Money — Paper 4 · IGCSE Mathematics 0580

9 Answer the whole of this question on a sheet of graph paper. A taxi company has “SUPER” taxis and “MINI” taxis. One morning a group of 45 people needs taxis. For this group the taxi company uses x “SUPER” taxis and y “MINI” taxis. A “SUPER” taxi can carry 5 passengers and a “MINI” taxi can carry 3 passengers. So 5x + 3y 45. (a) The taxi company has 12 taxis. Write down another inequality in x and y to show this information. [1] (b) The taxi company always uses at least 4 “MINI” taxis. Write down an inequality in y to show this information. [1] (c) Draw x and y axes from 0 to 15 using 1 cm to represent 1 unit on each axis. [1] (d) Draw three lines on your graph to show the inequality 5x + 3y 45 and the inequalities from parts (a) and (b). Shade the unwanted regions. [6] (e) The cost to the taxi company of using a “SUPER” taxi is $20 and the cost of using a “MINI” taxi is $10. The taxi company wants to find the cheapest way of providing “SUPER” and “MINI” taxis for this group of people. Find the two ways in which this can be done. [3] (f) The taxi company decides to use 11 taxis for this group. (i) The taxi company charges $30 for the use of each “SUPER” taxi and $16 for the use of each “MINI” taxi. Find the two possible total charges. [3] (ii) Find the largest possible profit the company can make, using 11 taxis. [1]

16 marks

Mark scheme: 9 (a) x + y ≤ 12 o.e B1 x + y < 13 (b) y ≥ 4 o.e. B1 y > 3 (c) Scales correct – full length S1 (d) x + y = 12 ruled and long enough L1 or broken line x + y = 13 y = 4 ruled and long enough L1 or broken line y = 3. F.t from x ≥ 4 only in (b) 5x + 3y = 45 ruled and long enough B2 SC1 for either point correct (1 mm at (9, 0) and (0, 15) if extended) Unwanted regions shaded B2√ SC1 for wanted regions shaded f.t. from minor slips in the lines that do not compromise the shape and position of the triangle or from x ≥ 4 in (b) and x = 4 drawn (e) 6 super, 5 mini and 5 super, 7 mini B3 SC2 for 1 correct and no more than 1 wrong (no extras) SC1 for any point(s) in their region selected Can write as (6, 5) and (5, 7) (enclosed by 3 lines or 2 lines + 1 axis) (f)(i) (7, 4) or (6, 5) s.o.i. M1 ($) 274 A1 ($) 260 A1 If 0 scored, SC1 for evidence of 30x + 16y written or used (f)(ii) ($) 94 c.a.o. B1 16

This question in 0580/41 May/June 2005

1 A Spanish family went to Scotland for a holiday. (a) The family bought 800 pounds (£) at a rate of £1 = 1.52 euros (€). How much did this cost in euros? [1] (b) The family returned home with £118 and changed this back into euros. They received €173.46. Calculate how many euros they received for each pound. [1] (c) A toy which costs €11.50 in Spain costs only €9.75 in Scotland. Calculate, as a percentage of the cost in Spain, how much less it costs in Scotland. [2] (d) The total cost of the holiday was €4347.00. In the family there were 2 adults and 3 children. The cost for one adult was double the cost for one child. Calculate the cost for one child. [2] (e) The original cost of the holiday was reduced by 10% to €4347.00. Calculate the original cost. [2] (f) The plane took 3 hours 15 minutes to return to Spain. The length of this journey was 2350 km. Calculate the average speed of the plane in (i) kilometres per hour, [2] (ii) metres per second. [1]

11 marks

Mark scheme: 1 (a) 1216 B1 (b) 1.47 B1 (c) 11 . 5 − 9 . 75 M1 × 100 11 . 5 15.2 A1 ww2 SC1 for 17.9 (d) 4347 ÷ 7 o.e. M1 621 A1 ww2 (e) 4347 ÷ 0 . 9 o.e. M1 4830 A1 ww2 (f)(i) 2350 M1 Must deal with the minutes correctly o.e. 3 . 25 723 to 723.1 A1 ww2 (ii) 200.9 to 201 A1ft their (i) ÷ 3.6 r.o.t. to 3sf or better [11]

