Standard form — Paper 3 · IGCSE Mathematics 0580

1 A bookshop sold a total of 2750 books in January. Examiner's Use (a) The ratio hardback books sold : paperback books sold was 4 : 7. Calculate how many paperback books were sold. Answer(a) [2] (b) 24% of the 2750 books sold were non-fiction. Calculate how many non-fiction books were sold. Answer(b) [2] (c) 330 cookery books were sold. Write 330 as a fraction of 2750 in its lowest terms. Answer(c) [2] (d) In February, the bookshop sold 14% more than the 2750 books sold in January. Calculate the number of books sold in February. Answer(d) [3] (e) The total value of the books sold in January was $9480 correct to the nearest 10 dollars. Write down the lower bound for this amount. Answer(e) $ [1] (f) 35000 books were sold in a year. Write this number in standard form. Answer(f) [1]

11 marks

Mark scheme: Qu. Answers Mark Part Marks 771 (a) 1750 2 M1 × 2750 oe 4 + 7 24× 2750 (b) 660 2 M1 100 3 (c) 2 W1 for equivalent fractions 25 114 (d) 3135 cao 3 M2 × 2750 oe 100 14 If M0 then M1 for × 2750 or 385 seen 100 (e) 9475 1 cao (f) 3.5 × 104 1 cao

This question in 0580/33 May/June 2010

2 The distance between Geneva and Gstaad is 150 km. For Examiner's (a) Write 150 in standard form. Use Answer(a) [1] 1 (b) A car took 1 hours to travel from Geneva to Gstaad. 2 Calculate the average speed of the car. Answer(b) km/h [1] (c) A bus left Gstaad at 10 15. It arrived in Geneva at 12 30. Calculate the time, in hours and minutes, that the bus took for the journey. Answer(c) h min [1] (d) Another bus left Geneva at 13 55. It travelled at an average speed of 60 km/h. Find the time it arrived in Gstaad. Answer(d) [2] (e) The distance of 150 km is correct to the nearest 10 km. Complete the statement for the distance, d km, from Geneva to Gstaad. Answer(e) Y d I [2]

7 marks

Mark scheme: 2 (a) 1.5(0) × 102 cao 1 (b) 100 cao 1 (c) 2 hours 15 minutes cao 1 (d) 16(:) 25 (pm) or (0)425 pm 2 M1 for 2.5 (oe), 2hrs 30 min (e) 145 ≤ d < 155 2 B1 for each value in correct place

This question in 0580/31 Oct/Nov 2011

9 (a) (i) Calculate the cube root of 68 921. Answer(a)(i) … [1] (ii) Write 68 921 in standard form. Answer(a)(ii) … [1] (iii) Write 68 921 correct to 2 significant figures. Answer(a)(iii) … [1] (b) 96 550 kg is reduced to 88 826 kg. Calculate the percentage reduction. Answer(b) … % [3] (c) (i) Work out 5–2. Answer(c)(i) … [1] 2 (ii) Simplify ^ 5 h . Answer(c)(ii) … [1] (iii) Explain why 6 is not a prime number. Answer(c)(iii) … … [1] (iv) Explain the term ‘irrational number’. Answer(c)(iv) … … [1]

10 marks

Mark scheme: 9 (a) (i) 41 1 (ii) 6.8921 × 104 1 (iii) 69 000 1 96550 − 88826 (b) 8% 3 M2 for × 100 oe 96550 88826 or M1 for 7724 seen or 96550 1 (c) (i) or 0.04 1 25 (ii) 5 1 (iii) Has more than 2 factors oe 1 (iv) A decimal that is not truncated and it 1 does not recur (or can’t be written as a fraction) oe

