Ratio and proportion — Paper 4 · IGCSE Mathematics - International 0607

5 Nitini flies from New Delhi to Singapore for a holiday. (a) Nitini changes 119 050 Indian rupees (INR) to Singapore dollars (SGD). The exchange rate is 1 SGD = 47.62 INR. Find how many Singapore dollars he receives. … SGD [2] (b) The flight from New Delhi to Singapore takes 5 hours and 45 minutes. The distance of the flight is 4150 km. (i) The time in New Delhi when the flight leaves is 21 55. The time in Singapore is 2 12 hours ahead of the time in New Delhi. Find the time in Singapore when the flight arrives. … [2] (ii) Find the average speed of the aircraft. … km / h [3] (iii) On the return flight the average speed is 750 km / h. Find the time of this flight in hours and minutes. … h … min [3]

10 marks

Mark scheme: 5(a) 2500 2 M1 for 119 050 ÷ 47.62 5(b)(i) [0]6 10 or 6 10 am oe 2 B1 for [0]0 25 or [0]3 40 or 28 h 130 min oe seen 5(b)(ii) 722 or 721.7 ... 3 M1 for 4150 ÷ their 5h 45 min B1 for 5.75 oe 5(b)(iii) 5 h 32 (or 31.8 to 32[.0] ) min 3 M1 for 4150 ÷ 750 soi by 5.53 or 5.53 ... B1FT for correct conversion to hours and minutes

This question in 0607/42 May/June 2017

4 (a) Marie has $260.50 and Luk has $208.40 . (i) Find, in its simplest form, the ratio Marie’s money : Luk’s money. Marie’s money : Luk’s money = … : … [2] (ii) Marie spends 16% of her money to buy a new coat. Calculate the cost of the coat. $ … [2] (iii) In a sale, the prices of all books are reduced by 10%. Luk buys a book for $11.25 . Calculate the original price of the book. $ … [3] (iv) Marie invests $200 at a rate of 2% per year simple interest. Calculate the total value of this investment at the end of 25 years. $ … [3] (v) Luk invests $190 at a rate of 2% per year compound interest. Calculate the value of this investment at the end of 25 years. $ … [3] (b) Fredrik invests $120 at a rate of 5.7% per year compound interest. Calculate the number of complete years it will take until the value of this investment is first greater than $300. … [3]

16 marks

Mark scheme: 4(a)(i) 5 : 4 2 B1 for any other correct ratio 4(a)(ii) 41.68 2 M1 for 0.16 × 260.5[0] oe 4(a)(iii) 12.5[0] 3 M2 for 11.25 ÷ 0.9 oe or M1 for recognising 11.25 as 90% 4(a)(iv) 300 nfww 3 200 × 2 × 25 M2 for + 200 oe 100 200 × 2 × 25 or M1 for oe (implied by 100 100 nfww) 4(a)(v) 311.72 3 M2 for 190 × 1.0225 oe or M1 for 190 × 1.02n oe where n > 1 4(b) 17 3 B2 for 16.5 or 16.52 to 16.53  300  log    120  or M2 for or appropriate sketch log1.057 or 120 × 1.057n = 300 and at least 2 trials which reach from 250 to 350 or M1 for 120 × 1.057n [ = 300]

This question in 0607/43 May/June 2017

2 Alan, Brendan and Cieran work as gardeners. (a) The total amount of money they earn is shared in the ratio of the time each person works. One day Alan works for 2 hours 40 minutes, Brendan works for 5.5 hours and Cieran works for 200 minutes. They earn, in total, $379.50 . By changing all the times into minutes, find the amount of money each person earns. Alan $ … Brendan $ … Cieran $ … [5] (b) (i) Alan needs to buy some gardening tools. In shop A, the price of the tools is $70.20 . In shop B, the price of the tools is 5% less than in shop A. Find the price of the tools in shop B. $ … [2] (ii) The price of $70.20 is 8% higher than it was last year. Find the price last year. $ … [3] (c) (i) Brendan invests $450 for 5 years at a rate of 3.5% per year simple interest. Show that the total value of this investment after 5 years is $528.75 . [2] (ii) Cieran invests $450 for 5 years at a rate of x % compound interest. The value of Cieran’s investment after 5 years is $530.60 . Find the value of x. x = … [3]

15 marks

Mark scheme: 2(a) 88, 181.5, 110 5 B4 for any two correct or all three correct values seen OR M1 for converting times to same units e.g. 160 : 330 : 200 M2 for correct method to find any part their 160or330or200 e.g. × 379.5 oe their 690 or M1 for correct use of total 379.5 e.g. soi 0.55 their 690 A1 for any one value correct, correctly placed 2(b)(i) 66.69 2 M1 for 70.2 × 0.95 oe 2(b)(ii) 65[.00] cao 3 70.2 M2 for oe 1.08 or M1 for 70.2 = 108% soi 2(c)(i) 3.5 3.5 M1 450 × [ × 5] or 5 × [ × 450] or 100 100 better 3.5 A1 i.e. full and correct conclusion to 450 + 78.75 450 + 450 × 5 × [ = 528.75] 100 leading to 450 + 78.75 or better. 2(c)(ii) 3.35 or 3.350… 3 530.6 M2 for 5 450 or M1 for 450 × [ ]5 = 530.6 oe

