Ratio and proportion — Paper 4 · IGCSE Mathematics 0580

1 The Smith family paid $5635 for a holiday in India. The total cost was divided in the ratio travel : accommodation : entertainment = 10 : 17 : 8. (a) Calculate the percentage of the total cost spent on entertainment. … % [2] (b) Show that the amount spent on accommodation was $2737. [2] (c) The $5635 was the total amount Mr Smith received from an investment he made 5 years ago. Compound interest at a rate of 2.42% per year was paid on this investment. Calculate the amount he invested 5 years ago. $ … [3] (d) Mr Smith, his wife and their three children visit a theme park. The tickets cost 2500 Rupees for an adult and 1650 Rupees for a child. Calculate the total cost of the tickets. … Rupees [2] (e) One day the youngest child spent 130 Rupees on sweets. On this day the exchange rate was 1 Rupee = $0.0152 . Calculate the value of the sweets in dollars, correct to the nearest cent. $ … [2]

11 marks

This question in 0580/42 Feb/March 2017

1 (a) Annie and Dermot share $600 in the ratio 11 : 9. (i) Show that Annie receives $330. [1] (ii) Find the amount that Dermot receives. $ … [1] (b) (i) Annie invests $330 at a rate of 1.5% per year compound interest. Calculate the amount that Annie has after 8 years. Give your answer correct to the nearest dollar. $ … [3] (ii) Find the amount of interest that Annie has, after the 8 years, as a percentage of the $330. … % [2] (c) Dermot has $70 to spend. He spends $24.75 on a shirt. (i) Find $24.75 as a fraction of $70. Give your answer in its lowest terms. … [1] (ii) The $24.75 is the sale price after reducing the original price by 10%. Calculate the original price. $ … [3] (d) After one year, the value of Annie’s car had reduced by 20%. At the end of the second year, the value of Annie’s car had reduced by a further 15% of its value at the end of the first year. (i) Calculate the overall percentage reduction after the two years. … % [2] (ii) After three years the overall percentage reduction in the value of Annie’s car is 40.84%. Calculate the percentage reduction in the third year. … % [2]

15 marks

Mark scheme: Question Answer Marks Part marks 1(a)(i) 600 ÷ (11+ 9) × 11 [ =330] M1 Could be in separate steps with no errors seen 1(a)(ii) 270 1 1(b)(i) 372 cao nfww 3 B2 for answer 371.7…  1.5  8 or M1 for 330 × 1 + oe not spoiled    100  After zero scored, SC1 for answer 42 or 41.7… 1(b)(ii) 12.6 or 12.7 or 12.63 to 12.73 2 their (b)(i) − 330 their (b)(i) M1 for or × 100 soi by 112.7 330 330 or 113 After zero scored, SC1 for answer 12% 1(c)(i) 99 1 cao final answer 280 1(c)(ii) 27.5[0] 3 100 − 10 M2 for 24.75 ÷ oe 100 or M1 for recognising 24.75 as 90[%] oe 1(d)(i) 32 cao 2  20  15  M1 for  1 −  1 −  [x]oe  100  100  or for 0.15 × 0.8 [x] oe 1(d)(ii) 13 cao 2  20  15  M1 for  1 −  1 −  × x = 40.84 – 32 oe seen  100  100    their (d)(i)   or for their (d)(i) +  1 −    x = 40.84 oe   100  

This question in 0580/42 May/June 2017

1 (a) A library has a total of 10 494 fiction and non-fiction books. The ratio fiction books : non-fiction books = 13 : 5. Find the number of non-fiction books the library has. … [2] (b) The library has DVDs on crime, adventure and science fiction. The ratio crime : adventure : science fiction = 11 : 6 : 10. The library has 384 more science fiction DVDs than adventure DVDs. Calculate the number of crime DVDs the library has. … [2] (c) Every Monday, Sima travels by car to the library. The distance is 20 km and the journey takes 23 minutes. (i) Calculate the average speed for the journey in kilometres per hour. … km/h [2] (ii) One Monday, she is delayed and her average speed is reduced to 32 km/h. Calculate the percentage increase in the journey time. … % [5] (d) In Spain, the price of a book is 11.99 euros. In the USA, the price of the same book is $12.99 . The exchange rate is $1 = 0.9276 euros. Calculate the difference between these prices. Give your answer in dollars, correct to the nearest cent. $ … [3] (e) 7605 books were borrowed from the library in 2016. This was 22% less than in 2015. Calculate the number of books borrowed in 2015. … [3]

17 marks

Mark scheme: Question Answer Marks Partial marks 1(a) 2915 2 M1 for 10 494 ÷ (13 + 5) oe 1(b) 1056 2 M1 for 384 ÷ (10 – 6) oe 1(c)(i) 2 M1 for 20 ÷ 23 or 20 × 60 or 23 ÷ 60 isw 52.2 or 52.17… If zero scored, SC1 for answer 52.6 (from use of 0.38) 1(c)(ii) 63[.0] or 63.03 to 63.05… 5 their 52.17... − 32 M4 for × 100 oe 32 their 52.17... − 32 or M3 for oe or 32 their 52.17... × 100 oe 32 OR 5 B2 for [hours] oe or 37.5 [minutes] 8 or M1 for 20 ÷ 32 or better and their 37.5 − 23 M2 for × 100 oe 23 their 37.5 − 23 their 37.5 or M1 for or ×100 23 23 1(d) 0.06 final answer nfww 3 M1 for 11.99 ÷ 0.9276 or 12.99 × 0.9276 A1 for 12.93 or 12.925 to 12.926 1(e) 9750 3  22  M2 for 7605 ÷  1 −  oe  100  or M1 for (100 – 22)[%] correctly associated with 7605 seen

This question in 0580/41 Oct/Nov 2017

1 Adele, Barbara and Collette share $680 in the ratio 9 : 7 : 4. (a) Show that Adele receives $306. [1] (b) Calculate the amount that Barbara and Collette each receives. Barbara $ … Collette $ … [3] (c) Adele changes her $306 into euros (€) when the exchange rate is €1 = $1.125 . Calculate the number of euros she receives. € … [2] (d) Barbara spends a total of $17.56 on 5 kg of apples and 3 kg of bananas. Apples cost $2.69 per kilogram. Calculate the cost per kilogram of bananas. $ … [3] 1 (e) Collette spends half of her share on clothes and of her share on books. 5 Calculate the amount she has left. $ … [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 9 1 × 680 9 + 7 + 4 1(b) 238 136 3 B2 for 238 or 136 7 or M1 for × 680 oe or 9 + 7 + 4 4 × 680 oe seen 9 + 7 + 4 1(c) 272 2 M1 for 306 ÷ 1.125 1(d) 1.37 3 M2 for (17.56 −×5 2.69 ) ÷ 3 or M1 for 17.56 − 5 × 2.69 or B1 for 13.45 [cost of apples] 1(e) 40.8[0] 3 3FT for 0.3 × their 136 from part (b) 1 1 or M2 for their 136( + ) or better 2 5 1 1 or M1 for their 136 × or their 136 × 2 5 3 or B1 for 68 or 27.2 or or 0.3 seen 10

This question in 0580/41 May/June 2018

1 (a) Here is a list of ingredients to make 20 biscuits. 260 g of butter 500 g of sugar 650 g of flour 425 g of rice (i) Find the mass of rice as a percentage of the mass of sugar. … % [1] (ii) Find the mass of butter needed to make 35 of these biscuits. … g [2] (iii) Michel has 2 kg of each ingredient. Work out the greatest number of these biscuits that he can make. … [3] (b) A company makes these biscuits at a cost of $1.35 per packet. These biscuits are sold for $1.89 per packet. (i) Calculate the percentage profit the company makes on each packet. … % [3] (ii) The selling price of $1.89 has increased by 8% from last year. Calculate the selling price last year. $ … [3] (c) Over a period of 3 years, the company’s sales of biscuits increased from 15.6 million packets to 20.8 million packets. The sales increased exponentially by the same percentage each year. Calculate the percentage increase each year. … % [3] (d) The people who work for the company are in the following age groups. Group A Group B Group C Under 30 years 30 to 50 years Over 50 years The ratio of the number in group A to the number in group B is 7 : 10. The ratio of the number in group B to the number in group C is 4 : 3. (i) Find the ratio of the number in group A to the number in group C. Give your answer in its simplest form. … : … [3] (ii) There are 45 people in group C. Find the total number of people who work for the company. … [3]

21 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 85 1 1(a)(ii) 455 2 M1 for 260 ÷ 20 × 35 oe 1(a)(iii) 61 3 B2 for 61.5… seen or M1 for 2000 ÷ 650 soi x 20 or for = oe or other attempt at 2000 650 scaling up with 650 or for 650 ÷ 20 oe 1(b)(i) 40 3 1.89 − 1.35 M2 for [× 100] oe 1.35 1.89 or × 100 oe 1.35 or M1 for oe 1.89[× 100] soi 1.35 1(b)(ii) 1.75 nfww 3  100 + 8  M2 for 1.89 ÷   or better  100  or M1 for 1.89 associated with 108 [%] 1(c) 10.1 or 10.06… 3 20.8 M2 for 3 oe 15.6 or M1 for 15.6 × k 3 = 20.8 oe 1(d)(i) 14:15 3 B2 for correct unsimplified 3 term ratio A: B: C or correct unsimplified two term ratio A : C or M1 for attempt to find common multiple of 4 and 10 or other common value for B 4 10 or for 7 × oe or 3 × oe 10 4 1(d)(ii) 147 3 45 M2 for (14 + 20 [ +15] ) oe or 15 45 ÷ 3 × 4 + (45 ÷ 3 × 4) ÷ 10 × 7 [+ 45] or M1 for 45 ÷ 3 oe or 45 ÷ their (d)(i) value for C shown

