Ratio and proportion — 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

9 (a) Calculate the size of one exterior angle of a regular heptagon (seven-sided polygon). For Give your answer correct to 1 decimal place. Examiner's Use Answer(a) [3] (b) D A E so to ro NOT TO SCALE 130o po qo F B C G In the diagram above, DAE and FBCG are parallel lines. AC = BC and angle FBA = 130°. (i) What is the special name given to triangle ABC? Answer(b)(i) [1] (ii) Work out the values of p, q, r, s and t. Answer (b)(ii) p = q = r = s = t = [5] (c) J J, K and L lie on a circle centre O. yo L KOL is a straight line and angle JKL = 65°. NOT TO Find the value of y. 65o O SCALE K Answer(c) y = [2]

11 marks

Mark scheme: 9 (a) 51.4 3 2 for 51 or M1 for any complete method (b) (i) Isosceles 1 (ii) p = 50 1 q = 80 1√ ft for 180 – 2p r = 50 1√ ft for = p s = 50 1√ ft for = p t = 80 1√` ft for = q or 180 – 2p (c) 25 2 M1 for 90 – 65 oe [11]

This question in 0580/31 Oct/Nov 2005

6 For Examiner's 20 cm Use NOT TO 10 cm SCALE brick face Part of the wall (a) A builder estimates the number of bricks in a wall by dividing the area of the wall by the area of the face of a brick. A brick wall is 10 metres long and 1.5 metres high. Each brick is 20 centimetres long and 10 centimetres high. Calculate how many bricks the builder estimates are in the wall. Show all your working. Answer(a) bricks [3] (b) Another wall will need 720 bricks. The builder adds an extra 5% to this number to allow for mistakes. (i) Calculate how many bricks the builder needs to buy. Answer(b) (i) bricks [2] (ii) Bricks are sold in packs of 100 which can not be split. How many packs should the builder buy? Answer(b) (ii) packs [1] (c) The builder mixes sand and cement in the ratio 5:2 to make mortar. He wants 14 buckets of mortar. (i) How many buckets of sand and how many buckets of cement does he need? Answer(c) (i) He needs buckets of sand and buckets of cement. [2] (ii) One bag of cement fills 3.5 buckets. How many bags of cement must the builder buy? Answer(c) (ii) bags [1]

9 marks

Mark scheme: 6 (a) 750cao 3 M1 Figs 10 ÷ figs 20 and figs 15 ÷ figs 10. OR M1 Figs 10 x Figs 15 and Figs 20 x Figs 10 M1 dep bricks in length × bricks in height. M1 dep. area of wall ÷ area of brick. If MO then SC1 for Figs 75 (b) (i) 756 2 M1 for 720 × 1.05 oe (ii) 8 1ft Their (b)(i) rounded up to the number of hundreds (c) (i) 10 1 4 1 (ii) 2 1ft Their cement buckets ÷ 3.5 and rounded up to next whole number 9

This question in 0580/31 Oct/Nov 2006

2 Marguerite earns $336 per month. For She divides her earnings between bills, food, savings and personal spending. Examiner's Use (a) Her bills take 2 of her earnings. 7 Show that $240 is left for her other items. Answer(a) [2] (b) She divides the $240 between food, savings and personal spending in the ratio 5 : 3 : 4. Calculate how much she spends on food. Answer(b) $ [2] (c) She saves the same amount each month. Show that she saves $720 in one year. Answer(c) [2] (d) She invests the $720 in a bank which pays 6% per year compound interest. How much will this be worth after 2 years? Answer(d) $ [3]

9 marks

Mark scheme: 2 5 2 (a) 336 − × 336 or × 336 M1 7 7 (=) 240 E1 240 must be seen for this mark (b) 5 ÷ their(5 + 4 + 3) × 240 M1 100 A1cao www 2 1 3 (c) 3 ÷ their(5 + 4 + 3) × 240 × 12 M1 Allow 2880 for 240 × 12 and for . 4 12 (=) 720 E1 720 must be seen for this mark (d) 720 × 1.06 2 oe M2 Implied by 88.99(2) or 89(total interest)seen M1 for 720 × 1.06 (implied by 763.2 seen) 808.99(2) or 809 A1 SC1 for 806.(4) (Simple Interest) www 3 for 808.99(2) or 809 [9] IGCSE – May/June 2007 0580/0581 03 1

