Limits of accuracy — Paper 3 · IGCSE Mathematics 0580

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

1 A bookshop sold a total of 2750 books in January. Examiner's Use (a) The ratio hardback books sold : paperback books sold was 4 : 7. Calculate how many paperback books were sold. Answer(a) [2] (b) 24% of the 2750 books sold were non-fiction. Calculate how many non-fiction books were sold. Answer(b) [2] (c) 330 cookery books were sold. Write 330 as a fraction of 2750 in its lowest terms. Answer(c) [2] (d) In February, the bookshop sold 14% more than the 2750 books sold in January. Calculate the number of books sold in February. Answer(d) [3] (e) The total value of the books sold in January was $9480 correct to the nearest 10 dollars. Write down the lower bound for this amount. Answer(e) $ [1] (f) 35000 books were sold in a year. Write this number in standard form. Answer(f) [1]

11 marks

Mark scheme: Qu. Answers Mark Part Marks 771 (a) 1750 2 M1 × 2750 oe 4 + 7 24× 2750 (b) 660 2 M1 100 3 (c) 2 W1 for equivalent fractions 25 114 (d) 3135 cao 3 M2 × 2750 oe 100 14 If M0 then M1 for × 2750 or 385 seen 100 (e) 9475 1 cao (f) 3.5 × 104 1 cao

This question in 0580/33 May/June 2010

2 The distance between Geneva and Gstaad is 150 km. For Examiner's (a) Write 150 in standard form. Use Answer(a) [1] 1 (b) A car took 1 hours to travel from Geneva to Gstaad. 2 Calculate the average speed of the car. Answer(b) km/h [1] (c) A bus left Gstaad at 10 15. It arrived in Geneva at 12 30. Calculate the time, in hours and minutes, that the bus took for the journey. Answer(c) h min [1] (d) Another bus left Geneva at 13 55. It travelled at an average speed of 60 km/h. Find the time it arrived in Gstaad. Answer(d) [2] (e) The distance of 150 km is correct to the nearest 10 km. Complete the statement for the distance, d km, from Geneva to Gstaad. Answer(e) Y d I [2]

7 marks

Mark scheme: 2 (a) 1.5(0) × 102 cao 1 (b) 100 cao 1 (c) 2 hours 15 minutes cao 1 (d) 16(:) 25 (pm) or (0)425 pm 2 M1 for 2.5 (oe), 2hrs 30 min (e) 145 ≤ d < 155 2 B1 for each value in correct place

This question in 0580/31 Oct/Nov 2011

6 James and Wei have a car. For Each year James drives 3 600 km and Wei drives 4 800 km. Examiner's Use (a) Write 3 600 : 4 800 as a ratio in its simplest form. Answer(a) : [1] (b) A garage charges $420 to service the car. James and Wei share the $420 in the ratio James : Wei = 2 : 3 . Find the amount that James pays. Answer(b) $ [2] (c) On a 268 km journey the car uses 22.8 litres of fuel. By writing these numbers to 1 significant figure, estimate the distance travelled using one litre of fuel. Show all your working. Answer(c) km [2] (d) On another journey the car uses 46.3 litres of fuel. Fuel costs $1.48 per litre. Work out the cost of the fuel for this journey. Answer(d) $ [2] (e) The table shows some information about the car. For Examiner's Use Fuel tank capacity 64 litres (to the nearest litre) Width 1810 mm (to 3 significant figures) (i) Write down the upper bound of the fuel tank capacity. Answer(e)(i) litres [1] (ii) Write down the minimum width of the car. Answer(e)(ii) mm [1]

9 marks

Mark scheme: 6 (a) 3 : 4 cao 1 (b) 168 2 M1 420 ÷ (2 + 3) or 84 seen (c) 300 ÷ 20 = 15 2 250 / 260 / 270 / 300 if 0 scored SC1 for 20 / 23 / 25 or 15 ww (d) 68.5(2) 2 M1 for 46.3 × 1.48, 68.53 or 68.524 (e) (i) 64.5 1 (ii) 1805 1

This question in 0580/33 May/June 2012

1 (a) Angelica goes to watch a football match. For She entered the stadium at 19 20 and left at 22 05. Examiner's Use Work out the number of hours and minutes she was in the stadium. Answer(a) hours minutes [1] (b) The number of people watching the football match was 25 926. Write 25 926 correct to the nearest thousand. Answer(b) [1] (c) The football club buys lemonade in 5 litre bottles. Work out the number of 250 millilitre drinks that can be poured from one bottle. Answer(c) [2] (d) The table shows the number of goals scored in each match by Mathsletico Rangers. Number of goals scored Number of matches 0 4 1 11 2 6 3 3 4 2 5 1 6 2 (i) Draw a bar chart to show this information. For Complete the scale on the frequency axis. Examiner's Use Frequency 0 1 2 3 4 5 6 Number of goals scored [3] (ii) Write down the mode. Answer(d)(ii) [1] (iii) Calculate the mean. Answer(d)(iii) [3]

11 marks

Mark scheme: Qu. Part Answers Mark Part Marks 1 (a) 2 hours 45 minutes oe 1 (b) 26 000 1 (c) 20 2 M1 5 ÷ 0.25 or 5000 ÷ 250 (d) (i) fully correct bar chart 3 B1 correctly scaled frequency axis B2 correct height of bars ,width and spaces or B1 correct height of 5 or 6 bars or all bars correct height but unequal widths or gaps (ii) 1 1 (iii) 1.97 (1.9655….) 3 M1 attempt to multiply implied by 0, 11, 12, 9, 8, 5, 12 added implied by 57 M1 dep ft 57 ÷ their 29 or B2 1.96 or 2.103