This question in 0607/43 Oct/Nov 2017

2 Conrad, Delia and Eli share $8000 in the ratio Conrad : Delia : Eli = 5 : 7 : 8 . (a) Show that Eli receives $3200. [2] (b) Conrad buys a toy for $65. He sells it for $55. Calculate the percentage loss. … % [3] (c) Delia invests $2500 at a rate of 2.5% per year simple interest. Calculate the interest Delia has at the end of 8 years. $ … [2] (d) Eli invests $2400 at a rate of 2.4% per year compound interest. Calculate the interest Eli has at the end of 8 years. $ … [3] (e) Conrad buys a coat in a sale. The sale price is $79.80 after a reduction of 5%. Calculate the original price of the coat. $ … [3]

13 marks

Mark scheme: 2(a) 8000 M2 M1 for 8000 ÷ (5 + 7 + 8) × 8 [ = 3200] 5 + 7 + 8 3200 If 0 scored SC1 for × 20 = 8000 oe 8 2(b) 15.4 or 15.38… 3 65 − 55[× 100] or 55 × 100 or 1 − 55 M2 for 65 65 65 55 or M1 for 65 − 55 or 65 2(c) 500 2 2500 × 2.5 × 8 M1 for oe 100 2(d) 501.42 3 M2 for 2400 × 1.0248 oe (2901 or 2901.4[0] or 2901.42…) or M1 for 2400 × 1.024n oe where n > 1 2(e) 84 3  5  M2 for 79.80 ÷ 1 − oe    100  or M1 for recognising 79.80 is 95%

This question in 0607/41 May/June 2018

1 (a) Work out. 3 402 .315 2 … [1] (b) Write 130.47 correct to (i) one decimal place, … [1] (ii) one significant figure. … [1] (c) Work out 23% of $76.80 . $ … [2] (d) $4200 is shared in the ratio 3 : 4 : 6 : 8 . Find the difference between the largest share and the smallest share. $ … [3] (e) Write down an irrational number less than 10. … [1] (f) Work out 7.31 # 10 - 2 + 1.56 # 10 - 1 . Give your answer in standard form. … [2]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 0.744 or 0.7437 to 0.7438 1 1(b)(i) 130.5 final answer 1 1(b)(ii) 100 [.00] final answer 1 1(c) 17.66 2 M1 for 0.23 × 76.8 oe 1(d) 1000 3 8 − 3 M2 for × 4200 oe 3 + 4 + 6 + 8 4200 or M1 for [×3 or 8] oe 3 + 4 + 6 + 8 1(e) Any irrational number less than 10 1 e.g. π , 12 , e ; and not with decimal or fractional equivalent 1(f) 2.29[1] × 10−1 final answer 2 B1 for figs 229[1]

This question in 0607/42 May/June 2018

1 Louis and Maria share $50 in the ratio 11 : 14. (a) Show that Louis receives $22. [1] (b) Louis and Maria each spend $6 from their share of the $50. Find the new ratio Louis’ money : Maria’s money. … : … [2] 17 (c) Louis spends of his remaining money to buy a bus ticket. 32 Calculate the cost of the bus ticket. $ … [1] (d) In a sale, a bookshop reduces the price of each book by 10%. Maria buys two of these books. (i) The first book Maria buys has an original price of $6. Calculate how much Maria pays for this book. $ … [2] (ii) Maria pays $3.69 for her second book. Calculate the original price of this book. $ … [3]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 11 11 M1 × 50 or × 50 oe 11 + 14 25 1(b) 16 : 22 oe isw 2 M1 for 22 – 6 and 50 –22 – 6 oe If 0 scored, SC1 for 22 : 16 oe 1(c) 8.5[0] 1 1(d)(i) 5.4[0] 2 M1 for 0.9 × 6 oe 1(d)(ii) 4.1[0] nfww 3 .369 M2 for oe 9.0 or M1 for associating 3.69 with 90%

This question in 0607/42 May/June 2019

3 Alana and Bill share some money in the ratio 5 : 4. Alana’s share is $160. (a) Show that Bill’s share is $128. [1] (b) Alana spends $x. The ratio of Alana’s money : Bill’s money is now 4 : 5. Find the value of x. x = … [3] (c) A shop has a sale. Bill buys a jacket in the sale for $32. (i) Write $32 as a percentage of $128. … % [1] (ii) The original price of the jacket was reduced by 20% to $32. Work out the original price. $ … [3]

8 marks

Mark scheme: 3(a) 4 1 160 × oe 5 3(b) 57.60 3 4 160 − x 4 M2 for 128 × or = 5 128 5 128 160 − x or M1 for or or 160 − x :128 = 4:5 5 4 3(c)(i) 25 1 3(c)(ii) 40 3 100 M2 for 32 × oe 80 or M1 equating 32 to 80%

