Exponential growth and decay — Paper 3 · IGCSE Mathematics 0580

2 Marguerite earns $336 per month. For She divides her earnings between bills, food, savings and personal spending. Examiner's Use (a) Her bills take 2 of her earnings. 7 Show that $240 is left for her other items. Answer(a) [2] (b) She divides the $240 between food, savings and personal spending in the ratio 5 : 3 : 4. Calculate how much she spends on food. Answer(b) $ [2] (c) She saves the same amount each month. Show that she saves $720 in one year. Answer(c) [2] (d) She invests the $720 in a bank which pays 6% per year compound interest. How much will this be worth after 2 years? Answer(d) $ [3]

9 marks

Mark scheme: 2 5 2 (a) 336 − × 336 or × 336 M1 7 7 (=) 240 E1 240 must be seen for this mark (b) 5 ÷ their(5 + 4 + 3) × 240 M1 100 A1cao www 2 1 3 (c) 3 ÷ their(5 + 4 + 3) × 240 × 12 M1 Allow 2880 for 240 × 12 and for . 4 12 (=) 720 E1 720 must be seen for this mark (d) 720 × 1.06 2 oe M2 Implied by 88.99(2) or 89(total interest)seen M1 for 720 × 1.06 (implied by 763.2 seen) 808.99(2) or 809 A1 SC1 for 806.(4) (Simple Interest) www 3 for 808.99(2) or 809 [9] IGCSE – May/June 2007 0580/0581 03 1

This question in 0580/31 May/June 2007

1 Falla buys 3000 square metres of land for a house and garden. For The garden is divided into areas for flowers, vegetables and grass. Examiner's Use He divides the land in the following ratio. house : flowers : vegetables : grass = 4 : 7 : 8 : 5 (a) (i) Show that the area of land used for flowers is 875 m2. Answer(a)(i) [2] (ii) Calculate the area of land used for the house. Answer(a)(ii) m2 [2] (b) Write down the fraction of land used for vegetables. Give your answer in its simplest form. Answer(b) [2] (c) During the first year Falla plants flowers in 64% of the 875 m2. For Examiner's Calculate the area he plants with flowers. Use Answer(c) m2 [2] (d) Falla sells some of the vegetables he grows. These vegetables cost $85 to grow. He sells them for $105. Calculate his percentage profit. Answer(d) % [3] (e) To buy the land Falla borrowed $5000 at a rate of 6.4% compound interest for 2 years. Calculate the total amount he pays back at the end of the 2 years. Give your answer correct to the nearest dollar. Answer(e) $ [3]

14 marks

Mark scheme: Qu. Answers Mark Part Marks 77 1 (a) (i) 3000 ÷ ( 4 + 7 + 8 + 5) 2 M2 for × 3000 24 and multiply by 7 M1 for 3000 ÷ (24 or their clear attempt at total) (ii) 500 www cao 2 M1 for 4 ÷ their 24 × 3000 oe or 74 × 875 1 8 4 2 2 (b) 2 B1 for or or oe seen or SC1 3 24 12 6 5 (c) 560 2 M1 for 64 ÷ 100 × 875 or 0.64 × 875 oe (d) 23.5 or 23.52 to 23.53 3 W1 for 105 − 85 implied by 20 M1dep for their (105 − 85) ÷ 85 × 100 (e) 5660 3 B2 for 5660.48 or 5660.5 or 660 4.6 4.6 If B0 then M1 for 5000 × 1( + ) × 1( + ) or 100 100 better

