TopicalMathematics 0580NumberStandard formPaper 2

Standard form — Paper 2 · IGCSE Mathematics 0580

E1.8· 44 questions · 93 marks · 112 min · 2009–2025· Structured questions

Every Cambridge IGCSE Mathematics Paper 2 question on standard form, laid out as 12 A4 pages with the mark scheme below. Nothing is left out. Free to read, no account.

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Questions12 pages

Question 1: (a) There are 109 nanoseconds in 1 second. For Find the number of nanoseconds in 5 minutes, giving your answer in standard form. Examiner's…Question 2: Calculate the value of 5(6 × 103 + 400), giving your answer in standard form. Examiner's Use Answer [2]Question 3: Change 64 square metres into square millimetres. Give your answer in standard form. Answer mm2 [2]Question 4: Write 0.00658 (a) in standard form, Answer(a) [1] (b) correct to 2 significant figures. Answer(b) [1]1 / 12
Question 5: A hummingbird beats its wings 24 times per second. ForFor Examiner'sExaminer's (a) Calculate the number of times the hummingbird beats its …Question 6: (a) Write 16 460 000 in standard form. Answer(a) [1] (b) Calculate 7.85 ÷ (2.366 × 102), giving your answer in standard form. Answer(b) [2]Question 7: The population of a city is 128 000, correct to the nearest thousand. (a) Write 128 000 in standard form. Answer(a) [1] (b) Write down the …2 / 12
Question 8: The price of a ticket for a football match is $124 . For Examiner's (a) Calculate the amount received when 76 500 tickets are sold. Use Ans…Question 9: Calculate, giving your answers in standard form, For Examiner′s Use (a) 2 × (5.5 × 104) , Answer(a) .......................................…Question 10: p = 4 × 105 q = 5 × 104 Find, giving your answer in standard form, (a) pq, Answer(a) ................................................ [2] q…3 / 12
Question 11: (a) Write 2.8 × 102 as an ordinary number. Answer(a) ................................................ [1] (b) Work out 2.5 × 108 × 2 × 10–2…Question 12: Work out 4 × 10–5 × 6 × 1012. Give your answer in standard form. Answer ................................................ [2] ______________…Question 13: Write 1.7 × 10–4 as an ordinary number. Answer ................................................ [1] _______________________________________…4 / 12
Question 14: (a) Write 2016 as the product of prime factors. ................................................... [3] (b) Write 2016 in standard form. ..…Question 15: Write 1.27 × 10–3 as an ordinary number. ....................................................[1]Question 16: (a) Write 5 -3 as a fraction. ................................................. [1] (b) Write 0.004 56 in standard form. ..................…5 / 12
Question 17: (a) Write 14 835 correct to the nearest thousand. ................................................. [1] (b) Write your answer to part (a) i…Question 18: Write in standard form. (a) 2 470 000 ................................................. [1] (b) 0.0079 ....................................…Question 19: (a) Write 0.0605 in standard form. ................................................. [1] (b) Calculate 0.1 # 5.1 # 104 , giving your answer…Question 20: Write .517 # 10 -3 as an ordinary number. .............................................. [1]6 / 12
Question 21: Work out, giving your answer in standard form. 1.2 # 10 40 + 1. 2 # 10 41 .............................................. [2]Question 22: Write 0.000 038 7 in standard form. .............................................. [1]Question 23: Here are some numbers written in standard form. .34 # 10 -1 .136 # 106 .79 # 100 .24 # 105 .521 # 10 -3 .43 # 10 -2 From these numbers, wri…Question 24: (a) Write .482 # 10 -3 as an ordinary number. ................................................. [1] (b) Write 52 million in standard form. …Question 25: Work out 6 .4 # 10 7 + 9. 6 # 10 6 ^ h ^ h. Give your answer in standard form. .................................................[2]7 / 12
Question 26: Write 23 000 in standard form. ................................................ [1]Question 27: (a) Write the number five million, two hundred and seven in figures. .................................................[1] (b) Write 0.008 1…Question 28: (a) Write 0.046 875 correct to 2 significant figures. .................................................... [1] (b) Write 2 760 000 in stand…Question 29: (a) Write 0.047 883 correct to 2 significant figures. ............................................... [1] (b) Write 0.005 27 in standard fo…Question 30: Write 15 060 (a) in words, ................................................................................................................…8 / 12
Question 31: Write in standard form. (a) 72 000 .................................................... [1] (b) 0.0018 ....................................…Question 32: Calculate the value of ( 2.3 # 10 -3 ) + ( 6. 8 # 10 -4 ) . Give your answer in standard form. ............................................…Question 33: Calculate ( 3 # 10 - 3 ) 3 . Give your answer in standard form. ................................................. [1]Question 34: Work out ( 3 # 10 199 ) + ( 2 # 10 201 ) . Give your answer in standard form. ................................................. [2]Question 35: Calculate 4.8 # 10 6 + 3.7 # 10 7 . Give your answer in standard form. ................................................. [1]9 / 12
Question 36: (a) Write 0.006 54 in standard form. ................................................. [1] (b) The number .1467 # 10102 is written as an or…Question 37: Simplify 2.1 # 10 p + 2.1 # 10 p - 1 . Give your answer in standard form. ................................................. [2]Question 38: Calculate 0.04 2 + 0.03 # 0.28 . Give your answer in standard form. ................................................. [2]Question 39: Work out 2 # 10 100 - 2 # 10 98 , giving your answer in standard form. ................................................. [2]10 / 12
Question 40: Calculate .032 . Give your answer in standard form. ................................................. [2]Question 41: Write 174 000 in standard form. ................................................. [1]Question 42: Work out, giving each answer in standard form. (a) `.21 # 10 101j # `8 # 10 101j ................................................. [2] (b) …11 / 12
Question 43: (a) Write 0.007 08 in standard form. ................................................. [1] (b) Work out ( 3. 8 # 10 22 ) + ( 3. 8 # 10 23 )…Question 44: (a) Write 66 000 in standard form. ................................................. [1] (b) Work out `3.7 # 10 8j + `3. 7 # 10 7j. Give yo…12 / 12