This question in 0580/42 May/June 2018

1 Marianne sells photos. (a) The selling price of each photo is $6. (i) The selling price for each photo is made up of two parts, printing cost and profit. For each photo, the ratio printing cost : profit = 5 : 3. Calculate the profit she makes on each photo. $ … [2] (ii) Calculate her profit as a percentage of the selling price. … % [1] (iii) Calculate the selling price of a photo in euros (€) when the exchange rate is €1 = $1.091 . € … [2] (b) Marianne sells two sizes of photo. These photos are mathematically similar rectangles. The smaller photo has length 15 cm and width 12 cm. The larger photo has area 352.8 cm2. Calculate the length of the larger photo. … cm [3] (c) In a sale, Marianne buys a new camera for $483. This is a reduction of 8% on the original price. Calculate the original price of the camera. $ … [3]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 2.25 final answer 2 3 6 M1 for or oe 5 + 3 5 + 3 1(a)(ii) 37.5 1 (a)(i) FT their × 100 6 1(a)(iii) 5.5[0] or 5.499 to 5.500 2 M1 for 6 ÷ .1091 1(b) 21 3 3528. M2 for 15 × oe 15 × 12 or SC2 for answer 16.8 352 8. 15× 12 or M1 for or seen 15 × 12 352 8. or M1 for a correct implicit statement for the length 1(c) 525 3 483 M2 for [× 100] oe 100 − 8 or M1 for 483 associated with 92 [%]

This question in 0580/41 Oct/Nov 2018

2 (a) A school has 240 students. The ratio girls : boys = 25 : 23. (i) Show that the number of boys is 115. [1] (ii) One day, there are 15 girls absent and 15 boys absent. Find the ratio girls : boys in school on this day. Give your answer in its simplest form. … : … [2] (iii) Next year, the number of students will increase by 15%. Calculate the number of students next year. … [2] (iv) Since the school was opened, the number of students has increased by 60%. There are now 240 students. Calculate the number of students when the school was opened. … [3] (b) The population of a city is increasing exponentially at a rate of 2% each year. The population now is 256 000. Calculate the population after 30 years. Give your answer correct to the nearest thousand. … [3] (c) A bacteria population increases exponentially at a rate of r% each day. After 32 days, the population has increased by 309%. Find the value of r. r = … [3]

14 marks

Mark scheme: 2(a)(i) 240 M1 × 23 (23 + 25) 2(a)(ii) 11 : 10 2 M1 for 110 : 100 or better or SC1 for 10 : 11, following boys 100, girls 110 2(a)(iii) 276 2  15  M1 for 240 ×  1 +  oe  100  or B1 for 36 seen 2(a)(iv) 150 3 240 M2 for [× 100] oe 100 + 60 or M1 for evidence of 160[%] associated 240 2(b) 464 000 3 30  2  M1 for 256 000 ×  1 +  oe  100  A1 for 463 700 to 463 710 B1 for their more accurate answer seen and rounded to nearest 1000 2(c) 4.5[0] 3 M2 for [x =] 32 .409 oe 32 = .409 oe or M1 for ( x ) If 0 scored, SC2 for answer 3.6 or 3.59 or 3.588… or SC1 for 32 3.09 or 1.0358 to 1.036 seen

This question in 0580/43 Oct/Nov 2018

1 Amol and Priya deliver 645 parcels in the ratio Amol : Priya = 11 : 4. (a) Calculate the number of parcels Amol delivers. … [2] (b) Amol drives his truck at an average speed of 50 km/h. He leaves at 07 00 and arrives at 11 15. Calculate the distance he drives. … km [2] (c) Priya drives her van a distance of 54 km. She leaves at 10 55 and arrives at 12 38. Calculate her average speed. … km/h [3] (d) Priya has 50 identical parcels. Each parcel has a mass of 17 kg, correct to the nearest kilogram. Find the upper bound for the total mass of the 50 parcels. … kg [1] (e) 67 of the 645 parcels are damaged on the journey. Calculate the percentage of parcels that are damaged. … % [1] (f) (i) 29 parcels each have a value of $68. By writing each of these numbers correct to 1 significant figure, find an estimate for the total value of these 29 parcels. $ … [1] (ii) Without doing any calculation, complete this statement. The actual total value of these 29 parcels is less than the answer to part (f)(i) because … [1]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 473 2 M1 for 645 ÷ (11 + 4) 1(b) 212.5 2 M1 for 50 × 4.25 1(c) 31.5 or 31.45 to 31.46 3 43 M2 for 54 ÷ 160 oe or M1 for time =1h 43min or 103 [mins] or 54 ÷ their time 1(d) 875 1 1(e) 10.4 or 10.38 to 10.39 1 1(f)(i) 30 [×] 70 and 2100 1 1(f)(ii) both numbers rounded up oe 1

This question in 0580/42 Feb/March 2019

4 The diagram shows an incomplete scale drawing of a market place, ABCD, where D is on CX. The scale is 1 centimetre represents 5 metres. X C A B Scale : 1 cm to 5 m D lies on CX such that angle DAB = 75°. (a) On the diagram, draw the line AD and mark the position of D. [2] (b) Find the actual length of the side BC of the market place. … m [2] (c) In this part, use a ruler and compasses only. Street sellers are allowed in the part of the market place that is • more than 35 metres from A and • nearer to C than to B and • nearer to CD than to BC. On the diagram, construct and shade the region where street sellers are allowed. [7] (d) Write the scale of the drawing in the form 1 : n. 1 : … [1]

12 marks

Mark scheme: 4(a) Correct ruled line with D marked 2 B1 for correct ruled line or short line 4(b) 47.5 2 B1 for 9.5 or 95 mm seen or for answer figs 465 to figs 485 4(c) Correct arc radius 7 cm 2 B1 for complete arc other radius, centre A or correct but short arc Correct ruled perpendicular bisector of 2 B1 for correct perpendicular bisector BC with correct pairs of arcs without correct arcs or for correct arcs, no/incorrect line Correct ruled bisector of angle BCD with 2 B1 for correct angle bisector without correct pairs of arcs correct arcs or for correct arcs, no/incorrect line correct region shaded 1 Dep on at least B1B1B1 and five boundaries one of which is an arc 4(d) [1 :] 500 1

This question in 0580/42 Feb/March 2019

2 (a) Ali and Mo share a sum of money in the ratio Ali : Mo = 9 : 7. Ali receives $600 more than Mo. Calculate how much each receives. Ali $ … Mo $ … [3] (b) In a sale, Ali buys a television for $195.80 . The original price was $220. Calculate the percentage reduction on the original price. … % [3] (c) In the sale, Mo buys a jacket for $63. The original price was reduced by 25%. Calculate the original price of the jacket. $ … [3]

9 marks

Mark scheme: 2(a) [Ali] 2700 3 B2 for one correct or for correct values [Mo] 2100 reversed or M1 for 600 ÷ (9 – 7) or for any equation that would lead to an answer of 300, 2700 or 2100, or 4800 (for the total) 2(b) 11 3 220 − 1958. M2 for [× 100] or for 220 1958. [100 − ] × 100 220 195 8. or M1 for 220 – 195.8 or for or a 220 correct implicit equation for percentage 195.8 − 220 reduction or for 220 2(c) 84 3 63 M2 for oe 25 1 − 100 or M1 for associating 63 with (100 – 25)% or a correct implicit equation for the original price.

This question in 0580/41 Oct/Nov 2019

1 (a) Mohsin has 600 pear trees and 720 apple trees on his farm. (i) Write the ratio pear trees : apple trees in its simplest form. … : … [1] (ii) Each apple tree produces 16 boxes of apples each year. One box contains 18 kg of apples. Calculate the total mass of apples produced by the 720 trees in one year. Give your answer in standard form. … kg [3] (b) (i) One week, the total mass of pears picked was 18 540 kg. For this week, the ratio mass of apples : mass of pears = 13 : 9. Find the mass of apples picked that week. … kg [2] (ii) The apples cost Mohsin $0.85 per kilogram to produce. He sells them at a profit of 60%. Work out the selling price per kilogram of the apples. $ … [2] (c) Mohsin exports some of his pears to a shop in Belgium. The shop buys the pears at $1.50 per kilogram. The shop sells the pears for 2.30 euros per kilogram. The exchange rate is $1 = 0.92 euros. Calculate the percentage profit per kilogram made by the shop. … % [5] (d) Mohsin’s earnings increase exponentially at a rate of 8.7% each year. During 2018 he earned $195 600. During 2027, how much more does he earn than during 2018? $ … [3]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 5 : 6 1 1(a)(ii) 2.0736[0] × 105 final answer 3 B2 for 207360 oe or M1 for 16 × 18 × 720 1(b)(i) 26780 2 M1 for 18540 ÷ 9 soi 1(b)(ii) 1.36 2 M1 for 0.85 × 1.6 oe or B1 for 0.51 or 51 1(c) 66.7 or 66.66 to 66.67 5 (2.3 − 1.5 × M4 for 0.92)[× 100] oe or 1.5 × 0.92 2.3 × 100 oe 1.5 × 0.92 OR Working in euros B2 for [€]1.38 or M1 for 1.5[0] × 0.92 M2dep on B2 or M1 for 2.3 − their 1.38[× 100] oe their 1.38 2.3 − their 1.38 or × 100 oe their 1.38 2.3 or M1 for 2.3 – their 1.38 or their 1.38 OR Working in dollars B2 for [$]2.50 or M1 for or 2.3[0] ÷ 0.92 M2dep on B2 or M1 for their 5.2 − 5.1 their 2.5 [×100] oe or × 100 5.1 1.5 their 2.5 or M1 for their 2.5 – 1.5 or 1.5 1(d) 219 000 3 B2 for 414000 or 414414[.3.…] rounded to 4 or 218814[.3.…] rounded to 4 sf or sf or more more 9  8.7  or M2 for 195600 ×  1 +  [– 195600]  100   8.7  k or M1 for 195600 ×  1 +  or better  100  (k >1 and an integer)