This question in 0580/32 May/June 2011

2 Aminata buys a business costing $23 000. For Examiner's (a) She pays part of this cost with $12 000 of her own money. Use Calculate what percentage of the $23 000 this is. Answer(a) % [1] (b) Aminata’s brother gives her 32% of the remaining $11 000. Show that $7 480 is still needed to buy the business. Answer(b) [2] (c) Aminata borrows the $7 480 at a rate of 3.5 % per year compound interest. Calculate how much money she owes at the end of 3 years. Answer(c) $ [3] (d) In the first year Aminata spent $11 000 on salaries, equipment and expenses. 2 of this money was spent on salaries, 0.45 of this money was spent on equipment and the 5 remainder was for expenses. Calculate how much of the $11 000 was spent on (i) salaries, Answer(d)(i) $ [1] (ii) equipment, Answer(d)(ii) $ [1] (iii) expenses. Answer(d)(iii) $ [1] (e) The three items in part (d) are in the ratio salaries : equipment : expenses = 0.4 : 0.45 : 0.15 . Write this ratio in its simplest form. Answer(e) : : [2]

11 marks

Mark scheme: 2 (a) 52.2(%) or 52.17… 1 (b) 11000 − (32 ÷ 100 × 11000) M1 or (68 ÷ 100 × 11000) (=) 7480 E1 Must see this for the second mark. (c) 8293 or 8290 or 8293.2 3 Either M1 for 7480 × 1.0352 oe or 8293.21 as final answer or M1 for 7480 × 1.035 = 7741.8 and their 7741.8 × 1.035 (M1 implied by 8012.76...) Then M1 dep for completion of method for the third year If zero SC1 for answer 813.(2…) (d) (i) 4 400 1 (ii) 4 950 1 (iii) 1 650 1ft 11 000 − their (d)(i) − their (d)(ii) (e) 8 : 9 : 3 cao 2 B1 for 40 : 45 : 15 oe seen or correct non-integer ratio IGCSE – October/November 2011 0580 32 ( ) (i) ( ) −2 

This question in 0580/32 Oct/Nov 2011

1 (a) Vince and Wendy share $2000 in the ratio Vince : Wendy = 19 : 21. For Examiner's Calculate the amount of money that Vince receives. Use Answer(a) $ [2] (b) Wendy has $265 to spend on some chairs. The chairs cost $37 each. Work out the largest number of chairs she can buy. Answer(b) [2] (c) Wendy shares $200 between her three children Jake, Karl and Lana. 2 She gives 27% of the money to Jake and of the money to Karl. 5 Work out the amount of money she gives to Lana. Answer(c) $ [3] (d) Wendy invests $500 at a rate of 4% per year compound interest. Calculate the total amount of interest she receives at the end of 2 years. Give your answer correct to the nearest dollar. Answer(d) $ [4]

11 marks

Mark scheme: Qu. Answers Mark Part Mark 1 (a) 950 2 M1 for 2000 ÷ (19 + 21) 265 (b) 7 cao 2 M1 for seen oe e.g. adding up 37s 37 (c) 66 3 M1 for 54 seen M1 indep for 80 seen Or 33 67 M2 for × 200 or M1 for × 200 100 100 (d) 41 4 M1 for (500 × 1.04) × (1.04) oe A1 for 540.8 M1 dep for ‘their 540.8’ – 500 B1 ft for ‘their 40.8’ rounded to 41 Alt Method M1 for [500 + (500×0.04)] × 0.04 M1 dep ‘their 20’ + ‘their 20.8’ A1 for 40.8 B1 ft for ‘their 40.8’ rounded to 41

This question in 0580/31 May/June 2012

1 Adam owns a farm. For Examiner′s Use (a) He plans to keep twenty hens. He works out what he thinks this will cost. Complete the following table. Item Cost ($) Equipment 500 20 hens costing $12 each 3 years supply of feed costing $25 per month TOTAL [3] (b) The equipment actually costs $600. The ratio of costs is equipment : hens : feed = 5 : 3 : 9 . (i) Show that the total cost is now $2040. Answer(b)(i) [2] (ii) Adam actually buys more than 20 hens, each costing $12. How many hens does he buy? Answer(b)(ii) … [2] (c) Adam makes $2920 from selling his hens’ eggs. For Examiner′s Use Calculate his percentage profi t on the $2040. Answer(c) … % [2] (d) Adam borrows $1500 for 3 years at a rate of 5.5% per year compound interest. Calculate the interest he will pay, correct to the nearest cent. Answer(d) $ … [3] _____________________________________________________________________________________

