Percentages — Paper 4 · IGCSE Mathematics - International 0607

1 In 2016, Carla’s salary was $23 970 per year. (a) From her salary she pays tax at a rate of 20%. She is paid monthly in equal amounts. Calculate the amount Carla receives each month after tax has been paid. $ … [3] (b) Carla’s salary of $23 970 was 2% more than her salary in 2015. (i) Calculate her yearly salary in 2015. $ … [3] (ii) From 2016, Carla’s employer agrees to pay her an increase of 3% each year. Calculate the year in which her salary is first greater than $30 000. … [3]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1598 final answer 3 M2 for (23 970 × 0.8) ÷ 12 oe or M1 for 23 970 × 0.2 or better or for 23 970 ÷ 12 1(b)(i) 23 500 nfww 3 M2 for 23 970 ÷ 1.02 oe or M1 for 23 970 = 102% 1(b)(ii) 2024 nfww 3  30000  log    23970  M2 for oe soi by 7.59...or sketch log1.03 leading to 7.59 or 2 trials, one giving 7 and one giving 8  3  n or M1 for 23 970 ×  1 +  [= 30 000] oe seen  100  or reasonable sketch or 3 trials of 23 970 × 1.03n or 1 trial giving 8.

This question in 0607/42 May/June 2017

2 In a sale, a shop reduces all of its prices by 15%. (a) Jake buys a jacket which had an original price of $65. (i) Calculate how much Jake pays for the jacket. $ … [2] (ii) After paying for the jacket, Jake has $24.75 left. Work out $24.75 as a fraction of the total amount of money Jake had before he bought the jacket. Give your answer in its lowest terms. … [2] (b) In the sale, Amy pays $80.75 for a coat. Calculate the original price of the coat. $ … [3] (c) One day the shop reduces its sale prices by 10%. Calculate the overall percentage reduction of the original prices. … % [2]

9 marks

Mark scheme: 2(a)(i) 55.25 2 M1 for 65 × 0.85 oe 2(a)(ii) 99 2 B1 for 80 cao or M1 for 24.75 + their 55.25 320 2(b) 95[.00] 3 M2 for 80.75 ÷ 0.85 oe or M1 for recognising 80.75 as 85%. 2(c) 23.5 2 0.9 × their ( a )( i ) M1 for 0.85 × 0.90 oe or 65 oe 0.765 implies M1

This question in 0607/42 Oct/Nov 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

2 Flavia makes china cats. They each cost $22.60 to make. (a) Flavia sells some of them to Ari. She makes a profit of 35% on each cat. Calculate the price Ari pays for each cat. $ … [2] (b) Ari sells each cat for $43. Calculate Ari’s percentage profit. … % [3] (c) Jean buys 92 of Flavia’s cats. This is 15% more than the number Ari bought. Calculate the number of cats that Ari bought. … [3] (d) Jean bought the cats for $32 each. He sells some of the cats for $45 each. For the rest of the cats he reduces the price by 5% each day. Find the number of reductions he has made when the price first falls below $32. … [3]

11 marks

Mark scheme: 2(a) 30.51 2  35  M1 for 22.6 ×  1 +  oe  100  2(b) 40.9 or 40.93 to 40.94 3 43 − their 30.51 M2 for [× 100] oe their 30.51 43 or M1 for 43 – their 30.51 or their 30.51 2(c) 80 3  15  M2 for 92 ÷  1 +  oe  100  or M1 for 92 = 115% oe 2(d) 7 nfww 3 log( 3245 ) M2 for soi by 6.64 to 6.65 log0.95 or trials as far as n = 5 or M1 for 45 × 0.95n oe soi