This question in 0580/31 May/June 2007

1 Alphonse, his wife and child fly from Madrid to the Olympic Games in Beijing. For The adult plane fare is 450 euros. Examiner's The child fare is 68% of the adult fare. Use (a) Show that the total plane fare for the family is 1206 euros. Show all your working clearly. Answer (a) [3] (b) The ratio of the money spent on plane fares : accommodation : tickets = 6 : 5 : 3. Calculate the total cost. Answer(b) euros [3] (c) Alphonse changes 500 euros into Chinese Yuan at a rate of 1 euro = 9.91 Chinese Yuan. How many Chinese Yuan does he receive? Answer(c) Yuan [2] (d) Their plane leaves Madrid at 05 45. The journey takes 11 hours 35 minutes. Beijing time is 6 hours ahead of Madrid time. Find the time in Beijing when they arrive. Answer(d) [2]

10 marks

Mark scheme: 1 (a) 0.68 x 450 M1 = 306 A1 2 x 450 + 306 (= 1206) M1 dep allow 900 or 450 + 450 SCM3 for 2.68 x 450 (= 1206) (b) 2814 B3 M1 for 1206 ÷ 6 (implied by 201) or 450 ÷ 6 or 306 ÷ 6 M1 dep for x (6 + 5 + 3) implied by 14 SCM2 for 1206 + 1005 + 603 (c) 4955 B2 M1 for 500 x 9.91 implied by figs 4955 (d) 2320 or 11 20 pm B2 SC1 for 1720 or 1120 seen SC1 for any arrival time + 6 soi [10]

This question in 0580/31 May/June 2008

1 Aida, Bernado and Cristiano need $30 000 to start a business. For Examiner's 2 Use (a) (i) They borrow of this amount. 5 Show that they still need $18 000. Answer (a)(i) [1] (ii) They provide the $18 000 themselves in the ratio Aida : Bernado : Christiano = 5 : 4 : 3. Calculate the amount each of them provides. Answer(a)(ii)Aida $ Bernado $ Cristiano $ [3] (b) (i) Office equipment costs 35 % of the $30 000. Calculate the cost of the equipment. Answer(b)(i)$ [2] (ii) Office expenses cost another $6500. Write this as a fraction of $30 000. Give your answer in its lowest terms. Answer(b)(ii) [2] (iii) How much remains of the $30 000 now? Answer(b)(iii)$ [1] (c) They invest $12 500. After one year this has increased to $15 500. Calculate this percentage increase. Answer(c) % [3]

12 marks

Mark scheme: Qu Answers Mark Part Marks 1 (a) (i) 3 × 30 000 M1 Must see evidence of fractions 5 or 30 000 − 52 × 30 000 (ii) Aida $7500 5 or 4 or 3 W3 M1 for 5+ 4 + 3 × 18000 Bernado $6000 A1 for 1 correct answer Christiano $4500 (b) (i) 10 500 W2 M1 for 10035 × 30 000 or 0.35 × 30 000 (ii) 13 6500 60 W2 W1 for 30000 seen or other ‘correct’ fraction. (iii) ($)13 000 W1ft 15500 (c) 24 W3cao M1 for 15 500 − 12500 or 12500 × 100 M1 for 12500' 3000 ' × 100 or ‘124’− 100

This question in 0580/31 Oct/Nov 2008

9 The quadrilateral ABCD is a scale drawing of a park. For Angle ABC = 90° and 1 centimetre represents 10 metres. Examiner's Use D A B C (a) Write down (i) the actual length, in metres, of the side CD, Answer(a)(i) m [1] (ii) the size of angle BAD. Answer(a)(ii) [1] (b) Two straight paths cross the park. One path is the same distance from AB as from BC. The other path is the same distance from A as from D. (i) Using a straight edge and compasses only, construct the lines which show each path. [4] (ii) Tennis courts in the park are situated in a region closer to AB than to BC and closer to A than to D. Label this region T. [1] (c) Keith cycles past the park, so that he is always 30 metres outside the boundary ABC. Construct the locus of points which shows this part of his route. [2]

