Percentages — Paper 2 · IGCSE Mathematics 0580

8 In 1997 the population of China was 1.24 × 109. In 2002 the population of China was 1.28 × 109. Calculate the percentage increase from 1997 to 2002. Answer % [2]

2 marks

Mark scheme: 8 3.23 2* figs 4 figs 128 − figs 124 M1 or figs 124 figs 124 Note 3.13 is M0

This question in 0580/21 Oct/Nov 2004

5 In 1970 the population of China was 8.2 x 108. For In 2007 the population of China was 1.322 x 109. Examiner's Calculate the population in 2007 as a percentage of the population in 1970. Use Answer %[2]

2 marks

Mark scheme: 5 161 2 M1 1.322 × 109 / 8.2 × 108 (× 100)

This question in 0580/21 Oct/Nov 2009

17 (a) In 2007, a tourist changed 4000 Chinese Yuan into pounds (£) when the exchange rate was £1 = 15.2978 Chinese Yuan. Calculate the amount he received, giving your answer correct to 2 decimal places. Answer(a) £ [2] (b) In 2006, the exchange rate was £1 = 15.9128 Chinese Yuan. Calculate the percentage decrease in the number of Chinese Yuan for each £1 from 2006 to 2007. Answer(b) % [2]

4 marks

Mark scheme: 17 (a) 261.48 cao 2 M1 4000 / 15.2978 (b) (±)3.86(48…) or 3.865 2 M1 (15.9128 – 15.2978)/15.9128 (× 100) or (“261.48 – 4000/15.9128) / “261.48”

This question in 0580/21 Oct/Nov 2009

17 (a) In 2007, a tourist changed 4000 Chinese Yuan into pounds (£) when the exchange rate was £1 = 15.2978 Chinese Yuan. Calculate the amount he received, giving your answer correct to 2 decimal places. Answer(a) £ [2] (b) In 2006, the exchange rate was £1 = 15.9128 Chinese Yuan. Calculate the percentage decrease in the number of Chinese Yuan for each £1 from 2006 to 2007. Answer(b) % [2]

4 marks

Mark scheme: 17 (a) 261.48 cao 2 M1 4000 / 15.2978 (b) (±)3.86(48…) or 3.865 2 M1 (15.9128 – 15.2978)/15.9128 (×100) oe or (“261.48” – 4000/15.9128) / “261.48”

This question in 0580/22 Oct/Nov 2009

5 Amalie makes a profit of 20% when she sells a shirt for $21.60. Examiner's Use Calculate how much Amalie paid for the shirt. Answer $ [2]

2 marks

Mark scheme: 5 18 2 M1 for 21.6 ÷ 1.2 oe 8

This question in 0580/23 May/June 2010

10 Nikhil invests $200 for 2 years at 4% per year compound interest. Calculate the exact amount Nikhil has after 2 years. Answer $ [2]

2 marks

Mark scheme: 10 216.32 cao 2 M1 200 × (1 + (4/100))2 oe

This question in 0580/23 Oct/Nov 2010

1 A concert hall has 1540 seats. ForFor Examiner'sExaminer's Calculate the number of people in the hall when 55% of the seats are occupied. UseUse Answer [1]

1 marks

Mark scheme: g g Qu. Answers Mark Part Mark 1 847 1

This question in 0580/21 May/June 2011

9 Eva invests $120 at a rate of 3% per year compound interest. Calculate the total amount Eva has after 2 years. Give your answer correct to 2 decimal places. Answer $ [3]

3 marks

Mark scheme: 9 127.31 cao 3 M1 for 120 × 1.032 A1 for 127.308 If M0 award SC2 for 7.31 or 247.31

This question in 0580/23 May/June 2011

6 Pedro invested $800 at a rate of 5% per year compound interest. Calculate the total amount he has after 2 years. Answer $ [2]

2 marks

Mark scheme: 6 882 2 M1 800 × 1.05 × 1.05 1 1

This question in 0580/23 Oct/Nov 2011

10 Maria decides to increase her homework time of 8 hours per week by 15%. Calculate her new homework time. Give your answer in hours and minutes. Answer h min [3]