This question in 0607/43 May/June 2018

5 The number of fish in a lake decreases by 4% each year. In January 2018 there are 30 000 fish in the lake. (a) Calculate the number of fish in the lake in (i) January 2019, … [2] (ii) January 2029, … [3] (iii) January 2017. … [3] (b) Find the last year in which there were at least 50 000 fish in the lake. … [4] (c) Philip runs a fishing business and he works 50 weeks every year. In 2018, he catches 800 kg of fish in each of these weeks. He sells all the fish he catches at a price of $3.50 for each kilogram. (i) Calculate the total amount he receives in 2018. $ … [3] (ii) For each of the 50 weeks, Philip’s business costs $2240 to run. Calculate his profit as a percentage of $2240. … % [3] (d) In 2019, Philip’s business costs 8% more to run than in 2018. The selling price of fish decreases by 10%. Find the amount of fish, in kilograms, Philip will need to catch each week to keep the percentage profit found in part (c)(ii) the same. … kg [4]

22 marks

Mark scheme: 5(a)(i) 28 800 2 100 − 4 M1 for 30000 × oe 100 5(a)(ii) 19 147 or 19 100 nfww 3 FT their 0.96, must be <1 and not 0.04 M2 for 30000 × (their 0.96)11 or 28800 × (their 0.96)10 or M1 for 30000 × ( their 0.96) k , k > 1 oe 5(a)(iii) 31 250 3 M2 for 30000 ÷their (0.96) or M1 for 30000 = their 0.96[ x ] 5(b) 2005 nfww 4 30000 M3 for n log(their 0.96) = log oe 50000 or M2 for (their 0.96) n = 0.6 oe or M1 for 50000 × (0.96) n = 30000 oe OR M3 for T and I with ‘12 and13’ seen or M2 for at least 3 correct trials or M1 for 50000 × (0.96) n = 30000 oe 5(c)(i) 140 000 3 M2 for 800 × 50 × 3.5 or M1 for multiplying any two 5(c)(ii) 25 3 their ( i ) − 2240 × M2 for 50[× 100] oe 2240 × 50 their ( i ) or × 100 oe 2240 × 50 800 × 3.5 − 2240 or [× 100 ] oe 2240 800 × 3.5 or × 100 2240 or M1 for their ( i ) − 2240 × 50 their ( i ) or 2240 × 50 or 800 × 3.5 − 2240 800 × 3.5 or 2240 5(d) 960 4 2240 × 1.08 × 1.25 M3 for oe 3.5 × 0.9 x× 3.5 × 0.9 − 2240 × 1.08 or for 2240 × 1.08 their ( c )( ii ) = oe 100 or B1 for 3.15 or 157.50 and B1 for 2419.2 or 120 960 or 3024

This question in 0607/41 Oct/Nov 2018

1 Adila has $10 000. (a) She uses some of the money to buy a car. The salesman reduces the price from $3800 to $3610. Calculate the percentage reduction. … % [3] (b) Adila invests the remaining $6390 at a rate of 3% per year compound interest. (i) Find the value of the investment at the end of 5 years. $ … [3] (ii) Find the least number of complete years after which the value of the investment is more than $9000. … [4]

10 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 5% 3 3800 − 3610 M2 for [× 100] oe 3800 3610 or × 100 3800 3610 or M1 for oe 3800 1(b)(i) 7410 or 7407 to 7408 3 3 5 M2 for 6390 × (1 + ) oe 100 3 k or M1 for 6390 × (1 + ) oe, k > 1 100 1(ii) 12 nfww 4  9000  M3 for nlog 1.03 = log   soi by 11.6  6390  or 11.58... oe or correct trials as far as 11 and 12 oe 9000 or M2 for 1.03n = 6390 or at least 3 correct trials with n ⩾ 5 or M1 for 6390 × 1.03n = 9000 soi.

This question in 0607/42 Oct/Nov 2018

1 In a sale, a shop reduces all its prices by 15%. (a) Calculate the sale price of a television originally costing $630. $ … [2] (b) The price of a fridge in the sale is $952. Calculate the original price. $ … [3] (c) After one week the shop reduces the price of the television in part (a) by a further 5% each week until it is sold. Calculate the number of weeks from the start of the sale until the television reaches half the original price. … [4]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 535.5[0] final answer 2  15  M1 for 630 ×  1 −  oe  100  1(b) $1120 3  15  M2 for 952 ÷  1 −  oe  100  or M1 for 85% associated with 952 1(c) 12 nfww 4  5   12 (630)  M3 for nlog  1 −  = log    100   their 535.50  oe soi by 10.3 or 10.4 or 10.34 to 10.36… or correct trials as far as 10 and 11 or suitable sketch(es) e.g. y = 535.5 × 0.95x and y = 315  5  n  12 (630)  or M2 for  1 −  =   oe  100   their 535.50  or at least 3 correct trials or final answer 11 nfww  5  n 1 or M1 for their 535.5 ×  1 −  = 2 (630)  100  soi oe