9 marks

Mark scheme: 9 (a) (i) 99 to 101 (metres) W1 (ii) 103° to 105° W1 (b) (i) Bisector of angle ABC W2 W1 correct bisector without arcs (45 ± 1 to BC) with arcs Bisector of AD with arcs W2 W1 correct bisector without arcs. Bisector about ±1mm from centre of AD 89° to 91° to AD by eye and centre within 2mm by and 89° to 91° to AD. eye. (ii) Closed region T indicated W1 Dependent on at least W1 for each bisector. Allow T omitted if region is clear. IGCSE – October/November 2008 0580 and 0581 03

This question in 0580/31 Oct/Nov 2008

1 (a) Roberto owns 6000 square metres of land. For He divides it between himself and his two children, Stefano and Tania, in the ratio Examiner's Use Roberto : Stefano : Tania = 7 : 5 : 3. (i) Show that Roberto now has 2800 square metres of land. Answer(a)(i) [2] (ii) Calculate the area of land that Stefano and Tania each have. Answer(a)(ii) Stefano m2 Tania m2 [2] (b) Roberto receives a rent of $1.40 per month for each square metre of his land. (i) Calculate the rent he receives in one year from his 2800 square metres of land. Answer(b)(i) $ [2] 3 (ii) Roberto uses of this amount to buy more land. 5 Calculate the amount that he uses to buy more land. Answer(b)(ii) $ [2] (c) Stefano builds a house on his land. For He borrows $5000 from a bank at 8% per year simple interest. Examiner's Find the total amount of interest he will have paid at the end of 3 years. Use Answer(c) $ [2] (d) Tania sells her land for $12 000. She invests the money for 3 years at 6% per year compound interest. Calculate the total amount of money she will have at the end of the 3 years. Give your answer to the nearest dollar. Answer(d) $ [4]

14 marks

Mark scheme: Qu Answers Mark Part marks 1 (a) (i) 6000 ÷ (7 + 5 + 3) 1 M1 6000 ÷ clear attempt at total Multiply by 7 1 M1 Dependent on first mark. (ii) (Stephano) 2000 www 1 Must be clearly Stephano. (Tania) 1200 www 1 Must be clearly Tania. (b) (i) ($)47040 2 M1 1.40 × 12 × 2800 (ii) ($)28224 2ft M1 3 × ‘47040’ or 0.6 × ‘47040’ 5 (c) ($)1200 2 M1 5000 × 8 × 3 ÷ 100 SC1 for final answer 6200 (d) ($) 14292 4 M2 12000 × (1.06)3 Or M1(12000+12000 × 0.06) × 0.06 M1 dep. Correct method for the next 2 years A1cao ($)14292(.19(2)) W1ft Their answer rounded to the nearest dollar. If M0 then maximum SC2 for ($) 2292 or SC1 for ($) 2292.2 or ($) 2292.19(2) or ($) 2300 IGCSE – May/June 2009 0580, 0581 03 2 (a) One-third of 360 oe 1

This question in 0580/31 May/June 2009

10 Examiner's Use Diagram 1 Diagram 2 Diagram 3 Diagram 4 Look at the sequence of diagrams. (a) Diagram 2 has a height of 2. Write down the height of (i) Diagram 5, Answer(a)(i) [1] (ii) Diagram 10, Answer(a)(ii) [1] (iii) Diagram n. Answer(a)(iii) [1] (b) Diagram 2 has a width of 3. Find the width of (i) Diagram 5, Answer(b)(i) [1] (ii) Diagram 10, Answer(b)(ii) [1] (iii) Diagram n. Answer(b)(iii) [2] (c) There are 6 squares in Diagram 2 and 15 squares in Diagram 3. (i) Write down how many squares there are in Diagram 5. Answer(c)(i) [1] (ii) Explain how this is found from the height and width of the diagram. Answer(c)(ii) [1] (iii) Write down, in terms of n, how many squares there are in Diagram n. Answer(c)(iii) [1]