This question in 0580/41 Oct/Nov 2005

9 Peter wants to plant x plum trees and y apple trees. For Examiner's He wants at least 3 plum trees and at least 2 apple trees. Use (a) Write down one inequality in x and one inequality in y to represent these conditions. Answer(a) , [2] (b) There is space on his land for no more than 9 trees. Write down an inequality in x and y to represent this condition. Answer(b) [1] (c) Plum trees cost $6 and apple trees cost $14. Peter wants to spend no more than $84. Write down an inequality in x and y, and show that it simplifies to 3x + 7y Y 42. Answer(c) [1] (d) On the grid, draw four lines to show the four inequalities and shade the unwanted regions. For Examiner's y Use 12 11 10 9 8 7 6 5 4 3 2 1 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 [7] (e) Calculate the smallest cost when Peter buys a total of 9 trees. Answer(e) $ [2] Question 10 is printed on the next page.

13 marks

Mark scheme: 9 (a) x [=3 y [=2 1, 1 (b) x + y Y 9 1 (c) 6x + 14y Y 84 1 (d) x = 3 y = 2 1, 1 Accept clear and freehand lines long enough to define the correct quadrilateral x + y = 9 2 SC1 for line through (0, 9) or (9, 0) Line from (0, 6) to (14, 0) 2 B1 for through (0, 6) or (14, 0) Correct quadrilateral unshaded or clearly 1 indicated (e) $ 70 2 B1 for considering (7, 2)

This question in 0580/41 May/June 2011

5 (a) The cost of a bottle of juice is 5 cents more than the cost of a bottle of water. For Mohini buys 3 bottles of water and 6 bottles of juice. Examiner's The total cost is $5.25. Use Find the cost of a bottle of water. Give your answer in cents. Answer(a) cents [4] (b) The cost of a biscuit is x cents. The cost of a cake is (x + 3) cents. The number of biscuits Roshni can buy for 72 cents is 2 more than the number of cakes she can buy for 72 cents. (i) Show that x2 + 3x O 108 = 0. Answer(b)(i) [3] (ii) Solve the equation x2 + 3x O 108 = 0. Answer(b)(ii) x = or x = [3] (iii) Find the total cost of 2 biscuits and 1 cake. Answer(b)(iii) cents [1]

11 marks

Mark scheme: 5 (a) 55 www B4 M3 for 3w + 6(w + 5) = 525 oe in $ or (3j – 5) + 6j = 525 oe in $ or M2 for j = w + figs5 oe and 3w + 6j = figs525 or M1 for w and w + figs5 or j and j – figs5 72 72 72 72 (b) (i) = 2 oe M2 M1 for or x −x + 3 x x + 3 72(x + 3) – 72x = 2x(x + 3) oe M1 Dep on 3 terms above Fractions removed, isw − 3 ± 441 (ii) –12, 9 www 3 M2 for (x + 12)(x – 9) or 2 or SC1 for ( x + a )( x + b ) where ab = –108 − 3 ± 3 2 − 4 × 1 × − 108 or a + b = 3 or 2 (iii) 30 1 ft 3 × a positive root + 3

This question in 0580/43 Oct/Nov 2011

10 Hassan stores books in large boxes and small boxes. For Each large box holds 20 books and each small box holds 10 books. Examiner's He has x large boxes and y small boxes. Use (a) Hassan must store at least 200 books. Show that 2x + y [ 20. Answer(a) [1] (b) Hassan must not use more than 15 boxes. He must use at least 3 small boxes. The number of small boxes must be less than or equal to the number of large boxes. Write down three inequalities to show this information. Answer(b) [3] (c) On the grid, show the information in part (a) and part (b) by drawing four straight lines and shading the unwanted regions. y 20 18 16 14 12 10 8 6 4 2 x 0 2 4 6 8 10 12 14 16 18 20 [6] (d) A large box costs $5 and a small box costs $2. For Examiner's (i) Find the least possible total cost of the boxes. Use Answer(d)(i) $ [1] (ii) Find the number of large boxes and the number of small boxes which give this least possible cost. Answer(d)(ii) Number of large boxes = Number of small boxes = [2] Question 11 is printed on the next page.