This question in 0607/41 May/June 2019

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

4 NOT TO SCALE 3 cm l cm The diagram shows a solid made from a cylinder and two hemispheres. The radius of the cylinder and each hemisphere is 3 cm. The total volume of the solid is 144r cm3. (a) The length of the cylinder is l cm. Find the value of l. l = … [3] (b) The solid is made of steel. 1 cm3 of steel has a mass of 7.8 g. Calculate the mass of the solid. Give your answer in kilograms. … kg [2] (c) The solid is melted down and made into 20 cubes each of side length 2.8 cm. Calculate the volume of steel not used for the cubes as a percentage of the 144r cm3. … % [3] (d) A solid that is mathematically similar to the original solid has a volume of 18r cm3. Find the radius of the new cylinder. … cm [3]

11 marks

Mark scheme: 4(a) 12 cao final answer 3 B2 for 11.98 to 12.02 2 2 3 or M1 for π × 3 × l + 2 × × π × 3 [ = 144π] 3 oe 4(b) 3.53 or 3.528 to 3.529... 2 M1 for 144 π × 8.7 soi by figs 353 or 3528 to 3529 4(c) 2.95 or 2.96 or 2.950 to 2.963... 3 144 π − 20 × 8.2 3 M2 for [× 100 ] 144 π 20 × 8.2 3 or × 100 oe 144 π 3 20 × 8.2 3 or M1 for 144 π − 20 × 8.2 or oe 144 π 4(d) 1.5 oe cao final answer 3 B2 for 1.498 to 1.502 18π or M2 for 3 × 3 oe 144 π 18π 144 π or M1 for 3 or 3 oe or better 144 π 18π  3 3 144π or for = oe    x  18π

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

1 Ernst makes chairs. (a) The total cost of making a chair is $250. Total cost = cost of materials + $26 for each hour worked 1 Ernst works for 6 hours to make a chair. 2 Calculate the cost of the materials as a percentage of the total cost of $250. … % [3] (b) Ernst sells the chairs to a shop. The shop makes 24% profit when they sell a chair for $396.80 . Calculate the amount the shop pays Ernst for a chair. $ … [2] (c) In a sale the shop reduces the price, $396.80, of each chair by 3% each day until it is sold. Find the number of days until the price first goes below $200. … [4]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 32.4 3 250 − 6.5 × 26 M2 for [× 100 ] oe 250 6.5 × 26 or × 100 250 or M1 for 250 – 6.5 × 26 soi by 81 6.5 × 26 or 250 1(b) 320 2  24  M1 for ( ) ×  1 +  = 396.8 or  100  better 1(c) 23 4 B3 for 22.49… or 22.5 or 22 as answer or M3 for  3   200  n log  1 −  = log   oe  100   396.8  or correct trials as far as 22 and 23 or sketch indicating value between 22 and 23  3  n 200 or M2 for  1 −  = oe  100  396.8 or at least 3 correct trials or a sketch that could lead to solution e.g. y = 0.97x and y = 200  3  n or M1 for 396.8 ×  1 −  = 200  100  soi. or at least 2 correct trials

This question in 0607/42 May/June 2021

2 (a) Increase $55 by 250%. $ … [2] (b) (i) Beatrice invests $500 at a rate of 1.5% per year simple interest. Find the amount Beatrice has at the end of 12 years. $ … [3] (ii) Dan invests $500 at a rate of 1.5% per year compound interest. Find the difference between Dan’s amount and Beatrice’s amount at the end of 12 years. $ … [3] (c) Eva invests an amount of money at a rate of 2.1% per year compound interest. Find the number of complete years it takes for Eva’s investment to double in value. … [4] (d) Each year the value of Fred’s car reduces by 15% of its value at the start of that year. The value of the car is now $5158.65 . Find the value of Fred’s car 3 years ago. $ … [3]

