Ratio and proportion — Paper 3 · IGCSE Mathematics (9-1) 0980

4 The scale drawing shows town A, town B and town C on a map. There is a straight road between town A and town B. The scale of the map is 1 centimetre represents 8 kilometres. North A North C North B Scale: 1 cm to 8 km (a) Measure the bearing of town A from town B. … [1] (b) Work out the actual distance, in kilometres, between town A and town B. … km [2] (c) Write the scale of the map in the form 1 : n. 1 : … [1] (d) A straight road from town C is on a bearing of 246°. It meets the road from town A to town B at point X. On the map, draw the road from town C to point X. Label the position of X. [1] (e) (i) Josie is at point X at 10 50. She arrives at town B 37 minutes later. Work out the time that she arrives at town B. … [1] (ii) Sammy leaves town A and travels to town B at a constant speed of 75 km/h. (a) Work out the time for this journey. Give your answer in hours and minutes, correct to the nearest minute. … h … min [3] (b) Sammy wants to arrive at town B at the same time as Josie. Work out the time that Sammy must leave town A. … [1]

10 marks

Mark scheme: 4(a) 322 1 4(b) 96 2 B1 for [AB =] 12 cm 4(c) 800 000 1 4(d) Ruled line CX drawn on map 1 4(e)(i) 11 27 1 4(e)(ii)(a) 1[h] 17 [min] 3 FT their(b) their (b) M2 for × 60 oe 75 their(b) or M1 for 75 4(e)(ii)(b) 10 10 1 FT their (e)(i) and their (e)(ii)(a)

This question in 0980/32 May/June 2019

9 Zach goes on holiday. (a) The mass, m kilograms, of his suitcase is 23.5 kg, correct to the nearest 500 g. Complete this statement about the value of m. … G m 1 … [2] (b) The ratio of the costs flights : hotels = 3 : 8. The cost of the flights is $861. Work out the total cost of flights and hotels. $ … [2] (c) $1 = 0.88 euros £1 = 1.15 euros Zach changes $575 into euros. He spends 45% of the euros in France. He changes the euros he does not use into pounds (£) to spend in England. Work out how many pounds he receives. £ … [4]

8 marks

Mark scheme: 9(a) 23.25 23.75 2 B1 for each If 0 scored, SC1 for both correct and in reverse order 9(b) 3157 2 861 oe M1 for ×  ( 3 + 8 ) or × 8  3 9(c) 242 4 M1 for changing to euros M1FT for 45% or 55% calculated M1FT for changing to pounds or M1 for 45% or 55% calculated M1FT for changing to euros M1FT for changing to pounds

This question in 0980/32 May/June 2019

4 Alexa, Ben and Chloe own a restaurant. (a) Alexa records some temperatures. Fridge 4 °C Cool box -3 °C Freezer -19 °C (i) Find the difference in temperature between the fridge and the cool box. … °C [1] (ii) Find the difference in temperature between the cool box and the freezer. … °C [1] (iii) The temperature in the cold room is 5 °C lower than the fridge. Find the temperature in the cold room. … °C [1] (b) Alexa, Ben and Chloe share the profits from their restaurant in the ratio 2 : 6 : 7. One year the restaurant makes a profit of $60 000. Work out how much each receives. Alexa = $ … Ben = $ … Chloe = $ … [3] (c) They invest $12 000 at a rate of n% per year simple interest. At the end of 3 years the value of the investment is $12 900. Find the value of n. n = … [3]

9 marks

Mark scheme: 4(a)(i) 7 1 4(a)(ii) 16 1 4(a)(iii) −1 1 4(b) 8000 3 B2 for one correct 24 000 60000 or M2 for × k 28 000 2 + 6 + 7 60000 or M1 for 2 + 6 + 7 4(c) 2.5 3 12900 − 12000 M1 for 3 their 300 M1dep for [× 100] 12000

This question in 0980/32 May/June 2020

1 Sean is the manager of a museum. (a) He buys a Chinese pot costing 1200 yuan. The exchange rate is $1 = 6.4 yuan. Work out the cost of this pot in dollars. $ … [1] (b) Sean records the maximum and minimum temperatures, in °C, at the museum. Some of the results for one week are shown in the table. Day Mon Tue Wed Thu Fri Sat Sun Maximum 8 12 15 14 11 7 4 temperature (°C) Minimum - 5 - 2 - 4 - 1 3 temperature (°C) (i) Find the difference between the maximum temperature and the minimum temperature on Wednesday. … °C [1] (ii) The minimum temperature on Saturday was 2 °C higher than the minimum temperature on Monday. Find the minimum temperature on Saturday. … °C [1] (iii) In this week the range of temperatures was 23 °C. Find the minimum temperature on Sunday. … °C [1] (c) These are the opening times for the museum. Monday to Friday 09 00 to 17 00 Saturday and Sunday 10 00 to 16 00 During opening hours the museum has 4 security guards working. Each guard works a maximum of 30 hours each week. Work out the smallest number of guards needed each week. … [4] (d) The entry price to the museum is $18. This price is increased by 28%. Find the increased entry price. $ … [2]

