The four operations — Paper 3 · IGCSE Mathematics 0580

1 Juana is travelling by plane from Spain to England. For Examiner's (a) Her case weighs 17.2 kilograms. Use The maximum weight allowed is 20 kilograms. By how much is the weight of her case below the maximum allowed? Answer (a) kg [1] (b) She changes 150 euros (€) into pounds (£). The exchange rate is €1 = £0.71. Calculate how much she receives. Answer (b) £ [1] (c) She travels from her home to the airport by train. She catches a train at 09 55 and the journey takes 45 minutes. (i) Write down the time she arrives at the airport. Answer (c)(i) [1] (ii) She has to wait until 12 10 to get on her plane. Work out how long she has to wait. Answer (c)(ii) h min [1] (d) The plane takes off at 12 40 Spanish time, which is 11 40 English time. 1 The flight takes 2 4 hours. What is the time in England when she arrives? Answer (d) [1] (e) The plane has seats for 420 passengers. 15% of the seats are empty. How many passengers are on the plane? Answer (e) [3]

8 marks

Mark scheme: Question Answer Marks Comments 1 (a) 2.8 1 ignore minus sign, accept 2800 g (b) 106.5(0) 1 107 is X (but remember to look back for 106.5) (c) (i) 10 40 1 accept 10.40, 10:40, 10.40 am (ii) 1 (hour) 30 (mins) 1 f.t. f.t. from (c)(i) [f.t. is (c)(i) > 12 10] accept 1 ½ (hours), 1.5 (hours), 90 (mins) (d) 13.55 1 accept 1.55 (pm) but 01 55 and 1.55 am are X (e) 357 3 M2 for 420 – 15 x 420/100, 420 x 85/100 o.e. or M1 for 15 x 420/100 o.e. answer of 63 is M1 implied 8

This question in 0580/31 May/June 2005

3 (a) (i) Calculate the interior angle of a regular heptagon (seven-sided polygon). For Write down all the figures on your calculator display. Examiner's Use Answer(a) (i) [2] (ii) Round your answer to part (a)(i) to 1 decimal place. Answer(a) (ii) [1] (b) xº NOT TO 80º 95º SCALE 3yº The diagram shows four angles around a point. (i) Write down an equation in x and y. Answer(b) (i) [1] (ii) Simplify your equation. Answer(b) (ii) [1] (iii) Find y when x = 65. Answer(b) (iii) y = [2] (c) (i) For A Examiner's Use aº NOT TO SCALE 70º 2bº C B Explain why a + 2b = 110 in the triangle above. Answer(c) (i) [1] (ii) NOT TO SCALE bº aº Explain why a + b = 90 in the semi-circle above. Answer(c) (ii) [1] (iii) Solve the equations a + 2b = 110, a + b = 90. Answer(c) (iii) a = b = [2] (iv) Work out the size of angle ABC in the triangle in part (c)(i). Answer(c) (iv) Angle ABC = [1]

12 marks

Mark scheme: 3 (a) (i) 128.571…… or 128° 3 4 ′ (….) 2 M1 for 180 – 360/7 oe (ii) 128.6 1 ft Follow through their (a)(i). (b) (i) x + 3y + 80 + 95 = 360 (or better) 1 (ii) x + 3y = 185 oe 1 Both marks may be gained in (b)(i) (iii) 40 2 ft M1 for x correctly substituted into the linear equation. Follow through their (b)(ii) provided linear in x and y. (c) (i) 180° or angle sum of triangle mentioned 1 (ii) Angle in a semi-circle mentioned. 1 (iii) (a =) 70 1 SC1 for a = 20 b = 70 (b =) 20 1 (iv) 40 1ft 2 × their value for b provided 0 < b < 55. 12

This question in 0580/31 Oct/Nov 2006

6 (a) Pencils cost 5 cents each and erasers cost 4 cents each. For Examiner's (i) Work out the total cost of 10 pencils and 7 erasers. Use Answer(a)(i) cents [1] (ii) Write down, in terms of p and e, the total cost of p pencils and e erasers. Answer(a)(ii) cents [1] (b) The cost of a pen is x cents and the cost of a ruler is y cents. 2 pens and 3 rulers have a total cost of 57 cents. 5 pens and 1 ruler have a total cost of 58 cents. (i) Write down two equations in x and y. Answer(b)(i) [2] (ii) Find the value of x and the value of y. Answer(b)(ii) x = y = [4]

8 marks

Mark scheme: 6 (a) (i) 78 B1 cao (ii) 5p + 4e B1 cao (b) (i) 2x + 3y = 57 B1 5x + y = 58 B1 SC1 for different variables (ii) 15x + 3y = 174 M1 oe, for useful mult. or substitution (2 terms correct) x = 9 A1 cao 18 + 3y = 57 M1 oe, for using first answer correctly and sensibly y = 13 A1 cao [8] www4 ft for M marks only for linear equations in 2 variables √ √

This question in 0580/31 Oct/Nov 2007

1 (a) Indira buys 1250 square metres of land to build a hotel. For Each square metre of land costs $12 . Examiner's Use Calculate the cost of the land. Answer(a) $ [1] (b) The cost of the land is 3% of the cost of the hotel. Calculate the cost of the hotel. Answer(b) $ [2] (c) The hotel has 84 rooms. The types of room are in the ratio family : double : single = 3 : 5 : 4 . Calculate the number of double rooms. Answer(c) [2] (d) Each single room is a cuboid, 4.5 m long, 3.2 m wide and 2.8 m high. Calculate the volume of a single room. Answer(d) m3 [2] (e) The total hotel income for the first year was $992 000 . For 3 Examiner's (i) The hotel spent of the total hotel income on staff wages. Use 8 Calculate the staff wages. Answer(e)(i) $ [1] (ii) The hotel also spent $420 000 on food. Calculate how much of the total hotel income was left. Answer(e)(ii) $ [2] (iii) Calculate $420 000 as a percentage of $992 000 . Give your answer correct to 1 decimal place. Answer(e)(iii) % [2] (f) To make improvements, Indira borrows $3 500 at a rate of 6% per year simple interest. She pays back all the amount at the end of 3 years. Calculate the total amount she needs to repay. Answer(f) $ [3]

15 marks

Mark scheme: Qu. Answers Mark Part Mark 1 (a) ($) 15 000 1 (b) ($) 500 000 2ft M1 for their 15 000 ÷ 3 × 100 (c) 35 2 M1 for 84 ÷ ( 3 + 5 + 4) or 84 ÷ 12 (d) 40.32 or 40.3 2 M1 for 4.5 × 3.2 × 2.8 (e) (i) ($) 372 000 1 (ii) ($) 200 000 2ft M1 for 992 000 − (their (e)(i) + 420 000) (iii) 42.3 cao 2 M1 for 420 000 ÷ 992 000 × 100 or better (f) ($) 4130 3 M1 for 3500 × 3 × 6 ÷ 100 oe A1 for 630 soi After M1A0 then SCB1 for their 630 + 3500

This question in 0580/32 May/June 2012

1 (a) The minimum temperatures at Beijing Airport, for five days, are given in this table. For Examiner's Use Day Monday Tuesday Wednesday Thursday Friday Temperature (°C) –3 5 –1 2 –4 (i) Write down the lowest temperature. Answer(a)(i) °C [1] (ii) Write these temperatures in order, starting with the lowest. Answer(a)(ii) < < < < [1] (iii) What is the difference between the temperatures on Monday and Tuesday? Answer(a)(iii) °C [1] (b) The table shows part of the timetable for flights from Beijing to Hong Kong. Beijing 07 45 08 00 09 30 Hong Kong 11 20 11 40 13 05 (i) At what time does the first plane after midday arrive in Hong Kong? Answer(b)(i) [1] (ii) How long, in hours and minutes, does the 07 45 flight from Beijing to Hong Kong take? Answer(b)(ii) h min [1] (c) A plane travels 1708 km in 3.5 hours. Work out the average speed of the plane. Give the units of your answer. Answer(c) [2]

7 marks

Mark scheme: Qu. Answers Mark Part Mark 1 (a) (i) –4 1 (ii) –4 –3 –1 2 5 1 (iii) 8 1 allow –8 (b) (i) 1305 1 (ii) 3 (h) 35 (m) cao 1 (c) 488 1 km/h 1

This question in 0580/33 May/June 2012

9 (a) Each day from Monday to Saturday Caroline buys a newspaper, costing d cents. For On Sunday she buys a newspaper costing 160 cents. Examiner's Use The total amount she spends on newspapers in a week is 430 cents. (i) Write down an equation in d, to show this information. Answer(a)(i) [1] (ii) Solve your equation to find d. Answer(a)(ii) d = [2] (iii) The price of the Sunday newspaper is increased by 15%. Calculate the price of the Sunday newspaper after this increase. Answer(a)(iii) cents [2] (b) Potatoes cost p cents per kilogram and carrots cost c cents per kilogram. (i) Bernard buys 3 kilograms of potatoes and 2 kilograms of carrots. An expression for the amount he spends is 3p + 2c. He spends 92 cents on these items. Write down an equation, in p and c, to show this. Answer(b)(i) [1] (ii) Eleanor buys 2 kilograms of potatoes and 5 kilograms of carrots. She spends 153 cents on these items. Write down an equation, in p and c, to show this. Answer(b)(ii) [2] (iii) Solve your equations to find p and c. Answer(b)(iii) p = c = [4]

12 marks

Mark scheme: 9 (a) (i) 6d + 160 = 430 oe 1 (ii) 45 2ft Ft for pd + q = r p, q and r ≠ 0 and p ≠ 1 M1ft for1st step correct SC1 for 270 (iii) 184 or $1.84 2 M1 for 1.15 × 160 oe SC1 for answer 1.84 (b) (i) 3p + 2c = 92 oe 1 Final answer (ii) 2p + 5c = 153 oe 2 B1 for 2p + 5c seen IGCSE – October/November 2012 0580 32 (iii) (p =) 14 (c =) 25 cao 4 M2ft for correct method to eliminate 1 variable A1 for a correct answer If not M2 M1 for 2 equations with common coefficients of p or c seen or M1 for correct rearrangement to p= or c= seen

This question in 0580/32 Oct/Nov 2012

1 (a) On a map, the height of Hillibar Station is 1047 m and the height of Sular Junction is 297 m. For Examiner′s Use (i) Calculate the difference in these heights. Answer(a)(i) … m [1] (ii) The temperature falls by 1°C for every 100 m increase in height. One day the temperature in Sular Junction is 19°C. Work out the temperature at Hillibar Station. Answer(a)(ii) … °C [1] (iii) Write 297 correct to the nearest ten. Answer(a)(iii) … [1] (iv) Write 1047 correct to the nearest hundred. Answer(a)(iv) … [1] (b) (i) Kim arrives at Hillibar Station at 12 35. The taxi to her hotel takes 27 minutes. Work out the time Kim arrives at her hotel. Answer(b)(i) … [1] (ii) Henry takes 17 minutes to walk from his home to Sular Junction. He must arrive there by 10 43. Work out the latest time he can leave home. Answer(b)(ii) … [1] (c) Here is part of a train timetable. For Examiner′s Each journey from Sular Junction to Hillibar Station takes the same time. Use Sular Junction departs 10 59 12 32 14 48 Hillibar Station arrives 12 35 14 08 (i) Complete the timetable. [2] (ii) The distance between Sular Junction and Hillibar Station is 64 km. Calculate the average speed, in kilometres per hour, of a train between these two stations. Answer(c)(ii) … km/h [2] (iii) Joel arrives at Sular Junction at 11 48. At what time is the next train to Hillibar Station due to depart? Answer(c)(iii) … [1] _____________________________________________________________________________________