This question in 0580/42 Oct/Nov 2019

1 (a) In a cycling club, the number of members are in the ratio males : females = 8 : 3. The club has 342 females. (i) Find the total number of members. … [2] (ii) Find the percentage of the total number of members that are female. … % [1] (b) The price of a bicycle is $1020. Club members receive a 15% discount on this price. Find how much a club member pays for this bicycle. $ … [2] (c) In 2019, the membership fee of the cycling club is $79.50 . This is 6% more than last year. Find the increase in the cost of the membership. $ … [3] (d) Asif cycles a distance of 105 km. On the first part of his journey he cycles 60 km in 2 hours 24 minutes. On the second part of his journey he cycles 45 km at 20 km/h. Find his average speed for the whole journey. … km/h [4] (e) Bryan invested $480 in an account 4 years ago. The account pays compound interest at a rate of 2.1% per year. Today, he uses some of the money in this account to buy a bicycle costing $430. Calculate how much money remains in his account. $ … [3] 1 2(f) The formula s = at is used to calculate the distance, s, travelled by a bicycle. 2 When a = 3 and t = 10 , each correct to the nearest integer, calculate the lower bound of the distance, s. … [2]

17 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 1254 2 M1 for 342 ÷ 3 1(a)(ii) 27.3 or 27.27… 1 1(b) 867 2 15 M1 for 1020 × oe 100  15  or 1020 ×  1 −  oe  100  1(c) 4.5[0] 3 79.5 [ 0 M2 for ][× 6 ] oe 100 + 6 79.5 [ 0 ] or × 100 oe 100 + 6 or M1 for 79.5[0] associated with 106[%] 1(d) 22.6 or 22.58… nfww 4 45 M1 for or better 20 and 60 + 45 M2 for 45 their 2h 24min + their 20 45 or M1 for their + their 2h 24min 20 1(e) 91.6[0] to 91.61 3 4  2.1  M2 for 480 × 1 + − 430 oe    100   2.1  4 OR M1 for 480 × 1 + oe    100  A1 for 522, 521.6[0] to 521.61 1(f) 112.8125 2 B1 for 2.5 or 9.5 seen

This question in 0580/43 Oct/Nov 2019

1 (a) In 2018, Gretal earned $32 000. (i) She paid tax of 24% on these earnings. Work out the amount she paid in tax in 2018. $ … [2] (ii) In 2019, Gretal’s earnings increased by 7%. Work out her earnings in 2019. $ … [2] (b) Gretal invests $5000 at a rate of 2% per year compound interest. Calculate the value of her investment at the end of 3 years. $ … [2] (c) One month, Gretal spent a total of $360 on presents. She spent 15 of this total on presents for her parents. She spent 23 of the remaining money on presents for her friends. She spent the rest of the money on presents for her sisters. Calculate the percentage of the $360 that she spent on presents for her sisters. … % [4] (d) Arjun earned $36 515 in 2019. This was an increase of 9% on his earnings in 2018. Work out his earnings in 2018. $ … [2] (e) Arjun and Gretal each pay rent. In 2018, the ratio of the amount each paid in rent was Arjun : Gretal = 5 : 7. In 2019, the ratio of the amount each paid in rent was Arjun : Gretal = 9 : 13. Arjun paid the same amount of rent in both 2018 and 2019. Gretal paid $290 more rent in 2019 than she did in 2018. Work out the amount Arjun paid in rent in 2019. $ … [4]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 7680 2 M1 for 0.24 × 32 000 oe 1(a)(ii) 34 240 2 100 + 7 M1 for 32 000 × oe 100 1(b) 5306.04 2 3  2  M1 for 5000 ×  1 +  oe  100  1(c) 26.7 or 26.66... to 26.67 4 96 B3 for 96 or oe 360 OR 1 M3 for (1 − ) × (1 −2 ) × 100 oe 5 3 1 or M2 for (1 − ) and (1 −2 ) oe 5 3 OR M1 for 360 ÷ 5 [× 4] oe M1 for their 288 ÷ 3 [× 2] 1(d) 33 500 2 100 + 9 M1 for 36 515 ÷ oe 100 1(e) 6525 4  65 63  M3 for  −  [ A ] = 290 oe  45 45   13 7  or M2 for  −  [ A ] = 290 oe  9 5  or M1 for correct attempt to convert to a common ratio value for Arjun 13 7 or for − oe 9 5

This question in 0580/41 May/June 2020

1 (a) (i) Divide $24 in the ratio 7 : 5. $ … , $ … [2] (ii) Write $24.60 as a fraction of $2870. Give your answer in its lowest terms. … [2] (iii) Write $1.92 as a percentage of $1.60 . … % [1] (b) In a sale the original prices are reduced by 15%. (i) Calculate the sale price of a book that has an original price of $12. $ … [2] (ii) Calculate the original price of a jacket that has a sale price of $38.25 . $ … [2] (c) (i) Dean invests $500 for 10 years at a rate of 1.7% per year simple interest. Calculate the total interest earned during the 10 years. $ … [2] (ii) Ollie invests $200 at a rate of 0.0035% per day compound interest. Calculate the value of Ollie’s investment at the end of 1 year. [1 year = 365 days.] $ … [2] (iii) Edna invests $500 at a rate of r % per year compound interest. At the end of 6 years, the value of Edna’s investment is $559.78 . Find the value of r. r = … [3]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 14, 10 2 M1 for 24 ÷ (7 + 5) 1(a)(ii) 3 2 B1 for correct fraction not in lowest terms 350 1(a)(iii) 120 1 1(b)(i) 10.2[0] 2 15 M1 for × 12 oe or better 100 1(b)(ii) 45 2 38.25 M1 for oe 15 1 − 100 1(c)(i) 85 2 500 × 1.7 × 10 M1 for oe 100 1(c)(ii) 203 or 202.5 to 202.6 2 365  0.0035  M1 for 200 ×  1 +   100  1(c)(iii) 1.9 3 559.78 M2 for 6 500  r 6 or M1 for 500  1 +  = 559.78  100 

This question in 0580/42 May/June 2020

1 (a) Campsite fees (per day) Tent … $15.00 Caravan … $25.00 The sign shows the fees charged at a campsite. Today there are 54 tents and 18 caravans on the site. Calculate the fees charged today. $ … [2] (b) In September the total income at the campsite was $37 054. This was a decrease of 4.5% on the total income in August. Calculate the total income in August. $ … [2] (c) The visitors to the campsite today are in the ratio men : women = 5 : 4 and women : children = 3 : 7. (i) Calculate the ratio men : women : children in its simplest form. … : … : … [2] (ii) Today there are 224 children at the campsite. Calculate the total number of men and women. … [3] (d) The space allowed for each tent is a rectangle measuring 8 m by 6 m, each correct to the nearest metre. Calculate the upper bound for the area of the space allowed for each tent. … m2 [2] (e) The value of the campsite has increased exponentially by 1.5% every year since it opened 30 years ago. Calculate the value of the campsite now as a percentage of its value 30 years ago. … % [2]

13 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1260 2 M1 for 15 × 54 + 25 × 18 1(b) 38 800 2  4.5  M1 for 37054 ÷  1 −  oe  100  1(c)(i) 15 : 12 : 28 2 M1 for correct attempt to find a common multiple for the women oe 1(c)(ii) 216 3 M2 for 224 ÷ their 28 × their (15 + 12) or M1 for 224 ÷ their 28 1(d) 55.25 2 M1 for 8 + 0.5 or 6 + 0.5 seen 1(e) 156 or 156.3… 2 30  1.5  M1 for  1 +   100 

This question in 0580/43 May/June 2020

2 (a) A plane has 14 First Class seats, 70 Premium seats and 168 Economy seats. Find the ratio First Class seats : Premium seats : Economy seats. Give your answer in its simplest form. … : … : … [2] (b) (i) For a morning flight, the costs of tickets are in the ratio First Class : Premium : Economy = 14 : 6 : 5. The cost of a Premium ticket is $114. Calculate the cost of a First Class ticket and the cost of an Economy ticket. First Class $ … Economy $ … [3] (ii) For an afternoon flight, the cost of a Premium ticket is reduced from $114 to $96.90 . Calculate the percentage reduction in the cost of a ticket. … % [2] (c) When the local time in Athens is 09 00, the local time in Berlin is 08 00. A plane leaves Athens at 13 15. It arrives in Berlin at 15 05 local time. (i) Find the flight time from Athens to Berlin. … h … min [1] (ii) The distance the plane flies from Athens to Berlin is 1802 km. Calculate the average speed of the plane. Give your answer in kilometres per hour. … km/h [2]