10 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 187.5[0] 1 1(b)(i) 19 1 1(b)(ii) −3 1 1(b)(iii) −8 1 1(c) 7 nfww 4 M1 for 8 × 5 + 6 × 2 oe and M2 for their 52 × 4 ÷ 30 oe or M1 for their 52 × 4 oe or their 52 ÷ 30 oe 1(d) 23.04 2 28 M1 for 18 × (1 + ) oe 100 or B1 for 5.04

This question in 0980/31 Oct/Nov 2020

1 Alex is building a house. The materials cost 1 12 times the cost of the land. The wages cost 1 14 times the cost of the land. (a) Show that the ratio of costs, in its simplest form, is land : materials : wages = 4 : 6 : 5. [2] (b) The wages cost $47 500. Show that the total cost of land, materials and wages is $142 500. [2] (c) Work out the cost of (i) the land, $ … [2] (ii) the materials. $ … [1] (d) Alex borrows $28 000 for 6 years at a rate of 5.5% per year compound interest. Calculate the amount he repays at the end of the 6 years. Give your answer correct to the nearest dollar. $ … [3] (e) When Alex sells the house, he makes a profit of 27% on the $142 500. Calculate the selling price of the house. $ … [2]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1 1 B1 1 : 1.5 : 1.25 or 1 : 1 :1 2 4 Working shown leading to 4 : 6 : 5 M1 1(b) 47 500 ÷ 5 × (4 + 6 + 5) M2 M1 for 47 500 ÷ 5 1(c)(i) 38 000 2 M1 for 142 500 ÷ 15 [× 4] or 47 500 ÷ 5 [× 4] oe soi 1(c)(ii) 57 000 1 FT for 95 000 – their (c)(i) 1(d) 38 608 cao 3 6  5.5  M1 for 28 000 ×  1 +  oe  100  A1 for 38 607.5… or 38 607.6 or 38 607 or 38 610 or 38 600 B1 for their correctly rounded answer 1(e) 180 975 2  27  M1 for 142 500 ×  1 +  oe  100  or B1 for 38 475

This question in 0980/32 May/June 2021

3 (a) 50 Australian dollars = 540 South African rands 600 550 500 450 400 350 South African 300 rand 250 200 150 100 50 0 0 5 10 15 20 25 30 35 40 45 50 Australian dollar (i) On the grid, draw a conversion graph between Australian dollars and South African rands. [2] (ii) A watch costs 1350 South African rands. Find the cost of this watch in Australian dollars. … Australian dollars [2] (b) (i) A plane leaves Sydney at 21 48 local time to fly to Johannesburg. The flight takes 14 hours 15 minutes. The local time in Sydney is 8 hours ahead of the local time in Johannesburg. Find the local time in Johannesburg when the plane arrives. … [3] (ii) On the plane there are 315 people. The ratio of children : adults = 7 : 8. Work out the number of adults on the plane. … [2] (iii) Another plane has 420 seats. 90% of the seats are occupied. Work out the number of seats that are occupied. … [2]

11 marks

Mark scheme: 3(a)(i) Ruled line joining (0, 0) to 2 B1 for plotting point (50, 540) or for a ruled (50, 540) line from (0, 0) to their point (50, 520 – 560) 3(a)(ii) 125 or 123 to 127 2 B1 for 108 to 135 as answer 50 or M1 for 1350  oe 540 or for a valid method e.g. look up ‘50’ × 27 3(b)(i) 04 03 3 B2 for 28 03 or B1 for 36 03 or 12 03[pm] or 6h 15(m) or 13 48 or 1 48pm or 20 03 or 8 03pm seen or M1 for their arrival time – 8 hours 3(b)(ii) 168 2 315 M1 for × k where k = 1,7 or 8 oe 7  8 3(b)(iii) 378 2 90 M1 for 420 × oe 100