11 marks

Mark scheme: Qu. Answers Mark Part Answers 1 (a) (i) 750 1 (ii) 11, 11.5 or 12 1ft (iii) 300 1 (iv) 1000 1 (b) (i) 13 02 1 (ii) 10 26 1 (c) (i) 16 24 2 B1 for 1 (h) 36 or 2 (h) 16 or 3 (h) 49 or 96 or 136 or 229 or 4.24(pm) soi. (ii) 40 cao 2 M1 for 64 ÷ their time (e.g. 1(h) 36(m) ) (iii) 12 32 1

This question in 0580/31 May/June 2013

8 For Examiner′s Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Use Average temperature in °C –4.4 –4.2 –2.7 0.3 4.8 9.1 11.8 10.8 6.7 2.7 –1.1 –3.3 The table shows the average temperature for Tromso, Norway each month. (a) (i) Write down the month which had the highest average temperature. Answer(a)(i) … [1] (ii) How much warmer was it in September than in February? Answer(a)(ii) … °C [1] (iii) The lowest temperature in October was 12.3°C below the average temperature for that month. Work out the lowest temperature in October. Answer(a)(iii) … °C [1] (b) In a survey, some tourists were asked how they had travelled to Norway. The pie chart shows the results. Road Boat Train Plane (i) 150 of these tourists travelled by boat. For Examiner′s Use Show that 600 tourists took part in the survey. Answer(b)(i) [1] (ii) Calculate the number of these tourists who travelled by plane. Answer (b)(ii) … [3] (c) A train ticket from Oslo to Stavanger costs 885 krone. There is a discount of 12% on the total cost of the tickets for a group of 10 or more people. Calculate the cost of tickets for a group of 15 people. Answer(c) … krone [3] (d) On 1 January 2000, the population of Norway was 4 480 000, correct to 3 signifi cant fi gures. (i) Write this number in standard form. Answer(d)(i) … [1] (ii) On 1 January 2011, the population of Norway was 4 920 000, correct to 3 signifi cant fi gures. Calculate the percentage increase in the population. Answer(d)(ii) … % [3] _____________________________________________________________________________________

14 marks

Mark scheme: 8 (a) (i) July or Jul 1 (ii) 10.9 1 (iii) – 9.6 1 90 360 (b) (i) 150 ÷ oe 1 Accept 150 × , 150 × 4 360 90 (ii) 250 3 M1 for their 150/360 × 600 or their 150 × 150/90 and B1 for 150 seen as angle (c) 11682 3 M2 for 885 × 15 × 0.88 oe M1 for 885 × 0.88 oe or 885 × 15 × 0.12 oe (d) (i) 4.48 × 106 cao 1 4920000− 4480000 (ii) 9.82 3 M2 for × 100 oe 4480000  4920000  or  −1 × 100 oe  4480000  or B1 for 440000 or 0.44 or 1.098(….) or 109.8(…..) IGCSE – October/November 2013 0580 31

This question in 0580/31 Oct/Nov 2013

9 (a) The table shows some information about minimum and maximum temperatures in Moscow one For Examiner′s January and February. Use Temperature January February Maximum –9°C 2°C Minimum –16°C (i) Find the difference between the maximum and minimum temperatures in January. Answer(a)(i) … °C [1] (ii) The difference between the maximum and minimum temperatures in February was 34°C. Find the minimum temperature in February. Answer(a)(ii) … °C [1] (iii) The minimum temperature in Moscow in December was 5°C higher than the minimum temperature in January. Work out the minimum temperature in December. Answer(a)(iii) … °C [1] (b) The table shows the population of some cities in Russia. For Examiner′s Use City Population Kaliningrad 4.30 × 105 Moscow Novosibirsk 1.40 × 106 Omsk 1.13 × 106 Saint Petersburg 4.58 × 106 (i) The population of Moscow is 10 500 000. Complete the table by writing the population of Moscow in standard form. [1] (ii) Write the population of Saint Petersburg as an ordinary number. Answer(b)(ii) … [1] (iii) Which city has the smallest population? Answer(b)(iii) … [1] (iv) Find the difference between the population of Novosibirsk and the population of Omsk. Give your answer in standard form. Answer(b)(iv) … [2] _____________________________________________________________________________________ Question 10 is printed on the next page.

8 marks

Mark scheme: 9 (a) (i) 7 1 Allow –7 (ii) –32 1 (iii) –11 1 (b) (i) 1.05 × 107 1 (ii) 4 580 000 1 (iii) Kaliningrad 1 (iv) 2.7 × 105 2 B1 for figs 27

This question in 0580/32 Oct/Nov 2013

5 (a) Write in fi gures six million three thousand and seventy six. Answer(a) … [1] (b) (i) Work out the value of p when p = –0.6 ÷ 1.6 . Answer(b)(i) p = … [1] (ii) Work out the value of q when q = –0.6 – 1.6 . Answer(b)(ii) q = … [1] (iii) Use one of the symbols >, <, [, Y, = to complete this statement. p … q [1] (c) Mount Robson in Canada has a height of 3950 metres, correct to the nearest 10 metres. Complete the following statement about the height, h m, of Mount Robson. Answer(c) … Y h < … [2] 1 1 . (d) Calculate 2 ÷ 1 12 4 Give your answer as a decimal, correct to 4 signifi cant fi gures. Answer(d) … [2] (e) (i) Write down the value of 80. Answer(e)(i) … [1] (ii) Work out 5–3. Write your answer as a fraction. Answer(e)(ii) … [1] (iii) Simplify the expression. 8x5 × 3x4 Answer(e)(iii) … [2] __________________________________________________________________________________________

12 marks

Mark scheme: 5 (a) 6 003 076 1 (b) (i) –0.375 1 (ii) –2.2 1 (iii) > 1FT FT their answers to (i) and (ii) (c) 3945, 3955 1, 1 SC1 for both correct but reversed 2 (d) 1.667 cao 2 B1 for 1 3 or better (e) (i) 1 1 1 (ii) 1 125 (iii) 24x9 2 B1 for 24xk or kx9

This question in 0580/31 Oct/Nov 2014

9 Nina is going on a holiday to Dubai from her home in Mumbai. (a) At the airport she buys 2 packets of sandwiches and 3 magazines. Complete her shopping bill in Indian rupees. 2 packets of sandwiches at 325 rupees per packet = … rupees 3 magazines at 75 rupees per magazine = … rupees Total = … rupees [3] (b) She changed 10 000 rupees to dirhams when the exchange rate was 18.3 rupees = 1 dirham. How much did she receive? Answer(b) … dirhams [2] (c) The flight from Mumbai to Dubai takes 2 hours 50 minutes. The distance from Mumbai to Dubai is 1937 km. (i) Show that the average speed of the flight is 684 km / h, correct to the nearest whole number. Answer(c)(i) [2] (ii) Nina’s flight leaves Mumbai at 13 15. 1 The local time in Mumbai is 1 2 hours ahead of the local time in Dubai. Find the time of arrival in Dubai. Give your answer in the 24-hour clock. Answer(c)(ii) … [2]

9 marks

Mark scheme: 9 (a) 650 1 225 1 875 1FT (b) 546 or 546.4 or 546.44 or 546.45 2 M1 for 10 000 ÷ 18.3 (c) (i) 1937 ÷ 2.83[3…] or M1 1937 ÷ 170 × 60 683.6 to 684.4 … A1 but not 684 (ii) 14 35 2 B1 for 16 05 [time in Mumbai on arrival] or B1 for 11 45 [time in Dubai on departure from Mumbai] or M1 for 2 hours 50 mins – 1 hour 30 mins + 1315 or SC1 for answer 2 35pm

This question in 0580/32 May/June 2015

1 (a) Write down in figures the number twenty one million. Answer(a) … [1] (b) Write down the four factors of 21. Answer(b) … , … , … , … [2] (c) Write 21% as a fraction. Answer(c) … [1] (d) Put brackets in this calculation to make it correct. 210 + 21 ÷ 2.1 + 21 = 10 [1] (e) Write down the first two prime numbers after 21. Answer(e) … and … [2] (f) Fill in the missing number. 21 210 = 210 ff [1] (g) Calculate 21 2 - 21 . Answer(g) … [1] (h) Work out ( 21 ) 2. Answer(h) … [1] (i) Write down the value of 210. Answer(i) … [1] (j) Write 0.0021 in standard form. Answer(j) … [1] (k) Write down the lowest common multiple (LCM) of 21 and 15. Answer(k) … [2]

14 marks

Mark scheme: Question Answer Mark Part marks 1 (a) 21 000 000 1 (b) 1, 3, 7, 21 2 M1 for 3 correct and one incorrect (or missing) or for 4 correct and one extra 21 (c) 1 100 (d) (210 + 21) ÷ (2.1+ 21) 1 (e) 23 1 If zero scored SC1 for any two other prime 29 1 numbers greater than 21 (f) 2100 1 (g) 436 or 436.4... 1 (h) 21 1 (i) 1 1 (j) 1.2 × 10 − 3 1 (k) 105 2 M1 for [1 ×] 3 × 5 × 7 or 105k or for [1], 3, 7 and [1], 3, 5 seen or for [1], 3, 5, 7 (maybe in a table) or for listing multiples of 15 and 21 to at least 105 with not more than one error

This question in 0580/32 Oct/Nov 2015

2 Kylie, Rio and Choi buy a horse for $21 600. (a) They pay for the horse in the ratio Kylie : Rio : Choi = 2 : 3 : 4. Calculate the amount that they each pay. Answer(a) Kylie $ … Rio $ … Choi $ … [3] (b) It costs $14 000 to keep the horse for one year. (i) Food costs 30% of the $14 000. Calculate the cost of the food. Answer(b)(i) $ … [2] (ii) Stable fees are $8000. Write this as a fraction of the $14 000. Give your answer in its lowest terms. Answer(b)(ii) … [2] (iii) It costs $600 for vets’ fees and the rest of the $14 000 is spent on equipment. Work out how much is spent on equipment. Answer(b)(iii) $ … [2] (c) They later sell the horse for $17 280. Calculate the percentage loss on the $21 600 they paid for the horse. Answer(c) … % [3] (d) Rio invests $5500 for 3 years at a rate of 2.5% per year compound interest. Calculate how much interest he receives after the 3 years. Answer(d) $ … [3] __________________________________________________________________________________________

15 marks

Mark scheme: 2 (a) 4800 M2 for 1 correct value in correct place 7200 3 M1 for 21600 ÷ (2 + 3 + 4) or better 9600 If zero scored SC1 for all correct values in incorrect order (b) (i) 4200 2 M1 for 0.3 × 14000 oe 4 8000 (ii) cao 2 B1 for correct fraction other than 7 14000 (iii) 1200 2 FT M1FT for (14000 – their (b)(i) – 8000 – 600)

This question in 0580/33 Oct/Nov 2015

7 Burton City is a football team. (a) Burton City has 1732 supporters who want to travel to the next game. The football club hires some buses. Each bus seats 52 supporters. (i) Work out the number of buses needed to take these supporters to the game. … [2] (ii) The cost of the buses will be shared equally amongst these supporters. Each bus costs $198 to hire. Work out the amount that each supporter must pay. Give your answer correct to the nearest 10 cents. $ … [3] (b) Adam and Mabel are two supporters. The scale drawing shows the positions of Adam’s home, A, and Mabel’s home, M. The scale is 1 centimetre represents 500 metres. North A North Scale: 1 cm to 500 m M (i) Work out the distance in kilometres from A to M. … km [2] (ii) Burton City’s football ground is on a bearing of 105° from A and on a bearing of 068° from M. Mark the position of the football ground on the scale drawing. [3] (c) Teams are given points for winning or drawing games. A win is given w points and a draw is given d points. No points are given when the team loses. (i) Burton City has 24 points after winning 2 games and drawing 5 games. Complete the equation. 2w + 5d = … [1] (ii) Sowton Rovers is another football team. Sowton Rovers has 29 points after winning 3 games and drawing 4 games. Write this information as an equation. … = … [2] (iii) Solve your two equations to find the number of points for a win and the number of points for a draw. You must show all your working. w = … d = … [4] (iv) Another team, Cranbrook United, has played 12 games. It has won 4 games, drawn 5 games and lost 3 games. Work out the number of points Cranbrook United has after 12 games. … [1]