3 marks

Mark scheme: 10 9 h 12 min 3 M1 for 8 × 1.15 A1 for 9.2 B1 ft independent for their 9.2 correctly converted into hours and minutes

This question in 0580/23 Oct/Nov 2011

13 During a marathon race an athlete loses 2 % of his mass. At the end of the race his mass is 67.13 kg. Calculate his mass before the race. Answer kg [3]

3 marks

Mark scheme: 13 68.5 www 3 M2 for 67.13 ÷ 0.98 or M1 for 67. 13 is 98% 2 43 πr 3 2

This question in 0580/23 Oct/Nov 2011

1 For 10 Shania invests $750 at a rate of 2 2 % per year simple interest. Examiner's Use Calculate the total amount Shania has after 5 years. Answer $ [3]

3 marks

Mark scheme: 750 × 5 × 5.2 10 843.75 3 M2 for + 750 oe 100 750 × 5 × 5.2 or M1 for oe 100 or SC2 for answer 93.75 IGCSE – May/June 2012 0580 21

This question in 0580/21 May/June 2012

11 Boris invests $280 for 2 years at a rate of 3% per year compound interest. Calculate the interest Boris receives at the end of the 2 years. Give your answer correct to 2 decimal places. Answer $ [4]

4 marks

Mark scheme: 11 17.05 cao www 4 3 M1 for 280 × (1 + )2 oe 100 k M1 subtracting 280 from 280(1 + )2 any k 100 A1 for 17.052 or SC2 297.05 on answer line IGCSE – May/June 2012 0580 23

This question in 0580/23 May/June 2012

8 Acri invested $500 for 3 years at a rate of 2.8% per year compound interest. Calculate the final amount he has after 3 years. Answer $ [3]

3 marks

Mark scheme: 8 543.19 3 M2 for 500 × 1.0283 oe or long method or M1 for 500 × 1.028n , n = 2 or 4

This question in 0580/21 Oct/Nov 2012

5 Maria pays $84 rent. For The rent is increased by 5%. Examiner's Use Calculate Maria’s new rent. Answer $ [2]

2 marks

Mark scheme: 5 88.2(0) 2 M1 for 84 × 1.05 oe

This question in 0580/23 Oct/Nov 2012

1 Work out 72 cents as a percentage of 83 cents. For Examiner′s Use Answer … % [1] _____________________________________________________________________________________

1 marks

Mark scheme: Qu. Answers Mark Part Marks 1 86.7 or 86.74 to 86.75 1

This question in 0580/21 Oct/Nov 2013

4 Calculate 17.5% of 44 kg. Answer … kg [2] _____________________________________________________________________________________

2 marks

Mark scheme: 4 7.7 2 175. M1 for 44 × oe 100

This question in 0580/21 Oct/Nov 2013

17 Thailand NOT TO Hong SCALE Kong Singapore 150° Malaysia A travel brochure has 72 holidays in four different countries. The pie chart shows this information. (a) There are 24 holidays in Thailand. Show that the sector angle for Thailand is 120°. Answer(a) [2] (b) The sector angle for Malaysia is 150°. The sector angle for Singapore is twice the sector angle for Hong Kong. Calculate the number of holidays in Hong Kong. Answer(b) … [3] __________________________________________________________________________________________

5 marks

Mark scheme: 17 (a) correct working 2 M1 for 1 holiday = 5 or 360 ÷ 72 = 5 and B1 for 24 × 5 [= 120] or 24 M2 for × 360 [=120] oe 72 (b) 6 nfww 3 M1 for 150 + 120 + x + 2x = 360 oe A1 for 30 identified as the required angle 1 1 10 4

This question in 0580/21 May/June 2014

7 The population of Dubai at the end of 2012 was 2.1 million. This was predicted to increase at a rate of 6% each year. Calculate the predicted population of Dubai at the end of 2015. Answer … million [3] __________________________________________________________________________________________

3 marks

Mark scheme: 6 )3 oe7 2.5[0] or 2.501… nfww 3 M2 for 1.2 × (1 + 100 6 )n oe where n ≥ 2 or M1 for 1.2 × (1 + 100 6 3 or for figs 21 × (1 + 100 ) oe