13 marks

Mark scheme: 10 (a) 20x + 10y ≥ 200 1 In (a), (b) −1 once for wrong symbol (b) x + y ≤ 15, y ≥ 3, y ≤ x 3 B1 for each (c) All lines long enough to make full boundary of region, accept dashed or solid lines, 2 mm acc at intercepts 2x + y = 20 ruled B2 B1 for ruled line through (10, 0) or (0, 20) x + y = 15 ruled B1 y = x ruled B1 y = 3 ruled B1 −1 once, freehand Quadrilateral identified R1 Allow if slight inaccuracy(s) in diagonal lines Allow any clear indication of region (d) (i) 47 cao 1 (ii) 7, 6 cao 2 M1 for any 5x + 2y in their region evaluated to equal their 47 IGCSE – October/November 2011 0580 43 8 

This question in 0580/43 Oct/Nov 2011

1 David sells fruit at the market. For Examiner′s Use (a) In one week, David sells 120 kg of tomatoes and 80 kg of grapes. (i) Write 80 kg as a fraction of the total mass of tomatoes and grapes. Give your answer in its lowest terms. Answer(a)(i) … [1] (ii) Write down the ratio mass of tomatoes : mass of grapes. Give your answer in its simplest form. Answer(a)(ii) … : … [1] (b) (i) One day he sells 28 kg of oranges at $1.56 per kilogram. He also sells 35 kg of apples. The total he receives from selling the oranges and the apples is $86.38 . Calculate the price of 1 kilogram of apples. Answer(b)(i) $ … [2] (ii) The price of 1 kilogram of oranges is $1.56 . This is 20% more than the price two weeks ago. Calculate the price two weeks ago. Answer(b)(ii) $ … [3] (c) On another day, David received a total of $667 from all the fruit he sold. The cost of the fruit was $314.20 . 1 David worked for 10 2 hours on this day. Calculate David’s rate of profi t in dollars per hour. Answer(c) … dollars/h [2] _____________________________________________________________________________________

9 marks

Mark scheme: Qu Answers Mark Part Marks 1 2 (a) (i) cao 1 5 (ii) 3 : 2 cao 1 (b) (i) 1.22 2 M1 for 86.38 – 28 × 1.56 (ii) 1.3 [0] nfww 3 M2 for 1.56 ÷ 1.2 oe or M1 for 1.56 = 120% soi (c) 33.6[0] 2 M1 for (667 – 314.2) ÷ 10.5 oe

This question in 0580/41 Oct/Nov 2013

1 An energy company charged these prices in 2013. Electricity price Gas price 23.15 cents per day 24.5 cents per day plus plus 13.5 cents for each unit used 5.5 cents for each unit used (a) (i) In 90 days, the Siddique family used 1885 units of electricity. Calculate the total cost, in dollars, of the electricity they used. $ … [2] (ii) In 90 days, the gas used by the Khan family cost $198.16 . Calculate the number of units of gas used. … units [3] (b) In 2013, the price for each unit of electricity was 13.5 cents. Over the next 3 years, this price increased exponentially at a rate of 8% per year. Calculate the price for each unit of electricity after 3 years. … cents [2] (c) Over these 3 years, the price for each unit of gas increased from 5.5 cents to 7.7 cents. (i) Calculate the percentage increase from 5.5 cents to 7.7 cents. … % [3] (ii) Over the 3 years, the 5.5 cents increased exponentially by the same percentage each year to 7.7 cents. Calculate the percentage increase each year. … % [3] (d) In 2015, the energy company divided its profits in the ratio shareholders : bonuses : development = 5 : 2 : 6 . In 2015, its profits were $390 million. Calculate the amount the company gave to shareholders. $ … million [2] (e) The share price of the company in June 2015 was $258.25 . This was an increase of 3.3% on the share price in May 2015. Calculate the share price in May 2015. $ … [3]