This question in 0607/42 Oct/Nov 2019

1 Adam and Brenda share $560 in the ratio Adam : Brenda = 4 : 3. (a) Show that Adam receives $320. [1] (b) Adam spends 15% of his $320 on some software. Calculate how much Adam spends on this software. $ … [2] (c) In a sale, Brenda buys a computer for $179.40 . This is 8% less than the original price. Calculate the original price of the computer. $ … [2] (d) Adam spends a further $29.60 on a train ticket. Adam and Brenda then work out how much money each of them has left. Show that Adam has 4 times as much left as Brenda. [3]

8 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 560 M1 × 4 oe 7 1(b) 48 2 15 M1 for × 320 oe 100 1(c) 195 2 100 − 8 M1 for x × = 179.40 oe or better 100 1(d) 320 – their 48 – 29.60 = 242.40 M1 Clear working to 242.40 their 240 – 179.40 = 60.60 M1 Clear working to 60.60 60.60 × 4 = 242.40 cao A1 Clear statement using 242.40 and 60.60

This question in 0607/43 Oct/Nov 2020

2 (a) Write 260 512 correct to 3 significant figures. … [1] (b) Write 0.000 000 576 in standard form. … [1] (c) Calculate 27 2 - 6 # 31 0 .3 . Give your answer correct to 1 decimal place. … [2] (d) (i) Work out 37% of $820. $ … [2] (ii) Work out $36 as a percentage of $150. … % [1] (e) An amount of money is shared between Alan, Bjorn and Carlo in the ratio 3 : 7 : 5. Carlo receives $695. (i) Find the total amount of money shared. $ … [3] (ii) Carlo invests 40% of his $695 at a rate of 1.2% per year compound interest. Calculate the value of his investment at the end of 5 years. $ … [3] (f) Dana invests $2100 for 12 years at a rate of x% per year compound interest. At the end of the 12 years, the value of her investment is $2663.31 . Calculate the value of x. x = … [3]

16 marks

Mark scheme: 2(a) 261 000 1 2(b) 5.76 × 10−7 1 2(c) 26.7 2 B1 for 26.68 to 26.69 or answer 26.6 2(d)(i) 303.4[0] cao final answer 2 37 × 820 M1 for oe soi by 303 100 2(d)(ii) 24 1 2(e)(i) 2085 3 695 M1 for soi 5 M1 for (their 139) × (3 + 5 + 7) 2(e)(ii) 295.09 3 M2 for 0.4 × 695 × 1.0125 oe or M1 for 0.4 × 695 soi by 278 or A × 1.0125 2(f) 2[.00] or 1.998 to 2.001... 3 2663.31 M2 for 12 oe 2100 or M1 for 2100 × r12 = 2663.31 seen

This question in 0607/42 Feb/March 2021

11 y A (– 2, 4) NOT TO SCALE P O x B (8, – 1) A is the point (-2, 4) and B is the point (8, -1). P divides AB in the ratio 3 : 2. (a) Show that the coordinates of P are (4, 1). ( … , … ) [2] (b) The line L is perpendicular to AB and passes through P. Find the equation of line L. … [4] (c) The point C has coordinates (6, 5). Show that point C lies on line L. [1] (d) (i) Find the distance AB. Give your answer in surd form. … [2] (ii) Calculate the area of triangle ABC. … [3]

12 marks

Mark scheme: 11(a) 8 – –2 = 10, 3 : 2 = 6 : 4, M2 M1 for each coordinate x = –2 + 6 = 4 oe 4 to –1 = 5, y = 4 – 3 = 1 oe 11(b) y = 2x – 7 oe final answer 4 B3 for 2x – 7 as final answer OR −−1 4 M1 for gradient of AB = 8 −−( 2 ) −1 M1 for m =  1  their  −   2  M1 for 1 = (their2) × 4 + c or y – 1 = their2(x – 4)) 11(c) 2 × 6 – 7 = 5 oe 1 11(d)(i) 5 5 or 125 final answer 2 M1 for (8 – (–2))2 + ((–1) – 4)2 oe 11(d)(ii) 25 [.0] cao nfww 3 M1 for (6 – 4)2 + (5 – 1)2 M1 dep on first M1 for 1 × their ( d )( i ) × their 20 2

This question in 0607/42 May/June 2021

5 (a) Alana and Beau share $200 in the ratio x : y. 200x An expression for the amount of money Alana receives is . x + y (i) Write down an expression for the amount of money Beau receives. … [1] (ii) Alana and Beau are each given an extra $50. The ratio of the total amount of money that each person now has is 3 : 1. x Find the value of . y x = … [5] y (b) (i) On 1 January each year Bruno invests $1000 in Bank A. Bank A pays simple interest at a rate of 4% per year. Show that the total value of Bruno’s investment in Bank A at the end of 4 years is $4400. [3] (ii) On 1 January each year Bruno also invests $1000 in Bank B. Bank B pays compound interest at a rate of 3.5% per year. Find the total value of Bruno’s investment in Bank B at the end of 4 years. $ … [3]