18 marks

Mark scheme: 1732 7 (a) (i) 34 2 M1 for 52 198 ×their 34 (ii) 3.90 3FT M1FT for 1732 A1FT 3.88 to 3.89 A1FT their answer rounded to nearest 10c (b) (i) 3.9 2 M1 for 7.8 If zero scored SC1 for figs 38 to 40 (ii) football ground indicated in 3 B1 for bearing of 105° from A correct position B1 for bearing of 068° from M B1FT for indication of the football ground’s position, dpt on at least one B1

This question in 0580/32 Feb/March 2016

3 Paul and Mary go on a 14 night cruise in the Mediterranean. (a) The price of the cruise is $237 per person per night. A tax of 6% is added to this price. Find the total amount Paul and Mary pay for this cruise. $ … [3] (b) At a port Mary buys 2 bottles of sun cream. Each bottle costs $7.89 . Work out the change she receives from $20. $ … [2] (c) Paul and Mary leave the ship at 09 23 to tour Pisa. 3 The tour lasts for 6 hours. 4 Find the time when the tour finishes. … [2] (d) The ship leaves at 18 40 to sail to the next port. It sails 270 km at an average speed of 32.4 km/h. Find the time when the ship arrives. … [3] (e) There are 1800 passengers on the ship. They are in the ratio males : females = 5 : 4. Work out the number of male passengers. … [2]

12 marks

Mark scheme: 3 (a) 7034.16 3 M2 for 14 × 237 × 2 × 1.06 oe or M1 for 14 × 237 × 2 oe or 237 × 1.06 oe or 237 × 2 × 1.06 oe or 237 × 1.06 × 14 oe (b) 4.22 2 M1 for 20 – 2 × 7.89 (c) 16 08 or 4 08 pm 2 B1 for 45 min soi (d) 03 00 or 3 am 3 M1 for 270 ÷ 32.4 or 8.33[…] or 8 (h) 20 (min) M1dep for 18 40 + their 8.33 (e) 1000 2 M1 for 18004 + 5 [×5] oe

This question in 0580/31 May/June 2016

4 (a) The table shows the temperature at noon each day for one week in a city. Monday Tuesday Wednesday Thursday Friday Saturday Sunday 5 °C 2 °C −3 °C −1°C 0 °C 1°C −2 °C (i) Which day had the lowest noon temperature? … [1] (ii) Find the difference between the noon temperatures on Tuesday and Wednesday. … °C [1] (iii) Write these seven temperatures in order, starting with the lowest. … , … , … , … , … , … , … [1] lowest (iv) On Sunday the noon temperature was −2 °C. The next day the noon temperature fell by 4 °C. Find the noon temperature on the next day. … °C [1] (b) The number of houses in the city is 1 935 364. Write this number correct to the nearest million. … [1] (c) The height, h metres, of a tower in the city is 120 m, correct to the nearest 10 m. Complete this statement about the value of h. … G h < … [2] (d) The diagram shows the cross section of a circular tunnel in the city. NOT TO SCALE 8 m 1 m Calculate the shaded area. … m2 [4]

11 marks

Mark scheme: 4 (a) (i) Wednesday 1 (ii) 5 1 accept –5 (iii) –3 –2 –1 0 1 2 5 1 (iv) –6 1 (b) 2 million or 2 000 000 1 (c) 115 125 2 B1 for either correct or both correct but reversed (d) 28.3 or 28.27 to 28.28 4 B1 for radius of 5 cm or 4 cm soi M2 for π × 52 – π × 42 soi or M1 for π × 52 or π × 42 soi If 0 scored SC2 for π × 102 – π × 82 or SC1 for π × k2

This question in 0580/31 May/June 2016

1 Here is part of the menu in a café. Item Price Tea … $2.40 Coffee … $2.80 Fruit juice … $1.85 Pizza … $4.15 Vegetable pasty ... $3.60 Chicken curry … $5.20 Ice cream … $2.80 Cake … $3.25 Yoghurt … $1.40 (a) Jenna buys 3 coffees and 2 cakes. Work out how much she spends altogether. $ … [3] (b) Find the maximum number of pizzas Harry can buy for $20. Work out the change he receives from a $20 note. Number of pizzas = … Change = $ … [3] (c) Priti’s meal costs $7.60 . She gives the waitress 15% extra for service. Work out the total amount she pays. $ … [2] (d) Elena and Maria are waitresses in the café. One day they receive $96 for service. They share the $96 in the ratio Elena : Maria = 3 : 1. Work out how much Elena receives. $ … [2] (e) The café’s opening hours are shown below. Day Opening hours Monday CLOSED Tuesday 11 00 to 15 00 and 17 00 to 22 00 Wednesday 11 00 to 15 00 and 17 00 to 22 00 Thursday 11 00 to 15 00 and 17 00 to 22 00 Friday 11 00 to 15 00 and 17 00 to 22 00 Saturday 10 30 to 23 00 Sunday 09 30 to 21 00 (i) Find the number of hours the café is open during one week. … hours [2] (ii) During opening hours the café needs 3 people on duty. Each person works 36 hours in a week. Find the number of people the café needs in a week. … [3] (f) The café owner pays rent. The monthly rent is $6.40 for each square metre of floor area. The floor area is 72.5 m2. Calculate the total rent the café owner pays in one year. $ … [3]

18 marks

Mark scheme: Question Answer Mark Part marks 1(a) 14.9[0] 3 M2 for 3 × 2.8[0] + 2 × 3.25 or better or B1 for 8.4[0] or 6.5[0] 1(b) 4 1 3.4[0] 2 M1 for 20 – (their 4 × 4.15) 1(c) 8.74 2 M1 for 7.60 × 1.15 oe 1(d) 72 2 M1 for 96 ÷ 4 [× 3] 1(e)(i) 60 2 B1 for two from 9 or 36, 12.5, 11.5 1(e)(ii) 5 nfww 3 M2 for (their 60 × 3) ÷ 36 or better or M1 for their 60 × 3 or better or their 60 ÷ 36 1(f) 5568 3 M2 for 6.4[0] × 72.5 × 12 or better or M1 for 6.4[0] × 72.5 or 6.4[0] × 12

This question in 0580/32 May/June 2017

2 Jeff owns a clothes shop. (a) Shirt Tie Coat $24 $12.50 $46 A customer buys 3 shirts, 5 ties and 1 coat. Calculate the total cost. $ … [3] (b) A jacket has a price of $64. Jeff increases this price by 8%. Calculate the new price. $ … [2] (c) Jeff also increases the price of a dress from $250 to $280. Calculate the percentage increase in the price of the dress. … % [3] (d) The shop has a rectangular floor measuring 5.5 m by 8.5 m. The floor covering costs $12 per square metre. Calculate the cost of the floor covering. $ … [3] (e) Jeff invests $3600 for 3 years at a rate of 6% per year compound interest. Work out the value of the investment at the end of the 3 years. $ … [3]

14 marks

Mark scheme: 2(a) 180.5[0] 3 M2 for 3 × 24 + 5 × 12.50 + 46 oe or M1 for 3 × 24 or 5 × 12.50 or better, soi by 72 or 62.5 2(b) 69.12 2 M1 for 64 × 1.08 oe 2(c) 12 3 M2 for ( 280250 – 1) × 100 or 280250− 250 × 100 oe or M1 for 280250 – 1 or 280250 × 100 or 280250− 250 oe 2(d) 561 3 M1 for 5.5 × 8.5 soi by 46.75 M1 for their 46.75 × 12 2(e) 4287.66 3 M2 for 3600 × (1 + 1006 )3 oe or M1 for 3600 × (1 + 1006 )2 oe soi by 4044.96 If zero scored, SC2 for 687.6576, 687.658, 687.66, 687.65, 687.7, 688 or 690

This question in 0580/31 Oct/Nov 2017

1 (a) Martha makes hats. Each week she makes 160 hats. (i) Work out how many hats she makes in 5 weeks. … [1] (ii) The hats are made in the ratio small : medium : large = 2 : 5 : 3. Work out how many of the 160 hats are large. … [2] (iii) She sells 3 of the 160 hats. 8 Work out how many hats she sells. … [1] (b) Nina sells T-shirts. The prices are shown in the table. Type Plain Striped Logo Price $7.50 $9.50 $10.50 (i) Sam buys 3 plain T-shirts and 2 logo T-shirts. Work out how much she pays altogether. $ … [2] (ii) One day, Nina reduces all prices by 20%. Work out the new price of a striped T-shirt. $ … [2] (c) Nina sold 300 T-shirts in September. She wants to show how many of each type she sold using a pie chart. Type Number sold Pie chart sector angle Plain 100 120° Striped 85 Logo 115 (i) Complete the table. [2] (ii) Complete the pie chart. [2] (d) Nina paid $22.50 for a dress. She sold the dress for $31.50 . Work out her percentage profit. … % [3]

15 marks

Mark scheme: Question Answer Marks Partial marks 1(a)(i) 800 1 1(a)(ii) 48 2 160 M1 for [ × 3] 2 + 5 + 3 1(a)(iii) 60 1 1(b)(i) 43.5[0] 2 M1 for 3 × 7.5[0] + 2 × 10.5[0] 1(b)(ii) 7.6[0] 2  20  M1 for 9.5  1 −  oe  100  1(c)(i) 102 2 85 115 M1 for × 360 or × 360 or 138 300 300 120 120 × 85 or × 115 oe 100 100 1(c)(ii) 3 correct sectors 2FT FT if their angles add to 240° B1FT for one correct sector 1(d) 40 3 31.50 − 22.50 M2 for × 100 or 22.50  31.50   − 1  × 100 oe  22.50  31.50 − 22.50 or M1 for or 22.50 31.50 31.50 − 1 or × 100 oe 22.50 22.50

This question in 0580/33 Oct/Nov 2017

2 (a) Fill in the missing number in each calculation. (i) 6 + 2 # … = 24 [1] (ii) (10 – … ) ÷ 3 = 2 [1] (b) Find the value of (i) .196, … [1] (ii) 163. … [1] 7. 82 - 4. 15 (c) Work out . 5.25 # 16. 4 Give your answer correct to 2 significant figures. … [2] 1 2 (d) V = a h 3 Calculate V when a = 4.5 and h = 9.6 . V = … [2] (e) Put a ring around the irrational number in the list below. 2 5 4 5 - 36 1 [1] 3 7 5 (f) Written as a product of its prime factors, T = 22 # 3 # 52 . (i) Work out the value of T. T = … [1] (ii) Write 80 as a product of its prime factors. … [2] (iii) Find the highest common factor (HCF) of T and 80. … [2]

14 marks

Mark scheme: 2(a)(i) 9 1 2(a)(ii) 4 1 2(b)(i) 1.4 1 2(b)(ii) 4096 1 2(c) [0].043 cao 2 367 M1 for 0.0426… or 8610 2(d) 64.8 2 1 2 324 M1 for × 4.5 × 9.6 or 3 5 2(e) 5 indicated 1 2(f)(i) 300 1 2(f)(ii) 24 × 5 or 2 × 2 × 2 × 2 × 5 2 M1 for 2, 2, 2, 2, 5 or 24,5 or 1 × 2 × 2 × 2 × 2 × 5 or 1 × 24 × 5 2(f)(iii) 20 2 B1 for 2 or 4 or 5 or 10 as answer or 22 × 5 as answer