This question in 0580/33 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

3 (a) A shop has maps arranged in bookcases. For Examiner′s Use (i) The length of one wall in the shop is 7.35 m. Each bookcase is 120 cm wide. Work out the maximum number of bookcases that will fi t along this wall. Answer(a)(i) … [2] (ii) Each bookcase weighs 45 kg correct to the nearest 5 kg. Write down the upper bound for the weight of a bookcase. Answer(a)(ii) … kg [1] (b) During July and August the shop sells a total of 160 maps. Some of these maps are driving maps and the rest are walking maps. (i) Complete the table below. Driving maps Walking maps Total July 15 August 65 Total 40 160 [2] (ii) Write down the fraction of the total number of walking maps that are sold in July. Give your answer in its simplest form. Answer(b)(ii) … [2] (c) The shopkeeper buys each map for $5.50 . For Examiner′s He sells each map for $6.60 . Use (i) Calculate his percentage profi t. Answer(c)(i) … % [3] (ii) Each map has a price in dollars ($) and euros (€). The price is $6.60 or €3.52 . Work out the exchange rate for €1 . Answer(c)(ii) €1 = $ … [2] (d) The shop is open for 312 days each year. The shopkeeper pays 3 employees $47.66 each per day. The total annual wage bill for the three employees is given by 3 × 312 × 47.66 . (i) Rewrite this calculation so that each number is rounded to 1 signifi cant fi gure. 3 × … × … [1] (ii) Use your answer to part (d)(i) to work out an estimate for the total annual wage bill. Answer(d)(ii) $ … [1] _____________________________________________________________________________________

14 marks

Mark scheme: 3 (a) (i) 6 cao 2 M1 for 735/120 oe implied by 6.125 or SC1 for figs ‘61 … ’ (ii) 47.5 1 (b) (i) 55 ---- 70 2 M1 for 3 or 4 correct numbers ---- 25 90 120 ---- --- 3 15 3 (ii) cao 2 B1 for or seen 8 40 8 20 (c) (i) 3 B1 for 6.6 - 5.5 or better M1 for ‘their 1.1’ / 5.5 OR (an alternative method) M1 for 6.6/5.5 M1 for ‘their 1.2’ –1 oe 1.875 cao (ii) 2 M1 for 6.60/3.52, imp by 1.87 or 1.88 300, 50 (d) (i) 1 45000 (ii) 1 SC1 43200

This question in 0580/32 May/June 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

2 Olga owns a fruit and vegetable shop. (a) An apple weighs 70 g correct to the nearest 5 g. Complete the statement about the mass, m grams, of this apple. Answer(a) … G m 1 … [2] (b) The number of strawberries in each of 12 boxes is shown below. 23 21 21 20 21 20 22 22 21 20 20 20 (i) Find the range. Answer(b)(i) … [1] (ii) Write down the mode. Answer(b)(ii) … [1] (iii) Find the median. Answer(b)(iii) … [2] (iv) Calculate the mean. Answer(b)(iv) … [2] (v) Find the probability that a box chosen at random has 22 or 23 strawberries in the box. Answer(b)(v) … [1] (c) The shop sells potatoes in bags A, B and C. 20 kg 8 kg $6.92 5 kg $2.75 $1.74 BAG C BAG B BAG A Work out which bag is the best value. You must show all your working. Answer(c) … [3] (d) The price of plums is $2.40 per kilogram. Olga reduces this price by 35%. Calculate the new price per kilogram. Answer(d) $ … [2] __________________________________________________________________________________________

14 marks

Mark scheme: 2 (a) 67.5 1 SC1 for both answers correct but reversed 72.5 1 (b) (i) 3 1 (ii) 20 1 (iii) 21 2 M1 for 7 or more in order (iv) 20.9 or 20.91 to 20.92 2 M1 for clear attempt to add numbers and divide by 12 3 (v) oe 1 12 (c) complete correct method shown and 3 M2 for completely correct method Bag B oe or M1 for one correct calculation seen (d) 1.56 2 M1 for (100 – 35) × 2.40 / 100 oe

This question in 0580/32 Feb/March 2015

6 A sweet shop sells lots of different types of sweets. (a) (i) Each large bag of mixed sweets is divided in the ratio mints : jellies : toffees = 5 : 2 : 8. Each large bag has a total of 180 sweets. Calculate the number of sweets of each type in a large bag. Answer(a)(i) Mints = … Jellies = … Toffees = … [3] (ii) The mass, m grams, of a small bag of sweets is 75 g, correct to the nearest gram. Complete the statement about the value of m. Answer(a)(ii)…………….  m  ………….. [2] (b) There are 156 g of sugar in a 240 g bar of chocolate. (i) Write 156 as a percentage of 240. Answer(b)(i) … % [1] (ii) Work out the number of grams of sugar in a 1.2 kilogram bar of chocolate. Answer(b)(ii) … g [2] (iii) Another bar of chocolate is made. The mass is 35% greater than the 240 g bar. Work out the mass of this chocolate bar. Answer(b)(iii) … g [2] (c) A girl buys a large piece of fudge. She eats 103 herself and divides the rest equally between 4 friends. Work out the fraction of this fudge that each friend receives. Answer(c) … [2] (d) Gabriella and Max buy some bags of mints and some bags of toffees from the shop. The cost of one bag of mints is m cents and the cost of one bag of toffees is t cents. (i) Gabriella buys 3 bags of mints and 5 bags of toffees for $4.70 . Complete the equation. 3m + 5t = … [1] (ii) Max buys 4 bags of mints and 3 bags of toffees for $3.70 . Write this information as an equation. Answer(d)(ii) … = … [2] (iii) Solve your two equations to find the cost of a bag of mints and the cost of a bag of toffees. You must show all your working. Answer(d)(iii) Cost of a bag of mints = … cents Cost of a bag of toffees = … cents [4]