This question in 0580/32 Feb/March 2015

1 (a) Write down (i) two factors of 12, Answer(a)(i) … [1] (ii) the next prime number after 19, Answer(a)(ii) … [1] (iii) the cube root of 64, Answer(a)(iii) … [1] (iv) two million five hundred and seven in figures, Answer(a)(iv) … [1] (v) two multiples of 75, Answer(a)(v) … [1] (vi) the value of π correct to 5 significant figures. Answer(a)(vi) … [1] (b) Write as a percentage. (i) 1.63 Answer(b)(i) … % [1] 3 (ii) 40 Answer(b)(ii) … % [1] (c) (i) Write 63 521.769 correct to 1 decimal place. Answer(c)(i) … [1] (ii) Write 63 521.769 correct to the nearest hundred. Answer(c)(ii) … [1] (d) (i) Change 234 mm into metres. Answer(d)(i) … m [1] (ii) Change 876 m2 into square centimetres. Answer(d)(ii) … cm2 [1] __________________________________________________________________________________________

12 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) At least two of 1, 2, 3, 4, 6, 12 1 No incorrect factors (ii) 23 1 (iii) 4 1 (iv) 2 000 507 1 (v) e.g. 75, 150 1 Accept any 75k, k > 0 (vi) 3.1416 1 (b) (i) 163 1 (ii) 7.5 1 (c) (i) 63521.8 1 (ii) 63500 cao 1 (d) (i) [0].234 1 (ii) 8 760 000 1

This question in 0580/31 May/June 2015

3 (a) Luis buys a season ticket to watch his local football team. The season ticket costs $595. (i) Luis buys the season ticket online and gets a 5% discount on the $595. Work out how much Luis pays for the season ticket online. Answer(a)(i) $ … [2] (ii) A ticket to watch one match costs $38. Luis watches 16 matches. How much did Luis save by buying a season ticket online instead of 16 tickets at $38 each? Answer(a)(ii) $ … [2] (b) The football stadium has 26 272 seats. The number of people who attend one match is 23 854. Calculate the percentage of the 26 272 seats that are empty. Answer(b) … % [2] (c) The total number of people attending matches at the stadium last season was 506 762. Write 506 762 in standard form, correct to 3 significant figures. Answer(c) … [2] (d) Last season the team played a total of 45 matches. The table shows the results of these matches. Result Number of matches Pie chart sector angle Won 20 160° Drawn 15 Lost 10 (i) Complete the table. [3] (ii) Complete the pie chart. Won [1] (e) The table shows the total attendance figures for all the teams in the league for two seasons. Season Total attendance A 9.76 × 106 B 1.36 × 107 Work out how much greater the attendance was in season B than in season A. Give your answer in standard form. Answer(e) … [2] __________________________________________________________________________________________

14 marks

Mark scheme: 3 (a) (i) 565.25 2 M1 for − 1 5  × 595 oe  100  (ii) 42.75 2FT 2FT if positive difference (ie (a)(i) < 608) M1 for 38 × 16 (or 608) – their (a)(i) (b) 9.2[0…] 2 M1 for  26272 − 23854  × 100 oe or  26272  − 1 23854  × 100 oe or  26272  23854 100 − × 100 oe 26272 (c) 5.07 × 105 cao 2 B1 for figs 507 or for a × 105 (a ≠ 0) (d) (i) 120° 3 B2 for one correct 80° 15 10 160 or M1 for × 360 or × 360 or × 15 45 45 20 160 or × 10 or better 20 (ii) Pie chart correct 1FT FT if their angles add to 200° (e) 3.84 × 106 2 B1 for answer figs 384

This question in 0580/31 Oct/Nov 2015

1 (a) Write down in figures the number twenty one million. Answer(a) … [1] (b) Write down the four factors of 21. Answer(b) … , … , … , … [2] (c) Write 21% as a fraction. Answer(c) … [1] (d) Put brackets in this calculation to make it correct. 210 + 21 ÷ 2.1 + 21 = 10 [1] (e) Write down the first two prime numbers after 21. Answer(e) … and … [2] (f) Fill in the missing number. 21 210 = 210 ff [1] (g) Calculate 21 2 - 21 . Answer(g) … [1] (h) Work out ( 21 ) 2. Answer(h) … [1] (i) Write down the value of 210. Answer(i) … [1] (j) Write 0.0021 in standard form. Answer(j) … [1] (k) Write down the lowest common multiple (LCM) of 21 and 15. Answer(k) … [2]