This question in 0580/21 Oct/Nov 2014

17 Alex invests $200 for 2 years at a rate of 2% per year simple interest. Chris invests $200 for 2 years at a rate of 2% per year compound interest. Calculate how much more interest Chris has than Alex. Answer $ … [4] __________________________________________________________________________________________

4 marks

Mark scheme: 17 [0.]08 4 M3 for 200 × + 1 2  2 − 200 − 200 × 2 × 2 oe  100  100 or M1 for 200 × + 1 2  2  100  200 × 2 × 2 and M1 for [+200] 100

This question in 0580/22 Oct/Nov 2014

10 Maryah borrows $12 000 to start a business. The loan is for 3 years at a rate of 5% per year compound interest. The loan has to be paid back at the end of the 3 years. Calculate the total amount to be paid back. Answer $ … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 5 10 13891.5[0] 3 M2 for 12000 × + 1  oe  100  n 5  or M1 for 12000 × + 1  oe n > 2  100  1

This question in 0580/23 Oct/Nov 2014

10 In a sale, the cost of a coat is reduced from $85 to $67.50 . Calculate the percentage reduction in the cost of the coat. Answer … % [3]

3 marks

Mark scheme: 85 − 675. 67 5. 10 20.6 or 20.58 to 20.59 3 M2 for × 100 or − 1  × 100 85  85  85 − 67 5. 675. or M1 for or × 100 85 85 675. − 85 If zero scored SC1 for × 100 85

This question in 0580/23 May/June 2015

16 Hazel invests $1800 for 7 years at a rate of 1.5% per year compound interest. Calculate how much interest she will receive after the 7 years. Give your answer correct to the nearest dollar. Answer $ … [4] __________________________________________________________________________________________

4 marks

Mark scheme: 16 198 4 B3 for 197.7…. or answer 198.00 or 7 5.1  M2 for 1800 × + 1  – 1800  100  or B2 for answer 1998 or 7 5.1  M1 for 1800 × + 1   100  If B0 then B1 for seeing their answer in decimal form correctly written to the nearest integer

This question in 0580/21 Oct/Nov 2015

8 Robert buys a car for $8000. At the end of each year the value of the car has decreased by 10% of its value at the beginning of that year. Calculate the value of the car at the end of 7 years. Answer $ … [2]

2 marks

Mark scheme: 8 3826 or 3826.38 2 M1 for 8000 × −1 10  7 oe  100  k × 50 000 × 50 000

This question in 0580/22 Oct/Nov 2015

10 Jason receives some money for his birthday. 11 He spends 15 of the money and has $14.40 left. Calculate how much money he received for his birthday. Answer $ … [3]

3 marks

Mark scheme: 15 10 54 3 M2 for 14 4. × oe 4 4 or M1 for 14.4 ÷ 4 or associated with 14.4 15 If zero scored SC1 for final answer 19.6[4] 2 2

This question in 0580/22 Oct/Nov 2015

14 Jasjeet and her brother collect stamps. When Jasjeet gives her brother 1% of her stamps, she has 2475 stamps left. Calculate how many stamps Jasjeet had originally. Answer … [3]

3 marks

Mark scheme: 1  oe14 2500 nfww 3 M2 for 2475 ÷ 1   −100  or M1 for 2475 associated with 99% ( )( )

This question in 0580/22 Oct/Nov 2015

2 From a sample of 80 batteries, 3 are faulty. Work out the percentage of faulty batteries. … % [1]

1 marks

Mark scheme: 2 3.75 or 3¾ 1

This question in 0580/21 May/June 2016

19 At the start of an experiment there are 20 000 bacteria. The number of bacteria increases at a rate of 30% per hour. (a) Work out the number of bacteria after 4 hours. … [2] (b) After how many whole hours, from the start of the experiment, will the number of bacteria be greater than one million? … hours [2]

4 marks

Mark scheme: 19 (a) 57 122 2 M1 for 20 000 × (1 + 10030 ) 4 oe (b) 15 2 M1 for two substitutions greater than 4 e.g. 20 000 × (1 + 10030 )k where k > 4