19 marks

Mark scheme: 6 (a) (i) 60, 24, 96 3 180 M2 for × k where k is 5, 2 or 8 (5 + 2 + 8) or better 180 or M1 for or better (5 + 2 + 8) If zero scored SC1 for all correct answers in incorrect order (ii) 74.5 1 SC1 for both answers correct but reversed 75.5 1 (b) (i) 65 1 (ii) 780 2 M1FT for their 65 156 × 2.1 × 1000 or × 2.1 × 1000 oe 100 240 If zero scored SC1 for figs 78 (iii) 324 2 M1 for 240 × 1.35 oe 7 k 3  (c) 2 M1 for − 1  ÷ 4 oe 40 k  10  (d) (i) 470 1 (ii) 4m + 3t = 370 2 B1 for 4m + 3t seen (iii) Correct working and 4 M1FT for correctly equating one set of [m] 40 coefficients [t] 70 M1FT for correct method to eliminate one variable A1 for m = 40 A1 for t = 70 If zero scored SC1 for either: 2 correct answers given or 2 values satisfying one of their original equations

This question in 0580/32 Oct/Nov 2015

1 (a) Chip flies from New York to St Petersburg. The plane takes off at 02 30 and arrives in St Petersburg at 19 35. The local time in New York is 8 hours behind the local time in St Petersburg. How long does the flight take? Answer(a) … hours … min [2] (b) Chip books a bus tour of St Petersburg. The cost is $290 for each adult and $163 for each child. There are 37 adults and 8 children on the bus. (i) Calculate how much is paid altogether. Answer(b)(i) $ … [3] (ii) The bus has 53 seats for passengers. Calculate the percentage of seats that are occupied. Answer(b)(ii) … % [2] (iii) Chip pays $290 for the bus tour. The exchange rate is $1 = 33.2 rubles. Work out the cost of the tour in rubles. Answer(b)(iii) … rubles [1] (c) St Isaac’s cathedral in St Petersburg is 101 m high, correct to the nearest metre. Complete the statement about the height, h metres, of St Isaac’s cathedral. Answer(c) …  h < … [2] (d) Chip went on a cruise ship from St Petersburg. It visited four other ports. 30 guests are asked which port they enjoyed the most. Each reply is listed below. Stockholm St Petersburg St Petersburg Helsinki Tallinn St Petersburg Tallinn Helsinki Tallinn Copenhagen Tallinn Copenhagen St Petersburg St Petersburg Stockholm St Petersburg Stockholm Helsinki Helsinki St Petersburg Tallinn Tallinn St Petersburg St Petersburg Stockholm Tallinn St Petersburg Helsinki Tallinn Copenhagen (i) Complete the frequency table. You may use the tally column to help you. Port Tally Frequency Copenhagen Helsinki St Petersburg Stockholm Tallinn Total 30 [2] (ii) Draw a bar chart to show this information. Complete the scale on the frequency axis. Frequency Copenhagen Helsinki St Petersburg Stockholm Tallinn [3] __________________________________________________________________________________________

15 marks

Mark scheme: Question Answer Mark Part marks 1 (a) 9 hours 5 minutes 2 B1 for 17 hrs 5 mins or using 10 30 or 11 35 (b) (i) 12034 3 M2 for 290 × 37 + 163 × 8 or M1 for either 290 × 37 or 163 × 8 (ii) 84.9 2 M1 for (37 + 8) ÷ 53 or better (iii) 9628 1 (c) 100.5 1 SC1 for correct but reversed 101.5 1 (d) (i) Copenhagen 3 2 B1 for 3 or 4 correct or fully correct tallies if frequency Helsinki 5 column blank or correct frequencies in tally column St Petersburg 10 Stockholm 4 Tallinn 8 (ii) Correct bar chart 3FT B3 All bars correct height same width and same gaps between bars and linear scale B2 for all bars correct height same width and same gaps between bars B1 for linear scale on y-axis B1 FT 3 or 4 correct heights

This question in 0580/33 Oct/Nov 2015

1 Whisper is a horse. (a) Whisper eats three apples every day. Work out how many apples she eats in 52 weeks. … [1] (b) Whisper is exercised twice a day. The first time is for 30 minutes. The second time is for 1 12 hours. (i) Write down the fraction of a day that Whisper is exercised. Write your answer in its simplest form. … [2] (ii) Write down the fraction of a day that she is not being exercised. … [1] (c) Whisper weighs 429 kg, correct to the nearest kilogram. Complete the statement about her weight, w kg. …  w  … [2]

6 marks

Mark scheme: Question Answer Mark Part marks 1 (a) 1092 1 1 2 120 (b) (i) cao 2 M1 for or oe 12 24 1440 11 1 (ii) oe 1FT FT is for 1– their 12 12 (c) 428.5 1 SC1 for both answers correct but reversed 429.5 1