Mark scheme44 answers

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Mathematics 0580 · Standard form — Paper 2

IGCSE · topical answer key — answer key (teacher use)

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Questions as text

Q1 · There are 109 nanoseconds in 1 second 0580/21 May/June 2009

14 (a) There are 109 nanoseconds in 1 second. For Find the number of nanoseconds in 5 minutes, giving your answer in standard form. Examiner's Use Answer(a) [2] (b) Solve the equation 5 ( x + 3 × 106 ) = 4 × 107. Answer(b) x = [2]

4 marks

Mark scheme: 14 (a) 3 × 1011 2 M1 60 × 5 × 109 or better (b) 5 000 000 or 5 × 106 or 5 million 2 M1 0.8 × 107 – 3 × 106 oe or M1 5x = 4 × 107 – 15 × 106 oe If m is used for a million it must be used consistently

This question in 0580/21 May/June 2009

Q2 · Calculate the value of 5(6 × 103 + 400), giving your answer in standard form 0580/21 May/June 2010

5 Calculate the value of 5(6 × 103 + 400), giving your answer in standard form. Examiner's Use Answer [2]

2 marks

Mark scheme: 5 3.2(0) × 104 2 B1 32000 or 32 × 103 etc

This question in 0580/21 May/June 2010

Q3 · Change 64 square metres into square millimetres 0580/22 May/June 2010

6 Change 64 square metres into square millimetres. Give your answer in standard form. Answer mm2 [2]

2 marks

Mark scheme: 6 6.4 × 107 2 M1 64 × 1002 × 102 or 64 000 000 oe

This question in 0580/22 May/June 2010

Q4 · Write 0.00658 (a) in standard form, Answer(a) [1] (b) correct to 2 significant figures 0580/22 Oct/Nov 2010

6 Write 0.00658 (a) in standard form, Answer(a) [1] (b) correct to 2 significant figures. Answer(b) [1]

2 marks

Mark scheme: 6 (a) 6.58 × 10–3 1 × and 10 essential (b) 0.0066 cao 1 Allow 6.6 × 10–3 1