15 marks

Mark scheme: 2(a) 192.5[0] 2 250 M1 for 55 × oe or better 100 2(b)(i) 590 3 500 × 1.5 × 12 M2 for 500 + oe 100 500 × 1.5 × 12 or M1 for 100 2(b)(ii) 7.81 3 B2 for 597.8 … or 598 seen OR  1.5 12 M2 for 500  1 +  − their (b)(i) oe  100   1.5 12 or M1 for 500  1 +  oe  100  2(c) 34 4 B3 for 33.4 or 33.35... OR  2.1  M3 for n log  1 +  = log2 oe  100  or for trials reaching 33 and 34 or good sketch indicating value between 33 and 34  2.1  n or M2 for  1 +  = 2 oe  100  or for at least 3 correct trials or for suitable graph  2.1  n or M1 for  1 +  oe soi by two trials  100  For M2 and M1 oe includes use of a sum of money 2(d) 8400 3 3  100 − 15  M2 for 5158.65 ÷   oe  100   100 − 15  n or M1 for 5158.65 ÷   , including n = 1  100 

This question in 0607/43 May/June 2021

2 (a) Find 12 kg as a percentage of 80 kg. … % [1] (b) Find 19% of $250. $ … [2] (c) Xavier invests $500 at a rate of 1.5% per year simple interest. At the end of y years, the value of Xavier’s investment is $612.50 . Find the value of y. y = … [3] (d) Each year the value of a car decreases by 12% of its value at the beginning of that year. The original value of the car is $20 000. (i) Calculate the value of the car at the end of 3 years. Give your answer correct to the nearest dollar. $ … [3] (ii) Find the number of complete years for the value of $20 000 to decrease until it is first below $1000. … [4] (e) Each year the value of another car decreases by r % of its value at the beginning of that year. At the end of 10 years, the value has decreased from $12 000 to $4673. Find the value of r. r = … [3]

16 marks

Mark scheme: 2(a) 15 1 2(b) 47.5[0] 2 19 M1 for × 250 oe 100 2(c) 15 3 500 × 1.5 × y M2 for 500 + = 612.50 oe 100 500 × 1.5 × y or M1 for oe 100 or for one year’s interest = 7.5[0] 2(d)(i) 13629 cao 3 B2 for 13630 or 13629. ...  12  3 or M1 for 20000 ×  1 −  oe  100  2(d)(ii) 24 nfww 4 B3 for 23.4 or 23.43... OR  12   1000  M3 y log  1 −  = log   oe  100   20000  or correct trials reaching 23 and 24 or good sketch indicating value between 23 and 24  12  y 1000 or M2 for  1 −  = oe  100  20000 or at least 3 correct trials or suitable graph with y > 1  12  y or M1 for 20000 ×  1 −  = 1000 oe soi by at  100  least 2 correct trials with n > 3 2(e) 9[.00] or 8.999 to 9.000... 3 4673 M2 for 10 12000 or M1 for 12 000 × ( … )10 = 4673

This question in 0607/42 Feb/March 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

6 The lifetimes, x hours, of 80 electric light bulbs are shown in the table. Lifetime (x hours) Frequency 850 1 x G 870 4 870 1 x G 890 6 890 1 x G 900 12 900 1 x G 920 18 920 1 x G 940 16 940 1 x G 950 20 950 1 x G 1000 4 (a) Calculate an estimate of the mean lifetime. … h [2] (b) Complete the cumulative frequency table. Lifetime (x hours) Cumulative frequency x G 870 4 x G 890 x G 900 x G 920 x G 940 x G 950 x G 1000 80 [1] (c) On the grid below, draw a cumulative frequency curve. 80 70 60 50 Cumulative 40frequency 30 20 10 0 x 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 Lifetime (hours) [3] (d) Use your graph in part (c) to find an estimate for (i) the median lifetime, … h [1] (ii) the interquartile range. … h [2] (e) Find the percentage of bulbs that have a lifetime of more than 900 hours. … % [2]