14 marks

Mark scheme: Question Answer Mark Part marks 1 (a) 21 000 000 1 (b) 1, 3, 7, 21 2 M1 for 3 correct and one incorrect (or missing) or for 4 correct and one extra 21 (c) 1 100 (d) (210 + 21) ÷ (2.1+ 21) 1 (e) 23 1 If zero scored SC1 for any two other prime 29 1 numbers greater than 21 (f) 2100 1 (g) 436 or 436.4... 1 (h) 21 1 (i) 1 1 (j) 1.2 × 10 − 3 1 (k) 105 2 M1 for [1 ×] 3 × 5 × 7 or 105k or for [1], 3, 7 and [1], 3, 5 seen or for [1], 3, 5, 7 (maybe in a table) or for listing multiples of 15 and 21 to at least 105 with not more than one error

This question in 0580/32 Oct/Nov 2015

9 (a) The area of Cuba, in square kilometres, is one hundred and five thousand eight hundred and six. Write this number in figures. … [1] (b) The population of an island is 103 000. Write this number in standard form. … [1] (c) The table shows some populations in 2014. Population Puerto Rico 3.68 × 106 St Maarten 4.61 × 104 Haiti 1.05 × 107 US Virgin Islands 1.07 × 105 (i) Write the population of St Maarten as an ordinary number. … [1] (ii) Complete the statement. The population of Haiti is approximately … times the population of the US Virgin Islands. [1] (iii) Find the difference between the population of Haiti and the population of Puerto Rico. Give your answer in standard form. … [2] (d) In 2013 the population of a town was 30 405. In 2014 the population was 30 851. Calculate the percentage increase in the population. … % [3]

9 marks

Mark scheme: 9 (a) 105 806 1 (b) 1.03 × 105 1 (c) (i) 46 100 1 (ii) 100 1 (iii) 6.82 × 106 2 B1 for figs 682  30 851  (d) 1.47 or 1.466 to 1.467 3 M2 for  − 1  [×100] oe soi by 0.0146….  30 405  or 0.0147  30 851 or  × 100 [–100] oe soi by 101.46….  30 405  or 101.47  30 851  or M1 for   soi by 1.0146……. or 1.0147  30 405  Alternative method 30 851 − 30 405 M2 for [× 100 ] oe soi by 0.0146…. 30 405 or 0.0147 or B1 for 30 851 – 30 405 soi by 446

This question in 0580/31 Oct/Nov 2016

2 (a) The diameter of the Earth is 12 756 km. Write 12 756 km in metres. … m [1] (b) The distance from the Earth to the Moon is 384 000 km. Work out the time it would take a car travelling at 100 km/h to travel 384 000 km. Give your answer in days. … days [2] (c) The distance from the Sun to the Earth is 149.6 million kilometres. Write 149.6 million in standard form. … [2] (d) The diameter of a grain of salt is 1 × 10−4 metres. (i) Write 1 × 10−4 as an ordinary number. … [1] (ii) Write 1 × 10−4 metres in millimetres. … mm [1]

7 marks

Mark scheme: 2(a) 12 756 000 1 2(b) 160 2 384000 M1 for 100 2(c) 1.496 × 108 2 M1 for 1.496 × 10k or 149 600 000 oe If zero scored, SC1 for 1.496 × 102 million 2(d)(i) 0.0001 1 2(d)(ii) 0.1 oe 1

This question in 0580/33 May/June 2017

9 (a) By rounding each number correct to 1 significant figure, show that an estimate for this calculation is 20. 9. 78 + 31. 562 0.381 # 5 .09 [2] (b) Write these numbers in order, smallest first. 22 333 3.142 3.1416 7 106 … 1 … 1 … 1 … [2] smallest (c) The length, p cm, of a pencil is 9.8 cm, correct to 2 significant figures. Complete the statement about the value of p. … G p 1 … [2] 5 2163 (d) Calculate .3142 - . 16 604 Give your answer in standard form correct to 2 significant figures. … [2]