10 marks

Mark scheme: 2(a) 1 : 5 : 12 2 1 5 12 M1 for 2 : 10 : 24 or 7 : 35 : 84 or : : 18 18 18 2(b)(i) 266 and 95 3 B2 for 266 or 95 or 266 and 95 reversed 114 or M1 for 6 2(b)(ii) 15 2 114 − 96.9 M1 for [× 100] oe 114 96.9 or × 100 114 2(c)(i) 2h 50min 1 2(c)(ii) 636 2 M1 for 1802 ÷ their 2h 50min

This question in 0580/41 Oct/Nov 2020

1 Karel travelled from London to Johannesburg and then from Johannesburg to Windhoek. (a) The flight from London to Johannesburg took 11 hours 10 minutes. The average speed was 813 km/h. Calculate the distance travelled from London to Johannesburg. Give your answer correct to the nearest 10 km. … km [3] (b) The total time for Karel’s journey from London to Windhoek was 15 hours 42 minutes. The total distance travelled from London to Windhoek was 10 260 km. (i) Calculate the average speed for this journey. … km/h [2] (ii) The cost of Karel’s journey from London to Windhoek was $470. (a) Calculate the distance travelled per dollar. … km per dollar [1] (b) Calculate the cost per 100 km of this journey. Give your answer correct to the nearest cent. $ … per 100 km [2] (c) Karel changed $300 into 3891 Namibian dollars. Complete the statement. $1 = … Namibian dollars [1]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 9080 cao 3 B2 for 9078 to 9081… or M1 for 813 × their 11h 10min 1(b)(i) 654 or 653.5… 2 M1 for 10260 ÷ 15 h 42 min oe 1(b)(ii)(a) 21.8 or 21.82 to 21.83 1 1(b)(ii)(b) 4.58 or 4.59 cao 2 M1 for 470 ÷ (10260 ÷ 100) oe or 100 ÷ their (b)(ii)(a) 1(c) 12.97 1

This question in 0580/42 Oct/Nov 2020

10 (a) A box is a cuboid with length 45 cm, width 30 cm and height 42 cm. The box is completely filled with 90.72 kg of sand. Calculate the density of this sand in kg/m3. [Density = mass ÷ volume] … kg/m3 [3] (b) A bag contains 15000 cm 3 of sand. Some of this sand is used to completely fill a hole in the shape of a cylinder. The hole is 30 cm deep and has radius 10 cm. Calculate the percentage of the sand from the bag that is used. … % [3] (c) Sand costs $98.90 per tonne. This cost includes a tax of 15%. Calculate the amount of tax paid per tonne of sand. $ … [3] (d) Raj buys some sand for 3540 rupees. Calculate the cost in dollars when the exchange rate is $1 = 70.8 rupees. $ … [2]

11 marks

Mark scheme: 10(a) 1600 3 B2 for answer figs 16 or M2 for 90.72 ÷ (figs45 × figs3 × figs42) or M1 for volume = figs 45 × figs 3 × figs 42 isw 10(b) 62.8 or 62.83 to 62.84 3 π× 10 2 × 30 M2 for × 100 15000 or M1 for π × 10 2 × 30 10(c) 12.9[0] 3 B2 for 86 OR 98.9 98.9 M2 for × 0.15 oe or 98.9 − oe 15 15 1 + 1 + 100 100  15  or M1 for  1 +  a = 98.9 oe isw  100  10(d) 50 2 M1 for 3540 ÷ 70.8

This question in 0580/42 Feb/March 2021

4 (a) The exchange rate is 1 euro = $1.142 . (i) Johann changes $500 into euros. Calculate the number of euros Johann receives. Give your answer correct to the nearest euro. … euros [2] (ii) Johann buys a computer for $329. The same computer costs 275 euros. Calculate the difference in cost in dollars. $ … [2] 3 (b) Lucy spends of the money she has saved this month on a book that costs $5.25 . 8 Calculate how much money Lucy has saved this month. $ … [2] (c) Kamal invests $6130 at a rate of r% per year compound interest. The value of his investment at the end of 5 years is $6669. Calculate the value of r. r = … [3]

9 marks

Mark scheme: 4(a)(i) 438 cao 2 500 M1 for 1.142 4(a)(ii) 14.95 2 M1 for [329 –] 275 × 1.142 oe 4(b) 14 2 8 M1 for 5.25 × oe 3 4(c) 1.7[0] or 1.699… 3 6669 M2 for 5 6130 or M1 for 6669 = 6130 ( k ) 5

This question in 0580/41 May/June 2021

1 (a) A 2.5-litre tin of paint costs $13.50 . In a sale, the cost is reduced by 14%. (i) Work out the sale price of this tin of paint. $ … [2] (ii) Work out the cost of buying 42.5 litres of paint at this sale price. $ … [2] (b) Henri buys some paint in the ratio red paint : white paint : green paint = 2 : 8 : 5. (i) Find the percentage of this paint that is white. … % [1] (ii) Henri buys a total of 22.5 litres of paint. Find the number of litres of green paint he buys. … litres [2] (c) Maria paints a rectangular wall. The length of the wall is 20.5 m and the height is 2.4 m, both correct to 1 decimal place. One litre of paint covers an area of exactly 10 m2. Calculate the smallest number of 2.5-litre tins of paint she will need to be sure all the wall is painted. Show all your working. … [4]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 11.61 final answer 2  14  M1 for 13.5[0] ×  1 −  oe  100  or B1 for 1.89 1(a)(ii) 197.37 final answer 2 FT 17 × their (a)(i) exact or correct to nearest cent M1 for 42.5 ÷ 2.5 1(b)(i) 53.3 or 53.33… 1 1(b)(ii) 7.5 2 M1 for 22.5 ÷ (2 + 8 + 5) oe soi 1(c) 20.55 × 2.45 oe M2 M1 for 20.5 + 0.05 oe seen or 2.4 + 0.05 oe seen If 0 scored, SC1 here for 20.45 × 2.35 oe 3 nfww A2 M1 for their area ÷ 10 ÷ 2.5 oe

This question in 0580/42 May/June 2021

8 (a) A cuboid has length L cm, width W cm and height H cm. L cm H cm NOT TO SCALE 20.1 cm W cm 37.8 cm The diagram shows the net of this cuboid. The ratio W : L = 1 : 2. Find the value of L, the value of W and the value of H. L = … W = … H = … [5] (b) E NOT TO SCALE 24 cm D C 15 cm A 18 cm B The diagram shows a solid pyramid with a rectangular base ABCD. E is vertically above D. Angle EDC = angle EDA = 90°. AB = 18 cm, BC = 15 cm and EC = 24 cm. (i) The pyramid is made of wood and has a mass of 800 g. Calculate the density of the wood. Give the units of your answer. 1 [The volume, V, of a pyramid is V = # area of base # height.] 3 [Density = mass ' volume] … … [5] (ii) Calculate the angle between BE and the base of the pyramid.

14 marks

Mark scheme: 8(a) [L =] 11.8 5 M1 for L = 2W oe soi [W =] 5.9 M1 for W + 2H = 20.1 oe [H =] 7.1 M1 for 2L + 2H = 37.8 oe B1 for at least one correct answer 8(b)(i) 0.559 to 0.56[0…] B4 1 2 2 M2 for × 18 × 15 × 24 − 18 isw 3 conversion or M1 for h2 + 182 = 242 oe or better M1 for figs 800 ÷ figs their volume isw g/cm3 or g cm–3 final answer B1 8(b)(ii) 34.1 or 34.11 to 34.12 4 2 2 24 − 18 M3 for tan [ ] = oe 18 2 + 15 2 or M2 for 18 2 + 15 2 isw or 24 2 + 15 2 isw or M1 for 182 + 152 isw or 242 + 152 isw or M1 for indicating required angle is EBD

This question in 0580/42 May/June 2021

1 (a) (i) Yasmin and Zak share an amount of money in the ratio 21 : 19. Yasmin receives $6 more than Zak. Calculate the total amount of money shared by Yasmin and Zak. $ … [2] (ii) In a sale, all prices are reduced by 15%. (a) Yasmin buys a blouse with an original price of $40. Calculate the sale price of the blouse. $ … [2] (b) Zak buys a shirt with a sale price of $29.75 . Calculate the original price of the shirt. $ … [2] (b) Xavier’s salary increases by 2% each year. In 2010, his salary was $40 100. (i) Calculate his salary in 2015. Give your answer correct to the nearest dollar. $ … [3] (ii) In which year is Xavier’s salary first greater than $47 500? … [3] (c) In January 2020, the population of a town was 5% more than its population in January 2018. In January 2021, the population of this town was 2% less than its population in January 2020. Calculate the overall percentage increase in the population from January 2018 to January 2021. … % [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 120 2 M1 for 6 ÷ (21 – 19) oe soi 2 x or for = 6 40 1(a)(ii)(a) 34 2 15 M1 for 40 – × 40 oe or better 100 or B1 for 6 1(a)(ii)(b) 35 2  15  M1 for  1 −  × p = 29.75 or better  100  1(b)(i) 44 274 cao 3 B2 for 44273 to 44274 or 44270  2  5 or M1 for 40100 ×  1 +  oe  100  1(b)(ii) 2019 nfww 3 M2 for one correct trial of n = 8 or n = 9 either to find a salary or, if working with 1.02n and 47 500÷ 40 100 [= 1.1845], to find a value of 1.02n or B2 for final answer 9 or 4 nfww or M1 for  2  n their 44 274 ×  1 +  = 47 500 oe  100   2  n or 40 100 ×  1 +  = 47 500 oe  100  or for at least one trial giving a value greater than their 44 274 1(c) 2.9 [increase] 2  5  2  M1 for  1 + × 1 −  oe  100  100  implied by 1.029 or 102.9[%]