12 marks

Mark scheme: 5(a)(i) 200 y 200 x 1 or 200 − x + y x + y 5(a)(ii) 7 5 M4 for 250 x + 50 y = 3(50 x + 250 y ) oe 250 x + 50 y or M3 for = 3 oe 50 x + 250 y or M2 for 250 x + 50 y or 250 y + 50 x oe 200 x 200 y or B1 for + 50 or + 50 x + y x + y OR M4 for x : y = 175: 25 oe or M3 for 225 − 50 or 75 − 50 oe 200 + 100 or M2 for oe 3 + 1 or B1 for 200 + 100 5(b)(i) 1000 × 4 × (4 + 3 + 2 + 1) M2 4 M1 for 1000 × oe or better 100 100 [= 400] oe 4000 + 400 [= 4400] A1 5(b)(ii) 4362.47 3 M2 for 1000 × (1.035 + 1.035 2 + 1.0353 + 1.035 4 ) oe or M1 for 1000 × 1.035 oe

This question in 0607/43 Oct/Nov 2021

4 (a) $216 is shared in the ratio 5 : 1. Work out the larger share. $ … [2] (b) Luis shares some money between Ali, Betty and Clare in the ratio 3 : 4 : 6. Ali receives $171. Find the total amount of money Luis shared. $ … [2] (c) Farima invests $1400 in a savings account paying simple interest at a rate of 2.5% per year. Calculate the total amount in the account at the end of 3 years. $ … [3] (d) Emir invests $3000 at a rate of 2% per year compound interest. (i) Calculate the value of Emir’s investment at the end of 4 years. $ … [2] (ii) Find the number of complete years until Emir’s investment is first worth more than $4000. … [4]

13 marks

Mark scheme: 4(a) 180 2 216 M1 for [ 5] 5  1 4(b) 741 2 171 M1 for 3 4(c) 1505 3 2.5 M2 for 1400 + 3(1400 × ) oe 100 2.5 or M1 for 3(1400 × ) oe 100 4(d)(i) 3247.30 or 3250 2 4  2  M1 for 3000  1  oe    100  4(d)(ii) 15 4 B3 for 14.5 or 14.52 to 14.53 seen  4000  or M3 for n log(1.02)  log   oe  3000  or for correct trials reaching 14 and 15 or good sketch indicating value between 14 and 15 4000 or M2 for 1.02n = 3000 or at least three correct trials for n > 4 or suitable graph or M1 for 3000 × 1.02n = 4000 soi by at least 2 correct trials for n > 4

This question in 0607/41 May/June 2022

5 (a) Alenia, Bob and Cara share some money in the ratio 5 : 3 : 4 . Alenia’s share is $1240. (i) Show that Bob’s share is $744. [1] (ii) Cara spends $x from her share. The ratio of Bob’s money : Cara’s money is now 4 : 3 . Find the value of x. x = … [3] (b) A shop has a sale and all prices are reduced by 20%. (i) Bob buys a coat. The original price of the coat was $92. Work out the sale price of the coat. $ … [2] (ii) Cara buys a jacket in the sale for $132. Work out the original price of the jacket. $ … [2] (c) On 1 January 2022 Alenia buys a scooter for $1240. On 1 January 2023 the value of the scooter is reduced by 18%. On 1 January 2024 the value of the scooter is reduced by 12% of its 1 January 2023 value. (i) Calculate the value of the scooter on 1 January 2024. $ … [3] (ii) After 1 January 2024, the value of the scooter is reduced by 12% each year. Find the year in which the value of the scooter on 1 January will first be below $310. … [4]

15 marks

Mark scheme: 5(a)(i) 1240 1  3[  744] 5 5(a)(ii) 434 3 744  3 M2 for  x   992  oe 4 744  3 or M1 for oe (558) (186 × 3) or 4 3  1302 seen 7 or for 992 seen 5(b)(i) 73.6[0] 2 20  92 M1 for 92  oe 100 or B1 for 18.4 5(b)(ii) 165[.00] 2 100  20 M1 for x   132 oe or better 100 5(c)(i) 894.78 3 1240  (100  18)  (100  12) M2 for oe 100  100 1240  (100  18) or M1 for or 100 (their 1016.8)  (100  12) 100 5(c)(ii) 2033 nfww 4 B3 for 9.3 or 9.288 to 9.29… OR 8.3 or 8.29 as final value 310 or M3 for n log0.88  log1240  0.82 or 310 n log0.88  log their 894.78 or correct trials reaching 9 and 10 or 8 and 9 or good sketch indicating value between 9 and 10 or between 8 and 9 n 310 or M2 for 0.88  or 1240  0.82 n 310 0.88  their 894.78 or at least 3 correct trials or sketch that could lead to solution e.g. y = 0.88x and y = 0.3 or M1 for 1240  0.82  0.88n = 310 or their 894.78  0.88n = 310 or at least 2 trials or suitable graph e.g. y = 0.88x