This question in 0580/32 Feb/March 2016

1 (a) A group of 20 children were asked to choose their favourite type of fruit juice. The results are listed below. Orange Apple Apple Pineapple Mango Tropical Orange Mango Apple Mango Pineapple Apple Apple Mango Orange Apple Mango Pineapple Orange Apple (i) Complete the frequency table for the results. You may use the tally column to help you. Type of juice Tally Frequency Orange Apple Pineapple Mango Tropical [2] (ii) Draw a bar chart to show these results. Remember to mark the scale on the frequency axis. Frequency Orange Apple Pineapple Mango Tropical [3] (iii) Sarah has a pack of 20 cartons of juice. 5 are orange, 5 are apple, 5 are pineapple and 5 are mango. She would like to give each child their favourite type of juice. How many children will not get their favourite type of juice? … [1] (b) One litre of a mixed fruit drink contains 550 millilitres of apple juice. Write down the fraction of the drink that is apple juice. Give your answer in its simplest form. … [2] (c) Amir wants to buy a bottle of fruit juice. There are three sizes of bottle. 0.9 litres 1.25 litres 1.35 litres $2.40 $3.15 $3.50 Work out which size of bottle gives the best value. Show how you decide. … [3] (d) The amount of juice in a glass, j millilitres, is 150 millilitres correct to the nearest 10 millilitres. Complete this statement about the value of j. … G j 1 … [2]

13 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) Frequencies 4, 7, 3, 5, 1 2 B1 for 3 or 4 correct in frequency column or for fully correct tally in tally column or for 4, 7, 3, 5, 1 in tally column (ii) Correct bar chart 3FT B1 for linear vertical scale B2FT for all bars correct height and equal width, with equal gaps or no gaps or B1FT for all bars correct height with unequal widths and/or gaps or at least four bars correct height and equal width, with equal gaps or no gaps (iii) 3 1 11 550 (b) final answer 2 M1 for oe seen 20 1000 (c) Three correct evaluated, to at least 3 M2 M2 implied by 2.67 or 2.66… and 2.52 and significant figures, consistent divisions 2.59… or M1 for one correct evaluated division soi, implied by one of 2.67 or 2.66…, 2.52, 2.59… [$/litre] or one of 2.40/0.9 = 2.7, 3.15/1.25 = 2.5, 3.50/1.35 = 2.6 1.25 litre bottle indicated A1 Dependent on M2 (d) 145 155 1, 1 B1 for both correct in reverse order

This question in 0580/32 May/June 2016

3 (a) Tariq wants to buy some orange juice. He sees these offers in a shop. Offer A Offer B Offer C 1-litre carton 2-litre carton Pack of 4 1-litre cartons $0.65 $1.25 $2.56 Work out the lowest amount Tariq could pay for 5 litres of orange juice. Show how you decide. Tariq buys … cartons. The lowest amount is $ … [3] (b) Bottle P contains 1.5 litres of lemonade. 1 Bottle Q contains 3 more lemonade than bottle P. Work out how much lemonade is in bottle Q. … litres [2] (c) Tariq makes a fruit drink. He mixes 500 ml of orange juice, 200 ml of pineapple juice and 1 litre of lemonade. (i) Write the ratio orange juice : pineapple juice : lemonade in its simplest form. … : … : … [2] (ii) Tariq makes more of this fruit drink. Work out the total amount of fruit drink he makes when he uses 2 litres of orange juice. Give your answer in litres. … litres [3] (d) Tariq pours 300 cm3 of fruit drink into a glass. The glass is in the shape of a cylinder with radius 3.5 cm. The height of the drink in the glass is h cm. NOT TO SCALE h cm 3.5 cm Work out the value of h. h = … [2] (e) The capacity of a jug is 750 ml correct to the nearest 10 ml. Write down the upper and lower bounds of the capacity of the jug. Upper bound = … ml Lower bound = … ml [2]

14 marks

Mark scheme: 3 (a) 2 B and 1 A selected, with 2 M1 for one correct cost for 5 litres at least one other or B1 for 0.625 or 0.64 combination and its value seen or 2 B and 1 A selected, with 1 Independent 0.625 and 0.64 seen 3.15 selected 1 (b) 2 2 M1 for [1.5 + ] × 1.5 oe soi by 0.5 3 (c) (i) 5 : 2 : 10 2 M1 for 500 : 200 : 1000 oe (ii) 6.8 3 B2 for answer 6800 or 2 M2 for × 17 oe or for 4 × (0.5 + 0.2 + 1) 5 or for 4 × (500 + 200 + 1000) oe 5 2000 or M1 for soi or for oe soi by 4 17 500 (d) 7.79 or 7.80 or 7.794 to 2 M1 for 300 = π × 3.52 × h or better implied by 7.795 300 (38.4to38.5) (e) 755 2 B1 for one correct or both values reversed 745

This question in 0580/32 Oct/Nov 2016

6 (a) A bag contains 5 white and 6 black marbles. (i) A marble is chosen at random from the bag and then replaced. Write down the probability that the marble is black. … [1] (ii) Delilah adds some more black marbles to the bag. The probability of choosing a black marble is now 23 . How many black marbles did she add to the bag? … [2] (b) A white marble costs w cents and a black marble costs b cents. (i) 2 white marbles and 5 black marbles cost 155 cents. Complete the equation. 2w + 5b = … [1] (ii) 3 white marbles and 10 black marbles cost 290 cents. Write down an equation to show this information. … [1] (iii) Solve your two equations to find the value of w and the value of b. You must show all your working. w = … b = … [3] (c) A black marble is weighed and its mass, m grams, is 35 g correct to the nearest 5 g. Complete the statement about the value of m. … G m 1 … [2] (d) Each marble is a sphere of diameter 3 cm. On the grid, draw an accurate net of the smallest closed box a marble can fit in. NOT TO SCALE [2]