18 marks

Mark scheme: Question Answer Marks Part marks 1(a)(i) 275.31 2 M1 for 90 × 23.15 + 1885 × 13.5 oe 1(a)(ii) 3202 3 198.16 – 90 × 0.245 M2 for oe 0.055 M1 for 90 × 0.245 or 90 × 24.5 oe 1(b) 17.[0] or 17.00 to 17.01 2 3 § 8 · M1 for 13.5 × ¨ 1 + ¸ © 100 ¹ 1(c)(i) 40 3 7.7 − 5.5 7.7 M2 for [×100] oe or ×100 5.5 5.5 7.7 or M1 for oe 5.5 1(c)(ii) 11.9 or 11.86 to 11.87 3 7.7 M2 for 3 oe 5.5 or M1 for 5.5 × x3 = 7.7 oe 1(d) 150 [million] oe 2 M1 for 390 [million] ÷ ( 5 + 2 + 6) 1(e) 250 nfww 3 M2 for 258.25 ÷ ((100 + 3.3) ÷ 100) or M1 for 258.25 associated with 103.3[%]

This question in 0580/41 May/June 2017

8 l h NOT TO SCALE 5 mm The diagram shows a solid made from a hemisphere and a cone. The base diameter of the cone and the diameter of the hemisphere are each 5 mm. 115r (a) The total surface area of the solid is mm2. 4 Show that the slant height, l, is 6.5 mm. [The curved surface area, A, of a cone with radius r and slant height l is A = rrl.] [The surface area, A, of a sphere with radius r is A = 4rr2.] [4] (b) Calculate the height, h, of the cone. h = … mm [3] (c) Calculate the volume of the solid. 1 [The volume, V, of a cone with radius r and height h is V = rr2h.] 3 4 [The volume, V, of a sphere with radius r is V = rr3.] 3 … mm3 [4] (d) The solid is made from gold. 1 cubic centimetre of gold has a mass of 19.3 grams. The value of 1 gram of gold is $38.62 . Calculate the value of the gold used to make the solid. $ … [3]

14 marks

Mark scheme: 8(a) 2 M2 2 5 4  5  115π 5 4  5  π × × l + × π × = oe M1 for π × × l or × π ×     2 2  2  4 2 2  2  115π 4  5  2 5 or – × π × = π × × l oe   4 2  2  2 5πl 65π B1 nfww = oe oe both terms must be written in terms of π 2 4  115π 2  or [ l = ]  − 2 × π × 2.5  ÷ 2.5π oe nfww  4  or correct complete method for l with decimals 65π × 2 65π A1 [l =] or oe = 6.5 Correct calculation with no errors and B1 earned 4 × 5π 10π 8(b) 6 3 2 2 M2 for 6.5 − 2.5 or M1 for h2 + 2.52 = 6.52 If zero scored, SC2dep for answer 4.15[3]… 8(c) 72[.0…] or 71.99… nfww 4 2 3 π  5  1 4π  5  M3 for × × their 6 + × ×     3  2  2 3  2  oe π  5  2 or M1 for × × their 6 oe   3  2  1 4π  5  3 and M1 for × × oe   2 3  2  If zero scored, SC3dep for π 2 1 4π 3 × ( 5 ) × their 4.15 + × × ( 5 ) oe 3 2 3 or π 2 SC1dep for × ( 5 ) × their 4.15 oe 3 1 4π 3 SC1dep for × × ( 5 ) oe 2 3 8(d) 53.7 or 53.65 to 53.67 3 M1 for figs (their (c)) × 19.3 × 38.62 or better M1 for ÷ 1000 soi