This question in 0607/42 May/June 2022

3 Alana, Bev and Cara work as decorators. (a) The total amount of money they earn is shared in the ratio of the time each person works. During one week Alana works for 16 hours 40 minutes, Bev works for 30 hours and Cara works for 1200 minutes. They earn a total of $1680.80 . Change all the times into minutes and find the amount of money each person earns. Alana $ … Bev $ … Cara $ … [4] (b) (i) Alana pays a weekly rent of $255 for her apartment. The price of this weekly rent is 2% higher than one year ago. Find the price of her weekly rent one year ago. $ … [2] (ii) Alana can pay one full year’s rent in advance. One year is 52 weeks. She will receive a discount of 3% on each weekly rent of $255. Calculate the cost of paying the full year’s rent in advance. $ … [2] (c) One week Bev earns $x. 1 2 She spends of these earnings on rent and on food. 4 9 1 She spends of the remaining money on clothes and saves the rest. 3 She saves $152. Find the value of x. x = … [3] (d) Cara invests $500 for 5 years at a rate of y % per year simple interest. The value of Cara’s investment at the end of 5 years is $530.75 . Find the value of y. y = … [3]

14 marks

Mark scheme: 3(a) 420.2[0] 4 B3 for one correct answer 756.36 or M2 for 1000 + 1800 + 1200 oe 504.24 or B1 for 1000 or 1800 seen 3(b)(i) 250 nfww 2  2  M1 for x   1 +  = 255 oe  100  3(b)(ii) 12862.2[0] 2 3 M1 for 255  52 − (255  52) oe 100 or B1 for 247.35 or 397.8 3(c) 432[.00] 3 19 35 B2 for oe or oe or 235 or 234.5... 54 54  1 2  or M1 for  1 − −  oe or better  4 9  3(d) 1.23 3 500  y  5 M2 for 500 + = 530.75 oe or better 100 500  y  5 or M1 for seen 100 or B1 for 6.15 If 0 scored, SC1 for 1.2[00] to 1.201 from compound interest used

This question in 0607/41 Oct/Nov 2022

1 Giselle flies from Paris (France) to Atlanta (USA). (a) She changes 8500 euros (€) to USA dollars ($). She receives $9520. Calculate the exchange rate. €1 = $ … [1] (b) The aircraft leaves at 10 35 local time and the flight takes 9 hours 30 minutes. The time in Atlanta is 6 hours behind the time in Paris. (i) Find the local time in Atlanta when the aircraft lands. … [2] (ii) On the return flight the aircraft leaves Atlanta at 23 08 local time and arrives in Paris the next day at 13 25 local time. The distance from Atlanta to Paris is 7072 km. Find the average speed for the flight from Atlanta to Paris. … km/h [4]

7 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1.12 1 1(b)(i) 14 05 2 B1 for 20 05 or 04 35 or 3h 30 min seen 1(b)(ii) 854 or 853.7 to 853.8 4 17 B2 for 8 or 8.28 or 8.283... 60 or B1 for 8 h 17 min or 497 min 17 M1 for 7072 ÷ their 8 60

This question in 0607/42 Oct/Nov 2022

5 (a) Kris and Laila share $200 in the ratio 2 : 3. (i) Show that Kris receives $80. [1] (ii) Kris spends 30.8% of his $80 on a book. Calculate the cost of the book. $ … [2] (iii) Laila invests her $120 at a rate of 1.16% per year simple interest. Calculate the total amount Laila has at the end of 5 years. $ … [3] (b) On 1 January 2020, Sangita invests an amount of money at a rate of 2% per year compound interest. On 1 January 2023 the value of the investment is $5306.04 . (i) Calculate the amount Sangita invested on 1 January 2020. $ … [2] (ii) Calculate the value of the investment on 1 January 2025. $ … [2] (c) Tomas invests an amount of money at a rate of 1.4% per year compound interest. Find the number of complete years it takes for the value of his investment to increase by 50%. … [4]

14 marks

Mark scheme: 5(a)(i) 2 1 200 2 + 3 5(a)(ii) 24.64 cao 2 30.8 M1 for  80 oe 100 5(a)(iii) 126.96 cao 3 120  1.16  5 M2 for 120 + oe 100 120  1.16  5 or M1 for 100 5(b)(i) 5000 cao 2 3  2  M1 for X  1 + = 5306.04 oe    100  5(b)(ii) 5520.4[0] nfww 2 2  2  M1 for 5306.04  1 + oe    100   2  5 or for their 5000  1 +    100  5(c) 30 nfww 4 B3 for 29.9 or 29.16… OR  1.4   150  or M3 for n log  1 +  = log    100   100  oe or good sketch indicating value between 29 and 30 or correct trials reaching 20 and 21  1.4  n 150 or M2 for 1 + = oe    100  100 or suitable graph with n > 1 or at least 3 correct trials or M1 for  1.4  150    1 +  n =   oe soi  100  100 by at least 2 trials with n > 1

This question in 0607/43 Oct/Nov 2022

11 A NOT TO SCALE O r cm B C The diagram shows an equilateral triangle ABC touching a circle, centre O and radius r cm. 3 3 2 (a) (i) Show that the area of triangle ABC is r cm 2. 4 [4] (ii) Find an expression, in terms of r and r, for the exact value of the shaded area. … cm2 [1] (b) D A NOT TO SCALE O r cm B C E F Another equilateral triangle DEF is touching the same circle. Find an expression, in terms of r and r, for the exact value of this shaded area. … cm2 [3] (c) Find in its simplest form the ratio perimeter of triangle ABC : perimeter of triangle DEF . … : … [2] Question 12 is printed on the next page.