This question in 0580/22 Oct/Nov 2010

Q5 · A hummingbird beats its wings 24 times per second 0580/21 May/June 2011

5 A hummingbird beats its wings 24 times per second. ForFor Examiner'sExaminer's (a) Calculate the number of times the hummingbird beats its wings in one hour. UseUse Answer(a) [1] (b) Write your answer to part (a) in standard form. Answer(b) [1]

2 marks

Mark scheme: ( ) 5 (a) 86400 1 (b) 8.64 × 104 1ft  3

This question in 0580/21 May/June 2011

Q6 · Write 16 460 000 in standard form 0580/23 May/June 2011

6 (a) Write 16 460 000 in standard form. Answer(a) [1] (b) Calculate 7.85 ÷ (2.366 × 102), giving your answer in standard form. Answer(b) [2]

3 marks

Mark scheme: 6 (a) 1.646 × 107 1 (b) 3.32 × 10–2 2 B1 for 0.0332 seen or 3.3 × 10–2 as answer or B1 for 3.32 × 10k

This question in 0580/23 May/June 2011

Q7 · The population of a city is 128 000, correct to the nearest thousand 0580/23 Oct/Nov 2011

5 The population of a city is 128 000, correct to the nearest thousand. (a) Write 128 000 in standard form. Answer(a) [1] (b) Write down the upper bound of the population. Answer(b) [1]

2 marks

Mark scheme: 5 (a) 1.28 × 105 1 (b) 128 500 1

This question in 0580/23 Oct/Nov 2011

Q8 · The price of a ticket for a football match is $124 0580/21 May/June 2012

1 The price of a ticket for a football match is $124 . For Examiner's (a) Calculate the amount received when 76 500 tickets are sold. Use Answer(a) $ [1] (b) Write your answer to part (a) in standard form. Answer(b) $ [1]

2 marks

Mark scheme: Qu Answers Mark Part marks 1 (a) 9486000 1 (b) 9.486 × 106 1ft

This question in 0580/21 May/June 2012

Q9 · Calculate, giving your answers in standard form, For Examiner′s Use (a) 2 × (5.5 × 104)… 0580/23 May/June 2013

9 Calculate, giving your answers in standard form, For Examiner′s Use (a) 2 × (5.5 × 104) , Answer(a) … [2] (b) (5.5 × 104) – (5 × 104) . Answer(b) … [2] _____________________________________________________________________________________

4 marks

Mark scheme: 9 (a) 1.1 × 105 2 B1 for 110 000 oe e.g.11 × 104 (b) 5 × 103 2 B1 for 5000 oe e.g. 0.5 × 104 IGCSE – May/June 2013 0580 23

This question in 0580/23 May/June 2013

Q10 · P = 4 × 105 q = 5 × 104 Find, giving your answer in standard form, (a) pq, Answer(a) …… 0580/21 May/June 2014

12 p = 4 × 105 q = 5 × 104 Find, giving your answer in standard form, (a) pq, Answer(a) … [2] q (b) . p Answer(b) … [2] __________________________________________________________________________________________

4 marks

Mark scheme: 12 (a) 2 × 1010 2 B1 for 20 × 109 or 20 000 000 000 (b) 1.25 × 10−1 2 B1 for 0.125 oe

This question in 0580/21 May/June 2014

Q11 · Write 2.8 × 102 as an ordinary number 0580/21 Oct/Nov 2014

9 (a) Write 2.8 × 102 as an ordinary number. Answer(a) … [1] (b) Work out 2.5 × 108 × 2 × 10–2. Give your answer in standard form. Answer(b) … [2] __________________________________________________________________________________________

3 marks

Mark scheme: 9 (a) 280 1 (b) 5 × 106 2 B1 for 5 000 000 oe or B1 for answer k × 10 6 or 5× 10 k

This question in 0580/21 Oct/Nov 2014

Q12 · Work out 4 × 10–5 × 6 × 1012 0580/23 Oct/Nov 2014

3 Work out 4 × 10–5 × 6 × 1012. Give your answer in standard form. Answer … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 3 4.2 × 10 8 2 B1 for 240 000 000 oe or B1 for k × 10 8 or 4.2 × 10 k