This question in 0580/33 Oct/Nov 2017

1 (a) The table shows the temperature at Lexford Station at 10 00 each day for a week. Day Mon Tue Wed Thu Fri Sat Sun Temperature - 3 4 - 1 0 - 5 2 1 (°C) (i) Write down the day which had the coldest temperature. … [1] (ii) Work out the difference in the temperature between Monday and Tuesday. … °C [1] (iii) The temperature falls 6°C from 10 00 to midnight on Sunday. Work out the temperature at midnight. … °C [1] (b) The distance between Lexford Station and Crowton Station is 6.5 km. (i) A train travels between these stations at an average speed of 39 km/h. Work out how long, in minutes, it takes the train to travel between these stations. … min [3] (ii) Each wheel on the train has a diameter of 1.8 m. Work out the number of complete turns each wheel makes in travelling the 6.5 km. … [4] (c) A northbound train leaves Lexford Station every 30 minutes. A bus leaves Lexford Station every 45 minutes. At 11 40 a northbound train and a bus leave the station together. Find the next time when this happens. … [3] (d) Here is part of a timetable for trains going east to west from Lexford Station. Lexford 09 14 09 47 10 21 11 15 11 48 Crowton 09 26 09 59 10 33 11 27 12 00 Doniton Halt 09 42 10 15 10 49 11 43 12 16 Mosshead 10 01 10 34 11 08 12 02 12 35 (i) Work out the number of minutes the 09 14 train takes to travel from Lexford to Mosshead. … min [1] (ii) Freda must arrive at Mosshead by 11 30. Write down the latest time she can catch a train from Lexford. … [1] (e) 437 people go on a coach trip. Each coach seats 62 people. How many coaches are needed? … [2]

17 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Fri[day] 1 1(a)(ii) 7 1 1(a)(iii) –5 1 1(b)(i) 10 cao 3 6.5 × 60 M2 for oe 39 or M1 for distance ÷ speed 1(b)(ii) 1149 4 M2 for (6.5 × 1000) ÷ (π × 1.8) oe or M1 for π × 1.8 oe A1 for 1149.3 to 1149.5 B1 for their answer to at least 1dp truncated to the integer 1(c) 13 10 3 M2 for [LCM=] 2 × 3 × 3 × 5 or 90 or M1 for [30=] 2 × 3 × 5 or [45=] 3 × 3 × 5 OR M2 for listing times or multiples to at least 13 10 or 90 or M1 for adding times i.e. one correct addition e.g. 12 10 1(d)(i) 47 1 1(d)(ii) 10 21 1 1(e) 8 2 M1 for 437 ÷ 62 oe implied by 7.04… or 7.05

This question in 0580/33 May/June 2018

3 (a) The table gives some information about the numbers of visitors at a leisure centre one day. Adult Child Total Male 144 240 Female 129 260 Total 225 275 500 (i) Complete the table. [1] (ii) Work out how many more child visitors than adult visitors there are. … [1] (iii) Write down the fraction of visitors that are adults. Give your answer in its lowest terms. … [2] (iv) Write the ratio number of males : number of females. Give your answer in its simplest form. … : … [2] (v) One of these visitors is selected at random. Find the probability that this visitor is a male child. … [1] (b) The number of people in each of 150 cars entering the leisure centre car park is recorded. The table shows the results. Number of people 1 2 3 4 5 Frequency 44 43 30 25 8 (i) Write down the mode. … [1] (ii) Calculate the mean. … [3] (c) In a survey of 50 visitors to the leisure centre, 18 used the gym. One day, 1500 people visited the leisure centre. Calculate an estimate for the number of people who used the gym on this day. … [2]

13 marks

Mark scheme: 3(a)(i) 96 144 240 1 both correct 129 131 260 225 275 500 3(a)(ii) 50 1 3(a)(iii) 9 2 225 45 B1 for or or 0.45 20 500 100 3(a)(iv) 12 : 13 2 B1 for 240 : 260 oe If 0 scored, SC1 for answer 13 : 12 3(a)(v) 144 1 oe 500 3(b)(i) 1 1 3(b)(ii) 2.4 3 M1 for 44 × 1 + 43 × 2 + 30 × 3 + 25 × 4 + 5 × 8 M1dep for their 360 ÷ 150 3(c) 540 2 18 1500 M1 for [× 1500 ] or [× 18] 50 50

This question in 0580/31 Oct/Nov 2018

1 Three people pick strawberries. The strawberries are sold in boxes. (a) (i) On Wednesday, they pick a total of 89 kg of strawberries. The mean mass of each strawberry is 22 g. Work out the number of strawberries they picked. Give your answer correct to the nearest 10. … [3] (ii) On Thursday, they pick a total of 4650 strawberries. They fill each box with 35 strawberries. How many boxes do they fill? … [2] (b) On Saturday, they sell 208 boxes of strawberries at $3.25 for each box. Work out how much money they receive. $ … [1] (c) On Monday, they receive $390 for their boxes of strawberries. They share this money in the ratio Alison : Bob : Jenny = 7 : 3 : 2. Work out how much money they each receive. Alison $ … Bob $ … Jenny $ … [3] (d) In 2016, they picked a total of 3500 kg of strawberries. In 2017, they picked a total of 3080 kg of strawberries. Work out the percentage decrease in the mass of strawberries they picked from 2016 to 2017. … % [3] (e) An open box in the shape of a cuboid is 7 cm long, 5 cm wide and 4 cm high. Complete the net of the box. The base of the box has been drawn for you. [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 4050 3 figs 89 M1 for figs 22 5 A1 for 4045[. …] or 4045 11 B1 for their answer seen (but not a multiple of 10) correctly rounded to the nearest ten, provided does not round to zero 1(a)(ii) 132 2 M1 for 4650 ÷ 35 1(b) 676[.00] 1 1(c) 227.5[0] 3 M2 for 390 ÷ (7 + 3 + 2) × k or better where 97.5[0] k is 7, 3 or 2 65[.00] or M1 for 390 ÷ (7 + 3 + 2) or better, implied by 32.5[0] 1(d) 12 3 3500 − 3080 M2 for [× 100] or 3500 3080 3080 (1 − ) [× 100] or [100 −] × 100 3500 3500 3080 or M1 for or 3500 – 3080 3500 1(e) Fully correct net 2 B1 for at least two correct faces drawn in the correct place

This question in 0580/32 Oct/Nov 2018

1 Here is part of the menu for Jamie’s café. Menu Price ($) Tea 2.35 Coffee 3.40 Lemonade 1.80 Cake 4.45 Biscuit 0.85 (a) Sue has one tea and one cake. Calculate how much she pays. $ … [1] (b) Derrick has one coffee and two biscuits. How much change does he receive from a $10 note? $ … [2] (c) Harriet works at the café for 34 hours each week. She is paid $8.25 for each hour. (i) Work out the amount she is paid each week. $ … [1] (ii) One week she works 8 hours extra. The extra hours are paid at 1.5 times her usual rate of $8.25 for each hour. Work out the total amount she is paid for that week. $ … [2] (d) Peter works these hours each week at the café. Day Time Monday 08 30 to 16 00 Tuesday 10 00 to 17 00 Thursday 08 30 to 16 30 Saturday 08 00 to 18 30 Work out the number of hours he works in one week. … hours [2] (e) Jamie buys a clock for the café from Japan for 9395 yen. The exchange rate is $1 = 110.27 yen. Work out the cost of the clock in dollars, correct to the nearest cent. $ … [3] (f) Jamie invests $12 000 at a rate of 5% per year compound interest. Calculate the value of his investment at the end of 3 years. $ … [3]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6.8[0] 1 1(b) 4.9[0] 2 M1 for 3.4[0] + 2 × [0].85 soi 1(c)(i) 280.5[0] 1 1(c)(ii) 379.5[0] 2 FT their (c)(i) + 99 M1 for 8 × 1.5 × 8.25 soi or (8 × 1.5 + 34) × 8.25 soi 1(d) 33 2 M1 for 7.5, 7, 8, 10.5 1(e) 85.20 cao 3 B2 for 85.1999… OR M1 for 9395 ÷ 110.27 B1 for their answer to at least 3 dp correctly rounded to 2 dp 1(f) 13 891.5[0] 3 M2 for 12 000 × (1 + 1005 )3 oe or M1 for 12 000 × (1 + 1005 )2 oe

This question in 0580/31 May/June 2019

2 (a) Work out 48 ' 3 - 5 # 2 . … [1] (b) Insert one pair of brackets to make this statement correct. 3 + 2 # 12 - 4 = 19 [1] (c) Write the following in order, starting with the smallest. 3 11 0.749 76% 4 15 … 1 … 1 … 1 … [2] smallest (d) Find the value of (i) 265.69, … [1] (ii) 83. … [1] (e) Write down the smallest prime number. … [1] (f) Write down all the factors of 18. … [2] (g) Write down a common factor of 16 and 72 that is greater than 2. … [1] 28(h) Write as a fraction in its simplest form. 140 … [1] (i) Jeff and his friends win a prize. 5 Jeff’s share is $160 which is of the prize. 11 Work out the value of the prize. $ … [2]

13 marks

Mark scheme: 2(a) 6 1 2(b) 3 + 2 × (12 – 4) = 19 1 2(c) 15 11 [0].749 34 76[%] 2 B1 for 3 in the correct order or 0.75, (0.749) , 0.76, 0.73… or 75%, 74.9%, (76%), 73….% 2(d)(i) 16.3 1 2(d)(ii) 512 1 2(e) 2 1 2(f) 1 2 3 6 9 18 2 B1 for 4 or 5 correct factors only or 6 correct factors with one extra or 1 × 18, 2 × 9, 3 × 6 2(g) 4 or 8 1 2(h) 1 5 cao 1 2(i) 352 2 M1 for 160 ÷ 5 [ × 11]

This question in 0580/31 May/June 2019

3 Mr Lester has a fruit and vegetable shop. (a) Apples cost 32 cents each. Suki buys 6 apples. Work out the change Mr Lester gives Suki when she pays with a $10 note. $ … [2] (b) Green grapes cost $3.10 per kilogram. Red grapes cost $2.80 per kilogram. Work out the total cost of buying 0.6 kg of green grapes and 34 kg of red grapes. $ … [3] (c) George spends $12 on fruit each week. The total amount he spends on food is $75. Work out the percentage of the $75 he spends on fruit. … % [1] (d) Mr Lester buys pineapples for $1.50 each. He makes 60% profit when he sells them. Work out the selling price of a pineapple. $ … [2] (e) The table shows the number of bananas bought by the last 50 customers. Number of Frequency bananas bought 0 14 1 0 2 2 3 5 4 11 5 8 6 10 (i) Find the range. … [1] (ii) Work out the median. … [1] (iii) Calculate the mean. … [3]

13 marks

Mark scheme: 3(a) 8.08 2 B1 for 192 or 1.92 or 808 or M1 for 10 −×6 0.32 or 1000 −×6 32 3(b) 3.96 3 3 M2 for 0.6 × 3.1 + 2.8 × oe 4 3 or M1 for 0.6 × 3.1 oe or 2.8 × oe 4 3(c) 16 1 3(d) 2.4[0] 2 60 M1 for [1.5 +] 1.5 × oe 100 3(e)(i) 6 1 3(e)(ii) 4 1 3(e)(iii) 3.26 3 M1 for ∑ fx M1 dep for ∑ fx ÷ 50