11 marks

Mark scheme: 6(a) 919 2 M1 for at least 5 correct midpoints soi 6(b) [ 4], 10, 22, 40, 56, 76, [80] 1 6(c) Correct curve or polygon and correct points 3 M1 for at least 6 horizontal plots correct plotted M1FT for at least 6 vertical plots correct (870, 4) (890, 10) (900, 22) (920, 40) (940, 56) (950, 76) (1000, 80) 6(d)(i) 920 1 6(d)(ii) 42 to 47 2 M1FT for [UQ =] 941 to 944 or [LQ =] 897 to 899 6(e) 72.5 2 B1 for 18+16+20+4 or 80 – 22 soi (58) or M1 for (80 – their 22)/80 × 100

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

3 (a) Sachin earns $63 000 per year before paying tax. He pays tax on his earnings at a rate of 16%. Calculate the amount Sachin has after paying tax. $ … [2] (b) Britte has $60 480 per year after paying tax at a rate of 16%. Calculate the amount that Britte earns before paying tax. $ … [2] (c) (i) Sachin opens a savings account with $1500 on 1 January. The account pays 1.8% per year simple interest. Show that the amount in Sachin’s account at the end of 3 years is $1581. [2] (ii) Britte also opens a savings account on 1 January. The account pays 2% per year compound interest. Britte pays $500 into her account on 1 January every year. Find who has the greater amount in their account at the end of 3 years. Give the difference correct to the nearest cent. … by $ … [4]

10 marks

Mark scheme: 3(a) 52 920 2 16 M1 for 63 000 × or better 100 3(b) 72 000 2  16  M1 for A   1 −  = 60 480 oe or  100  better 3(c)(i) 1.8 2 1.8 1500 + 1500 × 3 × oe M1 for 1500 3 100 100 3(c)(ii) Sachin 20.2[0] 4 B3 for 1560.8... or 20.2 or 20.19 to 20.20  2 3 or M2 for 500 1 + +    100   2  2  2  500  1 +  + 500  1 +  oe  100   100   2 3 or M1 for 500 1 + or    100   2  2 500 1 + oe    100 

This question in 0607/42 Oct/Nov 2022

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

4 (a) A group of 10 people were asked the time, correct to the nearest minute, they each spent listening to the news and reading the news on Monday. The results are shown in the table. Minutes listening (x) 1 9 3 3 11 8 2 7 1 4 Minutes reading (y) 5 10 9 7 2 1 3 6 11 5 (i) Complete the scatter diagram. The first six points have been plotted for you. y 12 10 8 Minutes 6 reading 4 2 x 0 2 4 6 8 10 12 Minutes listening [2] (ii) Find the median time spent reading the news on Monday. … min [1] (iii) Find the equation of the line of regression. Give your answer in the form y = mx + c . y = … [2] (iv) On Tuesday, each person spends the same time listening to the news as they did on Monday. They each spend 5 minutes longer reading the news than they did on Monday. Write down the equation of the line of regression for Tuesday. y = … [1] (b) In February Sancho read the news for a total of 8 hours. This was a reduction of 36% from January. Work out how long Sancho read the news in January. … hours [2] (c) The bar chart shows the number of news articles read one day by each of 23 people. 5 Number of 4 news articles read 3 2 0 1 2 3 4 5 6 7 8 9 10 Number of people Calculate the mean number of articles read. … [2]

10 marks

Mark scheme: 4(a)(i) 4 correct points plotted 2 B1 for 3 correct 4(a)(ii) 5.5 1 4(a)(iii)  y =  − 0.323 x + 7.48 2 B1 for [ y =] − 0.323 x + k or [y=] kx + 7.48 or [y=] −0.32 x + 7.5 4(a)(iv)  y =  − 0.323 x + 12.48 1 FT their (k) + 5 4(b) 12.5 2  100 − 36 = M1 for x   8 oe  100  4(c) 3.57 or 3.565... 2 M1 for 5 +5 4 +6 3 +9 2  3 implied by 82