This question in 0580/43 May/June 2021

2 Bob, Chao and Mei take part in a run for charity. (a) Their times to complete the run are in the ratio Bob : Chao : Mei = 4 : 5 : 7. (i) Find Chao’s time as a percentage of Mei’s time. … % [1] (ii) Bob’s time for the run is 55 minutes 40 seconds. Find Mei’s time for the run. Give your answer in minutes and seconds. … min … s [3] (b) Chao collects $47.50 for charity. (i) Bob collects 28% more than Chao. Find the amount Bob collects. $ … [2] (ii) Chao collects 60% less than Mei. Find how much more money Mei collects than Chao. $ … [3] (c) When running, Chao has a stride length of 70 cm, correct to the nearest 5 cm. Chao runs a distance of 11.2 km, correct to the nearest 0.1 km. Work out the minimum number of strides that Chao could take to complete this distance. … [4] (d) In 2015, a charity raised a total of $1.6 million. After 2015, this amount increased exponentially by 2.4% each year for the next 5 years. Work out the amount raised by the charity in 2020. $ … million [2]

15 marks

Mark scheme: 2(a)(i) 71.4 or 71.42 to 71.43 1 2(a)(ii) 97 [min] 25 [s] 3 B2 for 13 min 55 sec seen or 97.4 or 97.41 to 97.42 seen or 5845 seen OR M2 for 55.66… ÷ 4 × 7 oe or 3340 ÷ 4 × 7 oe or for 7/4 × 55 + 7/4 × 40 oe or M1 for 55 min 40 sec ÷ 4 oe or M1 for total time ÷ 16 soi 2(b)(i) 60.8[0] 2  28  M1 for 47.5 ×  1 +  oe  100  or B1 for 13.3[0] 2(b)(ii) 71.25 3 B2 for 118.75  60  Or M2 for 47.50 ÷  1 −  – 47.50  100   60  or M1 for x ×  1 −  = 47.50 oe or  100  better 2(c) 15 380 4 M3 for (1 120 000 – 5000) ÷ (70 + 2.5) oe or B2 for answer figs 15 379 to figs 15 380 or M2 for (1 120 000 ± 5000) ÷ (70 ± 2.5) oe or M1 for one of figs 675, 725, 1115, 1125 seen 2(d) 1.8[0] or 1.801 to 1.802 [million] nfww 2 5  2.4  M1 for figs 16 ×  1 +  oe  100 

This question in 0580/41 Oct/Nov 2021

1 (a) Malena has 450 fruit trees. The fruit trees are in the ratio apple : pear : plum = 8 : 7 : 3. (i) Show that Malena has 200 apple trees. [2] (ii) Find the number of plum trees. … [1] (iii) Malena wants to increase the number of pear trees by 32%. Calculate the number of extra pear trees she needs. … [2] (iv) Each apple tree produces 48.5 kg of apples. The apples have an average mass of 165 g each. Calculate the total number of apples produced by the 200 trees. Give your answer correct to the nearest 1000 apples. … [3] (b) Malena’s land is valued at three million and seventy-five thousand dollars. (i) Write this number in figures. … [1] (ii) Write your answer to part (b)(i) in standard form. … [1] (c) In 2020, each plum tree produced 37.7 kg of plums. This was 16% more than in 2019. Calculate the mass of plums produced by each plum tree in 2019. … kg [2] (d) Malena invests $1800 at a rate of 2.1% per year compound interest. Calculate the value of her investment at the end of 15 years. $ … [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 450 2 450 × 8 oe M1 for 8 + 7 + 3 8 + 7 + 3 1(a)(ii) 75 1 1(a)(iii) 56 2 32 M1 for × (450 – 200 – their 75) oe 100 32 450 or × × 7 oe 100 8 + 7 + 3 If 0 scored, SC1 for answer 231 1(a)(iv) 59 000 nfww 3 B2 for 58 600 to 58 800 or B1 for 293 to 294 figs485 × 200 or M1 for oe 165 If 0 scored, SC1 for their more accurate answer seen and rounded to the nearest 1000 1(b)(i) 3 075 000 1 1(b)(ii) 3.075 × 106 1 FT their (b)(i) 1(c) 32.5 2  16  M1 for x ×  1 +  = 37.7 or better  100  1(d) 2460 or 2458. … 2 15  2.1  M1 for 1800 1 +  oe  100 

This question in 0580/42 Oct/Nov 2021

1 A company employed 300 workers when it started and now employs 852 workers. (a) Calculate the percentage increase in the number of workers. … % [2] (b) Of the 852 workers, the ratio part-time workers : full-time workers = 5 : 7. Calculate the number of full-time workers. … [2] (c) The company makes 40 600 headphones in one year. Write this number (i) in words, … [1] (ii) in standard form. … [1] (d) In one month, the company sells 3 000 headphones. 3 Of these, 48% are exported, are sold to shops and the rest are sold online. 8 Calculate the number of headphones that are sold online. … [3] (e) One year, sales increased by 15%. The following year sales increased by 18%. Calculate the overall percentage increase in sales. … % [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 184 2 852 − 300 M1 for [× 100 ] oe 300 852 or for × 100 [ −100 ] oe 300 1(b) 497 2 852 M1 for × k oe where k = 1, 5 or 7 5 + 7 1(c)(i) Forty thousand six hundred 1 1(c)(ii) 4.06 × 10 4 1 1(d) 435 3  48 3  M2 for 3000 ×  1 − −  oe  100 8  or B2 for 2565, or 1440 and 1125 or 1875 and 1440 or 1560 and 1125 48 3  48 3  or M1 for 1 − − or 3000 ×  +  oe 100 8  100 8  or B1 for 1440 or 1125 or 1560 or 1875 If 0 scored SC1 for answer 975 1(e) 35.7 3 100 + 15 100 + 18 M2 for × [–1] oe or better 100 100 100 + 15 100 + 18 or M1 for k × × oe 100 100

This question in 0580/42 Feb/March 2022

2 (a) Alex, Bobbie and Chris share strawberries in the ratio Alex : Bobbie : Chris = 3 : 2 : 2. Chris receives 12 strawberries. Calculate the total number of strawberries shared. … [2] (b) In a sale, a shop reduces all prices by 12%. (i) Dina buys a book which has an original price of $6.50 . Calculate how much Dina pays for the book. $ … [2] (ii) Elu pays $11 for a toy. Calculate the original price of the toy. $ … [2] (c) Feri invests some money. The rate of interest for the first year is 2.5%. At the end of the second year the overall percentage increase of Feri’s investment is 6.6%. Find the rate of interest for the second year. … % [2] (d) A radioactive substance decays at an exponential rate of 2% per day. The initial mass is 80 g. (i) Find the mass at the end of 5 days. … g [2] (ii) Find how many more whole days, after day 5, it takes for the mass to reduce to less than 67 g. … [3]

13 marks

Mark scheme: 2(a) 42 2 M1 for 12 ÷ 2 or better 2(b)(i) 5.72 2 M1 for 100 12 6.50 100   oe or B1 for 0.88 oe 2(b)(ii) 12.5[0] 2 M1 for 100 12 11 100    x or better oe Question Answer Marks Partial Marks 2(c) 4 2 M1 for 100 2.5 100 6.6 [...] 100 100     oe 2(d)(i) 72.3 or 72.31... 2 M1 for 5 100 2 80 100        oe 2(d)(ii) 4 nfww 3 B2 for answer 9 nfww or M2 for correct trials with values giving either side of 67 or M1 for 100 2 80 100        n = 67 or  100 2 67 100          k their i or an evaluated trial with n ⩾ 6 or k ⩾ 1

This question in 0580/41 May/June 2022

1 (a) Find the lowest common multiple (LCM) of 30 and 75. … [2] (b) Share $608 in the ratio 4 : 5 : 7. $ … $ … $ … [3] 6 .39 # 10 4 (c) Work out 6 . 2 .45 # 10 Give your answer in standard form. … [2] (d) Write .027o o as a fraction. … [1] (e) A stone has volume 45 cm 3 and mass 126 g. Find the density of the stone, giving the units of your answer. [Density = mass ' volume] … … [2]

10 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 150 2 B1 for answer 150k or M1 for prime factors of 30 or 75 seen or a list of multiples of both 30 and 75 with at least 3 of each 30  75 or for oe 15 or for answer 2  3  52 1(b) 152 3 Accept in any order B2 for two correct answers 190 608 or M1 for  k oe where k =1, 4, 5, 7 4  5  7 266 1(c) 2.61  10–2 2.61  10 2 or 2 B1 for figs 2608 or 261 seen 2.608…  10–2 If 0 scored, SC1 for answer 2.6[0]  10–2 without more accurate value in standard form seen 1(d) 27 1 oe fraction 99 1(e) 2.8 1 g/cm3 or g cm–3 1