This question in 0580/23 May/June 2016

11 Ahmed paid $34 000 for a car. His car decreased in value by 40% at the end of the first year. The value at the end of the second year was 10% less than the value at the end of the first year. Calculate the value of Ahmed’s car after 2 years. $ … [2]

2 marks

Mark scheme:  40  10 11 18 360 2 M1 for 34 000 × 1 − × 1 − oe     100  100   1  4  5  3

This question in 0580/23 Oct/Nov 2016

10 Indira buys a television in a sale for $924. This was a reduction of 12% on the original price. Calculate the original price of the television. $ … [3]

3 marks

Mark scheme: (100 12 )10 1050 3 M2 for 924 ÷ oe 100 or M1 for 88[%] associated with 924 oe

This question in 0580/22 Feb/March 2017

5 Work out 85 cents as a percentage of $2.03 . … % [1]

1 marks

Mark scheme: 5 41.9 or 41.87 1

This question in 0580/22 May/June 2017

24 Marcel invests $2500 for 3 years at a rate of 1.6% per year simple interest. Jacques invests $2000 for 3 years at a rate of x% per year compound interest. At the end of the 3 years Marcel and Jacques receive the same amount of interest. Calculate the value of x correct to 3 significant figures. x = … [5]

5 marks

Mark scheme: 24 1.96 cao 5   2500 × 1.6 × 3     + 2000   M4 for ( (   3 100 − 1  ) − 1) [×   2000           100] oe or 1.96…or [0].0196... or 101.96… or 1.0196… or 2500 × 1.6 × 3 + 2000 3 100 M3 for 2000 or B2 for [SI =] 120 or [CI total=] 2120 2500 × 3 × 1.6 or M1 for 100 and 3 M1 for 2000 × ( k )

This question in 0580/23 May/June 2017

6 Write 55 g as a percentage of 2.2 kg. … % [2]

2 marks

Mark scheme: 6 2.5 2 B1 for 2200 or 0.055 seen or SC1 for answer figs 25

This question in 0580/22 Oct/Nov 2017

5 Increase $22 by 15%. $ … [2]

2 marks

Mark scheme: 5 25.3[0] 2 15 M1 for 22 × oe or better 100

This question in 0580/23 May/June 2018

7 The probability that Kim wins a game is 0.72 . In one year Kim will play 225 games. Work out an estimate of the number of games Kim will win. … [2]

2 marks

Mark scheme: 7 162 2 M1 for 225 × 0.72 oe

This question in 0580/23 May/June 2018

9 Jan invests $800 at a rate of 3% per year simple interest. Calculate the value of her investment at the end of 4 years. $ … [3]

3 marks

Mark scheme: 9 896 3 800 × 4 × 3 M2 for 800 + oe 100 800 × 4 × 3 or M1 for oe 100

This question in 0580/21 Oct/Nov 2018

3 Work out $1.45 as a percentage of $72.50 . … % [1]

1 marks

Mark scheme: 3 2 1

This question in 0580/23 Oct/Nov 2018

11 The number of passengers on a train increases from 63 to 77. Calculate the percentage increase. … % [3]

3 marks

Mark scheme: 11 2 3 77 − 22 or 22.2 or 22.22... M2 for 63[× 100] oe or 9 63 77 × 100 [– 100] oe 63 77 or M1 for oe 63

This question in 0580/22 Feb/March 2019

14 Eric invests an amount in a bank that pays compound interest at a rate of 2.16% per year. At the end of 5 years, the value of his investment is $6 999.31 . Calculate the amount Eric invests. $ … [3]

3 marks

Mark scheme: 14 6290[.0…] 3 6999.31 M2 for  2.16  5  1 +   100   2.16  5 or M1 for [ A] 1 +    100 

This question in 0580/22 Feb/March 2019

1 Work out $1.20 as a percentage of $16. … % [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 7.5 oe 1

This question in 0580/21 May/June 2019

15 Shona buys a chair in a sale for $435.60 . This is a reduction of 12% on the original price. Calculate the original price of the chair. $ … [3]

3 marks

Mark scheme: 15 495 3 100 − 12 M2 for 435.6 ÷ oe 100 or B1 for recognising 435.6 as 88[%]