12 marks

Mark scheme: 6 6 (a) (i) oe 1 11 1 (ii) 4 2 M1 for 10 black marbles or is 5 marbles 3 (b) (i) 155 1 (ii) 3 w + 10b = 290 oe 1 (iii) [w] 20 3 M1FT for correct method to eliminate one [b] 23 variable A1 for w = 20 A1 for b = 23 If zero scored, SC1 for either: 2 correct answers given or 2 values satisfying one of their original equations (c) 32.5 , 37.5 1,1 SC1 for both answers correct but reversed (d) correct net 2 M1 for 5 correctly placed 3 cm by 3 cm squares and one incorrect or missing

This question in 0580/32 Feb/March 2017

9 Zach goes on holiday. (a) The mass, m kilograms, of his suitcase is 23.5 kg, correct to the nearest 500 g. Complete this statement about the value of m. … G m 1 … [2] (b) The ratio of the costs flights : hotels = 3 : 8. The cost of the flights is $861. Work out the total cost of flights and hotels. $ … [2] (c) $1 = 0.88 euros £1 = 1.15 euros Zach changes $575 into euros. He spends 45% of the euros in France. He changes the euros he does not use into pounds (£) to spend in England. Work out how many pounds he receives. £ … [4]

8 marks

Mark scheme: 9(a) 23.25 23.75 2 B1 for each If 0 scored, SC1 for both correct and in reverse order 9(b) 3157 2 861 M1 for × oe  ( 3 + 8 ) or × 8  3 9(c) 242 4 M1 for changing to euros M1FT for 45% or 55% calculated M1FT for changing to pounds or M1 for 45% or 55% calculated M1FT for changing to euros M1FT for changing to pounds

This question in 0580/32 May/June 2019

8 (a) The scale drawing shows the positions of two buoys, A and B, in the sea. The scale is 1 centimetre represents 20 kilometres. North North B Land A Sea Scale : 1 cm to 20 km Land (i) Work out the actual distance between buoy A and buoy B. … km [2] (ii) Measure the bearing of buoy B from buoy A. … [1] (iii) Buoy C is 120 km from buoy B on a bearing of 300°. On the scale drawing, mark the position of buoy C. [2] (iv) Marco sails his boat so that he is always equidistant from buoy A and buoy B. On the scale drawing, use a straight edge and compasses only to construct the path of the boat. Show all your construction arcs. [2] (b) The amount of fuel, t litres, in the boat’s fuel tank is 135 litres, correct to the nearest litre. Complete the statement about the value of t. … G t 1 … [2] (c) Marco has ropes of four different colours. He takes a rope at random. Colour Brown White Red Green Probability 0.35 0.04 0.2 Complete the table. [2] (d) When Marco arrives at a port the temperature is 5 °C. At midnight the temperature has fallen by 7 °C. Find the temperature at midnight. … °C [1] (e) Last year the cost to keep a boat at the port was $14 per night. This year the cost has increased by 12%. Calculate the cost this year. $ … [2] (f) Marco watched 25 boats enter the port, of which 9 had a mast. There are a total of 200 boats in the port. Calculate an estimate of the number of boats in the port that have a mast. … [2] Question 9 is printed on the next page.

16 marks

Mark scheme: 8(a)(i) 220 2 M1 for 11 8(a)(ii) [0]80° 1 8(a)(iii) C in correct position 2 B1 for correct distance of 6 cm or bearing of 300° from B 8(a)(iv) Correct line drawn with 2 pairs of 2 B1 for correct line with no or incorrect arcs correct arcs or correct arcs but no line 8(b) 134.5, 135.5 2 B1 for one correct or both correct but reversed 8(c) 0.41 2 M1 for 1 – (0.35 + 0.04 + 0.2) 8(d) –2 1 8(e) 15.68 cao 2 12 M1 for (1+ ) ×14 oe 100 8(f) 72 2 9 M1 for × 200 oe 25

This question in 0580/31 Oct/Nov 2019

9 (a) By rounding each number correct to 1 significant figure, show that an estimate for this calculation is 20. 9. 78 + 31. 562 0.381 # 5 .09 [2] (b) Write these numbers in order, smallest first. 22 333 3.142 3.1416 7 106 … 1 … 1 … 1 … [2] smallest (c) The length, p cm, of a pencil is 9.8 cm, correct to 2 significant figures. Complete the statement about the value of p. … G p 1 … [2] 5 2163 (d) Calculate .3142 - . 16 604 Give your answer in standard form correct to 2 significant figures. … [2]

8 marks

Mark scheme: 9(a) 10 + 30 M1 [ 0 ] .4 × 5 40 A1 [= 20] 2 9(b) 333 22 2 B1 for 3.1428[…] or 3.143 and 3.1416 3.142 3.1415[…] 106 7 or for 3 in the correct order 9(c) 9.75 9.85 2 B1 for one correct or both correct and reversed 9(d) 4.1 × 10–4 cao 2 B1 for 4.07[6…] × 10-4 or 4.08× 10-4 or figs 41

This question in 0580/33 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

6 (a) Write 60 025 in words. … [1] (b) Write 849.481 correct to 1 decimal place. … [1] (c) Write down (i) all the factors of 21, … [2] (ii) a prime number between 40 and 50. … [1] 2 (d) Write as a decimal. 5 … [1] (e) Find the value of (i) 3 2744 , … [1] (ii) 70. … [1] (f) Gino invests $6000 for 5 years at a rate of 1.2% per year compound interest. Calculate the value of his investment at the end of the 5 years. Give your answer correct to the nearest dollar. $ … [3]