This question in 0580/42 May/June 2022

6 (a) At a festival, 380 people out of 500 people questioned say that they are camping. There are 55 300 people at the festival. Calculate an estimate of the total number of people camping at the festival. … [2] (b) 12 friends travel to the festival. 5 travel by car, 4 travel by bus and 3 travel by train. Two people are chosen at random from the 12 friends. Calculate the probability that they travel by different types of transport. … [4] (c) Arno buys a student ticket for $43.68 . This is a saving of 16% on the full price of a ticket. Calculate the full price of a ticket. $ … [2] (d) At a football match, there are 29 800 people, correct to the nearest 100. (i) At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people. Calculate the lower bound for the number of minutes it takes for all the people to leave. … min [3] (ii) At a cricket match there are 27 500 people, correct to the nearest 100. Calculate the upper bound for the difference between the number of people at the football match and at the cricket match. … [2]

13 marks

Mark scheme: 6(a) 42 028 2 380 M1 for oe soi isw 500 6(b) 47 4 0.712[1…] oe 66  5 4   4 3   5 3  M3 for 2   2   2         12 11   12 11   12 11  oe  5 4 4 3 3 2  or 1 –      oe    12 11 12 11 12 11  or M2 for sum of 3 or more correct product pairs and no incorrect pairs 5 4 4 3 3 2 or for      and no other 12 11 12 11 12 11 pairs k j or M1 for  seen 12 11 94 If 0 scored SC1 for answer oe 144 6(c) 52 2 100  16 M1 for x   43.68 oe or better 100 6(d)(i) 70 or 70.16[5…] or 70.17 or 70.2 3 29750 to 29800 29750 to 29800 M2 for or or 400  25 400  24 29800  50 400to425 or B1 for 29 750 or 29 850 or 29 849 or 375 or 425 or 424 seen 6(d)(ii) 2399 2 B1 for 27 450 or 27 550 or 27 549 or 29 850 or or 2400 nfww 29 849 seen

This question in 0580/42 May/June 2022

1 (a) (i) At a football club, season tickets are sold for seated areas and for standing areas. The cost of season tickets are in the ratio seated : standing = 5 : 3. The cost of a season ticket for the standing area is $45. Find the cost of a season ticket for the seated area. $ … [2] (ii) In 2021, the value of the team’s players was $2.65 million. In 2022 this value has decreased by 12%. Find the value in 2022. $ … million [2] (iii) The number of people at a football match is 1455. This is 6.25% of the total number of people allowed in the stadium. Find the total number of people allowed in the stadium. … [2] (iv) The average attendance increased exponentially by 4% each year for the three years from 2016 to 2019. In 2019 the average attendance was 1631. Find the average attendance for 2016. … [3] (b) Another club sells season tickets for individuals and for families. In 2018, the number of season tickets sold is in the ratio family : individual = 2 : 7. (i) The number of family season tickets sold is x. Write an expression, in terms of x, for the number of individual season tickets sold. … [1] (ii) In 2019, the number of family season tickets sold increases by 12 and the number of individual season tickets sold decreases by 26. Complete the table by writing expressions, in terms of x, for the number of tickets sold each year. Year Family tickets Individual tickets 2018 x 2019 [2] (iii) In 2019, the number of individual season tickets sold is 3 times the number of family season tickets sold. Write an equation in x and solve it to find the number of family tickets sold in 2018. x = … [4]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 75 2 45 M1 for [× k] where k is 1, 5 or 8 3 1(a)(ii) 2.332 oe 2  12  M1 for 2.65 [million]   1 −  oe  100  or B1 for 0.318[million] seen 1(a)(iii) 23 280 cao 2 6.25 M1 for  x = 1455 or better 100 1(a)(iv) 1450 or 1449 to 1450 3 3  4  M2 for 1631 = k 1 + oe or better    100   4 3 or B1 for 1 + oe seen    100   4  n or M1 for 1631 = k 1 + , n > 0 oe    100  1(b)(i) 7 x 1 oe 2 1(b)(ii) 7 x 2 FT their (b)(i) x + 12 – 26 oe B1 for x + 12 2 final answer 7 x B1 for their – 26 2 1(b)(iii) 7 x 4  7 x  − 26 = 3(x + 12) oe M1dep for their  − 26  = 3  their (x + 12) oe 2  2  leading to 124 M2dep for isolating x terms, dep on eqn with term in x and constant on each side and with a bracket or fraction. or M1dep for correctly removing brackets or dealing with fractions, dep on eqn with term in x and constant on each side and with a bracket or fraction.

This question in 0580/42 Oct/Nov 2022

1 (a) Here are the ingredients needed to make a pasta bake to serve 12 people. 250 g butter 600 g pasta 460 g mushrooms 280 g cheese 800 ml milk (i) Find the mass of the cheese as a percentage of the mass of the mushrooms. … % [1] (ii) Find the mass of butter needed to make a pasta bake to serve 18 people. … g [2] (iii) Monica has 2.2 litres of milk and 1.5 kg of each other ingredient. Calculate the greatest number of people she can serve with pasta bake. … [3] (b) In 2019, a packet of pasta cost $2.40 . This was an increase of 25% of the cost of a packet in 2018. (i) Work out the cost in 2018. $ … [2] (ii) In 2020, the cost of a packet increased by 15% from the cost in 2019. Work out the total percentage increase in the cost of a packet from 2018 to 2020. … % [3] (c) width NOT TO SCALE Pasta is sold in packets with width 11.5 cm, correct to the nearest 0.5 cm. A shop places these packets in a single line on a shelf of length 2 m, correct to the nearest 0.1 m. Find the maximum number of these packets that will fit along this shelf. You must show all your working. … [3]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 60.9 or 60.86 to 60.87 1 1(a)(ii) 375 2 250 M1 for [ 18] oe 12 1(a)(iii) 30 nfww 3 M1 for figs2200 ÷ 800 [× 12]oe M1 for 1500 ÷ 600 [× 12] oe 1(b)(i) 1.92 2  25  M1 for k   1 +  = 2.4[0] oe or better  100  1(b)(ii) 3 3 43.75 or 43 4   25  15   100 oe M2 for   1 +  1 +  [ −1]     100  100    25  15  or  1 +  1 +   100 [–100]  100  100   15  2.40   1 +  or for  100  100 [– 100] oe their(b)(i)  15   25   15  or M1 for 2.40 ×  1 +  or  1 +    1 +  oe  100   100   100  1(c) 18 nfww 3 200 to 210 200 + 5 M2 for or oe 11.5 − 0.25 11 to 11.5 or M1 for 200 + 5, 200 – 5, 11.5 + 0.25 or 11.5 – 0.25

This question in 0580/43 Oct/Nov 2022

1 (a) (i) Alain and Beatrice share $750 in the ratio Alain : Beatrice = 8 : 7. Show that Alain receives $400. [1] (ii) (a) Alain spends $150. Write $150 as a percentage of $400. … % [1] (b) He invests the remaining $250 at a rate of 2% per year simple interest. Calculate the amount Alain has at the end of 5 years. $ … [3] (iii) Beatrice invests her $350 at a rate of 0.25% per month compound interest. Calculate the amount Beatrice has at the end of 5 years. Give your answer correct to the nearest dollar. $ … [3] (b) Carl, Dina and Eva share 100 oranges. The ratio Carl’s oranges : Dina’s oranges = 3 : 5. The ratio Carl’s oranges : Eva’s oranges = 2 : 3. Find the number of oranges Carl receives. … [2] (c) Fred buys a house. At the end of the first year, the value of the house increases by 5%. At the end of the second year, the value of the house increases by 3% of its value at the end of the first year. The value of Fred’s house at the end of the second year is $60 564. Calculate how much Fred paid for the house. $ … [3] (d) Gabrielle invests $500 at a rate of r % per year compound interest. At the end of 8 years the value of Gabrielle’s investment is $609.20 . Find the value of r. r = … [3]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 750 M1  8 [= 400] 8 + 7 1(a)(ii)(a) 37.5 1 1(a)(ii)(b) 275 3 250 2 5 M2 for 250 + oe 100 250 2 5 or M1 for oe 100 1(a)(iii) 407[.00] cao nfww 3 B2 for 406.5 to 406.7  0.25  60 or M1 for 350  1 + oe isw    100  If 0 scored SC1 for answer 354 or answer 406 1(b) 24 2 M1 for [C : D =] 6 : 10 oe and [C : E =] 6 : 9 oe 6 or for [ 100] oe 6 + 10 + 9 1(c) 56 000 nfww 3  3   5  M2 for 60564  1 +  1 + oe      100   100   3  5  or M1 for [ x ] 1 +  1 +     100  100   3   5  or for 60564  1 + oe or 60564  1 +      100   100  If 0 scored, SC1 for answer 65499 to 65500 1(d) 2.5[0] or 2.499... 3 609.20 M2 for 8 oe 500 or M1 for 500  (...)8 = 609.2[0] oe