This question in 0580/22 May/June 2019

1 Work out 5% of $25. $ … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 1.25 1

This question in 0580/21 Oct/Nov 2019

12 Roberto buys a toy for $5.00 . He then sells it for $4.60 . Calculate his percentage loss. … % [2]

2 marks

Mark scheme: 12 8 2 5 − 4.60 4.60 M1 for [× 100 ] or × 100 5 5

This question in 0580/22 May/June 2020

9 (a) Ahmed increases 40 by 300%. From this list, put a ring around the correct calculation. 40 # 1.300 40 # 3 40 # 400 40 # 4 40 # 300 [1] 2 (b) Ahmed finds the magnitude of the vector e- 3o. From this list, put a ring around the correct calculation. 2 2 +- 3 2 2 2 - 3 2 2 2 - 3 2 2 2 + ( - 3 ) 2 2 2 + ( - 3 ) 2 [1]

2 marks

Mark scheme: 9(a) 40 × 4 1 9(b) 2 2 1 2 + ( − 3 )

This question in 0580/21 Oct/Nov 2020

5 Increase 42 by 16%. … [2]

2 marks

Mark scheme: 5 48.72 2 16 M1 for × 42 oe or better 100

This question in 0580/22 Oct/Nov 2020

16 The selling price of a shirt is $26.50 . This includes a tax of 6%. Calculate the price of the shirt before the tax was added. $ … [2]

2 marks

Mark scheme: 16 25 2  6  M1 for x ×  1 +  = 26.50 oe or better  100 

This question in 0580/22 Oct/Nov 2020

17 Adil and Brian are paid the same wage. Adil is given a 7% pay decrease and his new wage is $427.80 . Brian is given a 7% pay increase. Work out Brian’s new wage. $ … [3]

3 marks

Mark scheme: 17 492.2[0] 3 B2 for 32.2[0] OR  7  M1 for x ×  1 −  = 427.8[0] oe or  100  better  7  M1 for their 460 ×  1 +  oe  100  7 or their 460 × correctly evaluated 100

This question in 0580/23 Oct/Nov 2020

12 Chai invests some money. By the end of the first year, the value of the investment has decreased by 35%. By the end of the second year, the value of the investment has increased by 40% of its value at the end of the first year. Find the overall percentage change in the value of the investment. … % [3]

3 marks

Mark scheme: 12 [– ] 9 3  35   40  M2 for [k × ]  1 −  ×  1 +  oe or  100   100  better  35  35  40  or for [k × ]  −  1 −  ×   100  100  100   35  or M1 for [k × ]  1 −  oe  100   40  or [k × ]  1 +  or better  100 

This question in 0580/21 Oct/Nov 2021

1 Write 26 g as a percentage of 208 g. … % [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 12.5 1

This question in 0580/23 Oct/Nov 2021

6 Marek buys a computer for $420. He sells it at a loss of 15%. Calculate the selling price of this computer. $ … [2]

2 marks

Mark scheme: 6 357 2  15  M1 for  1 −  × 420 oe  100  or B1 for 63

This question in 0580/23 Oct/Nov 2021

15 The cost of a train journey is increased by 6% to a new cost of $153.70 . Calculate the original cost of the train journey. $ … [2]

2 marks

Mark scheme: 15 145 2 6  M1 for x 1 +  = 153.7 oe or better  100 

This question in 0580/23 Oct/Nov 2021

12 (a) Sanjay invests $700 in an account paying simple interest at a rate of 2.5% per year. Calculate the value of his investment at the end of 6 years. $ … [3] (b) Meera invests $700 in an account paying compound interest at a rate of r % per year. At the end of 17 years the value of her investment is $1030.35 . Find the value of r. r = … [3]

6 marks

Mark scheme: 12(a) 805 3 B2 for 105 700 × 2.5 × 6 or M2 for + 700 oe 100 700 × 2.5 [× 6 ] or M1 for oe 100 12(b) 2.3[0…] 3 1030.35 M2 for 17 oe 700 or M1 for 1030.35 = 700 ( k )17 oe for any k