12 marks

Mark scheme: Qu. Part Answers Mark Part Marks 1 (a) 240 900 1,1 [Total] 1640 1FT 500 + their 2 costs (b) (i) 600 ÷ 5 × 17 M2 M1 for 600 ÷ 5 or 17 ÷ 5 (ii) 30 2 M1 for 2040 ÷ 17 × 3 Or 120 × 3, soi by 360 2920 − 2040 (c) 43.1 2 M1 for × 100 oe 2040 2920 or ( − )1 × 100 oe 2040 2920 or × 100 − 100 oe 2040 (d) 261.36 cao 3 M1 for 1500 × 1.0553 oe M1FT for their 1761.36 – 1500 If only 1 scored SC1 for correctly rounding to 2 decimal places from at least 3 decimal places SC2 if only 1761.36 seen

This question in 0580/33 Oct/Nov 2013

7 Today it is Simon’s birthday. (a) Simon is x years old. Katy is twice as old as Simon. Bob is 8 years younger than Simon. (i) Write expressions, in terms of x, for the ages of Katy and Bob. Answer(a)(i) Katy … Bob … [2] (ii) The sum of their three ages is 40 years. Write an equation in terms of x. Answer(a)(ii) … [1] (iii) Solve your equation for x. Answer(a)(iii) x = … [2] (b) Simon’s birthday cake weighs 600 grams. 1 He eats of the cake. 8 Katy eats 25% of the cake. Bob eats 0.3 of the cake. Find the weight of the cake that is left. Answer(b) … g [4] (c) Aunty Millie gives Simon $150 for his birthday. He invests the money in a bank at a rate of 6% per year compound interest. Calculate the total amount Simon will have after 3 years. Answer(c) $ … [3] (d) One of Simon’s presents is a bag of sweets. He decides to eat the sweets in a sequence. On day 1 he eats 1 sweet, on day 2 he eats 5 sweets, on day 3 he eats 9 sweets and so on. (i) Describe in words the rule for continuing the sequence 1, 5, 9, 13, 17 … . Answer(d)(i) … [1] (ii) Write down an expression for the number of sweets he eats on day n. Answer(d)(ii) … [2] __________________________________________________________________________________________

15 marks

Mark scheme: 7 (a) (i) 2x 1, 1 x – 8 (ii) x + 2x + x – 8 = 40 or better 1FT FT if algebraic (iii) 12 cao 2 M1 FT for ax = b and a and b not zero (b) 195 cao 4 B1 for 75 B1 for 150 B1 for 180 (c) 178.65 3 M2 for 150 × 1.063 oe or 178.7 or or 179 M1 for 150 × 1.06 × 1.06 (d) (i) Add 4 oe 1 (ii) 4n – 3 oe, final answer 2 M1 for 4n + k (k not -3), qn–3 (q not 0 or 4) seen

This question in 0580/33 May/June 2014

4 (a) A farmer has 45 horses and 20 cows. (i) Write this as a ratio horses : cows. Give your answer in its simplest form. … : … [1] (ii) The farmer wants the ratio horses : cows to equal 5 : 3. He keeps his 45 horses but buys some more cows. Work out the number of cows he must buy. … [2] (b) Three years ago the farmer invested $3750 at a rate of 4% per year compound interest. (i) Calculate the total value of his investment after the 3 years. $ … [3] (ii) The farmer wants to spend his investment on buying goats. Goats cost $126 each. Work out the maximum number of goats he can buy and how much money is left over. Number of goats … Amount of money left over $ … [4] (c) The farmer grows carrots. In 2014 the selling price for carrots was $96 per tonne. In 2015 this selling price increased by 18%. Work out the increase in the selling price from 2014 to 2015. $ … [1] (d) The farmer has 20 female sheep. Each sheep has 0, 1, 2 or 3 lambs. The table shows this information. Number Number of of lambs sheep 0 1 1 4 2 12 3 3 (i) Calculate the mean number of lambs per sheep. … [3] (ii) The farmer takes 1 lamb away from each of the sheep with 3 lambs. These lambs are given to 3 of the 4 sheep that have 1 lamb. Complete the table after the farmer has done this. Number Number of of lambs sheep 0 1 2 3 0 [2] (iii) Explain why the mean number of lambs per sheep does not change. … [1]