This question in 0580/42 Feb/March 2023

1 (a) An orchard has 1250 trees. The trees are in the ratio apple : pear : cherry = 12 : 9 : 4. (i) Calculate the number of apple trees. … [2] (ii) Last year in the orchard, the mean mass of fruit produced was 64 kg per tree. Calculate the total mass of fruit produced last year. Give your answer in tonnes. [1 tonne = 1000 kg] … tonnes [2] (iii) Last year, the mean mass of pears produced was 54 kg per tree. This was a decrease of 10% on the mean mass of pears produced per tree from the year before. Calculate the mean mass of pears produced by each pear tree the year before. … kg [2] 1 (iv) The orchard loses of its total number of trees in a storm. 5 Calculate the number of trees that remain. … [2] (b) Paulo buys some pears from a market. Pears cost $0.54 each or 0.51 euros each. (i) Paulo pays in dollars for 12 pears. Calculate the change he receives from $10. $ … [2] (ii) The exchange rate is $1 = 0.826 euros. Calculate how much more Paulo pays for each pear when he pays in euros. Give your answer in dollars, correct to the nearest cent. $ … [3]

13 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 600 2 1250 M1 for  k where k = 1, 4, 9, 12 oe 12  9  4 1(a)(ii) 80 2 M1 for 1250 × 64 [÷ 1000] 1(a)(iii) 60 2  10  M1 for x  1   54 oe    100  1(a)(iv) 1000 2 M1 for 1250 – (1250 ÷ 5) oe or B1 for 250 1(b)(i) 3.52 2 M1 for [10 –] 12 × 0.54 or B1 for 6.48 1(b)(ii) 0.08 3 B2 for 0.077[4...] or M1 for 0.51 ÷ 0.826 If 0 or 1 scored award instead SC2 for 0.93 final answer OR If 0 scored SC1 for 0.06 as answer

This question in 0580/41 May/June 2023

1 (a) 42° NOT TO SCALE x° The diagram shows an isosceles triangle with the base extended. Find the value of x. x = … [3] (b) The diagram shows three lines meeting at a point. The ratio a : b : c = 3 : 4 : 5. Find the value of c. a° NOT TO c° b° SCALE c = … [3] (c) A regular pentagon has an exterior angle, d. A regular hexagon has an interior angle, h. d Find the fraction . h Give your answer in its simplest form. … [4] (d) S R x° ( x + 20)° NOT TO SCALE ( 3x – 40)° Q ( 2x – 5)° P Show that PQRS is a cyclic quadrilateral. [5] (e) B A 50° 9 cm NOT TO O SCALE The diagram shows a circle of radius 9 cm, centre O. The minor sector AOB, with sector angle 50°, is removed from the circle. Calculate the length of the major arc AB. … cm [3]

18 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 111 3  42 M2 for 180 –180 oe or 42 + 2 180  42 oe 2 180  42 or M1 for oe 2 1(b) 150 3 M1 for k ÷ (3 + 4 + 5) [×p] where p = 1, 3, 4 or 5 5 or oe 12 B1 for 360 used 1(c) 3 4 72 cao nfww B3 for 5 120 or B2 for [d = ] 72 or [h = ] 120 or M1 for 360 ÷ 5 oe isw or 180 – (360 ÷ 6) isw or for (6 – 2) × 180 [÷ 6] 1(d) x + 2x – 5 + x + 20 + 3x – 40 = 360 M1 Accept equivalent equation e.g. 7x – 25 = 360 7x = 360 + 5 – 20 + 40 or better M1 FT their equation, accept e.g. 7x = 385 x = 55 B1 55 and 125 B1dep Dep on M1M1B1 or 105 and 75 Accept 55 + 3 × 55 – 40 = 180 or 2 × 55 – 5 + 55 + 20 = 180 If B0 scored, SC1 for 55, 75, 105 and 125 Opposite angles sum to 180 oe A1 Dep on M1M1B1B1 [so PQRS is a cyclic quadrilateral ] 1(e) 48.7 or 48.69 to 48.70… 3 360  50 M2 for 2 π oe9 360 50 or M1 for  2  π oe9 360

This question in 0580/42 May/June 2023

1 (a) Tomas sells a computer, a bike and a phone. The amounts he receives are in the ratio computer : bike : phone = 14 : 17 : 9. (i) Calculate the amount he receives for the phone as a percentage of the total. … % [2] (ii) The total amount he receives is $560. Calculate how much he receives for the bike. $ … [2] (iii) Tomas originally bought the bike for $195. He wanted to make a profit of at least 25% when he sold it. Does Tomas make a profit of at least 25%? You must show all your working to support your decision. [3] (b) Ulla invests $725 for 6 years in an account paying simple interest at a rate of 1.3% per year. Calculate the total interest earned at the end of 6 years. $ … [2] (c) In a sale, all prices are reduced by 24%. Victor pays $36.86 for a pair of shoes in the sale. Calculate the original price of the shoes. $ … [2]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 22.5 2 9 M1 for [ 100] 14  17  9 1(a)(ii) 238 2 FT their 14 + 17 + 9 = N seen in (a)(i) 560 M1 for  k, their 14  17  9  where k = 1, 9, 14 or 17 1(a)(iii) METHOD 1 M2 25 M1 for  195 100 1.25  195 oe 243[.75] and No oe A1 Strict FT yes if their (a)(ii) > 243.75 If M0 scored, then SC1 for 243.75 and a correct conclusion. METHOD 2 (M2) their 238 M1 for = 1.22... oe 195 their 238 – 1 = 0.22… oe 195 22[%] (or better) and No oe (A1) Strict FT yes if their (a)(ii) gives answer > 25 If M0 scored, then SC1 for 22.05 and a correct conclusion. METHOD 3 (M2) M1 for 0.25  195 195  0.25 = 48.75 oe and their 238 – 195 = 43 43 and 48.75 and NO (A1) Strict FT yes if their (a)(ii) gives profit > 48.75 If M0 scored, then SC1 for 43 and 48.75 and a correct conclusion. METHOD 4 (M2)  25  M1 for x   1   = their 238  100  their 238  100 125 190.4 and NO (A1) Strict FT yes if their (a)(ii) gives answer > 195 If M0 scored then SC1 for 190.4 and a correct conclusion. 1(b) 56.55 2 725  1.3[ 6] M1 for oe 100 1(c) 48.5[0] 2  24  M1 for x   1   = 36.86 oe  100 

This question in 0580/43 May/June 2023

1 The table shows the amount received when exchanging $100 in some countries. Country Amount received for $100 Wales 77.05 pounds India 7437.05 rupees China 671.20 yuan Spain 85.35 euros (a) Brad changes $250 to Indian rupees. Calculate the amount he receives correct to the nearest rupee. … rupees [2] (b) Wang changes 5400 Chinese yuan into dollars. Calculate how much he receives in dollars, correct to the nearest cent. $ … [2] (c) Gretal lives in Spain and goes on holiday to Wales. She spends 3500 euros in total on travel and hotels in the ratio travel: hotels = 4 : 3 . (i) Work out how much Gretal spends, in euros, on travel. … euros [2] (ii) Work out how much she spends, in pounds, on hotels. … pounds [3] (iii) Gretal flies home to Spain. The plane flies a distance of 2200 km, correct to the nearest 100 km. The average speed of the plane is 740 km/h, correct to the nearest 20 km/h. Calculate the lower bound of the time taken, in hours and minutes, for this flight. … h … min [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 18593 cao 2 M1 for 7437.05  250 ÷ 100 oe 1(b) 804.53 cao 2 M1 for 5400 ÷ 671.20 [ 100] oe 1(c)(i) 2000 2 M1 for 3500 ÷ (4 + 3) [× k] oe 1(c)(ii) 1354.13 … 3 77.05 M2 for (3500 – their (c)(i))  oe 85.35 or M1 for (3500 – their (c)(i)) ÷ figs 85.35 oe 77.05 or for oe 85.35 or for (3500 – their (c)(i))  figs 77.05 1(c)(iii) 2 [h] 52 [min] nfww 3 2100 to 2200 2200 − 50 M2 for or 740 + 10 740 to 760 or M1 for 2200 + 50 or 2200 – 50 or 740 + 10 or 740 – 10

This question in 0580/43 Oct/Nov 2023

1 A grocer sells potatoes, mushrooms and carrots. (a) A customer buys 3 kg of mushrooms at $1.04 per kg and 4 kg of carrots at $1.28 per kg. Calculate the total cost. $ … [2] (b) In one week, the ratio of the masses of vegetables sold by the grocer is potatoes : mushrooms : carrots = 11 : 8 : 6. (i) Work out the mass of mushrooms sold as a percentage of the total mass. … % [2] (ii) The total mass of potatoes, mushrooms and carrots sold is 1500 kg. Find the mass of carrots the grocer sells this week. … kg [2] (iii) The profit the grocer makes selling 1 kg of carrots is $0.75 . Find the total profit the grocer makes selling carrots this week. $ … [1] (iv) On the last day of the week, the grocer reduces the price of 1 kg of potatoes by 8% to $1.15 . Calculate the original price of 1 kg of potatoes. $ … [2] (c) The grocer buys 620 kg of onions, correct to the nearest 20 kg. He packs them into bags each containing 5 kg of onions, correct to the nearest 1 kg. Calculate the upper bound for the number of bags of onions that he packs. … [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 8.24 cao 2 M1 for 3 1.04 + 4 1.28 1(b)(i) 32 2 8 M1 for  100  oe 11 + 8 + 6 1(b)(ii) 360 2 1500 M1 for  k where k = 1 , 11, 8 or 6 11 + 8 + 6 1(b)(iii) 270 1 FT 0.75 × their 360 1(b)(iv) 1.25 cao 2  8  M1 for x   1 −  = 1.15 oe or better  100  1(c) 140 nfww 3 620 to 640 620 + 10 M2 for or oe 5 − 0.5 4 to 5 or M1 for 620 +10 oe or 620 – 10 oe or 5 + 0.5 oe or 5 – 0.5 oe seen