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) Rowena buys and sells clothes. (i) She buys a jacket for $40 and sells it for $45.40 . Calculate the percentage profit. … % [3] (ii) She sells a dress for $42.60 after making a profit of 20% on the cost price. Calculate the cost price. $ … [3] (b) Sara invests $500 for 15 years at a rate of 2% per year simple interest. Calculate the total interest Sara receives. $ … [2] (c) Tomas has two cars. (i) The value, today, of one car is $21 000. The value of this car decreases exponentially by 18% each year. Calculate the value of this car after 5 years. Give your answer correct to the nearest hundred dollars. $ … [3] (ii) The value, today, of the other car is $15 000. The value of this car increases exponentially by x % each year. After 12 years the value of the car will be $42 190. Calculate the value of x. x = … [3]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 13.5 3 45.4[0] − 40 45.4[0] M2 for [× 100] or × 100 40 40 45.4[0] or M1 for [× 100] 40 1(a)(ii) 35.5[0] 3  20  M2 for 42.6[0] ÷ 1 + or better    100  or M1 for recognising 42.6[0] as 120[%] 1(b) 150 cao 2 500 × 2 × 15 M1 for oe 100 1(c)(i) 7800 cao 3 B2 for 7790 or 7785 to 7786  18  5 or M1 for 21000 × 1 − oe isw    100  If 0 or 1 scored, SC1 for their 7785… seen and rounded correctly to nearest 100 1(c)(ii) 9[.00…] 3 42190 M2 for 12 or better 15000  x 12 or M1 for 15000 1 + = [42190]    100 

This question in 0580/43 May/June 2018

8 (a) The price of a book increases from $2.50 to $2.65 . Calculate the percentage increase. … % [3] (b) Scott invests $500 for 7 years at a rate of 1.5% per year simple interest. Calculate the value of his investment at the end of the 7 years. $ … [3] (c) In a city the population is increasing exponentially at a rate of 1.6% per year. Find the overall percentage increase at the end of 20 years. … % [2] (d) The population of a village is 6400. The population is decreasing exponentially at a rate of r% per year. After 22 years, the population will be 2607. Find the value of r. r = … [3]

11 marks

Mark scheme: 8(a) 6 nfww 3 M2 for 2.65 − 2.50[× 100] or for 2.50 2.65 × 100 2.50 2.65 or M1 for 2.50 8(b) 552.5[0] 3 B2 for 52.5[0] 1.5 or M2 for 500 × × 7 + 500 oe 100 1.5 or M1 for 500 × [× 7] oe 100 8(c) 37.4 or 37.36… 2 20  1.6  M1 for 1 + oe soi 1.37…    100  8(d) 4[.00...] 3 2607 M2 for 22 6400 or M1 for 6400 × x22 = 2607 oe or better

This question in 0580/41 May/June 2019

4 (a) (i) Calculate the external curved surface area of a cylinder with radius 8 m and height 19 m. … m2 [2] (ii) This surface is painted at a cost of $0.85 per square metre. Calculate the cost of painting this surface. $ … [2] (b) A solid metal sphere with radius 6 cm is melted down and all of the metal is used to make a solid cone with radius 8 cm and height h cm. (i) Show that h = 13.5 . 4 3 [The volume, V, of a sphere with radius r is V = r r .] 3 1 2 [The volume, V, of a cone with radius r and height h is V = r r h .] 3 [2] (ii) Calculate the slant height of the cone. … cm [2] (iii) Calculate the curved surface area of the cone. [The curved surface area, A, of a cone with radius r and slant height l is A = r rl .] … cm2 [1] (c) Two cones are mathematically similar. The total surface area of the smaller cone is 80 cm2. The total surface area of the larger cone is 180 cm2. The volume of the smaller cone is 168 cm3. Calculate the volume of the larger cone. … cm3 [3] (d) The diagram shows a pyramid with a P square base ABCD. DB = 8 cm. NOT TO P is vertically above the centre, X, of SCALE the base and PX = 5 cm. D C X A B Calculate the angle between PB and the base ABCD. … [3]

15 marks

Mark scheme: 4(a)(i) 955 or 955.0 to 955.2 2 M1 for 2 × π × 8 × 19 oe 4(a)(ii) 812 or 811.7 to 811.9... 2 FT their (i) × 0.85 M1 for their (i) × 0.85 or their (i) × 85 4(b)(i) 4 3 M2 4 3 1 2 × π × 6 M1 for × π × 6 = × π × 8 × h 3 3 3 or cancelling clearly 1 2 × π × 8 3 seen to reach 13.5 4(b)(ii) 15.7 or 15.69... 2 M1 for 82 + 13.52 or better 4(b)(iii) 394 or 395 or 394.3 to 394.6... 1 FT π × 8 × their (b)(ii) 4(c) 567 3 3 168  80  2 M2 for =   oe or better V  180  1 1  180  2  80  2 or M1 for   or   oe seen or  80   180  better 4(d) 51.3 or 51.34... 3 5 M2 for tan = oe 4 or M1 for recognition of angle PBX