This question in 0580/32 May/June 2019

1 (a) Write this number in figures. One million three hundred and two thousand five hundred and ninety-six. … [1] (b) (i) Two numbers are added together to give the number in the box immediately above. 2 5 – 3 – 4 Complete the diagram. [2] (ii) Two numbers are multiplied together to give the number in the box immediately above. 5 – 3 – 4 Complete the diagram. [3] (c) Write these in order of size, starting with the smallest. 5 -1 18.4% .183 # 10 5-1 27 … 1 … 1 … 1 … [2] smallest (d) Work out 142 as a percentage of 304. … % [1] (e) (i) Find the highest common factor (HCF) of 28 and 98. … [2] (ii) Find the lowest common multiple (LCM) of 28 and 98. … [2] (f) The average distance from Earth to Mars is .225 # 108 km. A space ship travels from Earth to Mars at an average speed of .58 # 104 km/h. Find how long, in hours, the journey takes. … hours [2]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1 302 596 1 1(b)(i) −5 2 B1 for −7 −7 B1FT for 2 + their −7 1(b)(ii) −180 3 B1 for −15 −15 12 B1 for 12 and B1FT for their −15 × their 12 1(c) 5 2 M1 for 3 in correct order or for 1.83 × 10−1 18.4% 5−1 27 5 three of [ =]0.185 … , [18.4% =] 0.184, 27 [1.83 × 10−1 =] 0.183, [5−1=] 0.2 1(d) 46.7 or 46.71... 1 1(e)(i) 14 2 B1 for answer of 2 or 7 or 2 × 7 or 2 × 2 × 7 and 2 × 7 × 7 or list (28 =) 2, 2, 7 and (98 =)2, 7, 7 1(e)(ii) 196 2 B1 for 28, 56, 84, 112,… and 98, 196 or [1 ×]2 × 2 × 7 × 7 or 196k 1(f) 3880 or 3879[⋅…] 2 M1 for 2.25 × 108 ÷ 5.8 × 104 oe or 3.88(0...) × 103 or 3.879… × 103 or figs (388 or 3879…) as the answer

This question in 0580/33 May/June 2019

4 (a) Write the number four hundred and eighteen thousand and seventy two in figures. … [1] (b) Write down all the factors of 16. … [2] (c) Write down a prime number between 30 and 40. … [1] (d) Find the value of (i) 729, … [1] (ii) 183, … [1] (iii) 70. … [1] (e) Saskia has $600. 1 1 She spends of the $600 on a coat and gives of the $600 to her son. 5 3 What fraction of the $600 does she have left? Give your answer in its simplest form. … [3] (f) Find the lowest common multiple (LCM) of 15 and 27. … [2] (g) Write 432 as the product of its prime factors. … [2] (h) Ella invests $4000 for 3 years at a rate of 1.2% per year compound interest. Calculate the value of her investment at the end of the 3 years. $ … [3]

17 marks

Mark scheme: 4(a) 418 072 1 4(b) 1 2 4 8 16 2 B1 for 3 or 4 correct and no extra or all correct and one extra 4(c) 31 or 37 1 4(d)(i) 27 1 4(d)(ii) 5832 1 4(d)(iii) 1 1 4(e) 7 3 5 3 8k cao M2 for + or 15 15 15 15k 320 280 7 k or or or , k must be an 600 600 15k integer 1 1 or M1 for + 5 3 or 120 + 200 or 320 or 280 or 600 – 120 − 200 oe 47 If M0 scored, SC1 for answer of 100 467 4667 1000 10000 4(f) 135 2 M1 for listing at least 3 multiples of 15 and 27 or [15=]3 × 5 and [27=]3 × 3 × 3 or 3³ or B1 for 135k as final answer or B1 for 3 × 3 × 3 × 5 or 33 × 5 4(g) 24 × 33 or 2 × 2 × 2 × 2 × 3 × 3 × 3 2 M1 for a complete correct factor tree or 2,2,2,2,3,3,3 clearly identified as factors or B1 for a correct product that equals 432 4(h) 4145.7[3] or 4145.70 or 4150 or 4146 3  1.2  3 M2 for 4000 ×  1 +  oe  100   1.2  2 or M1 for 4000 ×  1 +  oe  100 

This question in 0580/31 Oct/Nov 2019

3 (a) Write down (i) all the factors of 18, … [2] (ii) a square number between 30 and 50, … [1] (iii) a prime number between 90 and 100. … [1] (b) Put one pair of brackets into each calculation to make it correct. (i) 24 ' 6 + 2 # 3 = 9 [1] (ii) 24 ' 6 + 2 # 3 = 2 [1] (c) Calculate. 4.85 # 6.14 8.91 + 3.89 Give your answer correct to 2 decimal places. … [2] (d) (i) Find the highest common factor (HCF) of 36 and 90. … [2] (ii) Find the lowest common multiple (LCM) of 36 and 90. … [2] (e) (i) Write .42 # 10 -3 as an ordinary number. … [1] (ii) Calculate (8. 1 # 10 5 ) + ( 7. 9 # 10 4 ) . Give your answer in standard form. … [2]

15 marks

Mark scheme: 3(a)(i) 1, 2, 3, 6, 9, 18 2 B1 for 4 or 5 correct and no extras or 6 correct and one extra 3(a)(ii) 36 or 49 1 3(a)(iii) 97 1 3(b)(i) 24 ÷ (6 + 2) × 3 1 3(b)(ii) 24 ÷ (6 + 2 × 3) 1 3(c) 2.33 nfww 2 B1 for 2.32[648…] If 0 scored, SC1 for rounding their answer given to 3dp or more correctly to 2dp 3(d)(i) 18 2 B1 for 2 or 3 or 6 or 9 or 2 × 3 × 3 as final answer or for [36 = ] 2 × 2 × 3 × 3 or 22 × 32 and [90 = ] 2 × 3 × 3 × 5 or 2 × 32 × 5 3(d)(ii) 180 2 B1 for answer 180k where k is a positive integer or 2 × 2 × 3 × 3 × 5 3(e)(i) [0].0042 1 3(e)(ii) 8.89 × 105 2 B1 for figs 889

This question in 0580/32 Oct/Nov 2019

5 (a) Write one hundred and twenty thousand and twenty in figures. … [1] (b) Find the value of 3481. … [1] (c) (i) Write down the fraction of the rectangle that is shaded. … [1] (ii) Find the percentage of the rectangle that is not shaded. … % [1] (d) Write these numbers in order, starting with the smallest. 5 7 27% 0.268 17 29 … 1 … 1 … 1 … [2] smallest (e) Write 0.3728 correct to 1 decimal place. … [1] (f) Write down the value of 190. … [1] (g) The height, h metres, of a tower is 128 m, correct to the nearest metre. Complete the statement about the value of h. … G h 1 … [2] (h) Find the highest common factor (HCF) of 126 and 180. … [2] (i) Write down an irrational number with a value between 6 and 7. … [1]

13 marks

Mark scheme: 5(a) 120 020 1 5(b) 59 1 5(c)(i) 5 1 8 5(c)(ii) 37.5 1 5(d) 7 5 2 B1 for 3 in the correct order 0.268 27% or M1 for .27 .29… [.268] .24… 29 17 5(e) 0.4 1 5(f) 1 1 5(g) 127.5 128.5 2 B1 for each or SC1 for both correct but reversed 5(h) 18 2 B1 for an answer of 2 or 3 or 6 or 9 or 2 × 3 × 3 or 2 × 32 as final answer or for [126 =] 2 × 3 × 3 × 7 or 2 × 32 × 7 and [180 =] 2 × 2 × 3 × 3 × 5 or 22 × 32 × 5 or for complete correct list of factors for 126 and 180 5(i) Any irrational number between 6 and 7 1

This question in 0580/31 Oct/Nov 2020

7 (a) W = 3a + 5c Find the value of W when a = 6 and c = 2 . W = … [2] (b) Factorise completely. 12b + 8b 2 … [2] (c) Make m the subject of the formula y = 4m - p . m = … [2] (d) Find the value of x when 5 x # 5 3 = 5 12 . x = … [1] (e) Find the value of (i) 30, … [1] (ii) 5 - 2 . … [1] (f) In this part, all measurements are in centimetres. (3x – 1) NOT TO SCALE (2x + 5) The diagram shows a kite with sides ( 2x + 5) and ( 3x - 1) . The perimeter of the kite is 33 cm. Work out the length of a shorter side. … cm [5]

14 marks

Mark scheme: 7(a) 28 2 M1 for 3 × 6 + 5 × 2 or better or B1 for 18 or 10 seen 7(b) 4b(3 + 2b) final answer 2 B1 for final answer 2(6b + 4b2) or 4(3b + 2b2) or 2b(6 + 4b) or b(12 + 8b) or 4b(3 + 2b) seen then spoilt 7(c) y + p y p 2 y p or + oe final answer M1 for 4m = y + p or = m − 4 4 4 4 4 7(d) 9 cao 1 7(e)(i) 1 1 7(e)(ii) 1 1 or 0.04 25 7(f) 6.5 5 M2 for 10x + 8 = 33 or 5x + 4 = 16.5 or M1 for [2 ×] (3x – 1 + 2x + 5) oe M1 for a correct first step in solving their linear equation A1 for [x =] 2.5 If A0 scored, SC1 for 3x – 1 correctly evaluated FT their positive x

This question in 0580/33 Oct/Nov 2020

2 A family go on a skiing holiday to America. (a) The hotel has 840 rooms. 735 rooms are occupied. Calculate the percentage of rooms that are occupied. … % [1] (b) The temperature in the hotel is 21 °C. The temperature in the hotel is 26.7 °C warmer than at the top of the mountain. The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain. Work out the temperature at the bottom of the mountain. … °C [2] (c) Hire cost ($) Equipment 3 days 4 days 7 days Ski equipment 80.80 94.60 128.00 Adult Snowboard equipment 96.80 112.60 151.20 Helmet 12.80 15.20 20.70 Ski equipment 47.60 55.40 75.80 Child Snowboard equipment 59.00 70.20 94.60 Helmet 10.40 12.00 16.70 There are two adults and one child in the family. They hire all their equipment. The child skis for 3 days and snowboards for 4 days. Both adults ski for 7 days. All three of them hire a helmet for 7 days. Work out the total cost of the equipment hire for the family. $ … [2] (d) A ski lift, when full, takes 4000 passengers per hour. This lift works for 10 hours a day. One day, this lift is 90% full for 3 hours and 75% full for 7 hours. Work out the number of passengers who take the lift that day. … [3] (e) The family buy their lift passes before the holiday for a total of 51 400 rupees. In America, the passes cost a total of $684. The exchange rate is 1 rupee = $0.0129 . Show that the family save 1620 rupees, correct to the nearest 10 rupees, by buying the passes before their holiday. [3] (f) The height, h metres, of the mountain is 2642 m, correct to the nearest metre. Complete this statement about the value of h. … G h 1 … [2]

13 marks

Mark scheme: 2(a) 87.5 1 2(b) −2.5 2 M1 for 21 − 26.7 or 26.7 − 3.2 2(c) 431.9[0] 2 M1 for 47.6 + 70.2 + 16.7 oe or 2 × 128 + 2 × 20.7 oe or B1 for 134.5, 148.7, 297.4, 58.1 or 373.8 or 283.2 2(d) 31 800 3 90 M2 for 3 × × 4000 oe 100 75 or 7 × × 4000 oe 100 90 or M1 for × 4000 oe 100 75 or × 4000 oe 100 2(e) 684 M1 or 684 − 51400 × 0.0129 0.0129 53023 − 51400 M1 20.94 or 0.0129 1623 A1 2(f) 2641.5 2642.5 2 B1 for each If 0 scored, SC1 for answers correct but reversed