17 marks

Mark scheme: 4 (a) (i) 9 : 4 1 3 (ii) 7 2 M1 for 5× 45 or 45 : 3 × 9 (b) (i) 4218.24 cao 3 M2 for 3750 × 1.043 oe or M1 for 3750 × 1.042 oe If zero scored SC2 for 468.24 4218.24 (ii) 33 2FT M1FT for their 126 60.24 2FT M1FT for their 4218.24 – 126 × their 33 4218.24 or (their – their33)×126 126 (c) 17.28 1 (d) (i) 1.85 3 M1 for 0 × 1 + 1 × 4 + 2 × 12 + 3 × 3 their 37 M1dep for 20 (ii) 1 2 B1 for 1 answer correct and total number of 1 sheep = 20 18 or 18 [0] (iii) Same total number of sheep and 1 same total number of lambs oe

This question in 0580/32 Feb/March 2016

2 Jeff owns a clothes shop. (a) Shirt Tie Coat $24 $12.50 $46 A customer buys 3 shirts, 5 ties and 1 coat. Calculate the total cost. $ … [3] (b) A jacket has a price of $64. Jeff increases this price by 8%. Calculate the new price. $ … [2] (c) Jeff also increases the price of a dress from $250 to $280. Calculate the percentage increase in the price of the dress. … % [3] (d) The shop has a rectangular floor measuring 5.5 m by 8.5 m. The floor covering costs $12 per square metre. Calculate the cost of the floor covering. $ … [3] (e) Jeff invests $3600 for 3 years at a rate of 6% per year compound interest. Work out the value of the investment at the end of the 3 years. $ … [3]

14 marks

Mark scheme: 2(a) 180.5[0] 3 M2 for 3 × 24 + 5 × 12.50 + 46 oe or M1 for 3 × 24 or 5 × 12.50 or better, soi by 72 or 62.5 2(b) 69.12 2 M1 for 64 × 1.08 oe 2(c) 12 3 M2 for ( 280250 – 1) × 100 or 280250− 250 × 100 oe or M1 for 280250 – 1 or 280250 × 100 or 280250− 250 oe 2(d) 561 3 M1 for 5.5 × 8.5 soi by 46.75 M1 for their 46.75 × 12 2(e) 4287.66 3 M2 for 3600 × (1 + 1006 )3 oe or M1 for 3600 × (1 + 1006 )2 oe soi by 4044.96 If zero scored, SC2 for 687.6576, 687.658, 687.66, 687.65, 687.7, 688 or 690

This question in 0580/31 Oct/Nov 2017

4 Leo, Kim and Priya own a shop. (a) (i) Pens cost $1.45 each. Andre has a $10 note. Find the greatest number of pens that he can buy and how much change he receives. Number of pens = … Change = $ … [3] (ii) The price of a pack of printer paper is $5.60 . In a sale this price is reduced by 15%. Calculate the sale price. $ … [2] (b) Each day, Kim records the number of people who buy a pen. The results for 10 days are shown below. 40 7 19 25 18 19 32 57 12 47 Find the median. … [2] (c) The shop makes a profit of $7000. The profit is shared in the ratio Leo : Kim : Priya = 6 : 3 : 5. Calculate the amount they each receive. Leo = $ … Kim = $ … Priya = $ … [3] (d) Leo changed $1400 into pounds (£). The exchange rate was £1 = $1.54 . Work out how many pounds Leo received. £ … [2] (e) Priya invested $2000 for 3 years at a rate of 2.6% per year compound interest. Calculate the value of her investment at the end of the 3 years. $ … [3]

