(a\). [1 mark]

\(\underline{\qquad\qquad} \leqslant a \lt \underline{\qquad\qquad}\)

(b) \(b \times 10^n\) is the number 7200 written in standard form.

Work out \(\quad b \times 10^{-n}\)

Write your answer as an ordinary number. [2 marks]

Foundation November 2022 Paper 2 Q24

AQAFoundationCurrent spec4 marksStandard FormUsing a Calculator / BIDMAS

24

(a) Work out \(\quad 2.8^4 + \sqrt{158.76}\)

Give your answer as a decimal. [2 marks]

(b) Work out \(\quad \dfrac{6.09 \times 10^{14}}{4.2 \times 10^9}\)

Give your answer in standard form. [2 marks]

Foundation November 2022 Paper 2 Q17

AQAFoundationCurrent spec1 markStandard Form

17 Complete this statement. [1 mark]

\[10^8 = \ldots\ldots\ldots\ldots \text{ million}\]

Foundation June 2022 Paper 1 Q18

AQAFoundationCurrent spec2 marksStandard Form

18 Work out \(80\,000\,000 \div 200\)

Give your answer in standard form. [2 marks]

Higher June 2022 Paper 1 Q5

AQAHigherCurrent spec2 marksStandard Form

5 Work out \(\quad 80\,000\,000 \div 200\)

Give your answer in standard form. [2 marks]

Foundation November 2021 Paper 1 Q27

AQAFoundationCurrent spec4 marksStandard Form

27

(a) Work out \(\quad 2000 \times 70\,000\)

Give your answer in standard form. [2 marks]

(b) Work out \(\quad \dfrac{1.8 \times 10^2}{3 \times 10^{-1}}\)

Give your answer as an ordinary number. [2 marks]

Higher November 2021 Paper 1 Q10

AQAHigherCurrent spec4 marksStandard Form

10

(a) Work out \(\quad 2000 \times 70\,000\)

Give your answer in standard form. [2 marks]

(b) Work out \(\quad \dfrac{1.8 \times 10^2}{3 \times 10^{-1}}\)

Give your answer as an ordinary number. [2 marks]

Foundation November 2020 Paper 1 Q29

AQAFoundationCurrent spec2 marksStandard Form

29

(a) Write \(\quad 360\,000 \quad\) in standard form. [1 mark]
(b) Write \(\quad 9.2 \times 10^{-3} \quad\) as an ordinary number. [1 mark]

Foundation November 2019 Paper 1 Q30

AQAFoundationCurrent spec4 marksStandard Form

30

(a) Work out \(\quad \dfrac{2 \times 10^{14}}{8 \times 10^9}\)

Give your answer in standard form. [2 marks]

(b) \(6200.07 = 6.2 \times 10^c + 7 \times 10^d\)

Work out the values of \(c\) and \(d\). [2 marks]

Higher November 2019 Paper 1 Q11

AQAHigherCurrent spec4 marksStandard Form

11

(a) Work out \(\quad \dfrac{2 \times 10^{14}}{8 \times 10^9}\)

Give your answer in standard form. [2 marks]

(b) \(6200.07 = 6.2 \times 10^c + 7 \times 10^d\)

Work out the values of \(c\) and \(d\). [2 marks]

Foundation June 2019 Paper 1 Q20

AQAFoundationCurrent spec3 marksStandard Form

20

(a) Write \(\quad 0.000\,97 \quad\) in standard form. [1 mark]
(b) Work out \(\quad \dfrac{3 \times 10^5}{4 \times 10^3}\)

Give your answer as an ordinary number. [2 marks]

Higher June 2019 Paper 1 Q5

AQAHigherCurrent spec3 marksStandard Form

5

(a) Write \(\quad 0.000\,97 \quad\) in standard form. [1 mark]
(b) Work out \(\quad \dfrac{3 \times 10^5}{4 \times 10^3}\)

Give your answer as an ordinary number. [2 marks]

Foundation November 2018 Paper 2 Q27

AQAFoundationCurrent spec2 marksStandard Form

27 Work out \(\quad \dfrac{9.12 \times 10^{10}}{3.2 \times 10^4}\)

Give your answer in standard form. [2 marks]

Higher November 2018 Paper 2 Q12

AQAHigherCurrent spec2 marksStandard Form

12 Work out \(\quad \dfrac{9.12 \times 10^{10}}{3.2 \times 10^4}\)

Give your answer in standard form. [2 marks]