This question in 0607/42 Oct/Nov 2023

2 Asif, Basheera and Chelsea make baskets. (a) The selling price of a basket increases by 8%. The new selling price is $4.86 . Find the original selling price of a basket. $ … [2] (b) Asif earns $4.70 per hour plus $1.21 for each basket he makes. Each week he works 8 hours a day for 5 days. Each day Asif makes 18 baskets. Calculate the total amount Asif earns in one week. $ … [3] (c) One day Basheera and Chelsea make a total of 36 baskets. They each work for 8 hours. Basheera takes x minutes to make a basket. Basheera takes 6 minutes longer than Chelsea to make a basket. (i) Write down an expression in terms of x for the number of baskets Chelsea makes. … [1] (ii) Write down an equation in terms of x and show that it simplifies to 3x 2 - 98x + 240 = 0 . [3] (iii) Solve the equation 3x 2 - 98 x + 240 = 0 . x = … or … [2] (iv) Find the number of baskets Chelsea makes. … [2]

13 marks

Mark scheme: 2(a) 4.5[0] 2  8  M1 for A   1 +  = 4.86 oe  100  2(b) 296.9[0] 3 M1 for 8 [× 5] × 4.7[0] oe M1 for [5 ×] 18 × 1.21 oe 2(c)(i) 480 1 oe x − 6 2(c)(ii) 480 480 M1 480 + = 36 oe Allow + their (i) = 36 x x − 6 x 480(x – 6) + 480x = 36x(x – 6) oe M1 Clearing fractions correctly (Dep on two fractions with different algebraic denominators) Completion to A1 3x2 – 98x + 240 [= 0] with no errors 2(c)(iii) 8 2 M1 for suitable sketch of parabola with 2 30, oe positive solutions 3 or (3x – 8)(x – 30) = 0 −−( 98)  ( −98) 2 − 4(3)(240) or 2  3 2(c)(iv) 20 2 480 M1 for their 30 − 6

This question in 0607/42 Feb/March 2024

4 (a) The price of a coat is $84. The price is reduced by 12%. Find the new price of the coat. $ … [2] (b) The price of a table is reduced by 25%. The price is now $960. Find the original price of the table. $ … [2] (c) Samir invests $600 in a bank that pays compound interest at a rate of 5.1% each year. (i) Find the value of Samir’s investment after 4 complete years. $ … [2] (ii) Find the number of complete years for the value of Samir’s investment to be first worth more than $1000. … [4] (d) Amir and Bob work together and share their earnings in the ratio 3 : 5. (i) Find the amount Bob receives when their earnings are $120. $ … [2] (ii) They decide to change the ratio for all further earnings. Amir’s share of the earnings is increased by 20% of his original share. Bob’s share of the earnings is decreased by 20% of his original share. Show that the ratio of their earnings is now 9 : 10. [3]

15 marks

Mark scheme: 4(a) 73.92 2 (100  12) M1 for 84  soi 100 or B1 for 10.08 4(b) 1280 2 100  25 M1 for x   960 oe 100 4(c)(i) 732.09 2 M1 for 600  1.0514 oe 4(c)(ii) 11 4 B3 for 10.3 or 10.26 to 10.27 1000 or M3 for n log1.051  log 600 or good sketch indicating value between 10 and 11 or correct trials reaching 10 and 11 n 1000 or M2 for 1.051  oe 600 or sketch that could lead to solution e.g. y  1.051x , y  1.67 or at least 3 correct trials with n > 4 or M1 for 600  1.051n  1000 oe or suitable graph e.g. y  1.051x or at least 2 trials with n > 4 4(d)(i) 75 2 5 M1 for [120  ]5  3 oe 4(d)(ii) 3[ k ](1  0.2) : 5[ k ](1  0.2) M2 M1 for 5[ k ](1  0.2) or 3[ k ](1  0.2) or for their (d)(i)(1 – 0.2) Leading to 9:10 A1 No errors seen