This question in 0580/41 Oct/Nov 2019

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

5 (a) $500 is invested at a rate of 3% per year. Calculate the total interest earned at the end of 7 years when (i) simple interest is paid, $ … [2] (ii) compound interest is paid. $ … [3] (b) The value of a car decreases exponentially by 10% each year. The value now is $6269.40 . Calculate the value of the car 3 years ago. $ … [3]

8 marks

Mark scheme: 5(a)(i) 105 2 3 M1 for × 500 [× 7 ] 100 5(a)(ii) 115 or 114.9... 3 7  3  M2 for 500 ×  1 +  [ −500 ]  100   3  k or M1 for 500 ×  1 +  , k integer ⩾ 2  100  5(b) 8600 3 6269.4 M2 for oe  10  3  1 −   100   10  3 or M1 for C ×  1 −  = 6269.4 oe  100 

This question in 0580/43 Oct/Nov 2021

7 Two rectangular picture frames are mathematically similar. (a) The areas of the frames are 350 cm2 and 1134 cm2. The width of the smaller frame is 17.5 cm. Calculate the width of the larger frame. … cm [3] (b) A picture in the smaller frame has length 15 cm and width 10.5 cm, both correct to the nearest 5 mm. Calculate the upper bound for the area of this picture. … cm2 [2] (c) In a sale, the price of a large frame is reduced by 18%. Parthi pays $166.05 for 5 large frames in the sale. Calculate the original price of one large frame. $ … [2] (d) Parthi advertises a large frame for a price of $57 or 48.20 euros. The exchange rate is $1= 0.88 euros. Calculate the difference between these prices, in dollars and cents, correct to the nearest cent. $ … [3]

10 marks

Mark scheme: 7(a) 31.5 3 1134 M2 for 17.5 × oe 350 1134 350 or M1 for oe isw or oe isw 350 1134 1134  x  2 or for =   oe 350  17.5  7(b) 15 2 B1 for 15 + 0.25 or 10.5 + 0.25 or better seen 163.937 5 or 16316 final answer 7(c) 40.5[0] 2  18  166.05 M1 for x ×  1 −  = oe  100  [ 5 ] 7(d) $2.23 final answer 3 B2 for 2.227… or 2.23 seen OR 48.2 M2 for 57 – oe 0.88 48.2 or M1 for oe 0.88 If 0 scored SC1 for 57 × 0.88 oe seen

This question in 0580/42 Feb/March 2022

4 (a) (i) Zak invests $500 at a rate of 2% per year simple interest. Calculate the value of Zak’s investment at the end of 5 years. $ … [3] (ii) Yasmin invests $500 at a rate of 1.8% per year compound interest. Calculate the value of Yasmin’s investment at the end of 5 years. $ … [2] (iii) Zak and Yasmin continue with these investments. How many more complete years is it before the value of Yasmin’s investment is greater than the value of Zak’s investment? … [3] (b) Xavier buys a car for $2500. The value of the car decreases exponentially at a rate of 10% each year. Calculate the value of Xavier’s car at the end of 5 years. Give your answer correct to the nearest dollar. $ … [3] (c) The number of a certain type of bacteria increases exponentially at a rate of r % each day. After 22 days, the number of this bacteria has doubled. Find the value of r. r = … [3]

14 marks

Mark scheme: 4(a)(i) 550 nfww 3 500 2 5 M2 for + 500 oe 100 500 2 5 or M1 for oe 100 4(a)(ii) 546.65 2 5  1.8  M1 for 500  1 + oe    100  4(a)(iii) 8 nfww 3 B2 for final answer 13 OR M2 for trials correctly comparing both investments to 7 and 8 more years or M1 for at least two trials correctly comparing both investments 4(b) 1476 cao 3 B2 for 1480 or 1476.2 ... OR  10 5 M1 for 2500  1 − oe    100  B1 for their more accurate answer seen correctly rounded to the nearest dollar. 4(c) 3.2[0] or 3.200 to 3.201 3 M2 for (...) = 22 2 oe isw or M1 for [N]  (...)22 = 2[N]