Foundation June 2018 Paper 1 Q32

AQAFoundationCurrent spec2 marksStandard Form

32 Put these numbers in order from smallest to largest. [2 marks]

\[8 \times 10^{-4} \qquad 4 \times 10^{-2} \qquad 6 \times 10^{-4} \qquad 0.07\]

Higher June 2018 Paper 1 Q12

AQAHigherCurrent spec2 marksStandard Form

12 Put these numbers in order from smallest to largest.

\[8 \times 10^{-4} \qquad 4 \times 10^{-2} \qquad 6 \times 10^{-4} \qquad 0.07\]

[2 marks]

Foundation November 2017 Paper 1 Q28

AQAFoundationCurrent spec2 marksStandard Form

28

(a) Write in standard form \(\qquad 12\,500\) [1 mark]
(b) Write as an ordinary number \(\qquad 3.4 \times 10^{-2}\) [1 mark]

Foundation June 2017 Paper 2 Q27

AQAFoundationCurrent spec2 marksStandard Form

27 Write these numbers in descending order.

\[9563 \qquad\qquad 9.56 \times 10^3 \qquad\qquad 9.56 \times 3^{10}\]

[2 marks]

Foundation June 2017 Paper 1 Q18

AQAFoundationCurrent spec2 marksStandard Form

18 Write the number   six million five thousand two hundred   in standard form. [2 marks]

Higher June 2017 Paper 1 Q13

AQAHigherCurrent spec2 marksStandard Form

13 Write the number \(\quad\) six million five thousand two hundred \(\quad\) in standard form. [2 marks]

Higher June 2017 Paper 2 Q11

AQAHigherCurrent spec2 marksStandard Form

11 Write these numbers in descending order.

\[9563 \qquad\qquad 9.56 \times 10^3 \qquad\qquad 9.56 \times 3^{10}\]

[2 marks]

Foundation June 2025 Paper 1 Q29

OCRFoundationCurrent spec5 marksCompound MeasuresStandard Form

29

(a) Write 0.0037 in standard form. [1]
(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 (km\(^2\))
South island\(1.2 \times 10^6\)\(1.5 \times 10^5\)
North island\(4.0 \times 10^6\)\(1.1 \times 10^5\)

Work out the overall population density of the country in June 2023. [4]

Higher June 2025 Paper 4 Q9

OCRHigherCurrent spec5 marksStandard Form

9

(a) Write 0.0037 in standard form. [1]
(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 (km\(^2\))
South island\(1.2 \times 10^6\)\(1.5 \times 10^5\)
North island\(4.0 \times 10^6\)\(1.1 \times 10^5\)

Work out the overall population density of the country in June 2023. [4]

Foundation November 2024 Paper 3 Q13

OCRFoundationCurrent spec5 marksStandard Form

13

(a) Write 0.001 025 in standard form. [1]
(b) A weather blogger writes:
  • \(1.655 \times 10^{12}\) raindrops fall in a storm
  • the mass of each raindrop is \(6 \times 10^{-5}\) grams.

Calculate the total mass of all of the raindrops that fall in the storm.
Give your answer in standard form in kilograms. [4]

Foundation November 2023 Paper 3 Q25

OCRFoundationCurrent spec6 marksCompound MeasuresStandard Form

25 A sheet of A4 card weighs \(1.19 \times 10^{-2}\) 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).\[W = \frac{\text{weight in grams}}{\text{area in square metres}}\]

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

Calculate \(W\) for this A4 card. [4]

Higher November 2023 Paper 6 Q5

OCRHigherCurrent spec6 marksCompound MeasuresStandard Form

5 A sheet of A4 card weighs \(1.19 \times 10^{-2}\) 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).\[W = \frac{\text{weight in grams}}{\text{area in square metres}}\]

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

Calculate \(W\) for this A4 card. [4]

Higher November 2023 Paper 6 Q3

OCRHigherCurrent spec4 marksFDPR Mixed ContextStandard Form

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

\(0.36\% \qquad \dfrac{1}{333} \qquad 0.03 \qquad 3.1 \times 10^{-3}\) [4]

Foundation June 2023 Paper 3 Q16

OCRFoundationCurrent spec3 marksStandard Form

16

(a) Write these numbers in order, starting with the smallest.\[2.4 \times 10^2 \qquad 1.3 \times 10^3 \qquad 4.9 \times 10^{-1} \qquad 9.5 \times 10^1\] [1]
(b) Work out.

\(5 \times 10^2 + 4 \times 10^3\)

Give your answer in standard form. [2]

Higher June 2023 Paper 4 Q5

OCRHigherCurrent spec6 marksCompound MeasuresStandard Form

5

(a) Write 0.003 86 in standard form. [1]
(b) The speed of sound is \(3.43 \times 10^{-1}\) km/s.
An object is travelling at the speed of sound.