This question in 0580/32 Feb/March 2021

1 (a) Strawberries cost $4.20 per kilogram and cream costs $8.56 per litre. Venus buys 1.2 kg of strawberries and 125 ml of cream. Work out the total cost. $ … [3] (b) Ravi has $20. A pineapple costs $1.45 . Work out the largest number of pineapples Ravi can buy and the change he receives. Number of pineapples … Change $ … [3] (c) Abraham has a box of 72 biscuits. 2 He gives of the biscuits to his grandmother. 9 3 He then gives of the biscuits that are left to his cousin. 7 Work out how many biscuits Abraham has now. … [3] (d) Flo makes 84 cakes. She sells 35 of these cakes. Calculate the percentage of the cakes that she sells. … % [1] (e) A bag contains 132 sweets. The sweets are shared between Beatrix and Volker in the ratio Beatrix : Volker = 5 : 7. Work out the number of sweets they each receive. Beatrix … Volker … [2] (f) Jed sells desserts for $24 each. Each dessert costs $12.80 to make. (i) Work out his percentage profit. … % [2] (ii) The cost to make each dessert increases to $13.60 . Jed wants to make the same percentage profit. Work out the new selling price. $ … [2]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6.11 3 M2 for 1.2 × 4.2 + 0.125 × 8.56 oe or M1 for 1.2 × 4.2 oe or figs125 × 8.56 or B1 for 0.125 1(b) 13 1.15 3 20 M1 for 1.45 M1 for 20 − 1.45 × k where k integer ⩽13 1(c) 32 3 7 4 M2 for × × 72 9 7 OR 2 7 M1 for 9× 72 or 9 × 72 4 and M1dep for × their 56 7 3 or × their 56 7 1(d) 41.7 or 41.66 to 41.67 1 1(e) 55 77 2 132 M1 for × k oe where k is 1 or 5 or 5 + 7 7 1(f)(i) 87.5 2 24 M1 for × 100 [ − 100 ] or 12.8 24 − 12.8 24 [× 100 ] or − 1[ × 100 ] 12.8 12.8 1(f)(ii) 25.5[0] nfww 2 FT their (f)(i)  their ( f )( i )  M1 for 13.6 ×  1 +  oe  100  or B1FT for 11.90 13.6 12.8 or M1 for = or better x 24

This question in 0580/31 May/June 2021

1 Ray owns an electrical shop. (a) The table shows the opening times of the shop. Sunday Closed Monday Closed Tuesday 08 00 to 12 30 and 13 30 to 17 00 Wednesday 08 00 to 12 30 and 13 30 to 17 00 Thursday 08 00 to 12 30 and 13 30 to 17 00 Friday 08 00 to 12 30 and 13 30 to 17 00 Saturday 08 00 to 13 00 and 14 00 to 19 00 Work out how many hours the shop is open in one week. … hours [3] (b) Saeed buys 2 ovens costing $440 each, 4 grills costing $184 each and 3 fridges costing $1280 each. Calculate the total cost. $ … [3] (c) Alice buys 3 batteries costing $2.85 each. Work out how much change she receives from $10. $ … [2] (d) Cherie works 32 hours one week and she is paid $8.48 per hour. In another week she works 37 hours. For each hour over 32 hours she works, she is paid 1.25 times her hourly rate. Calculate her pay for the week she works 37 hours. $ … [4] (e) Ray buys a toaster for $36. When he sells it he makes a profit of 40%. Calculate the selling price of this toaster. $ … [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 42 3 M1 for 4.5 + 3.5 or 9 – 1 M1 for 5 + 5 or 11 – 1 or M1 for 4.5 × 4 + 5 or 18 + 5 oe M1 for 3.5 × 4 + 5 or 14 + 5 oe 1(b) 5456 3 B2 for 880, 736 and 3840 or B1 for one of these or M1 for 2 × 440 or 4 × 184 or 3 × 1280 1(c) 1.45 2 M1 for 10 – 3 × 2.85 1(d) 324.36 cao 4 M1 for 32 × 8.48 M1 for 8.48 × 1.25 oe M1 for (37 – 32) × their 10.6[0] Accept alternative methods 1(e) 50.4[0] 2 M1 for 36 × 1.4 oe or B1 for 14.4[0]

This question in 0580/33 May/June 2021

5 (a) Find. (i) 320.41 … [1] (ii) 6.4 2 + 1. 2 3 … [1] (iii) the reciprocal of 2 … [1] (iv) 90 … [1] 3 (v) of $42 7 $ … [1] (vi) 12% of $62 $ … [1] (b) Insert one pair of brackets in each statement to make it correct. (i) 20 - 5 ' 5 - 3 = 0 [1] (ii) 20 - 5 ' 5 - 3 = 17.5 [1] (c) Write one of the symbols 1 , 2 or = in each statement to make it correct. 7 … 0.07 10 1 … 20% 5 3 … 0.38 8 [2] (d) (i) Write 90 as the product of its prime factors. … [2] (ii) Find the lowest common multiple (LCM) of 35 and 90. … [1] (iii) Find the highest common factor (HCF) of 35 and 90. … [1]

14 marks

Mark scheme: 5(a)(i) 17.9 1 5(a)(ii) 42.688 cao 1 5(a)(iii) 1 2 or 0.5 1 5(a)(iv) 1 1 5(a)(v) 18 1 5(a)(vi) 7.44 1 5(b)(i) (20 – 5) ÷ 5 – 3 = 0 1 5(b)(ii) 20 – 5 ÷ (5 – 3) = 17.5 1 5(c) 7 2 B1 for 2 correct > 0.07 10 1 = 20% 5 3 < 0.38 8 5(d)(i) 2 × 3 × 3 × 5 or 2 × 32 × 5 2 B1 for 2, 3, 3, 5 or M1 for correct factor tree / diagram / table 5(d)(ii) 630 1 5(d)(iii) 5 1

This question in 0580/33 May/June 2021

1 (a) In a café at a train station, a cup of coffee costs $3.25 and a glass of cola costs $2.15 . Gary buys 2 cups of coffee and 4 glasses of cola. Work out how much change he receives from a $20 note. $ … [3] (b) Roy spends $37.80 in the café on food and drink in the ratio food : drink = 7 : 2. Work out how much he spends on food. $ … [2] (c) The price of a $48 train ticket is increased by 12%. Find the new price of the ticket. $ … [2] (d) Here is part of the timetable for trains from Washby to Dunstley. All trains take the same time to travel from Washby to Dunstley. Washby 09 18 11 05 Dunstley 10 03 … Complete the timetable. [2] (e) On one day, Washby station sells 28 senior tickets, 192 adult tickets and some child tickets. Senior tickets 42° Complete the pie chart to show this information. [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 4.9[0] cao 3 M2 for 20 − (2 × 3.25 + 4 × 2.15) oe or M1 for 2 × 3.25 or 4 × 2.15 1(b) 29.4[0] cao 2 37.8 M1 for [× k] where k = 1, 2 or 7 7 + 2 1(c) 53.76 cao 2  12  M1 for 48 ×  1 +  oe  100  or B1 for 5.76 1(d) 11 50 2 B1 for 45 [min], 1 h 47 [min] or 107 [min] 1(e) Correct pie chart drawn 3 42 M2 for 192 × oe 28 or 42 M1 for oe 28

This question in 0580/32 Oct/Nov 2021

1 (a) Write the number six and a half million in figures. … [1] (b) Write 6538 correct to the nearest ten. … [1] (c) Work out 6 # 5 + 12 ' 3 . … [1] (d) 9 16 18 29 57 64 87 96 From this list of numbers, write down (i) a factor of 48, … [1] (ii) a cube number, … [1] (iii) a prime number. … [1] (e) Find the value of .0001225 . … [1] (f) Find the reciprocal of 8. … [1] (g) Find the value of 80. … [1] (h) (i) Write 180 as a product of its prime factors. … [2] (ii) Find the lowest common multiple (LCM) of 160 and 180. … [2] (i) The mass of an aircraft, m tonnes, is 473 tonnes, correct to the nearest tonne. Complete this statement about the value of m. … G m 1 … [2]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6 500 000 1 1(b) 6540 1 1(c) 34 1 1(d)(i) 16 1 1(d)(ii) 64 1 1(d)(iii) 29 1 1(e) 0.035 1 1(f) 1 1 8 or 0.125 1(g) 1 1 1(h)(i) 2  2  3  3  5 2 B1 for 2, 2, 3, 3, 5 or M1 for correct factor tree or table 1(h)(ii) 1440 2 B1 for 1440k as final answer or M1 for [160 =] 2  2  2  2  2  5 and [180 =] 2  2  3  3  5 or a list of multiples of 160 and 180 with at least the first three correct or two correct factor trees or tables or 2, 2, 2, 2, 2, 5, 3, 3 or 2  2  2  2  2  5  3  3 oe 1(i) 472.5 473.5 2 B1 for each If zero scored, SC1 for both correct but reversed

This question in 0580/31 May/June 2022

3 Sachin, his wife and three children go on a coach holiday. (a) Each adult ticket costs $375 and each child ticket costs $194. Work out the total cost of the tickets. $ … [2] (b) A meal costs $110 plus a service charge of 18%. Calculate the total cost of the meal. $ … [2] (c) One day, the temperature at midday is 16 °C. At midnight the temperature has fallen by 23 °C. Work out the temperature at midnight. … °C [1] (d) Sachin spends $768 on holiday. 3 He spends of this amount on presents. 8 Find how much he spends on presents. $ … [1] (e) There are 604 passengers on the holiday. (i) The coach company uses coaches which can carry 46 passengers. Work out the number of coaches needed. … [2] (ii) 268 of the 604 passengers are women. Find the percentage of the passengers that are women. … % [1] (f) A coach travels at an average speed of 54 km/h. Find how long, in hours and minutes, this coach takes to travel 126 km. … h … min [3]

12 marks

Mark scheme: 3(a) 1332 2 M1 for 2  375 + 3  194 oe 3(b) 129.8[0] 2 M1 for 110  (1  10018 ) oe or B1 for 19.8[0] 3(c) −7 1 3(d) 288 1 3(e)(i) 14 2 M1 for 604 ÷ 46 or 13.1[3…] 3(e)(ii) 44.4 or 44.37… 1 3(f) 2 (h) 20 (min) 3 M1 for 126 ÷ 54 A1 for 2.33… or 140 mins If A0 scored, SC1 for their (decimal time) correctly changed to hours and minutes

This question in 0580/31 May/June 2022

9 (a) Sami buys a new car. (i) She pays a deposit of $2250 and 36 equal monthly payments of $437.50 . Show that she pays a total amount of $18 000. [2] (ii) Sami later sells the car for $13 680. Calculate the percentage loss. … % [2] (b) Sami invests $12 750 for 6 years at a rate of 1.8% per year compound interest. Calculate the value of her investment at the end of the 6 years. $ … [2]

6 marks

Mark scheme: 9(a)(i) 2250 + 437.5  36 [= 18 000] 2 M1 for 437.5  36 9(a)(ii) 24 2 18000 –13680 M1 for  100  oe 18000  13680  or 1 –   [ 100] oe  18000  or 100 − 13680  100 oe 18000 9(b) 14 200 or 14 190 2  1.8  6 M1 for 12 750  1 +  oe or 14 190.5 or 14 190.47…  100 

This question in 0580/31 Oct/Nov 2022

9 (a) Write down the reciprocal of 1. 3 … [1] (b) Write down the value of 30. … [1] 3 4 (c) Find a fraction between and . 25 25 … [1] (d) Find the difference in temperature between −5 °C and 9 °C. … °C [1] (e) Write in standard form. (i) 5 600 000 … [1] (ii) 0.000 072 … [1] (f) Calculate ( 5.2 # 10 6 ) # (3 .8 # 10 -2 ) . Give your answer in standard form. … [1]

7 marks

Mark scheme: 9(a) 3 1 9(b) 1 1 9(c) Correct fraction e.g. 507 1 9(d) 14 1 9(e)(i) 5.6 × 106 1 9(e)(ii) 7.2 × 10-5 1 9(f) 1.976 × 105 1