11 marks

Mark scheme: 6(a) Sixty thousand [and] twenty five 1 6(b) 849.5 cao 1 6(c)(i) 1, 3, 7, 21 2 B1 for 3 factors and no extras or 4 correct and 1 extra 6(c)(ii) 41, 43 or 47 1 6(d) 0.4 cao 1 6(e)(i) 14 1 6(e)(ii) 1 1 6(f) 6369 cao 3  1.2  5 M1 for 6000 ×  1 +  or better  100  A1 for 6368.7 … , or 6368 or 6370 If A0 scored, SC1 for correctly rounding their decimal answer

This question in 0580/32 Oct/Nov 2020

1 (a) A cruise ship travels 2067 km. (i) Write 2067 in words. … [1] (ii) Write 2067 correct to the nearest hundred. … [1] (b) When full, the cruise ship carries 880 guests and 360 crew. Write the ratio guests : crew in its simplest form. … : … [1] (c) There are 480 cabins on the ship. On one cruise, 456 of these cabins were used. Find the percentage of cabins that were used. … % [1] (d) Last year the cost of a cruise was $4600. This year the cost of the same cruise is $4784. Work out the percentage increase in the cost. … % [2] (e) The cost of building the ship was $153 000 000. Write 153 000 000 in standard form. … [1] (f) There are 480 cabins on the ship. There are four types of cabin: Ocean-view, Balcony, Interior and Suite. Hannah starts to draw a pie chart to show the numbers of each type of cabin. Ocean-view 144° Balcony (i) Show that there are 120 Ocean-view cabins on the ship. [1] (ii) The table shows information about each type of cabin. Type of cabin Number of cabins Sector angle in a pie chart Ocean-view 120 90° Balcony 192 144° Interior 68 Suite 100 (a) Complete the table. [2] (b) Complete the pie chart. [1]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Two thousand [and] sixty-seven 1 1(a)(ii) 2100 1 1(b) 22 : 9 1 1(c) 95 1 1(d) 4 nfww 2 4784 − 4600 M1 for [× 100] 4600  4784  or  − 1  [× 100]  4600  4784 or × 100 [– 100] oe 4600 1(e) 1.53 × 108 1 1(f)(i) 90 1 × 480 [= 120] oe 360 1(f)(ii)(a) 51 2 68 100 M1 for either × 360 or × 360 oe 75 480 480 or better 1(f)(ii)(b) Correct pie chart 1 FT dep on their 51° and their 75° adding to 126°

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

74 (a) Put a ring around the fraction that is equivalent to . 12 35 20 49 82 64 62 36 84 144 110 [1] (b) Write these numbers in order, starting with the smallest. 7 8 2 0.6 58% 12 13 3 … 1 … 1 … 1 … 1 … [2] smallest (c) Write 0.724 as a fraction in its simplest form. … [1] (d) The mass, m grams, of a ball is 415 g, correct to the nearest 5 grams. Complete the statement about the value of m. … G m 1 … [2] (e) Ruth uses three-quarters of a bag of flour to make one cake. Work out the number of bags of flour she needs to buy to make 7 cakes. … [3] (f) A tin of soup costs $t and a packet of biscuits costs $p. (i) 3 tins of soup and 2 packets of biscuits cost $15.50 . Complete the equation. 3t + 2p = … [1] (ii) 5 tins of soup and 4 packets of biscuits cost $28.50 . Write down another equation in terms of t and p. … [1] (iii) Solve the two simultaneous equations. You must show all your working. t = … p = … [3]

14 marks

Mark scheme: 4(a) 49 1 84 4(b) 7 8 2 2 B1 for 4 in correct order 58% 0.6 or M1 for 0.583[...], [0.6], 0.58, 0.615[…] 12 13 3 or 0.61 or 0.62, 0.66[...] or 0.67 or 0.667 or 0.7 oe 4(c) 181 1 cao 250 4(d) 412.5 417.5 2 B1 for each If 0 scored, SC1 for both correct but reversed 4(e) 6 3 3 M1 for 7 × oe 4 1 A1 for 5.25 or 5 4 4(f)(i) 15.5[0] 1 4(f)(ii) 5t + 4p = 28.5[0] 1 4(f)(iii) For correct method to eliminate one M1 FT their two linear equations variable [t =] 2.5 A1 [p =] 4 A1 If 0 scored, SC1 for 2 values satisfying one of the correct equations or their (f)(i) or (f)(ii) or SC1 if no working shown, but 2 correct answers

This question in 0580/32 May/June 2021

7 Rita and Henry own an investment business. (a) They share the profit in the ratio Rita : Henry = 3 : 5. In one year they make a profit of $2 400 000. Calculate Rita’s share of the profit. $ … [2] (b) Henry invests $160 000 at a rate of 2.5% per year compound interest. Calculate the value of this investment at the end of 3 years. $ … [2] (c) Rita invests $12 000 at a rate of r % per year. The value of her investment at the end of one year is $12 408. Work out the value of r. r = … [2] (d) Rita and Henry decorate their office. The cost, $c, is $10 800, correct to the nearest hundred dollars. Complete this statement about the value of c. … G c 1 … [2]

8 marks

Mark scheme: 7(a) 900 000 2 2400000 M1 for × k 3 + 5 7(b) 172 302.5[0] cao 2 M1 for 160 000 × (1 + 1002.5 ) 3 oe 7(c) 3.4 2 12408 − 12000 M1 for [× 100] oe 12000 12408 or − 1 [ × 100 ] oe 12000 12408 or × 100 [ −100 ] oe 12000 7(d) 10 750 10 850 2 B1 for each If 0 scored, SC1 for both correct but reversed