Work out how far the object travels in one day. [2]

(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 \(n^3 \times\) 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 \(3.00 \times 10^5\) km/s.
  • The distance from Earth to Neptune is \(4.41 \times 10^9\) km.

Find the smallest possible warp \(n\) at which the spacecraft can travel.
You must show your working. [3]

Foundation November 2022 Paper 1 Q21

OCRFoundationCurrent spec6 marksShow That & ProofStandard Form

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

CountryPopulation
China\(1.44 \times 10^9\)
Kiribati\(1.19 \times 10^5\)
Tuvalu\(1.18 \times 10^4\)
(a) Calculate the approximate total population of Kiribati and Tuvalu in 2020.

Give your answer in standard form, correct to 3 significant figures. [4]

(b) Show that in 2020 the population of China was approximately 120 000 times the population of Tuvalu. [2]

Foundation November 2022 Paper 3 Q15

OCRFoundationCurrent spec4 marksStandard Form

15

(a) \(10^2\) is written in words as ‘one hundred’.

Write \(10^4\) in words. [2]

(b) Work out \((3.5 \times 10^{-1}) \times 100\), giving your answer in standard form. [2]

Higher November 2022 Paper 6 Q5

OCRHigherCurrent spec5 marksStandard Form

5 In space, distances can be measured in Astronomical Units.
In this question, use the conversion 1 Astronomical Unit = \(1.5 \times 10^8\) km.

(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]

(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. [2]

Higher November 2022 Paper 4 Q1

OCRHigherCurrent spec2 marksStandard Form

1

(a) Write 65 400 in standard form. [1]
(b) Write \(8.2 \times 10^{-4}\) as an ordinary number. [1]

Foundation June 2022 Paper 1 Q18

OCRFoundationCurrent spec2 marksStandard Form

18

(a) Write 6 050 000 in standard form. [1]
(b) Write \(4.58 \times 10^{-3}\) as an ordinary number. [1]

Foundation June 2022 Paper 2 Q12

OCRFoundationCurrent spec4 marksStandard Form

12 Dinosaurs first appeared on Earth \(2.4 \times 10^8\) years ago.
Dinosaurs became extinct on Earth \(7 \times 10^7\) years ago.

(a) Explain why it is appropriate to use standard form for these numbers. [1]
(b) Use the given information to work out how long dinosaurs existed on Earth.
Give your answer in standard form. [3]

Higher June 2022 Paper 5 Q3

OCRHigherCurrent spec4 marksStandard Form

3 Dinosaurs first appeared on Earth \(2.4 \times 10^8\) years ago.
Dinosaurs became extinct on Earth \(7 \times 10^7\) years ago.

(a) Explain why it is appropriate to use standard form for these numbers. [1]
(b) Use the given information to work out how long dinosaurs existed on Earth.
Give your answer in standard form. [3]

Higher June 2022 Paper 6 Q3

OCRHigherCurrent spec4 marksStandard FormUnits & Time

3 Light from the Sun travels 1 kilometre in \(3.3 \times 10^{-6}\) seconds.

The distance from the Sun to the Earth is \(1.5 \times 10^8\) kilometres.

How long does it take light to travel from the Sun to the Earth?
Give your answer in minutes and seconds. [4]

Higher June 2022 Paper 4 Q1

OCRHigherCurrent spec2 marksStandard Form

1

(a) Write 6 050 000 in standard form. [1]
(b) Write \(4.58 \times 10^{-3}\) as an ordinary number. [1]

Foundation November 2021 Paper 3 Q14

OCRFoundationCurrent spec7 marksStandard Form

14 This table shows the names and areas of five lakes.

Name of LakeArea in km\(^2\)
Ladoga\(1.81 \times 10^4\)
Mweru\(5.12 \times 10^3\)
Tana\(3.20 \times 10^3\)
Topozero\(9.86 \times 10^2\)
Victoria\(6.89 \times 10^4\)
(a) Write the area of Lake Mweru as an ordinary number. [1]
(b) Write the lakes in the order of their area, starting with the smallest. [2]
(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]

Higher November 2021 Paper 6 Q1

OCRHigherCurrent spec7 marksStandard Form

1 This table shows the names and areas of five lakes.

Name of LakeArea in km²
Ladoga\(1.81 \times 10^4\)
Mweru\(5.12 \times 10^3\)
Tana\(3.20 \times 10^3\)
Topozero\(9.86 \times 10^2\)
Victoria\(6.89 \times 10^4\)
(a) Write the area of Lake Mweru as an ordinary number. [1]
(b) Write the lakes in the order of their area, starting with the smallest. [2]
(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]