This question in 0580/32 Oct/Nov 2022

1 (a) List all the factors of 68. … [2] (b) Put one pair of brackets into each calculation to make it correct. (i) 7 + 3 # 5 - 1 = 19 [1] (ii) 12 + 16 ' 2 + 5 = 19 [1] (c) Find (i) the reciprocal of 2, 7 … [1] (ii) the value of 100. … [1] (d) Calculate. (i) 3 2 + 3 4 … [1] (ii) 3 # 12 … [1] (iii) 5 -3 … [1] (e) Write these numbers in order of size, starting with the smallest. 22 10 .3142 .182 r 7 … 1 … 1 … 1 … 1 … [2] smallest (f) By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of 136 + 47.2 . 62.9 ' 18.1 You must show all your working. … [2] (g) Write .473 # 106 as an ordinary number. … [1] (h) Write down a prime number between 30 and 40. … [1]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1, 2, 4, 17, 34, 68 2 B1 for 4 or 5 correct and no extras or 6 correct and one extra 1(b)(i) 7 + 3  (5 – 1) = 19 1 1(b)(ii) (12 + 16) ÷ 2 + 5 = 19 1 1(c)(i) 7 1 1 or 3.5 or 3 2 2 1(c)(ii) 1 1 1(d)(i) 90 1 1(d)(ii) 6 1 1(d)(iii) 1 1 or 0.008 125 1(e) 22 2 B1 for 4 in correct order π, 3.142, , 10 , 1.82 7 or M1 for [ 10 =] 3.16…, [1.82=] 3.24, 22 [π =] 3.141…, [ =] 3.1428 to 3.1429 or 7 3.143 1(f) 100 + 50 M1 60  20 50 cao nfww A1 If 0 scored, SC1 for 3 correct roundings or for all correct but with any trailing zeros 1(g) 4 730 000 1 1(h) 31 or 37 1

This question in 0580/33 Oct/Nov 2022

4 (a) Write 6479 correct to the nearest 100. … [1] (b) Write down the multiple of 13 that is between 100 and 110. … [1] (c) Find the reciprocal of 0.6 . … [1] (d) Work out. 3 + 4 # 2 … [1] (e) Write down an irrational number with a value between 15 and 20. … [1] (f) By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 423.8 - 78.4 . 23.5 You must show all your working. … [2]

7 marks

Mark scheme: 4(a) 6500 1 4(b) 104 1 4(c) 2 1 13 oe 4(d) 11 1 4(e) Any irrational number between 15 and 20 1 4(f) 400 − 80 M1 20 16 nfww A1 If 0 scored, SC1 for 2 correct roundings or all correct but with trailing zeros

This question in 0580/32 Feb/March 2023

1 (a) Write the number forty thousand and thirty-three in figures. … [1] (b) Find the value of 3 729 . … [1] 7 (c) Find the reciprocal of . 9 Give your answer as a decimal, correct to 3 decimal places. … [2] (d) Find the value of 6 5 ' 3 4 . … [2] (e) Work out ( - 9 ) # ( - 7 ) ' ( - 3) . … [1] (f) Work out. (i) 11 + 9 # 5 - 4 … [1] (ii) ( 11 + 9) # 5 - 4 … [1] 5(g) - 0 .67 123 49 3 .142 9 From this list, write down an irrational number. … [1] (h) (i) Find the lowest common multiple (LCM) of 24 and 104. … [2] (ii) Find the highest common factor (HCF) of 24 and 104. … [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 40 033 1 1(b) 9 1 1(c) 1.286 cao 2 B1 for 97 or 1.29 or 1.285 or 1.285…… 1(d) 96 2 B1 for 7776 or 81 1(e) −21 1 1(f)(i) 52 1 1(f)(ii) 96 1 1(g) √123 1 1(h)(i) 312 2 B1 for 312k as final answer or M1 for [24 =] 2 × 2 × 2 × 3 or 23 × 3 and [104 =] 2 × 2 × 2 × 13 or 23 × 13 or 2 correct factor trees or tables or a list of multiples of both 24 and 104 with at least 3 of each or 2 × 2 × 2 × 3 × 13 oe 1(h)(ii) 8 2 B1 for 2 or 4 or 2 × 2 × 2 or 23 as final answer, or for a complete list of factors of 24 and 104

This question in 0580/31 May/June 2023

2 A shop sells food and drink. (a) Bananas cost $1.20 per kilogram and apples cost $2.25 per bag. Work out the total cost of 3.5 kg of bananas and 2 bags of apples. $ … [3] (b) Students receive a 10% discount on their shopping. Before the discount, the cost of a student’s shopping is $16.80 . Work out the amount of the discount. $ … [1] (c) The cost of a cabbage increases by 15%. Calculate the new price if the original price is $1.80 . $ … [2] (d) Some customers have their shopping delivered to their home. The cost is $5 plus $1.50 for each kilometre travelled from the shop to their home. (i) Show that the cost for a customer living 10 km from the shop is $20. [1] (ii) 25 20 15 Cost ($) 10 5 0 0 1 2 3 4 5 6 7 8 9 10 Distance travelled (km) On the grid, draw a line to show the cost of having shopping delivered. [2] (e) A bottle of water costs $1.55 . Suki has $20. Work out the maximum number of bottles Suki can buy and the change she receives. Maximum number of bottles … Change $ … [3] (f) A farmer delivers eggs to the shop in trays of 50. The eggs are then put into boxes of 12. There are no eggs left in the trays and all of the egg boxes are full. Work out the smallest possible number of eggs that the farmer delivers. … [2] (g) The shop sells bottles of orange juice in three different sizes. Bottle A Bottle B Bottle C 0.5 litres 1.2 litres 2 litres $1.30 $3.20 $5.25 Work out which bottle is the best value. Show how you decide. Bottle … [3]

17 marks

Mark scheme: 2(a) 8.7[0] 3 M2 for 3.5  1.2  2  2.25 oe or B2 for 4.2[0] and 4.5[0] or M1 for 3.5  1.2 oe or 2  2.25 oe 2(b) 1.68 cao 1 2(c) 2.07 cao 2  15  M1 for  1    1.8 oe  100  or B1 for 0.27 2(d)(i) 5  10  1.5 [=20] 1 2(d)(ii) Ruled line from (0, 5) to (10, 20) 2 B1 for one correct point plotted 2(e) 12 3 M2 for 20  12  1.55 oe 1.4[0] or B2 for 18.6 20 or M1 for soi by 12.9… 1.55 or 12 in the answer space 2(f) 300 2 B1 for 300k as final answer or M1 for [12 =] 2 × 2 × 3 and [50 =] 2 × 5 × 5 or 2 correct factor trees/lists/tables or a list of multiples of both 12 and 50 with at least 3 of each or 2 × 2 × 3 × 5 × 5 or 2,2,3,5,5 12 or 50  oe 50  (12  4) 2(g) A 3 M2 for 3 correct comparable With correct comparisons made of the 3 values, or for a correct method to bottles with suitable accuracy shown compare 3 bottles shown but not evaluated to enough accuracy or M1 for 2 correct comparable values or for a correct method to compare 3 bottles but not evaluated

This question in 0580/33 May/June 2023

3 (a) Write the number fourteen thousand and ninety-seven in figures. … [1] (b) Write down a common multiple of 17 and 5. … [1] (c) Write 0.25 as a percentage. … % [1] (d) Find the value of (i) 75 … [1] (ii) 80. … [1] 5 (e) Ranjit buys some plants and sells of them. 11 He sells 190 plants. Work out how many plants he buys. … [2] (f) Factorise completely. 15x 3 y - 3x … [2] (g) Make n the subject of the formula V = 3n + t . n = … [2] (h) 7 15 ' 7 x = 7 9 Find the value of x. x = … [1]

12 marks

Mark scheme: 3(a) 14 097 1 3(b) Any correct multiple i.e. 85k 1 3(c) 25 1 3(d)(i) 16 807 1 3(d)(ii) 1 1 3(e) 418 2 M1 for 190 ÷ 5 soi by 38 3(f) 3x(5x2y – 1) final answer 2 B1 for 3(5x3y – x) or for x(15x2y – 3) or correct answer spoilt 3(g) V − t 2 V t oe final answer M1 for V – t =3n or = n + 3 3 3 3(h) 6 1

This question in 0580/32 Oct/Nov 2023

6 (a) Simplify. a + 4 a - 3a … [1] (b) Simplify. 8b - 4 # 7b … [1] (c) 4x + 3 x + 7 3x - 9 NOT TO SCALE 9x + 8 7x + 3 The perimeter of this shape is equal to the perimeter of a square. Find an expression for the length of one side of the square. Give your answer in its simplest form. … [4] (d) Victoria buys 5 cups of tea and 4 cakes for $15.69 . Isabella buys 3 cups of tea and 7 cakes for $17.97 . Write down a pair of simultaneous equations and solve them to find the cost of one cup of tea and the cost of one cake. You must show all your working. Tea $ … Cake $ … [6]

12 marks

Mark scheme: 6(a) 2a final answer 1 6(b) – 20b final answer 1 6(c) 6x + 3 final answer 4 24 x+12 B3 for seen or 6x + 3 seen then 4 spoilt 24 x + k kx+12 or B2 for 24x + 12 or or seen 4 4 k≠0 or M2 for 3 x – 9 + 4 x + 3 + x + 7 + 9 x + 8 + 7 x + 3 oe 4 or M1 for 3x – 9 + 4x + 3 + x + 7 + 9x + 8 + 7x + 3 oe or B1 for 24x + k or kx + 12 seen k≠0 6(d) 5t + 4c = 15.69 oe B1 3t + 7c = 17.97 oe B1 correctly equating one set of M1 coefficients correct method to eliminate one M1 variable t = 1.65 A1 c = 1.86 A1 If A0 scored, SC1 for 2 values satisfying one of the original equations or if no working shown, but 2 correct answers given

This question in 0580/32 Oct/Nov 2023

1 (a) Tom has a restaurant bill. Soup $ … Pasta $ 13.30 Ice cream $ 4.80 Drinks $ 3.81 Total cost $ 25.40 (i) Complete the bill to show the cost of soup. [2] (ii) Find the cost of drinks as a percentage of the total cost. … % [1] 2 (b) (i) Work out of $2400. 5 $ … [1] (ii) Decrease $3450 by 18%. $ … [2] (c) Amelia invests $14 000 at a rate of 1.6% per year compound interest. Calculate the value of her investment at the end of 5 years. Give your answer correct to the nearest dollar. $ … [3] (d) This conversion graph can be used to change between dollars and Swiss francs. 200 160 120 Swiss francs 80 40 00 40 80 120 160 200 Dollars (i) Use the graph to change (a) $80 to Swiss francs … Swiss francs [1] (b) 108 Swiss francs to dollars. $ … [1] (ii) Explain how you can use the graph to change $360 to Swiss francs. … … [1]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 3.49 2 M1 for 25.4[0] – (13.3[0] + 4.8[0] + 3.81) oe 1(a)(ii) 15 1 1(b)(i) 960 1 1(b)(ii) 2829 2  18  M1 for 3450 ×  1 −  oe  100  or B1 for 621 1(c) 15156 cao 3 5  1.6  M1 for 14000 ×  1 +  oe  100  A1 for 15156.4…, or 15156 or 15160 or 15200 If A0 scored, SC1 for correctly rounding their decimal answer to the nearest dollar 1(d)(i)(a) 72 1 1(d)(i)(b) 120 1 1(d)(ii) Correct explanation, using any correct 1 combination of values between 0 and 200 to reach 360 oe

This question in 0580/33 Oct/Nov 2023

7 (a) P = 3a + 5 Find the value of P when a = 2 . P = … [1] (b) Solve these equations. (i) 7x =-42 x = … [1] (ii) 9 ( 8x - 7) = 72 x = … [3] (c) 5 8 # 5 k = 5 -24 Find the value of k. k = … [1] (d) Solve the simultaneous equations. -6x - y = 13 8x + y =- 51 x = … y = … [2] (e) n is an integer where n 2- 3 and n G 1. Write down all the possible values of n. … [2] (f) A boy walks for 35 minutes at x metres per minute. He then runs for t minutes at 160 metres per minute. Write down an expression, in terms of x and t, for the total distance, in metres, the boy travels. … m [2] (g) NOT TO SCALE x – 2 x + 5 Find an expression for the area of this rectangle. Give your answer in the form x 2 + ax + b . … [3] Question 8 is printed on the next page.