15 marks

Mark scheme: 4(a)(i) 6 pens and 1.3[0] 3 10 M1 for 1.45 M1 for k × 1.45 where k is an integer 4(a)(ii) 4.76 2 15 M1 for 5.60 × ( 1 − ) oe 100 4(b) 22 2 M1 for ordered list of first 6 or last 6 or B1 for 19 and 25 both identified 4(c) 3000 3 7000 M2 for × k or better, where k is 6 or 3 1500 6 + 3 + 5 2500 or 5 7000 or M1 for or better implied by 500 6 + 3 + 5 If no working M2 implied by one correct answer in correct place If zero scored, M1 for all correct answers in wrong order 4(d) 909.09 or 909.1[0] or 909.0 or 909 2 1400 M1 for 1.54 4(e) 2160.09 or 2160.1[0] or 2160.0 or 3 2.6 M2 for 2000 ( 1 + )3 oe 2160 100 2.6 or M1 for 2000 ( 1 + )2 soi by 2105.35 100

This question in 0580/32 Oct/Nov 2017

3 Three boys each have $600. (a) Victor spends 40% of his $600. He spends the money in the ratio clothes : books : music = 10 : 2 : 3. (i) Work out how much he spends on music. $ … [3] (ii) Work out how much more he spends on clothes than books. $ … [2] (b) Walter invests his $600 for 3 years at a rate of 4.5% per year compound interest. Calculate the interest Walter receives at the end of the 3 years. $ … [3] (c) Xavier goes on holiday to Europe and changes his $600 into euros (€). He spends €325 whilst he is on holiday. When he gets home he changes the euros he has left back into dollars. The exchange rate is $1 = €0.864 . Work out how many dollars he has left after his holiday. Give your answer correct to the nearest cent. $ … [3]

11 marks

Mark scheme: 3(a)(i) 48 3 B1 for 240 [ their 240 M1 for ][× 3] soi by 16 10 + 2 + 3 3(a)(ii) 128 2 k M1 for × their 240 oe where k = 2, 10 or 8 15 or for their (a)(i) ÷3 ×k oe where k = 2, 10 or 8 3(b) 84.7[0] or 84.69 to 84.7 3 3  4.5  M2 for 600 ×  1 +  oe  100   4.5  2 or M1 for 600 ×  1 +  oe  100  3(c) 223.84 3 600 × 0.864 − 325 M2 for oe or better 0.864 or 325 M1 for 600×0.864 or 0.864

This question in 0580/31 May/June 2018

3 (a) Maia shares $3000 between her three children. She gives the eldest child $1200, the second eldest child $1000 and the rest to the youngest child. Write this information as a ratio in its simplest form. … : … : … [2] eldest youngest (b) Yani’s house is for sale. She decides to reduce the selling price of $240 000 by 15%. Calculate the new selling price. $ … [2] (c) Hawa invests $750 at a rate of 3.5% per year compound interest. Calculate the value of his investment at the end of 3 years. $ … [3]

7 marks

Mark scheme: 3(a) 6 : 5 : 4 2 M1 for 1200 : 1000 : 800 or better 3(b) 204 000 2  15  M1 for 240000 ×  1 −  oe  100  3(c) 832 or 831.5 or 831.53 or 831.54 or 3 3  3.5  831.538… M2 for 750×  1 +  oe  100   3.5  2 or M1 for 750×  1 +  oe  100 