This question in 0580/33 May/June 2021

3 360 people go on a school trip to one of four places. Some of the information is shown in the table. Adventure Botanic Wildlife Red castle Total park gardens centre Boys 65 12 36 Girls 9 62 163 Staff 15 3 37 Total 144 24 121 71 360 (a) Complete the table. [3] (b) Find the probability that (i) a girl, picked at random, visits the Wildlife centre, … [1] (ii) a person, picked at random from those visiting the Botanic gardens, is a girl, … [1] (iii) a person, picked at random, visits the Adventure park or the Botanic gardens. … [1] (c) The people who visit the Adventure park travel by coach. Each coach has 52 seats for passengers. Complete this statement. The least number of coaches needed for the trip to the Adventure park is … and there will be a total of … empty seats. [2] (d) The school hires one coach from each of two different companies for the trip to Red castle. A coach from Fast Track coaches costs $600 plus $0.72 per kilometre travelled. The total cost, in dollars, for travelling x kilometres is 600 + 0.72x . (i) A coach from Rapid coaches costs $550 plus $1.12 per kilometre travelled. Write an expression for the total cost, in dollars, for travelling x kilometres. … [1] (ii) Both companies charge the same amount for the trip. Write down an equation and solve it to find the distance travelled. … km [3] (e) The length, l km, of the journey to the Wildlife centre is 53 km, correct to the nearest kilometre. Complete this statement about the value of l. … G l 1 … [2] (f) Samira takes $31.50 to spend in the Botanic gardens. 2 (i) She spends of this money on food. 7 Work out how much Samira spends on food. $ … [1] (ii) At the end of the visit to the Botanic gardens, Samira has $4.50 left. What fraction of her money does Samira spend? Give your answer in its simplest form. … [2]

17 marks

Mark scheme: 3(a) 3 B2 for 4 or 5 correct A B W R Tot or B1 for 2 or 3 correct B 47 160 G 64 28 S 12 7 Tot 3(b)(i) 62 1 oe 163 3(b)(ii) 3 1 oe 8 3(b)(iii) 7 1 oe 15 3(c) 3, 12 2 B1 for 3 (coaches) nfww or M1 for 144 ÷ 52 3(d)(i) 550 + 1.12x 1 3(d)(ii) 600 + 0.72x = 550 + 1.12x 1 FT 600 + 0.72x = their (d)(i) 125 2 M1FT for isolating x terms and constant terms or better for their linear equation DEP on their (d)(i) of the form ax + b (a ≠ 0) 3(e) 52.5, 53.5 2 B1 for each If zero scored, SC1 for both values correct but reversed 3f(i) 9 1 3(f)(ii) 6 2 31.5 [ 0 ] − 4.5 [ 0 ] cao M1 for oe 7 31.5 [ 0 ]

This question in 0580/31 Oct/Nov 2021

6 (a) Write these in order, starting with the smallest. 11 17 0.5806 58% 19 29 … 1 … 1 … 1 … [2] smallest (b) Write 0.004 973 correct to (i) 3 decimal places, … [1] (ii) 2 significant figures. … [1] (c) The height of a flag pole, h metres, is measured as 37.84 metres, correct to 2 decimal places. Complete this statement about the value of h. … G h 1 … [2] (d) The population of Nigeria is 201 000 000, correct to 3 significant figures. Write this population in standard form. … [1] (e) The table shows the populations of some countries given in standard form, correct to 3 significant figures. Country Population Brazil .212 # 108 China .142 # 109 Eritrea .531 # 106 France .655 # 107 Maldives .452 # 105 New Zealand .479 # 106 Use the information in this table to find (i) the country with the smallest population, … [1] (ii) the country with the population that is nearest to 5 million, … [1] (iii) the difference between the population of Brazil and the population of France, … [1] (iv) the value of k, correct to 2 significant figures, where the population of China = k # the population of Eritrea. k = … [2]

12 marks

Mark scheme: 6(a) 11 17 2 M1 for 58% 0.5806 [0.5806] [0].57… [0].586… [0].58 19 29 or B1 for 3 in the correct order 6(b)(i) 0.005 cao 1 6(b)(ii) 0.0050 cao 1 6(c) 37.835 37.845 2 B1 for each If 0 scored, SC1 for both correct but reversed 6(d) 2.01 × 108 1 6(e)(i) Maldives 1 6(e)(ii) New Zealand 1 6(e)(iii) 146 500 000 or 1.465 × 108 1 6(e)(iv) 270 cao 2 M1 for (1.42 × 109) ÷ (5.31 × 106) oe or 267[. …] oe