This question in 0580/23 Oct/Nov 2014

Q13 · Write 1.7 × 10–4 as an ordinary number 0580/23 Oct/Nov 2015

3 Write 1.7 × 10–4 as an ordinary number. Answer … [1] __________________________________________________________________________________________

1 marks

Mark scheme: 3 [0].00017 1

This question in 0580/23 Oct/Nov 2015

Q14 · Write 2016 as the product of prime factors 0580/22 Feb/March 2016

13 (a) Write 2016 as the product of prime factors. … [3] (b) Write 2016 in standard form. … [1]

4 marks

Mark scheme: 13 (a) 2 5 × 32 × 7 oe final answer 3 B2 for product of two of 2 5 , 3 2 , 7 or B1 for 2, 3 and 7 seen or M1 for 2 × 1008 or 3 × 672 or 7 × 288 soi (b) 2.016 × 10 3 1 8 7 8 k k 7

This question in 0580/22 Feb/March 2016

Q15 · Write 1.27 × 10–3 as an ordinary number 0580/21 May/June 2016

3 Write 1.27 × 10–3 as an ordinary number. … [1]

1 marks

Mark scheme: 3 [0].00127 1

This question in 0580/21 May/June 2016

Q16 · Write 5 -3 as a fraction 0580/21 Oct/Nov 2016

5 (a) Write 5 -3 as a fraction. … [1] (b) Write 0.004 56 in standard form. … [1]

2 marks

Mark scheme: 5 (a) 1 125 (b) 1 4.56 × 10–3

This question in 0580/21 Oct/Nov 2016

Q17 · Write 14 835 correct to the nearest thousand 0580/22 Oct/Nov 2016

1 (a) Write 14 835 correct to the nearest thousand. … [1] (b) Write your answer to part (a) in standard form. … [1]

2 marks

Mark scheme: Question Answer Mark Part marks 1 (a) 15000 cao 1 (b) 1.5 × 10 4 1FT FT their (a)

This question in 0580/22 Oct/Nov 2016

Q18 · Write in standard form 0580/23 Oct/Nov 2016

4 Write in standard form. (a) 2 470 000 … [1] (b) 0.0079 … [1]

2 marks

Mark scheme: 4 (a) 2.47 × 106 1 (b) 7.9 × 10–3 1 18 5 18 k 5 k

This question in 0580/23 Oct/Nov 2016

Q19 · Write 0.0605 in standard form 0580/22 May/June 2017

11 (a) Write 0.0605 in standard form. … [1] (b) Calculate 0.1 # 5.1 # 104 , giving your answer in standard form. … [1]

2 marks

Mark scheme: 11(a) 6.05 × 10–2 1 11(b) 5.1 × 103 1

This question in 0580/22 May/June 2017

Q20 · Write .517 # 10 -3 as an ordinary number 0580/22 Oct/Nov 2017

2 Write .517 # 10 -3 as an ordinary number. … [1]

1 marks

Mark scheme: 2 [0].00517 1

This question in 0580/22 Oct/Nov 2017

Q21 · Work out, giving your answer in standard form 0580/22 Oct/Nov 2017

9 Work out, giving your answer in standard form. 1.2 # 10 40 + 1. 2 # 10 41 … [2]

2 marks

Mark scheme: 9 1.32 × 1041 2 M1 for 0.12 × 1041 or 12 × 1040 or SC1 for figs 132

This question in 0580/22 Oct/Nov 2017

Q22 · Write 0.000 038 7 in standard form 0580/21 May/June 2018

2 Write 0.000 038 7 in standard form. … [1]

1 marks

Mark scheme: 2 3.87 × 10−5 1

This question in 0580/21 May/June 2018

Q23 · Here are some numbers written in standard form 0580/22 May/June 2018

8 Here are some numbers written in standard form. .34 # 10 -1 .136 # 106 .79 # 100 .24 # 105 .521 # 10 -3 .43 # 10 -2 From these numbers, write down (a) the largest number, … [1] (b) the smallest number. … [1]