This question in 0580/22 Feb/March 2022

7 The price of a coat is $126. In a sale, this price is reduced by 18%. Find the sale price of the coat. $ … [2]

2 marks

Mark scheme: 7 103.32 cao 2  18  M1 for 126  1  oe    100  or B1 for 22.68

This question in 0580/22 May/June 2022

6 The price of a computer is $520. This price is reduced by 15% in a sale. Work out the sale price. $ … [2]

2 marks

Mark scheme: 6 442 2 100 − 15 M1 for  520 oe 100 or B1 for 78

This question in 0580/21 Oct/Nov 2022

12 Keita invests $4000 at a rate of 2.6% per year compound interest. Work out the interest earned on the investment at the end of 3 years. $ … [3]

3 marks

Mark scheme: 12 320.18 3 B2 for 4320.18  2.6 3 or M1 for 4000   1 +  [ – 4000] oe  100 

This question in 0580/23 Oct/Nov 2022

13 Anya invests $6000 in an account that pays compound interest at a rate of r % per year. At the end of 8 years, the account has earned $621.70 in interest. Calculate the value of r. r = … [3]

3 marks

Mark scheme: 13 1.24[0…] 3 6000  621.70 M2 8 oe 6000 or M1 for 6000  621.70  6000 k 8 oe

This question in 0580/21 May/June 2023

12 Oliver sent 22% more messages in June than in May. He sent 305 messages in June. Find how many more messages he sent in June than in May. … [3]

3 marks

Mark scheme: 12 55 3 B2 for 250 or M2 for (305 ÷ 122)  22 oe or better  22  or M1 for  1 +  m = 305 oe or better  100 

This question in 0580/23 Oct/Nov 2023

10 Amir invests $1500 in an account. The account pays compound interest at a rate of r % per year. At the end of 8 years the value of his investment is $1656.73 . Find the value of r. r = … [3]

3 marks

Mark scheme: 10 1.25 or 1.250… 3 1656.73 M2 for 8 oe 1500 or M1 for 1656.73  1500 k 8 oe for any k

This question in 0580/21 May/June 2024

15 At the start of an experiment there are 40 000 bacteria. The number of bacteria increases at a rate of 15% per hour. Calculate the number of bacteria after 3 hours. … [2]

2 marks

Mark scheme: 15 60835 2 3  15  M1 for 40 000  1 + oe    100 

This question in 0580/22 Oct/Nov 2024

11 A company sells items either on a website or in shops. The composite bar chart shows the percentage of sales on the website and in shops for January, February and March. 100 Sales in shops 90 Sales on website 80 70 60 Percentage 50 of sales 40 30 20 10 0 Jan Feb March April Month 17 (a) In April, of the company’s sales were on the website. 20 On the grid, draw the bar for April. [2] (b) In February, the company had sales of $3.5 million. Work out the value of sales in shops in February. $ … million [3] (c) In May, the company had sales of $6 million. In June, the company had sales of $7.5 million. Find the percentage increase in sales from May to June. … % [3] (d) In 2024, the company had total sales of $52 million. This was an increase of 30% on the total sales for 2023. Work out the total sales in 2023. $ … million [2]

10 marks

Mark scheme: 11(a) Graph completed 85% on website with 15% in 2 shops and correct shading M1 for 85 [%] soi 11(b) 1.4 [million] 3 B2 for 2.1 [million] 40 or M2 for  3.5  million  oe 100 60 or M1 for  3.5  million  oe 100 or B1 for 40 [%] oe If 0 scored SC1 for answer 1.96, 0.875 or 0.525 [million] oe 11(c) 25[%] 3 7.5 − 6 M2 for 100  or 6 7.5  100  −100  or 6  7.5   − 1   100  oe  6  7.5 or M1 for 6 11(d) 40 [million] 2  30  M1 for  1 +  k = 52  million  oe  100 

This question in 0580/22 Feb/March 2025

4 A computer costs $560. In a sale, this cost is reduced by 20%. Find the cost of the computer in the sale. $ … [2]

2 marks

Mark scheme: 4 448 2 M1 for 560 × 0.8 oe or B1 for 112

This question in 0580/22 Oct/Nov 2025