Foundation November 2020 Paper 1 Q17

OCRFoundationCurrent spec7 marksStandard Form

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

CountryBarrels of oil produced per day
USA\(1.17 \times 10^{7}\)
China\(3.98 \times 10^{6}\)
UK\(9.39 \times 10^{5}\)
Cameroon\(9.32 \times 10^{4}\)
Japan\(3.92 \times 10^{3}\)
(a) Write the number of barrels of oil produced per day by Cameroon as an ordinary number. [1]
(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]
(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]

Higher November 2020 Paper 4 Q1

OCRHigherCurrent spec3 marksStandard Form

1

(a) Write these numbers in standard form.
(i) 6500 [1]
(ii) 0.0584 [1]
(b) Work out \((4.2 \times 10^5) \times (1.8 \times 10^{-2})\), giving your answer in standard form. [1]

Foundation November 2019 Paper 1 Q17

OCRFoundationCurrent spec8 marksStandard Form

17 The table below shows the area, in square kilometres (km\(^2\)), of some countries.

CountryArea (km\(^2\))
Australia\(7.69 \times 10^{6}\)
Latvia\(6.46 \times 10^{4}\)
Luxembourg\(2.59 \times 10^{3}\)
Russia\(1.71 \times 10^{7}\)
Singapore\(7.24 \times 10^{2}\)
Sweden\(4.50 \times 10^{5}\)
(a) Write the area of Sweden as an ordinary number. [1]
(b) Which of the above countries has the smallest area? [1]
(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]

(d) Work out the total area of Russia and Australia.
Give your answer in standard form, correct to 2 significant figures. [4]

Higher November 2019 Paper 4 Q2

OCRHigherCurrent spec4 marksStandard Form

2 Use the formula \(F = \dfrac{s}{\sqrt{tm}}\) to find the value of \(F\) when

\(s = 5.8 \times 10^6\)
\(t = 4.1 \times 10^8\)
\(m = 3.7 \times 10^{-2}\).

Give your answer in standard form, correct to 2 significant figures. [4]

Foundation June 2019 Paper 3 Q18

OCRFoundationCurrent spec4 marksStandard Form

18 Tom researches the weights of plant seeds.

  • One poppy seed weighs \(3 \times 10^{-4}\) grams.
  • 250 pumpkin seeds weigh 21 grams.
  • One sesame seed weighs \(3.64 \times 10^{-6}\) 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. [4]

Foundation June 2019 Paper 3 Q17

OCRFoundationCurrent spec3 marksStandard Form

17 A grain of salt weighs \(6.48 \times 10^{-5}\) kg 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]
(b) Explain why your answer to part (a) is unlikely to be the actual number of grains of salt in the packet. [1]

Higher June 2019 Paper 6 Q2

OCRHigherCurrent spec4 marksStandard FormUnits & Time

2 Tom researches the weights of plant seeds.

  • One poppy seed weighs \(3 \times 10^{-4}\) grams.
  • 250 pumpkin seeds weigh 21 grams.
  • One sesame seed weighs \(3.64 \times 10^{-6}\) 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. [4]

Higher June 2019 Paper 5 Q1

OCRHigherCurrent spec2 marksStandard Form

1 Work out \((2 \times 10^3) \times (4 \times 10^4)\), giving your answer in standard form. [2]

Higher June 2019 Paper 6 Q1

OCRHigherCurrent spec3 marksStandard Form

1 A grain of salt weighs \(6.48 \times 10^{-5}\) kg 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]
(b) Explain why your answer to part (a) is unlikely to be the actual number of grains of salt in the packet. [1]

Foundation November 2018 Paper 3 Q22

OCRFoundationCurrent spec5 marksStandard Form

22 A newborn baby has an approximate mass of 3.5 kilograms.

A human cell has an approximate mass of \(2.7 \times 10^{-11}\) 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]

Foundation November 2018 Paper 2 Q13

OCRFoundationCurrent spec3 marksStandard Form

13

(a) Write 0.003 16 in standard form. [1]
(b) Work out.\[2 \times 10^2 \times 4 \times 10^5\]

Give your answer in standard form. [2]

Higher November 2018 Paper 6 Q3

OCRHigherCurrent spec5 marksStandard FormUnits & Time

3 A newborn baby has an approximate mass of 3.5 kilograms.
A human cell has an approximate mass of \(2.7 \times 10^{-11}\) 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]