This question in 0980/32 May/June 2023

9 (a) Pure gold costs $42 per gram. The fraction of pure gold in an object is measured in carats. 1 One carat means of the mass of an object is pure gold. 24 Henry buys a 9-carat gold bracelet weighing 16 g. The price of the bracelet is $204. Is the price of the bracelet more or less than the cost of the pure gold in it? You must show your working. [4] (b) A clock made of metals has a mass of 1080 g. The mass of each metal in the clock is in the ratio copper : zinc : other metals = 21 : 14 : 1. Calculate the mass of copper in this clock. … g [2] (c) There are 110 people in a group. G = { people who own gold jewellery } S = { people who own silver jewellery } 18 people own both gold jewellery and silver jewellery. 46 people own gold jewellery. 11 people own no gold jewellery and no silver jewellery. G S (i) Complete the Venn diagram. [2] (ii) Write down n ( G + S ) . … [1] (iii) One of the 110 people is chosen at random. Write down the probability that this person owns gold jewellery but not silver jewellery. … [1] (d) E F Use set notation to describe the shaded region. … [1]

11 marks

Mark scheme: 9(a) Less 4 1 M3 for  9  16  42 oe with working leading to 252 24 or M2 for three of these multiplied or M1 for any two of these multiplied 9(b) 630 2 1080 M1 for [ k] oe 21 + 14 + 1 where k =1,14 or 21 oe 9(c)(i) 2 B1 for two or three in the correct places 9(c)(ii) 18 1 FT their diagram 9(c)(iii) 28 1 FT their 28 from their diagram oe 110 9(d) E F cao 1

This question in 0980/31 Oct/Nov 2023

7 The area of some land is in the ratio park : gardens : playground = 11 : 2 : 3. The park has an area of 4620 m 2. (a) Work out the area of the gardens and the area of the playground. Gardens … m2 Playground … m2 [3] (b) The park area of 4620 m 2 is made up of paths and grassland. 18% of the park area is paths. (i) Show that the grassland area is 3788.4 m 2. [1] (ii) Seed for the grassland is sold in bags. The seed in one bag covers an area of 280 m 2. The bags cost $72 each for the first 5 bags and then $58 each for any extra bags. Calculate the cost of the seed needed to cover the grassland. $ … [4] (c) The owners of the land buy new equipment for the playground. They borrow $8500 for 4 years at a rate of 6.5% per year compound interest. Calculate the amount they repay at the end of the 4 years. Give your answer correct to the nearest dollar. $ … [3] (d) The café in the park sells water in bottles A, B and C. NOT TO SCALE Bottle A Bottle B Bottle C 330 ml 500 ml 750 ml $1.98 $3.20 $5.10 Work out which bottle is the best value. You must show all your working. Bottle … [3]

14 marks

Mark scheme: 7(a) 840 3 B2 for 1 correct answer in correct place 1260 or answers reversed or M1 for 4620 ÷ 11 × k (k = 1, 2, or 3) 7(b)(i) (100  18) M1 18  4620 accept 4620 –  4620 100 100 18 or 4620 ( 1 – ) 100 7(b)(ii) [$]882 4 B3 for 854.74, 853, 824 OR M3 for 5 × 72 + (their 14 – 5) × 58 oe or B2 for 14 [bags] or M1 for 3788.4 ÷ 280 OR M3 for 5 × 72 + (their 9 ) × 58 oe or B2 for 9 [bags] or M1 for (3788.4 – 5  280) ÷ 280 oe OR if 0 scored SC2 for 1056 or SC1 for 1027 or 998 7(c) [$]10935 cao 3 4  6.5  M1 for 8500 × 1  oe    100  A1 for 10934.96…… If A0 scored SC1 for their answer correct to at least 1 decimal place correctly rounded to nearest whole number. 7(d) A 3 With correct comparisons made of the 3 M2 for 3 correct comparable values bottles with suitable accuracy shown or for a correct method to compare 3 bottles shown but not evaluated to enough accuracy. or M1 for 2 correct comparable values or for a correct method to compare 3 bottles but incorrect or not evaluated.