This question in 0580/32 Feb/March 2019

1 Here is part of the menu for Jamie’s café. Menu Price ($) Tea 2.35 Coffee 3.40 Lemonade 1.80 Cake 4.45 Biscuit 0.85 (a) Sue has one tea and one cake. Calculate how much she pays. $ … [1] (b) Derrick has one coffee and two biscuits. How much change does he receive from a $10 note? $ … [2] (c) Harriet works at the café for 34 hours each week. She is paid $8.25 for each hour. (i) Work out the amount she is paid each week. $ … [1] (ii) One week she works 8 hours extra. The extra hours are paid at 1.5 times her usual rate of $8.25 for each hour. Work out the total amount she is paid for that week. $ … [2] (d) Peter works these hours each week at the café. Day Time Monday 08 30 to 16 00 Tuesday 10 00 to 17 00 Thursday 08 30 to 16 30 Saturday 08 00 to 18 30 Work out the number of hours he works in one week. … hours [2] (e) Jamie buys a clock for the café from Japan for 9395 yen. The exchange rate is $1 = 110.27 yen. Work out the cost of the clock in dollars, correct to the nearest cent. $ … [3] (f) Jamie invests $12 000 at a rate of 5% per year compound interest. Calculate the value of his investment at the end of 3 years. $ … [3]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6.8[0] 1 1(b) 4.9[0] 2 M1 for 3.4[0] + 2 × [0].85 soi 1(c)(i) 280.5[0] 1 1(c)(ii) 379.5[0] 2 FT their (c)(i) + 99 M1 for 8 × 1.5 × 8.25 soi or (8 × 1.5 + 34) × 8.25 soi 1(d) 33 2 M1 for 7.5, 7, 8, 10.5 1(e) 85.20 cao 3 B2 for 85.1999… OR M1 for 9395 ÷ 110.27 B1 for their answer to at least 3 dp correctly rounded to 2 dp 1(f) 13 891.5[0] 3 M2 for 12 000 × (1 + 1005 )3 oe or M1 for 12 000 × (1 + 1005 )2 oe

This question in 0580/31 May/June 2019

2 (a) The bar chart shows the number of cars sold by a garage in each of six months. 16 14 12 10Number of cars sold 8 6 4 2 0 Jan Feb Mar Apr May Jun Jul Month (i) In July, 11 cars were sold. Complete the bar chart. [1] (ii) How many more cars were sold in March than in May? … [1] (b) These are the opening times of the garage. Monday to Friday 8.30 am to 5.30 pm Saturday 8.30 am to 1.00 pm Sunday Closed Work out how many hours the garage is open in one week. … h [2] (c) Mohammed works at the garage. He works for 36 hours from Monday to Friday and for 2 hours on Saturday. He is paid $10.50 per hour from Monday to Friday. On Saturday he is paid 1 12 times this rate. Calculate how much Mohammed is paid for this week. $ … [3] (d) Viktor is saving to buy a car. He invests $8000 for 5 years at a rate of 2.4% per year compound interest. Calculate the value of Viktor’s investment at the end of the 5 years. Give your answer correct to the nearest dollar. $ … [3] (e) At the garage, Pierre, Luigi and Freda sell cars. They share a bonus of $12 000 in the ratio Pierre : Luigi : Freda = 8 : 4 : 3. Calculate the amount they each receive. Pierre $ … Luigi $ … Freda $ … [3]

13 marks

Mark scheme: 2(a)(i) Bar at height 11 1 2(a)(ii) 9 1 2(b) 49.5 2 M1 for 5 × 9 + 4.5 oe 2(c) 409.5[0] cao 3 M2 for 36 × 10.5 + 10.5 × 1.5 × 2 oe or M1 for 36 × 10.5 or 10.5 × 1.5 × 2 or 36 + 1.5 × 2 oe 2(d) 9007 cao nfww 3 B2 for 9007.[...] 2.4 or M1 for 8000 × (1 + )5 oe 100 If M0 or M1 scored, SC1 for their decimal answer correctly rounded to the nearest dollar 2(e) 6400 3 B2 for one correct answer in the correct 3200 place 2400 or M1 for 12 000 ÷ (8+4+3) [× k] where k is 8, 4, 3 or 1

This question in 0580/33 Oct/Nov 2021

17 Rick invests $6000 for 5 years at a rate of 9% per year compound interest. Calculate the total interest earned during the 5 years. $ … [3]

3 marks

Mark scheme: 17 3 230 or 3231 or 3232 or 3231.7… 3 B2 for 9230 or 9231 or 9232 or 9231.7… OR  9 5 M2 for 6000  1 + − 6000 oe    100   9 5 or M1 for 6000  1 + oe    100 

This question in 0580/32 May/June 2025