This question in 0580/41 Oct/Nov 2022

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

2 (a) Anil changes $830 into euros when the exchange rate is 1 euro = $1.16 . He spends 500 euros. He then changes the remaining money back into dollars at the same exchange rate. Work out how much, in dollars, Anil receives. $ … [3] (b) In 2021, Anil earns $37 000. (i) He spends $12 400 on bills in 2021. Calculate the percentage of his earnings he spends on bills. … % [2] (ii) His earnings of $37 000 increase by 3.2% in 2022. Calculate his earnings in 2022. $ … [2] (c) Anil invests $3500 in an account that pays a rate of 2.4% per year compound interest. (i) Calculate the total interest earned at the end of 5 years. $ … [3] (ii) Find the number of complete years before Anil has at least $5000 in this account. … years [3]

13 marks

Mark scheme: 2(a) 249.98 to 250[.0…] 3 M2 for 830 – 500 × 1.16 or M1 for 500 × 1.16 OR M1 for 830 ÷ 1.16 M1 for (their 715.5… – 500 ) × 1.16 2(b)(i) 33.5 or 33.51… 2 12400 M1 for [ 100] oe 37000 If 0 scored, SC1 for answer 66.5 or 66.48 to 66.49 2(b)(ii) 38 184 cao 2  3.2  M1 for 37 000   1   oe  100  or B1 for 1184 2(c)(i) 441 or 440.6 3 B2 for answer 3941 or 3940.6 or 3940.64 or 440.64 to 440.65 to 3940.65  2.4  5 or M2 for 3500 ×  1   – 3500  100   2.4  5 or M1 for 3500 ×  1   oe isw  100  2(c)(ii) 16 3 B2 for 15[.0] nfww to 15.1  2.4 15 or M2 for 3500 ×  1   oe seen  100   2.4 16 or 3500 ×  1   oe seen  100  or M1 for  2.4  n (3500 or their 3941) ×  1    100  associated with 5000 oe

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 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

9 (a) Janna and Kamal each invest $8000. At the end of 12 years, they each have $12 800. (i) Janna invests in an account that pays simple interest at a rate of r% per year. Calculate the value of r. r = … [3] (ii) Kamal invests in an account that pays compound interest at a rate of R% per year. Calculate the value of R. R = … [3] (b) The population of a city is growing exponentially at a rate of 1.8% per year. The population now is 260 000. Find the number of complete years from now when the population will first be more than 300 000. … years [3]

9 marks

Mark scheme: 9(a)(ii) 4[.0] or 3.99… 3 12800 M2 for 12 8000 or M1 for 12800 = 8000  k 12 for any k 9(b) 9 nfww 3 8  1.8  M2 for 260 000 ×  1 +  oe evaluated to 4  100  sf or better  1.8 9 or 260 000 ×  1 +  oe evaluated to 2 sf  100  or better  1.8  n or M1 for [300 000 = ] 260 000 ×  1 +   100  oe soi (Accept any inequality sign in [300 000 = ])

This question in 0580/42 Feb/March 2024

3 (a) Ed invests $500 in an account paying r % per year simple interest. At the end of 14 years the total amount in Ed’s account is $675. Find the value of r. r = … [3] (b) Eva invests $400 at a rate of 2.2% per year compound interest. Calculate the total interest earned at the end of 11 years. $ … [3] (c) Erin invests $700 at a rate of p% per month compound interest. At the end of 21 years the value of Erin’s investment is $1074, correct to the nearest dollar. Calculate the value of p. p = … [3]

9 marks

Mark scheme: 3(a) 2.5 3 500 r 14 M2 for = 675 − 500 oe 100 500 r 14 or M1 for or for 675 – 500 100 3(b) 108.18 3 B2 for 508.18... or 508.2 or 508  100 + 2.2 11 or M1 for 400   oe or  100  better 3(c) 0.17[0] or 0.1700... 3 1074 1074 M2 for either (12 21) or 252 or 700 700 better or M1 for 700 × [...](12×21 = 1074 oe If 0 scored SC1 answer 2.06 or 2.059...

This question in 0580/43 Oct/Nov 2024