15 marks

Mark scheme: 7(a) 11 1 7(b)(i) −6 1 7(b)(ii) 1.875 oe 3 M1 for a correct first step e.g. 8 x − 7 = 8 or 72 x− 63 = 72 M1FT for a correct second step e.g. 8 x = 15 or 72 x = 135 7(c) −32 1 7(d)  x =  − 19  y = 101 2 B1 for  x =  − 19 B1 for  y = 101 7(e) −2, −1, 0, 1 2 B1 for 3 correct and no extras or 4 correct and one extra 7(f) 35x + 160t final answer 2 B1 for 35x or 160t seen in final answer or 35 x + 160t seen and spoilt 7(g) x 2 + 3 x − 10 final answer 3 B2 for x 2 + 5 x − 2 x − 10 with at least 3 terms correct or B1 for ( x + 5 )( x − 2 ) oe

This question in 0580/32 Feb/March 2024

1 (a) The cost of a cinema ticket is $6.30 . (i) Work out the total cost of 4 tickets. $ … [1] (ii) The cinema sells 10 tickets for the price of 9 tickets. A group of 10 people go to the cinema. Work out how much each person must pay. $ … [2] (b) The cinema has 650 seats. (i) There are 26 seats in each row. Work out the number of rows. … [1] (ii) 84% of the seats are occupied. Work out how many seats are not occupied. … [2] (c) Suki buys a bag of popcorn and a bottle of water. A bag of popcorn costs twice as much as a bottle of water. She receives $3.55 change from $10. Work out the cost of a bag of popcorn and the cost of a bottle of water. Bag of popcorn $ … Bottle of water $ … [3] (d) (i) A film lasts for 155 minutes. Write 155 minutes in hours and minutes. … hours … minutes [1] (ii) Another film starts at 14 45 and lasts for 2 hours and 20 minutes. Work out the time that this film finishes. … [1] (e) The table shows the hours that Trevor works in the cinema each week. Monday No hours Tuesday No hours Wednesday 18 00 to 22 00 Thursday 18 00 to 22 00 Friday 12 00 to 17 30 Saturday 12 00 to 17 30 Sunday 13 00 to 18 00 Trevor is paid $11.50 per hour for the time he works before 18 00. He is paid 30% more for the time he works after 18 00. Work out how much Trevor is paid each week. $ … [4]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 25.2[0] 1 1(a)(ii) 5.67 2 M1 for 9  6.3   10  oe 1(b)(i) 25 1 1(b)(ii) 104 2  84  M1 for 650   1   oe  100  or B1 for 546 1(c) 4.3[0] 2.15 3 B2 for 4.3[0] or 2.15 in correct place or for both correct in the reverse order. 10  3.55 or M1 for k  oe k  1 or 2 3 1(d)(i) 2 [hours] 35 [minutes] 1 1(d)(ii) 1705 1 1(e) 303.6[0] 4 M3 for (4+4+5.5+5.5+5)×11.5 30 + (4+4)× (  11.5 ) oe 100 OR B2 for 59.8 (or 119.6) or 63.25 (or 126.5) or 57.5 or 184 or 276 or 27.6 seen OR M1 for 4 + 4 + 5.5 + 5.5 + 5 oe or 4 + 4 oe and 5.5 + 5.5 + 5 oe and 30 M1 for  11.5 oe 100  30  or  1    11.5 oe  100 

This question in 0580/31 May/June 2024

2 (a) Simplify. (i) 5a - 6a + 3a … [1] (ii) 6x 2 - 6x - 4x 2 - x … [2] (b) Find the value of c 2 + d 2 when c = 7 and d =- 5 . … [2] (c) The time, T minutes, to cook a chicken with a mass of m kg is T = 35m + 20 . (i) Make m the subject of the formula. m = … [2] (ii) Find the mass of a chicken that takes 83 minutes to cook. … kg [2] (d) Solve these simultaneous equations. You must show all your working. 5x - 6y = 24 15x + 8y = 33 x = … y = … [3]

12 marks

Mark scheme: 2(a)(i) 2a final answer 1 2(a)(ii) 2x2 – 7x final answer 2 B1 for 2x2 or −7x in final answer or for 2x2 – 7x seen then spoilt. 2(b) 74 2 B1 for 49 or 25 2(c)(i) T  20 2 T 20 [m =] final answer M1 for T – 20 = 35m or  m  35 35 35 2(c)(ii) 1.8 2 FT their (c)(i) for 2 marks or 1 mark M1 for (83 – 20) ÷ 35 2(d) Correctly eliminates one variable M1 Making the coefficients the same for one of the variables and correct consistent use of addition or subtraction using their equations alternative substitution method. M1 for correct rearrangement of one equation to make either x or y the subject and correct substitution of their rearrangement into 2nd equation. [x =] 3 A1 If A0 scored SC1 for 2 values satisfying one of the original equations. [y =] −1.5 A1

This question in 0580/32 May/June 2024

6 (a) In a sport, teams are given points using the formula number of points = number of wins # 4 + number of draws # 2 + bonus points. One team has 15 wins, 7 draws and 6 bonus points. Calculate the total number of points for this team. … [2] (b) Solve. x = 18 2 x = … [1] (c) Solve. 4x + 12 = 18 x = … [2] (d) Expand and simplify. 6 ( 3x - 4) + 5 ( x - 2) … [2] (e) T = 5r - 6 Make r the subject of this formula. r = … [2] (f) Bo has a green bag and a blue bag. Each bag contains some marbles. The green bag has x marbles. There are 5 times as many marbles in the blue bag than in the green bag. Bo now adds 6 marbles to each bag. There are now 4 times as many marbles in the blue bag than in the green bag. Use this information to write down an equation and solve it to find the value of x. x = … [5]

14 marks

Mark scheme: 6(a) 80 2 M1 for 15×4 + 7×2 + 6 oe 6(b) 36 1 6(c) 1 12 or 1.5 2 M1 for 4x = 18 – 12 or x  12  18 oe 4 4 6(d) 23x – 34 final answer 2 M1 for 23x or – 34 in the final answer or for 18x – 24 or 5x – 10 or 23x – 34 seen then spoilt 6(e) T  6 2 T 6 [r = ] oe final answer M1 for 5r = T + 6 or  r  5 5 5 6(f) 5x + 6 = 4(x + 6) oe B2 B1 for 5x or 5x + 6 or x + 6

This question in 0580/33 May/June 2024

1 (a) Onions cost $1.85 per kilogram and potatoes cost $2.34 per kilogram. Sophie buys 2.4 kg of onions and 4.5 kg of potatoes. Work out how much change she receives from $20. $ … [3] (b) Sophie gets on a bus at 10 47 and she gets off the bus 36 minutes later. Work out the time she gets off the bus. … [1] (c) Sophie uses two-thirds of a litre of milk each day. Milk is sold in 2-litre bottles. Show that she needs at least 3 bottles to have enough milk for 7 days. [2] (d) One month, Helen sells phones and computers in the ratio number of phones : number of computers = 3 : 5. She sells 40 computers. Work out how many phones she sells. … [2] (e) In 2022 Helen sells 520 phones. In 2023 she sells 35% more phones than in 2022. Calculate the number of phones she sells in 2023. … [2] (f) A television costs $840 in the USA. The same television costs 3549 ringgits in Malaysia. The exchange rate is $1 = 4.2 ringgits. In which country is the television cheaper and by how many dollars? Cheaper in … by $ … [2]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 5.03 3 B2 for 14.97 OR M2 for 20 – (2.4 × 1.85 + 4.5 × 2.34) oe or M1 for 2.4 × 1.85 or 4.5 × 2.34 soi 1(b) 11 23 1 1(c) Accept any correct method M1 2 2 14 Alt. method 2 ÷ = 3 [days] e.g. 7 3 = 3 3 e.g. their 143  2 = 73 [bottles] A1 1 Alt. method 7 ÷3 = 2 so 3 [bottles 1 3 2 so 3 [bottles needed] needed] 3 1(d) 24 nfww 2 40 M1 for [×k] , where k is 1,3 or 8 oe 5 1(e) 702 2 M1 for 520 × (1 + 10035 ) oe OR B1 for 182 1(f) USA 5 2 M1 for 3549 ÷ 4.2 oe or (3549 – (840 × 4.2)) ÷ 4.2 oe

This question in 0580/32 Oct/Nov 2024

1 (a) (i) Li has $20. A box of cereal costs $2.29 . Work out the maximum number of boxes of cereal that Li can buy. … [2] (ii) Each box of cereal has mass 615 g. Work out the total mass of 5 boxes of cereal. Give your answer in kilograms. … kg [2] (iii) The box of cereal is a cuboid. The cuboid measures 25 cm by 20 cm by 5 cm. Work out the volume of the cuboid. … cm3 [1] (b) A cereal bar is in a box. The box is a cuboid measuring 6 cm by 3 cm by 1 cm. NOT TO 6 cm SCALE 1 cm 3 cm On the 1 cm2 grid, complete a net of the cuboid. One face has been drawn for you. [3] (c) The cereal contains fat, protein, carbohydrate and fibre. The pie chart shows the information about the masses of fat and protein. Fat 36° Protein (i) Work out the percentage of the mass of the cereal that is fat. … % [1] (ii) 60% of the mass of the cereal is carbohydrate. Complete the pie chart. [2] (iii) Work out the mass of protein in 30 g of the cereal. … g [2]

13 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 8 2 M1 for 20 ÷ 2.29 1(a)(ii) 3.075 2 M1 for 615 × 5 1(a)(iii) 2500 1 1(b) Fully correct net 3 B2 for 3 or 4 correct extra faces in correct place B1 for 1 or 2 correct extra faces in correct place 1(c)(i) 10 1 1(c)(ii) Correct pie chart 2 B1 for 216º soi 1(c)(iii) 5.67 5.666 to 5.67 2 B1 for 68 OR k M1 FT for  30 oe 360

This question in 0580/33 Oct/Nov 2024

3 Put one pair of brackets into this calculation to make it correct. 80 ' 8 + 2 # 3 = 24 [1]

1 marks

Mark scheme: 3 80 ÷ (8 + 2) × 3 = 24 1

This question in 0580/33 May/June 2025

11 (a) Naz pays $76.25 per day to hire a car. He hires this car for 7 days. He also pays $146 for fuel. Calculate the total amount Naz pays. $ … [2] (b) Li pays $1400 to hire a car. $364 of this is insurance. Calculate the insurance as a percentage of the $1400. … % [1]

3 marks

Mark scheme: 11(a) 679.75 cao 2 M1 for 76.25 × 7 + 146 oe or B1 for 533.75 11(b) 26 1

This question in 0580/31 Oct/Nov 2025

14 Carl packs pens into boxes. Each box holds 68 pens. Carl has 980 pens and 14 boxes. Does Carl have enough boxes to pack all the pens? Show how you decide. … because … … [2]

2 marks

Mark scheme: 14 Correct working shown leading to 2 B1 for 980 ÷ 68 answer No with a correct statement. e.g. or No, he would need 15 boxes oe 980 ÷ 68 [= 14.4…] or 14 × 68 No, he would need 15 boxes oe or No, he can only pack 952 or or he has 28 remaining oe 14 × 68 [= 952] or 980 14 No, he can only pack 952 or he has 28 remaining oe or No, each box would need to hold 70 pens oe or 980 14 [ = 70] No, each box would need to hold 70 pens oe

This question in 0580/33 Oct/Nov 2025