2 marks

Mark scheme: 8(a) 1.36 × 106 oe 1 8(b) 5.21 × 10–3 oe 1

This question in 0580/22 May/June 2018

Q24 · Write .482 # 10 -3 as an ordinary number 0580/23 May/June 2018

8 (a) Write .482 # 10 -3 as an ordinary number. … [1] (b) Write 52 million in standard form. … [1]

2 marks

Mark scheme: 8(a) [0].004 82 cao 1 8(b) 5.2 × 107 1

This question in 0580/23 May/June 2018

Q25 · Work out 6 .4 # 10 7 + 9 0580/21 Oct/Nov 2018

4 Work out 6 .4 # 10 7 + 9. 6 # 10 6 ^ h ^ h. Give your answer in standard form. … [2]

2 marks

Mark scheme: 4 7.36 × 107 2 B1 for figs 736

This question in 0580/21 Oct/Nov 2018

Q26 · Write 23 000 in standard form 0580/22 Oct/Nov 2018

1 Write 23 000 in standard form. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 2.3 × 104 1

This question in 0580/22 Oct/Nov 2018

Q27 · Write the number five million, two hundred and seven in figures 0580/23 Oct/Nov 2018

6 (a) Write the number five million, two hundred and seven in figures. … [1] (b) Write 0.008 13 in standard form. … [1]

2 marks

Mark scheme: 6(a) 5 000 207 1 6(b) 8.13 × 10−3 1

This question in 0580/23 Oct/Nov 2018

Q28 · Write 0.046 875 correct to 2 significant figures 0580/22 Feb/March 2019

4 (a) Write 0.046 875 correct to 2 significant figures. … [1] (b) Write 2 760 000 in standard form. … [1]

2 marks

Mark scheme: 4(a) 0.047 1 4(b) 2.76 × 10 6 1

This question in 0580/22 Feb/March 2019

Q29 · Write 0.047 883 correct to 2 significant figures 0580/22 May/June 2019

8 (a) Write 0.047 883 correct to 2 significant figures. … [1] (b) Write 0.005 27 in standard form. … [1]

2 marks

Mark scheme: 8(a) 0.048 cao 1 8(b) 5.27 × 10−3 1

This question in 0580/22 May/June 2019

Q30 · Write 15 060 (a) in words, … [1] (b) in standard form 0580/21 Oct/Nov 2019

4 Write 15 060 (a) in words, … [1] (b) in standard form. … [1]

2 marks

Mark scheme: 4(a) Fifteen thousand [and] sixty 1 4(b) 1.506[0] × 104 1

This question in 0580/21 Oct/Nov 2019

Q31 · Write in standard form 0580/23 Oct/Nov 2019

5 Write in standard form. (a) 72 000 … [1] (b) 0.0018 … [1]

2 marks

Mark scheme: 5(a) 7.2 × 104 1 5(b) 1.8 × 10–3 1

This question in 0580/23 Oct/Nov 2019

Q32 · Calculate the value of ( 2.3 # 10 -3 ) + ( 6 0580/22 Feb/March 2020

8 Calculate the value of ( 2.3 # 10 -3 ) + ( 6. 8 # 10 -4 ) . Give your answer in standard form. … [1]

1 marks

Mark scheme: 8 2.98 × 10−3 1

This question in 0580/22 Feb/March 2020

Q33 · Calculate ( 3 # 10 - 3 ) 3 0580/22 May/June 2020

16 Calculate ( 3 # 10 - 3 ) 3 . Give your answer in standard form. … [1]

1 marks

Mark scheme: 16 2.7 × 10–8 1

This question in 0580/22 May/June 2020

Q34 · Work out ( 3 # 10 199 ) + ( 2 # 10 201 ) 0580/22 Oct/Nov 2020

14 Work out ( 3 # 10 199 ) + ( 2 # 10 201 ) . Give your answer in standard form. … [2]

2 marks

Mark scheme: 14 2.03 × 10201 2 B1 for figs 203 or [0].03 × 10201 or 200 × 10199

This question in 0580/22 Oct/Nov 2020

Q35 · Calculate 4.8 # 10 6 + 3.7 # 10 7 0580/22 Feb/March 2021

9 Calculate 4.8 # 10 6 + 3.7 # 10 7 . Give your answer in standard form. … [1]

1 marks

Mark scheme: 9 4.18 × 107 cao 1

This question in 0580/22 Feb/March 2021

Q36 · Write 0.006 54 in standard form 0580/22 May/June 2021

10 (a) Write 0.006 54 in standard form. … [1] (b) The number .1467 # 10102 is written as an ordinary number. Write down the number of zeros that follow the digit 7. … [1]