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

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 three hundred thousand and three in figures. … [1] (b) Write 15 896 correct to (i) the nearest thousand … [1] (ii) the nearest ten. … [1] (c) By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of 28.9 # 5.49 . 0.472 + 0.97 You must show all your working. … [2] (d) Find the value of (i) 1849 … [1] (ii) 5 0 - 5 -1 … [1] 5 sin 30 - 8 (iii) . 11 … [1] (e) A cyclist travels at a constant speed of 8.5 metres per second. (i) Work out how long the cyclist takes to travel a distance of 5.27 kilometres. Give your answer in minutes and seconds. … min … s [4] (ii) The cyclist increases speed from 8.5 m/s to 10.2 m/s. Work out the percentage increase in speed. … % [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 300 003 1 1(b)(i) 16 000 1 1(b)(ii) 15 900 1 1(c) 30  5 M1 0.5  1 100 A1 If 0 scored, SC1 for three correct from 30, 5, [0].5 and 1 or if all correct but with trailing zeros 1(d)(i) 43 1 1(d)(ii) 0.8 1 1(d)(iii) −0.5 1 1(e)(i) 10 (min) 20 (s) 4 B3 for 620 or 10.3… or 0.172… OR B1 for 5270 or 0.0085 or 510 or 30600 or 0.51 or 30.6 M1 for figs 527÷ figs 85 (imp by figs 62) or figs 527 ÷ figs 510 (imp by figs 103…) or figs 527 ÷ figs 306 (imp by figs172 … ) B1 for their time seen (assume time is in seconds unless units stated) and converted correctly to minutes and seconds (seconds must be correct to 3sf or better) 1(e)(ii) 20 2 10.2 8.5 M1 for [×100] oe 8.5 or (10.2  100 ) [–100 ] oe 8.5 or (10.2 )1 [×100] oe 8.5

This question in 0580/32 May/June 2023

8 (a) The length, l m, of a piece of wire is 18.7 metres, correct to the nearest 10 centimetres. Complete the statement about the value of l. … G l 1 … [2] (b) 850 metres of wire has a mass of 130.5 kilograms. Work out the length of wire, in metres, that has a mass of 900 grams. … m [3] (c) Aluminium is used to make the wire. The mass of 1 cm 3 of aluminium is 2.7 grams. Work out the mass, in grams, of 6000 cm 3 of aluminium. Give your answer in standard form. … g [2] (d) A 12 metre length of wire increases in length to 12.017 metres when its temperature rises. Calculate the percentage increase in the length of the wire. … % [2]

9 marks

Mark scheme: 8(a) 18.65 18.75 2 B1 for each If 0 scored, SC1 for both correct but reversed or 1865  l  1875 8(b) 5.86 or 5.862… 3 900 M2 for  850 oe 130500 OR B1 for a correct conversion 130.5 kg=130500 [g] or 900 g =0.9 [kg] figs 9 or M1 for  850 figs130.5 8(c) 1.62  10 4 cao 2 M1 for 2.7  6000 or their number correctly converted to standard form 8(d) 0.142 or 0.1416 to 0.1417 2 12.017  12 M1 for  100  12  12.017  100  or   1    12  12.017 or  100   100  12

This question in 0580/33 May/June 2023

1 (a) Write the number six and a half million in figures. … [1] (b) Write 37 508 correct to the nearest thousand. … [1] (c) 6 9 100 28 31 1000 32 36 From this list of numbers, write down (i) a factor of 18 … [1] (ii) a multiple of 12 … [1] (iii) a square number … [1] (iv) a prime number … [1] (v) an irrational number. … [1] (d) Put one pair of brackets in each statement to make it correct. (i) 24 - 4 # 3 + 2 = 62 [1] (ii) 24 - 4 # 3 + 2 = 4 [1] 3 (e) Write as a decimal. 4 … [1] 3(f) Work out of 126. 7 … [1] (g) Write down the value of the reciprocal of 0.5 . … [1] 2 1(h) Without using a calculator, work out 5 - 2 . 3 5 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6 500 000 1 1(b) 38 000 1 1(c)(i) 6 or 9 1 1(c)(ii) 36 1 1(c)(iii) 9 or 36 1 1(c)(iv) 31 1 1(c)(v) 1000 1 1(d)(i) (24 − 4)  3 + 2 = 62 1 1(d)(ii) 24 − 4  (3 + 2) = 4 1 1(e) 0.75 1 1(f) 54 1 1(g) 2 1 1(h) 17 11 B1 Correct step for dealing with mixed or 17 k 11k 3 5 numbers, allow e.g. or 3k 5 k 85 33 M1 FT Correct method to find a common and denominator 15 15 3 157 cao A1 Alternative methods 2 1 10 3 7 3 − B1, and M1, 3 15 cao 3 5 15 15 A1 510 and 3 M1, 3 157 cao B1 A1 15 215 10 3 7 and M1, 3 15 cao B1A1 15 15

This question in 0580/31 Oct/Nov 2023

27 The height, h metres, of a building is 105 m, correct to the nearest metre. Complete this statement about the value of h. … G h 1 … [2]

2 marks

Mark scheme: 27 104.5 105.5 2 B1 for each in correct position If 0 scored SC1 for both correct but reversed

This question in 0580/31 May/June 2025

22 (a) A train to town P leaves a station every 20 minutes. A train to town Q leaves the same station every 35 minutes. Both trains leave at 09 30. Find the next time both trains leave together. … [3] (b) The distance, d km, between town P and town Q is 97 km, correct to the nearest kilometre. Complete the statement about the value of d. … G d 1 … [2]

5 marks

Mark scheme: 22(a) 11 50 3 B2 for 140 or 2 hr 20 mins or M1 for 140k or 2  2  5  7 or [20 =] 2  2  5 and [35 =] 5  7 or two correct factor trees/tables of both 20 and 35 OR M2 for listing correct times/multiples of both 20 and 35 to at least 1150 or 140 or M1 for listing at least 3 correct of each or one full list 22(b) 96.5 97.5 2 B1 for each in correct position If 0 scored SC1 for both correct but reversed

This question in 0580/31 Oct/Nov 2025

17 Write 46.179 correct to 4 significant figures. … [1]

1 marks

Mark scheme: 17 46.18 cao 1

This question in 0580/33 Oct/Nov 2025