10 marks

Mark scheme: 11(a)(i) Fully correct method for area M3 2 1  3 r  e.g. [Area] =   2   sin60   2  2  1 2 or Area of BOC = r  sin120 2 1 2 3 = r  2 2 1 2 3 Area of ABC = 3× r  2 2 or Side by cosine rule = r 3 Then 0.5 × a2 × sin 60 or 3 2 3 2 ( side ) = ( r 3) 4 4 3 3 2 = r 4 or M2 for correct method length of side 3 or M1 for cos30 = oe 2 Completion to answer with no errors A1 11(a)(ii) 2 3 3 2 1 πr − r oe 4 11(b) [Area = ] 3 3 r 2 − πr 2 oe 3  2r  2 M2 for 0.5   sin60 oe    tan30  2r or M1 for EF = oe tan30 11(c) 1 : 2 2 B1 for unsimplified

This question in 0607/42 Feb/March 2023

1 25 students each record the number of logic problems they solve in one hour. The table shows the results. Number of logic problems solved 3 4 5 6 7 8 Frequency 1 3 8 7 5 1 (a) Find (i) the range … [1] (ii) the mode … [1] (iii) the median … [1] (iv) the interquartile range … [2] (v) the mean. … [2] (b) Nabile draws a pie chart. Calculate the angle that represents 7 logic problems solved. … [2] (c) Shabana draws a bar chart using these results. The bar that represents 4 logic problems solved has a height of 4.5 cm. Calculate the height of the bar that represents 5 logic problems solved. … cm [2]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 5 1 1(a)(ii) 5 1 1(a)(iii) 6 1 1(a)(iv) 1.5 2 B1 for [u.q. = ] 6.5 or [l.q. = ] 5 1(a)(v) 3 2 M1 for 5.6 or 5 5 (1  3 + 3  4 + 8  5 + 7  6 + 7  5 + 1  8)  25 1(b) 72 2 5 360 M1 for [360] or [5] 25 25 1(c) 12 2 8 4.5 M1 for [4.5] or [8] 3 3

This question in 0607/41 May/June 2023

4 (a) $x is divided in the ratio 3 : 5. The larger share is $42. Find the value of x. x = … [2] (b) (i) Increase 124 by 16%. … [2] 2 (ii) The price of a coat is reduced by in a sale. 9 The new price of the coat is $73.50 . Find the original price of the coat. $ … [2] (c) Xiong invests $2000 in Bank A which pays simple interest at a rate of 3% each year. Find the total amount of interest Xiong receives at the end of 5 years. $ … [2] (d) Wendi invests $400 in Bank B which pays compound interest at a rate of 1.6% each year. Find the total amount of interest Wendi receives at the end of 3 years. $ … [3] (e) Pedro invests $1000 in Bank C for 18 years. Pedro also invests $1000 in Bank D for 18 years. Bank C pays simple interest at a rate of x % each year. Bank D pays compound interest at a rate of 0.7x % each year. At the end of 18 years Pedro has exactly the same amount of money in Bank C and Bank D. 18 18x 0 .7 x (i) Show that 1 + = 1 + . 100 e 100 o [2] (ii) Given that 5 1 x 1 7 , use a graphical method to find x. x 5 7 x = … [3]

16 marks

Mark scheme: 4(a) 67.2[0] 2 M1 for 42  5  k  where k is 8 or 3 or 1 4(b)(i) 143.84 cao 2 16 M1 for 124  (1  ) oe 100 or B1 for 19.84 or 143.84 seen 4(b)(ii) 94.5 [0] 2  2  M1 for  1   x  73.5 oe  9  4(c) 300 2 M1 for 2000  [0].03  5 oe 4(d) 19.51 3 3  1.6  M2 for 400  1    400 oe  100   1.6 3 or M1 for 400  1   oe  100  4(e)(i) 1000  x  18 M1 1000  oe 100 18 M1  0.7 x  1000  1   oe  100  4(e)(ii) 5.76 or 5.756... 3  18 x  M2 for sketch of [ y ]  1   and  100   0.7 x 18 [ y  ]  1   oe  100  with distinct curve and line with clear point of intersection  18 x  or M1 for sketch of [ y ]  1   or  100   0.7 x 18 [ y  ]  1   oe  100 