2 marks

Mark scheme: 10(a) 6.54 × 10 –3 1 10(b) 99 1

This question in 0580/22 May/June 2021

Q37 · Simplify 2.1 # 10 p + 2.1 # 10 p - 1 0580/23 May/June 2021

20 Simplify 2.1 # 10 p + 2.1 # 10 p - 1 . Give your answer in standard form. … [2]

2 marks

Mark scheme: 20 2.31 × 10 p 2 B1 for 21 × 10 p −1 or 0.21 × 10 p or answer with figs 231

This question in 0580/23 May/June 2021

Q38 · Calculate 0.04 2 + 0.03 # 0.28 0580/23 Oct/Nov 2021

13 Calculate 0.04 2 + 0.03 # 0.28 . Give your answer in standard form. … [2]

2 marks

Mark scheme: 13 1[.0] × 10–2 cao 2 B1 for 0.01 oe

This question in 0580/23 Oct/Nov 2021

Q39 · Work out 2 # 10 100 - 2 # 10 98 , giving your answer in standard form 0580/21 May/June 2022

13 Work out 2 # 10 100 - 2 # 10 98 , giving your answer in standard form. … [2]

2 marks

Mark scheme: 13 1.98 × 10100 2 B1 for 200  10 98 or 0.02  10100 or answer with figs 198

This question in 0580/21 May/June 2022

Question 40 0580/22 Feb/March 2023

8 Calculate .032 . Give your answer in standard form. … [2]

2 marks

Mark scheme: 8 9  10−2 2 B1 for 0.09 oe or M1 for their decimal correctly converted to standard form if negative power

This question in 0580/22 Feb/March 2023

Q41 · Write 174 000 in standard form 0580/22 May/June 2024

10 Write 174 000 in standard form. … [1]

1 marks

Mark scheme: 10 1.74 ×105 1

This question in 0580/22 May/June 2024

Q42 · Work out, giving each answer in standard form 0580/23 May/June 2024

17 Work out, giving each answer in standard form. (a) `.21 # 10 101j # `8 # 10 101j … [2] (b) `2.1 # 10 101j + `2.1 # 10 100j … [2]

4 marks

Mark scheme: 17(a) 1.68  10 203 2 B1 for 16.8  10 202 17(b) 2.31  10101 2 B1 for figs 231

This question in 0580/23 May/June 2024

Q43 · Write 0.007 08 in standard form 0580/22 May/June 2025

11 (a) Write 0.007 08 in standard form. … [1] (b) Work out ( 3. 8 # 10 22 ) + ( 3. 8 # 10 23 ) . Give your answer in standard form. … [2]

3 marks

Mark scheme: 11(a) 7.08 × 10–3 cao 1 11(b) 4.18 × 1023 cao 2 B1 for figs 418 or M1 for 0.38 × 1023 or 38 × 1022 or 1022(3.8 + 3.8 × 10) or 1023(3.8 ÷ 10 + 3.8) oe

This question in 0580/22 May/June 2025

Q44 · Write 66 000 in standard form 0580/21 Oct/Nov 2025

15 (a) Write 66 000 in standard form. … [1] (b) Work out `3.7 # 10 8j + `3. 7 # 10 7j. Give your answer in standard form. … [2]

3 marks

Mark scheme: 15(a) 6.6 × 104 1 15(b) 4.07 × 108 2 M1 for figs 407 or for 0.37 × 108 or 37 × 107 or 107(3.7 × 10 + 3.7) or 108(3.7+ 3.7 ÷ 10) oe

This question in 0580/21 Oct/Nov 2025