8 marks

Mark scheme: 9(a) 10 + 30 M1 [ 0 ] .4 × 5 40 A1 [= 20] 2 9(b) 333 22 2 B1 for 3.1428[…] or 3.143 and 3.1416 3.142 3.1415[…] 106 7 or for 3 in the correct order 9(c) 9.75 9.85 2 B1 for one correct or both correct and reversed 9(d) 4.1 × 10–4 cao 2 B1 for 4.07[6…] × 10-4 or 4.08× 10-4 or figs 41

This question in 0580/33 Oct/Nov 2019

1 (a) A cruise ship travels 2067 km. (i) Write 2067 in words. … [1] (ii) Write 2067 correct to the nearest hundred. … [1] (b) When full, the cruise ship carries 880 guests and 360 crew. Write the ratio guests : crew in its simplest form. … : … [1] (c) There are 480 cabins on the ship. On one cruise, 456 of these cabins were used. Find the percentage of cabins that were used. … % [1] (d) Last year the cost of a cruise was $4600. This year the cost of the same cruise is $4784. Work out the percentage increase in the cost. … % [2] (e) The cost of building the ship was $153 000 000. Write 153 000 000 in standard form. … [1] (f) There are 480 cabins on the ship. There are four types of cabin: Ocean-view, Balcony, Interior and Suite. Hannah starts to draw a pie chart to show the numbers of each type of cabin. Ocean-view 144° Balcony (i) Show that there are 120 Ocean-view cabins on the ship. [1] (ii) The table shows information about each type of cabin. Type of cabin Number of cabins Sector angle in a pie chart Ocean-view 120 90° Balcony 192 144° Interior 68 Suite 100 (a) Complete the table. [2] (b) Complete the pie chart. [1]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Two thousand [and] sixty-seven 1 1(a)(ii) 2100 1 1(b) 22 : 9 1 1(c) 95 1 1(d) 4 nfww 2 4784 − 4600 M1 for [× 100] 4600  4784  or  − 1  [× 100]  4600  4784 or × 100 [– 100] oe 4600 1(e) 1.53 × 108 1 1(f)(i) 90 1 × 480 [= 120] oe 360 1(f)(ii)(a) 51 2 68 100 M1 for either × 360 or × 360 oe 75 480 480 or better 1(f)(ii)(b) Correct pie chart 1 FT dep on their 51° and their 75° adding to 126°

This question in 0580/33 Oct/Nov 2020

6 (a) Write these in order, starting with the smallest. 11 17 0.5806 58% 19 29 … 1 … 1 … 1 … [2] smallest (b) Write 0.004 973 correct to (i) 3 decimal places, … [1] (ii) 2 significant figures. … [1] (c) The height of a flag pole, h metres, is measured as 37.84 metres, correct to 2 decimal places. Complete this statement about the value of h. … G h 1 … [2] (d) The population of Nigeria is 201 000 000, correct to 3 significant figures. Write this population in standard form. … [1] (e) The table shows the populations of some countries given in standard form, correct to 3 significant figures. Country Population Brazil .212 # 108 China .142 # 109 Eritrea .531 # 106 France .655 # 107 Maldives .452 # 105 New Zealand .479 # 106 Use the information in this table to find (i) the country with the smallest population, … [1] (ii) the country with the population that is nearest to 5 million, … [1] (iii) the difference between the population of Brazil and the population of France, … [1] (iv) the value of k, correct to 2 significant figures, where the population of China = k # the population of Eritrea. k = … [2]

12 marks

Mark scheme: 6(a) 11 17 2 M1 for 58% 0.5806 [0.5806] [0].57… [0].586… [0].58 19 29 or B1 for 3 in the correct order 6(b)(i) 0.005 cao 1 6(b)(ii) 0.0050 cao 1 6(c) 37.835 37.845 2 B1 for each If 0 scored, SC1 for both correct but reversed 6(d) 2.01 × 108 1 6(e)(i) Maldives 1 6(e)(ii) New Zealand 1 6(e)(iii) 146 500 000 or 1.465 × 108 1 6(e)(iv) 270 cao 2 M1 for (1.42 × 109) ÷ (5.31 × 106) oe or 267[. …] oe