This question in 0607/43 May/June 2023

6 (a) Jade and Kim share $160. Jade receives $8 more than Kim. Find the ratio Jade’s money : Kim’s money. Give your answer in its simplest form. … : … [2] (b) Each year the height of a bush increases by x% of its height at the start of the year. It takes 6 years for the bush to grow from 1.2 m to 1.664 m. Find the value of x. x = … [3] (c) Work out, giving each answer in standard form. (i) ( 4. 5 # 10 85 ) # ( 3 # 10 36 ) … [2] (ii) ( 2 # 10 n ) + ( 2 # 10 n - 2 ) … [2]

9 marks

Mark scheme: 6(a) 21 : 19 cao 2 B1 for answer 84 : 76 or 1 1 M1 for (160) + 4 or (160) − 4 2 2 If 0 scored, SC1 for final answer of 19 : 21 6(b) 5.6[0] or 5.599 to 5.600 3 1.664 M2 for 6 oe 1.2 or M1 for 1.2 × [...]6 = 1.664 6(c)(i) 1.35 × 10122 cao 2 B1 for 13.5 × 10 121 oe seen 6(c)(ii) 2.02 × 10n cao 2 B1 for figs 202

This question in 0607/41 Oct/Nov 2023

2 (a) Yuri and Zoe share some money in the ratio 8 : 7. Zoe receives $210. Show that Yuri receives $240. [1] (b) Yuri uses some of his money to buy a set of books and a concert ticket. (i) He spends 21% of his $240 on the set of books. Calculate the cost of the set of books. $ … [1] (ii) He spends $75.50 on the concert ticket. Calculate the amount Yuri has remaining as a percentage of the $240. … % [2] (c) Zoe spends $140 on software. She is given a discount of 20% on the original price of the software. Calculate the original price of the software. $ … [2] (d) Find the ratio Yuri’s remaining money : Zoe’s remaining money. Give your answer in the form n : 1. … : 1 [2]

8 marks

Mark scheme: 2(a) 210 M1  8 oe 7 2(b)(i) 50.4[0] 1 2(b)(ii) 47.5 or 47.54... 2 75.50  their(i) M1 for  100 240 240  (75.50 their(i)) or 240 2(c) 175 2 100  20 M1 for X × = 140 oe or better 100 2(d) 1.63 [: 1] 2 M1 for (240 – 75.50 – their (b)(i)) : (210 – 140) 8 or  47.5 : 33.3 oe 7

This question in 0607/42 May/June 2024

2 (a) Ameera and Bertrand share some money in the ratio 4 : 5. Bertrand gets $3000. Calculate Ameera’s share. $ … [2] (b) Bertrand invests $3000 at a rate of r% per year simple interest. At the end of 10 years the value of the investment is $3840. Find the value of r. r = … [3] (c) Claudia invests $6000 at a rate of s% per year compound interest. At the end of 8 years the value of the investment is $7367.67 . Find the value of s. s = … [3] (d) Dieter invests $4000 at a rate of 1.8% per year compound interest. At the end of n complete years the value of the investment is more than $6000. Calculate the smallest value of n. n = … [4]

12 marks

Mark scheme: 2(a) 2400 2 3000 M1 for 5 2(b) 2.8 3 3000 r 10 M2 for = 840 oe 100 3000 r 10 or M1 for 100 or B1 for [1 year interest] = 84 2(c) 2.6[0] 3 7367.67 M2 for 8 oe 6000 or M1 for 6000  … 8  7367.67 2(d) 23 cao 4 B3 for 22.7 or 22.72 to 22.73 OR  1.8   6000  M3 n log  1    log   oe  100   4000  or good sketch indicating value between 22 and 23 or correct trials reaching 22 and 23  1.8  n 6000 or M2 for  1    oe  100  4000 or suitable graph with n > 1 or at least 3 correct trials  1.8  n or M1 for 4000   1    6000 oe soi by at least  100  2 correct trials with n > 1

This question in 0607/43 May/June 2024

4 (a) Alan, Beth and Imran share an amount of money in the ratio 3x : 2x : ( x + 1) where x is an integer. (i) Find the amount Beth receives when x = 4 and they share $400 in total. $ … [3] (ii) Find the amount that Alan receives when Beth receives $66. $ … [2] (iii) Find the value of x when Alan receives 2.5 times the amount Imran receives. x = … [2] (b) In a sale, a shop reduces the price of all furniture by 12%. (i) Find the sale price of a chair that has an original price of $90. $ … [2] (ii) Find the original price of a table that has a sale price of $440. $ … [2] (c) Kurt invests $X in a bank which pays simple interest at a rate of 4% each year. The total amount of money that Kurt has in the bank at the end of 6 years is $930. Show that X = 750 . [2] (d) Ivana invests $750 in a bank which pays compound interest at a rate of y % each year. The total amount of money that Ivana has in the bank at the end of 6 years is $921.94 . Find the value of y. y = … [3]