This question in 0980/32 May/June 2024

5 (a) The scatter diagram shows the distance travelled and the cost for each of 12 taxi journeys. 25 20 15 Cost ($) 10 5 0 0 2 4 6 8 10 Distance (km) (i) ‘The scatter diagram shows positive correlation.’ Is this statement true or false? Give a reason for your answer. … because … … [1] (ii) On one journey, the cost per kilometre travelled was much more expensive than on all of the other journeys. Draw a ring around this point on the scatter diagram. [1] (iii) Draw a line of best fit on the scatter diagram. [1] (iv) Another journey is 8 km long. Use your line of best fit to find an estimate for the cost of this journey. $ … [1] (b) Arit, Luke and Marie share the cost of a taxi journey. The cost is $26.40 . (i) Calculate how much Arit pays if they share the cost equally. $ … [1] (ii) They decide to share the cost in proportion to the distance they each travel in the taxi. Arit travels 12 km, Luke travels 3 km and Marie travels 7.5 km. (a) Write the ratio 12 : 3 : 7.5 in its simplest form. … : … : … [2] (b) Calculate how much more Arit pays than if they share the cost equally. $ … [3] (c) Jin invests some money from his taxi company. He invests $18 600 at a rate of 1.7% per year compound interest. Calculate the value of the investment at the end of 6 years. Give your answer correct to the nearest dollar. $ … [3]

13 marks

Mark scheme: 5(a)(i) True and correct description of 1 correlation e.g. as the distance increases the cost increases 5(a)(ii) (1, 15) circled 1 5(a)(iii) Acceptable ruled line of best fit drawn 1 5(a)(iv) 16 to 19 1 If 0 scored, FT their straight line of best fit with positive gradient 5(b)(i) 8.8[0] 1 5(b)(ii)(a) 8 : 2 : 5 2 M1 for any correct equivalent ratio 5(b)(ii)(b) 5.28 3 B2 for 14.08 26.40 or M1 for  m 12 + 3 + 7.5 where m = 1, 3 ,7.5 or 12 or M1FT for 26.40  k (their 8 + their 2 + their 5) where k = 1 or their 8 or their 2 or their 5 oe 5(c) 20 580 cao 3 B2 for answer 20 579.68[…] or 20 579.7[0] or 20 600[.00]  1.7  6 or M1 for 18600 1 + oe    100  B1 for their answer correctly rounded

This question in 0980/31 Oct/Nov 2024

6 (a) This is a recipe to make ice cream for 6 people. 270 ml cream 270 ml milk 100 g sugar 4 egg yolks Tom makes ice cream for 10 people. (i) Work out how much milk he uses. … ml [2] (ii) The mass of all the ingredients Tom uses is 1100 g. After Tom heats the mixture, this mass reduces by 15%. Find the mass of the mixture after heating. … g [2] (iii) Tom lets the mixture cool to 5°C. He then puts it into a freezer to cool to -18°C. Find the difference in these temperatures. … °C [1] (b) (i) In a factory, a machine fills 25 920 tubs of ice cream in 8 hours. Work out the number of tubs the machine fills in 1 minute. … [1] (ii) A pack of ice cream contains 6 tubs. There are 120 packs on a tray. There are 24 trays on a truck. Work out how many tubs of ice cream are on the truck. … [1] (c) Mario sells ice creams in five flavours. The table shows the relative frequency of some of the ice cream flavours Mario sells. Vanilla Chocolate Strawberry Coconut Banana Relative 0.34 0.18 0.12 frequency Mario sells three times as many chocolate ice creams as banana ice creams. (i) Complete the table. [3] (ii) One week Mario sells 450 ice creams. Find how many strawberry ice creams Mario expects to sell. … [1] (iii) The probability that any customer is an adult is 0.7 . First customer Second customer Adult 0.7 Adult 0.7 … Child Adult 0.7 … Child … Child (a) Complete the tree diagram. [1] (b) Find the probability that the first two customers are adults. … [2]

14 marks

Mark scheme: 6(a)(i) 450 2 M1 for 270[10] oe 6 6(a)(ii) 935 2  15  M1 for 1100 ×  1 −  oe  100  or B1 for 165 6(a)(iii) 23 1 6(b)(i) 54 1 6(b)(ii) 17 280 1 6(c)(i) 0.27 oe 3 B2 for either 0.27 oe or 0.09 oe in any 0.09 oe position in the table or M1 for 1 – ( 0.34 + 0.18 + 0.12) oe or better 6(c)(ii) 81 1 6(c)(iii)(a) Correct complete tree diagram: 1 0.3 0.3 0.3 6(c)(iii)(b) [0].49 oe 2 M1 for [0].7 × [0].7 oe

This question in 0980/31 Oct/Nov 2024

10 Anna and Bruno share some money in the ratio Anna : Bruno = 3 : 7. Bruno receives $36 more than Anna. Calculate the total amount of money they share. $ … [2]

2 marks

Mark scheme: 10 90 2 36 M1 for [ × k , where k = 1, 3, 7 or 10] oe 4

This question in 0980/31 Oct/Nov 2025