This question in 0580/32 Oct/Nov 2021

1 Roberto and his family fly from London to Los Angeles on a holiday. (a) The flight takes 11 hours 15 minutes. (i) The flight leaves London at 15 40 local time. The local time in Los Angeles is 8 hours behind the local time in London. Work out the local time in Los Angeles that the plane arrives. … [2] (ii) The plane flies a total of 8760 km. Calculate the average speed of the plane. … km/h [3] (b) Roberto hires a car. (i) The cost of hiring a car is $56 per day, plus a fixed cost of $436. Write down a formula for the cost, C dollars, of hiring a car for d days. … [2] (ii) Roberto is given a car at random. There are four colours of car. Colour Red Silver Black White Probability 0.17 0.24 0.3 Complete the table. [2] (c) The family visit a national park which has an area of 4986 km2. (i) Write 4986 correct to the nearest hundred. … [1] (ii) Write 4986 in standard form. … [1] (d) A ticket for the park costs $17.50 plus 8% tax. Calculate the amount of tax paid. $ … [1] (e) The scale drawing shows the positions of two viewing points, A and B, in the park. The scale is 1 centimetre represents 5 kilometres. North North B A Scale : 1 cm to 5 km (i) Work out the actual distance between point A and point B. … km [2] (ii) Point C is 20 km from point A on a bearing of 072°. On the scale drawing mark the position of point C. [2]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 18 55 2 B1 for 07 40 or 02 55 or 3[h] 15 [min] or M1 for departure time + 11h 15 min −8h evaluated as a time with one interval correctly added 1(a)(ii) 779 or 778.6 to 778.7 3 8760 M2 for 8760 ÷ 11.25 oe × 60 675 or B1 for 11.25 or M1 for 8760 ÷ their time 1(b)((i) C = 56d + 436 cao 2 B1 for C = 56d + 436 seen and spoilt or 56d + 436 as final answer 1(b)(ii) 0.29 2 M1 for 1 – (0.17 + 0.24 + 0.3) oe or better 1(c)(i) 5000 1 1(c)(ii) 4.986 × 103 1 1(d) 1.4[0] 1 1(e)(i) 35 2 B1 for 7 1(e)(ii) Correct length and bearing 2 B1 for length 4 cm from A B1 for bearing 072° from A

This question in 0580/33 Oct/Nov 2021

9 (a) Write down the reciprocal of 1. 3 … [1] (b) Write down the value of 30. … [1] 3 4 (c) Find a fraction between and . 25 25 … [1] (d) Find the difference in temperature between −5 °C and 9 °C. … °C [1] (e) Write in standard form. (i) 5 600 000 … [1] (ii) 0.000 072 … [1] (f) Calculate ( 5.2 # 10 6 ) # (3 .8 # 10 -2 ) . Give your answer in standard form. … [1]

7 marks

Mark scheme: 9(a) 3 1 9(b) 1 1 9(c) Correct fraction e.g. 507 1 9(d) 14 1 9(e)(i) 5.6 × 106 1 9(e)(ii) 7.2 × 10-5 1 9(f) 1.976 × 105 1

This question in 0580/32 Oct/Nov 2022

4.6 # 10 3 23 Calculate . 1 .84 # 10 5 Give your answer in standard form. … [2] Question 24 is printed on the next page

2 marks

Mark scheme: 23 2.5 × 10–2 cao 2 B1 for 0.025 or correct answer not in standard form e.g. 25 × 10–3 , 0.25 × 10–1

This question in 0580/31 Oct/Nov 2025

21 Calculate (5 .6 # 10 -3 ) ' ( 2.4 # 10 -5) . Write your answer in standard form. … [2]

2 marks

Mark scheme: 21 2.33 × 102 or 2.33[3…] × 102 2 B1 for 233[.3…] oe or correct value not in correct standard form or their value seen given in correct standard form if 0 scored SC1 for 2.3 × 102 as answer

This question in 0580/32 Oct/Nov 2025