16 marks

Mark scheme: 4(a)(i) 128 3 8 M2 for  400  12 + 8 + 5 or M1 for 12, 8, 5 or 25 4(a)(ii) 99 2 3 M1 for  66 oe 2 4(a)(iii) 5 2 M1 for 3 x = 2.5( x + 1) oe 4(b)(i) 79.2 [0] 2 100 − 12 M1 for 90  oe 100 or B1 for 10.8 4(b)(ii) 500 2 100 − 12 M1 for x  = 440 oe 100 4(c) 24 X M1 930 = X + oe 100 930 A1 X = oe 1.24 4(d) 3.5 or 3.4999.. 3 921.94 M2 for 6 750 or M1 for 750  ( k ) 6 = 921.94 oe

This question in 0607/41 Oct/Nov 2024

2 (a) Work out 24% of $15.50 . $ … [2] (b) The price of a bookcase is $123. This price is increased by 7%. Calculate the new price. $ … [2] (c) An amount of money is shared between Ali, Kat and Lena in the ratio 5 : 3 : 4. Lena’s share is $76. Work out the total amount of money. $ … [3] (d) A library has 32 800 books. Each year the number of books in the library increases by 300. Calculate the number of years it takes until there are 40 000 books in the library. … [2] (e) A different library has 32 695 books at the end of 2024. Each year the number of books increases by 0.6% of the number of books in the library at the end of the previous year. (i) Calculate the number of books the library had at the end of 2023. … [2] (ii) Calculate the number of complete years from 2024 that it takes for the number of books to first be greater than 40 000. … [4]

15 marks

Mark scheme: 2(a) 3.72 2 24 M1 for  15.5 oe 100 2(b) 131.61 final answer 2 100 + 7 M1 for  123 oe 100 or B1 for 8.61 2(c) 228 3 76 M2 for  ( 5 + 3 + 4 ) oe 4 76 or M1 for 4 2(d) 24 2 M1 for 300 +x 32 800 = 40 000 oe 2(e)(i) 32500 2  100 + 0.6 M1 for [...]  = 32 695 oe  100  2(e)(ii) 34 nfww 4 B3 for 33.71… or 33.7 OR 0.6 40 000 M3 for n log(1 + ) = log oe 100 32 695 or a good sketch indicating value between 33 and 34 or correct trials reaching 33 and 34  0.6  n 40 000 or M2 for 1 + = oe    100  32 695 or suitable graph or at least three correct trials  0.6  n or M1 for 32 695 1 + = 40 000 oe soi    100  or at least 2 trials with n > 1

This question in 0607/43 Oct/Nov 2024

3 (a) AC is a straight line. B is the mid-point of AC. A is the point (-1, 11) and B is the point (3, 8). (i) Find the length of AB. … [3] (ii) Find the coordinates of C. ( … , … ) [2] (iii) Find the equation of the perpendicular bisector of AC. … [4] (b) PQR is a straight line. P is the point (-6, -1) and Q is the point (-3, 1). Q divides the line PR in the ratio PQ : QR = 1 : 2 . Find the coordinates of R. ( … , … ) [2]

11 marks

Mark scheme: 3(a)(i) 5 3 M2 for (3 −−( 1)) 2 + (8 − 11) 2 soi or M1 for (3 −−( 1)) and (8 − 11) soi 3(a)(ii) (7, 5) 2 B1 for each 3(a)(iii) y = 43 x + 4 oe 4 M1 for gradient AC = 8 − 11 or better 3 −−( 1) M1 for perpendicular gradient = –1÷ their – 34 M1 for substituting (3, 8) into y = their mx + c 3(b) (3, 5) 2 B1 for one correct value or 3 M1 for  soi 2 or for suitable diagram seen e.g. a correct triangle with 2 sides marked

This question in 0607/43 Oct/Nov 2024

5 The exchange rate between pounds (£) and Chinese yuan (¥) is £1 = ¥ 8.3 . Change £549 to Chinese yuan. ¥ … [1]

1 marks

Mark scheme: 5 4556.7[0] final answer 1

This question in 0607/42 May/June 2025

3 In France, the price of a phone is 310 euros. In Dubai, the price of the same phone is 1185 dirhams. The exchange rate is 1 euro = 3.95 dirhams. Find the difference between the two prices. Give your answer in euros. … euros [2]

2 marks

Mark scheme: 3 10 2 M1 for 1185 ÷ 3.95 soi by 300 If 0 scored, SC1 for answer of 39.5

This question in 0607/41 Oct/Nov 2025

13 A is the point ( - 3 , 2) and B is the point ( 7 , - 3) . (a) Find the equation of the line AB. … [3] (b) C is a point on AB, and the ratio AC : CB = 3 : 2. Find the coordinates of C. ( … , … ) [2]

5 marks

Mark scheme: 13(a) 1 1 3 −−3 2 y = − x + oe final answer M1 for 2 2 7 −−( 3) ) M1 for substituting (–3, 2) or (7, –3) or  1   2, −  into  2  y = (their m)x + c oe 13(b) (3, – 1) 2 B1 for each or M1 for attempt to divide 10 and 5 in the ratio 3 : 2

This question in 0607/41 Oct/Nov 2025