This question in 0607/41 May/June 2024

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

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

12 A container is in the shape of a cuboid. The cuboid measures 41 cm by 32 cm by 25 cm. (a) Show that the capacity of the container is 32.8 litres. [2] (b) At 10 40 the container is empty. Water flows into the container at a rate of 2 litres per hour until the container is full. (i) At 12 10 there are x litres of water in the container. Find x as a percentage of 32.8 . … % [3] (ii) Find the time when the container is full. … [3]

8 marks

Mark scheme: 12(a) 41  32  25 M2 M1 for 41 × 32 × 25 or for dividing by 1000 seen 1000 = 32.8 with no errors 12(b)(i) 9.15 or 9.146… 3 B1 for 1.5 oe or 3 seen 2  their1.5[ 100] M1 for 32.8 12(b)(ii) [0]3 04 3 32.8 M1 for 2 M1 FT for correct conversion of their length of time to hours and minutes 16 hours 24 min

This question in 0607/42 Feb/March 2025

12 Paula bought a house on 1 January 2023. On 1 January 2024 the value of the house increased by 10%. On 1 January 2025 the value of the house increased by 6% of its value on 1 January 2024. The value of the house on 1 January 2025 was $215 710. (a) Calculate the amount Paula paid for the house in 2023. $ … [3] (b) From 2025 the value of the house increases exponentially at the rate of 6% each year. The value of the house on 1 January 2025 was $215 710. Find the year in which the value of the house on 1 January will first be greater than $400 000. … [4]

7 marks

Mark scheme: 12(a) 185 000 3 215710 M2 for oe or better (1 + 0.1)(1 + 0.06) or M1 for A (1 + 0.1) = 215710 or A (1 + 0.06) = 215710 oe 12(b) 2036 4 B3 for 11 or 10.59 to 10.6 OR 400000 log 215710  400000  M3 for [ n = ] or log1.06   log1.06  215710  or suitable graph showing correct solution or correct trials as far as 10 and 11 n 400000 or M2 for 1.06 = oe 215710 or graph of y = 1.06 n and y = k or at least 3 correct trials or M1 for 215710  1.06 n = 400000 oe or graph of y = 1.06 n

This question in 0607/42 May/June 2025

18 (a) Bruce buys a new car on 1 January 2022. On 1 January 2023 the value of the car has decreased by 20%. On 1 January 2024 the value of the car has decreased by 15% of its value on 1 January 2023. Find the overall percentage decrease in the value of the car on 1 January 2024. … % [2] (b) Sangita buys a car with a value of $20 000. The value of the car decreases exponentially at a rate of 5% per year. Calculate the number of complete years it will take for the value of the car to decrease from $20 000 to $8000. … [4] (c) Sunil buys a car. The value of the car decreases exponentially at a rate of 6% per year. At the end of 9 years the value of the car is $8022. Calculate the original value of the car. $ … [2]

8 marks

Mark scheme: 18(a) 32 2  20  15  M1 for  1 −  1 −   100  100  18(b) 18 4 B3 for 17.9 or 17.86... OR  5   8000  M3 for n log  1 −  = log   oe  100   20000  or good sketch indicating value between 17 and 18 or correct trials reaching 17 and 18  5  n 8000 or M2 for 1 − = oe    100  20000 or suitable graph with n > 1 or at least 3 correct trials, n > 1  5  n or M1 for 20000  1 − = 8000 oe soi by    100  at least 2 trials with n > 1 18(c) 14 000 2 9  6  M1 for [...] ×  1 −  = 8022 oe  100 

This question in 0607/43 May/June 2025

4 Aisha is paid $17.50 per hour. Aisha’s pay is increased to $19.30 per hour. Calculate the percentage increase in Aisha’s pay. … % [2]

2 marks

Mark scheme: 4 10.3 or 10.28 to 10.29 2 19.3 − 19.3 M1 for 17.5[ 100] or  100 oe 17.5 17.5

This question in 0607/41 Oct/Nov 2025