This question in 0580/42 Feb/March 2024

1 (a) A fruit drink is made using 1.5 litres of apple juice and 450 millilitres of mango juice. Write the ratio apple juice : mango juice in its simplest form. … : … [2] (b) One litre of fruit drink is shared between three cups. The amount in the cups is in the ratio 9 : 6 : 10. Calculate the number of millilitres in each cup. … ml , … ml , … ml [3] (c) A shop buys bottles of the fruit drink for $3.20 each. It sells them at a profit of 15%. Calculate the selling price of each bottle of fruit drink. $ … [2] (d) The number of bottles of fruit drink sold has grown exponentially at a constant rate of 2.5% per year. 5 years ago, the shop sold 16 620 bottles. Calculate the number of bottles sold this year. … [2] (e) d cm NOT TO 23 cm SCALE 18.5 cm The bottles of juice are 18.5 cm tall, correct to the nearest millimetre. They are stored on shelves. The distance between the shelves is 23 cm, correct to the nearest centimetre. Calculate the lower bound for the distance, d cm, between the top of a bottle and the shelf above it. … cm [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 10 : 3 final answer 2 M1 for 1500 : 450 oe in ratio form If 0 scored SC1 for answer 3 : 10 1(b) 360 240 400 3 B2 for answer 0.36 0.24 0.4 or for answer two of 360 240 400 1000 or M1 for [ k ] where k = 1, 9, 9  6  10 6 or 10 If 0 scored, SC1 for answer with 3 values in ratio 9 : 6 : 10 in that order 1(c) 3.68 cao 2  15  M1 for  1    3.2 oe  100  or B1 for answer 0.48 1(d) 18 804[.0...] 2  2.5  5 1 for 16620   1   oe  100  1(e) 3.95 3 M2 for 22.5 – (18.5 to 18.6) or (22 to 23) −18.55 or M1 for 23 – 0.5 oe seen or 23 + 0.5 oe seen or 18.5– 0.05 oe seen or 18.5 + 0.05 oe seen

This question in 0580/42 May/June 2024

4 (a) Enzo, Rashid and Blessy each swim as many lengths of a swimming pool as they can in 15 minutes. The results are shown in the table. Name Number of lengths Enzo 11.25 Rashid 18.75 Blessy 20 (i) Find the number of lengths Enzo swims as a percentage of the total number of lengths all three people swim. … % [2] (ii) Write the ratio of the number of lengths each person swims in the form Enzo : Rashid : Blessy. Give your answer in its simplest form. … : … : … [2] (iii) Each length of the pool is 25 m. (a) Work out Blessy’s average swimming speed for the 15 minutes. Give your answer in metres per second. … m/s [3] (b) Rashid continues to swim at the same rate. Calculate the time it takes Rashid to swim a total distance of 5 km. Give your answer in hours and minutes. … h … min [4] (iv) Blessy swims for one hour. The number of lengths she swims decreases by 5% every 15 minutes. Calculate the number of lengths she swims in the final 15 minutes. … [3] (b) Another swimmer, Adam, swims 450 m, correct to the nearest 25 metres. This takes 10 minutes, correct to the nearest minute. Calculate the minimum distance Adam swims in one hour at this rate. … m [3]

17 marks

Mark scheme: 4(a)(i) 22.5 2 11.25 M1 for 100  oe 11.25 + 18.75 + 20 4(a)(ii) 9 : 15 : 16 2 M1 for 1125 : 1850 : 2000 or better 4(a)(iii)(a) 5 3 or 0.556 or 0.5555 to 0.5556 9 20  25 M2 for oe 15[ 60] or M1 for 20 × 25 or for their distance ÷ (15 [× 60]) oe 4(a)(iii)(b) 2 h 40 mins 4 Approach 1 8 B3 for [h]oe or 160 [mins] or 9600[s] 3 Or M3 for 5000 ÷ (18.75 × 25 × 4)[h] oe or 5000 ÷ (18.75 × 25 ÷ 15)[mins] oe or 5000 ÷ ((18.75 × 25 × 4) ÷ (60 × 60))[secs] oe Or M2 for (18.75 × 25 × 4)[m/h] oe or (18.75 × 25 ÷ 15)[m/min] oe or (18.75 × 25 × 4) ÷ (60 × 60))[m/sec] oe Or B1 for 200 or 1 km =1000m soi After 0 scored SC1 for time Figs 267 or figs 2666 to 2667 or figs 16 or figs 96 Approach 2 B3 for 160 [mins] Or M3 for 15 × 5000 ÷ (18.75 × 25) [mins] oe Or M2 for 5000 ÷ (18.75 × 25) oe Or B1 for 200 or 1 km =1000m soi After 0 scored SC1 for time figs 16 4(a)(iv) 17.1 or 17.14 to 17.15 3 3  100 − 5  M2 for 20 ×   oe  100   100 − 5  k or M1 for 20 ×   where k is 2, or  100  4  100 − 5  3 or for 20 ×   oe seen and spoiled  100  4(b) 2500 3 425to450 450 − 12.5 M2 for or or 10 + 0.5 10 to 11 425 to 450 450 − 12.5 or 630 600 to 660 or M1 for 10.5 or 9.5 or 437.5 or 462.5 or 630[s] or 570[s]

This question in 0580/41 Oct/Nov 2024

4 (a) The angles of a quadrilateral are w°, x°, y° and z°. The ratio w : ( x + y + z) = 3 : 5. Find the value of w. w = … [2] (b) B M 105° P C NOT TO SCALE N 49° 45° A D Q A, B, C and D are points on a circle. PQ is the tangent to the circle at A. BMND is a straight line. Angle ACD = 49°, angle AMB = 105° and angle PAB = 45°. (i) Find angle BAM. Angle BAM = … [2] (ii) (a) Find angle BAD. Angle BAD = … [2] (b) Give a geometrical reason why BD is not the diameter of the circle. … … [1] (c) A B O NOT TO T D SCALE C A, B, C and D are points on a circle, centre O. TA and TC are tangents to the circle. OA = 6.75 cm and OT = 11.5 cm. (i) Show that angle AOC = 108.12°, correct to 2 decimal places. [3] (ii) Calculate the length of the minor arc ABC. … cm [2] (iii) Calculate the area of the major sector OCDA. … cm2 [3]

15 marks

Mark scheme: 4(a) 135 2 360 M1 for × k, where k = 1, 3 or 5 oe 5 + 3 4(b)(i) 26 2 B1 for ABD = 49 4(b)(ii)(a) 86 2 B1 for QAD = 49 or for BDA = 45 or for BCA = 45 4(b)(ii)(b) Angle in a semicircle = 90 1 4(c)(i) −1 6.75  M2 6.75 [2  ] cos   oe M1 for cos(…) = oe  11.5  11.5 108.117… A1 4(c)(ii) 12.7 or 12.73 to 12.74 2 108.12 M1 for  2  π  6.75 360 4(c)(iii) 100 or 100.1 to 100.2 3 360 − 108.12 M2 for  π  6.752 oe 360 108.12 or M1 for  π  6.752 360 360 − 108.12 If 0 scored, SC1 for  π  k 360

This question in 0580/42 Oct/Nov 2024

1 Dinari sells fruit and vegetables. (a) One day the mass of fruit and vegetables he sells is in the ratio fruit : vegetables = 9 : 8. He sells 48 kg of vegetables. Find the mass of the fruit he sells. … kg [2] (b) On another day he receives $280 for the fruit and vegetables he sells. The $280 is in the ratio fruit : vegetables = ( c + 3) : ( c - 1) . Find the amount he receives from selling the fruit. $ … [3] (c) In one week Dinari buys fruit and vegetables for $1620. He sells the fruit and vegetables for $1750. Calculate his percentage profit. … % [2] (d) In another week Dinari sells fruit and vegetables for $1738. He makes a profit of 10%. Calculate the amount he paid for the fruit and vegetables in that week. $ … [2]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 54 2 48 M1 for 8 1(b) 142 3 B2 for 2c = 278 or better or M1 for c + 3 + c – 1 = 280 OR B2 for 2x = 276 or better or M1 for c + 3 – (c – 1) = 4 1(c) 8.02 or 8.024 to 8.025 2 1750 − 1620 M1 for [100] 1620 1750 or for 100[ −100] 1620 1(d) 1580 2 + 10 M1 for 100...  =1738 oe or better 100

This question in 0580/43 Oct/Nov 2024

3 Mass of box A : Mass of box B = 4 : 7 The mass of box B is 2.4 kg more than the mass of box A. Calculate the mass of box A and the mass of box B. box A … kg box B … kg [3]

3 marks

Mark scheme: 3 [A =] 3.2 3 B2 for one correct or for both correct but [B =] 5.6 reversed 2.4 or M1 for  k where k = 1, 4, 7 or 11 oe 7 − 4 x 4 or for = oe x + 2.4 7

This question in 0580/42 May/June 2025