Higher November 2018 Paper 5 Q1

OCRHigherCurrent spec5 marksStandard Form

1 Work out.

(a) \(\sqrt[3]{64} \times 2^{-1}\) [2]
(b) \(4.3 \times 10^5 + 3.8 \times 10^4\)
Give your answer in standard form. [3]

Foundation June 2018 Paper 3 Q22

OCRFoundationCurrent spec3 marksShow That & ProofStandard Form

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

Two ellipses around the Sun: Earth on the inner ellipse and Pluto on the outer ellipse

Not to scale

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

Closest distance to
the Sun (km)
Earth\(1.47 \times 10^8\)
Pluto\(4.44 \times 10^9\)
(a) Show that the closest distance of Pluto to the Sun is roughly 30 times the closest distance of Earth to the Sun. [2]
(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]

Foundation June 2018 Paper 2 Q13

OCRFoundationCurrent spec6 marksFractionsStandard Form

13

(a) Calculate.\[\frac{3}{5} + \frac{5}{8}\]

Give your answer as a mixed number in its simplest form. [3]

(b) Work out.\[5 \times 10^4 - 1.6 \times 10^3\]

Give your answer in standard form. [3]

Higher June 2018 Paper 5 Q1

OCRHigherCurrent spec6 marksFractionsStandard Form

1

(a) Calculate.\[\frac{3}{5} + \frac{5}{8}\]

Give your answer as a mixed number in its simplest form. [3]

(b) Work out.\[5 \times 10^4 - 1.6 \times 10^3\]

Give your answer in standard form. [3]

Foundation November 2017 Paper 2 Q22

OCRFoundationCurrent spec3 marksShow That & ProofStandard Form

22

(a) Beth is given the following question.
Work out
\(4.1 \times 10^5 \times 3 \times 10^2\).
Give your answer in standard form.

This is Beth’s answer to the question.

\[12.3 \times 10^7\]

Explain why Beth’s answer is incorrect. [1]

(b) Show that\[4.5 \times 10^2 + 7.3 \times 10^3 = 7.75 \times 10^3.\]

[2]

Foundation November 2017 Paper 3 Q13

OCRFoundationCurrent spec9 marksStandard Form

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

Here are some facts.

\(1.47 \times 10^7\)
sweets are made every day		\(3.5 \times 10^5\)
packets of sweets are produced every day
(a) Calculate the mean number of sweets in one packet. [2]
(b) Sweets are made on 288 days each year.

Calculate the number of sweets made each year.
Give your answer in standard form. [3]

(c) The company has 152 machines making the sweets.
Each machine operates for 15 hours each day.
(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]
(ii) State one assumption you have made in part (c)(i). [1]

Higher November 2017 Paper 6 Q5

OCRHigherCurrent spec9 marksStandard Form

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

Here are some facts.

Two boxes: 1.47 × 10^7 sweets are made every day; 3.5 × 10^5 packets of sweets are produced every day
(a) Calculate the mean number of sweets in one packet. [2]
(b) Sweets are made on 288 days each year.

Calculate the number of sweets made each year.
Give your answer in standard form. [3]

(c) The company has 152 machines making the sweets.
Each machine operates for 15 hours each day.
(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]
(ii) State one assumption you have made in part (c)(i). [1]

Foundation June 2017 Paper 1 Q14

OCRFoundationCurrent spec3 marksStandard Form

14

(a) Write 543 000 in standard form. [1]
(b) Write \(6.3 \times 10^{-2}\) as an ordinary number. [1]
(c) Pierre is given this question.
Work out.
61 000 \(\times\) 4000
Give your answer in standard form.

Pierre’s answer is \(24.4 \times 10^7\).

Is Pierre correct?
Explain your answer. [1]

Higher June 2017 Paper 4 Q1

OCRHigherCurrent spec4 marksStandard FormUsing a Calculator / BIDMAS

1 Calculate.

(a) \(\sqrt{\dfrac{4.8^2 + 3.6^2}{4}}\) [2]
(b) \(\dfrac{1}{(2 \times 10^4) + (5 \times 10^3)}\) [2]

Higher June 2017 Paper 6 Q1

OCRHigherCurrent spec7 marksPercentagesStandard Form

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

CountryPopulation
England\(5.35 \times 10^7\)
Wales\(3.07 \times 10^6\)
Scotland\(5.31 \times 10^6\)
Northern Ireland\(1.82 \times 10^6\)
(a) Write the population of England as an ordinary number. [1]
(b) Work out the total population of Wales, Scotland and Northern Ireland.
Give your answer in standard form. [2]
(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]