10 marks

Mark scheme: 10 (a) (i) 5 1 (ii) 10 1 (iii) n 1 (b) (i) 9 1 (ii) 19 1 (iii) 2n − 1 oe 2 SC1 for 2n + k oe or jn – 1, j not = 0 (c) (i) 45 1 (ii) 5 × 9 1 Accept height × width (iii) n(2n – 1) oe or n(their (b)(iii)) 1ft Their (a)(iii) × their (b)(iii)

This question in 0580/31 May/June 2010

2 Francis earns $150 per week. Examiner's He has $132 left after he pays his tax. Use (a) Calculate what percentage of his $150 he pays in tax. Answer(a) % [3] (b) He divides the $132 between expenses, savings and family in the ratio Expenses : Savings : Family = 15 : 7 : 11. Calculate his expenses. Answer(b) $ [3] (c) His rent is $24 per week. What fraction of the $132 is this? Give your answer as a fraction in its simplest form. Answer(c) [2] (d) His earnings of $150 per week increase by 8%. Calculate his new earnings. Answer(d) $ [2]

10 marks

Mark scheme: 2 (a) 12 3 Either M1 for 150 − 132 soi M1 for ‘18’ ÷ 150 × 100 or M1 for 132/150×100 M1 for 100 – ‘88’ (b) 60 3 M1 for 15 + 7 +11 M1dep for 15 ÷‘33’ × 132, 132÷‘33’×15, 4×15 SC2 for 60:28:44 (c) 11 2 cao 2 W1 for 1266 or 448 or 336 or 224 (d) ($)162 2 M1 for 108 ÷ 100 × 150 or 150 + (8 ÷ 100 × 150) IGCSE – May/June 2010 0580 32

This question in 0580/32 May/June 2010

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

1 A drink consists of water and fruit juice. For Examiner's (a) 24% of the drink is water. Use Show that there is a total of 760 cm3 of fruit juice in one litre of the drink. Answer(a) [2] (b) What fraction of one litre of the drink is fruit juice? Give your answer in its simplest form. Answer(b) [2] (c) The 760 cm3 of fruit juice in one litre of the drink is made from apple, mango and peach in the following ratio. Apple : Mango : Peach = 6 : 15 : 17 Calculate the amount of apple juice. Answer(c) cm3 [2] (d) A shopkeeper buys bottles of the drink for 65 cents each. He sells them for 80 cents each. Calculate the percentage profit he makes on each bottle he sells. Answer(d) % [3]

9 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 0.76 × 1000 = 760 oe 2 B1 0.76 × 1000 or 1000 – 0.24 × 1000 19 760 76 38 (b) cao 2 B1 for or or 25 1000 100 50 (c) 120 2 M1 for 6 × 760 ÷ (6 + 15 + 17) or 6 ÷ (6 + 15 + 17) or 760 ÷ (6 + 15 + 17) or 20 (d) 23 or art 23.1 3 M1 for 80 – 65 (= 15) and M1 dep for ‘15’ ÷ 65 × 100

This question in 0580/32 Oct/Nov 2010

1 Mr and Mrs Clark and their three children live in the USA and take a holiday in Europe. For Examiner's (a) Mr Clark changes $500 into euros (€) when the exchange rate is €1 = $1.4593. Use Calculate how much he receives. Give your answer correct to 2 decimal places. Answer(a) € [2] (b) Tickets for an amusement park cost €62 for an adult and €52 for a child. Work out the cost for Mr and Mrs Clark and their three children to visit the park. Answer(b) € [3] (c) Mr Clark sees a notice: SPECIAL OFFER! Family ticket €200 Work out €200 as a percentage of your answer to part (b). Answer(c) % [1] (d) Mrs Clark buys 6 postcards at €0.98 each. For She pays with a €10 note. Examiner's Use Calculate how much change she will receive. Answer(d) € [2] (e) Children under a height of 130 cm are not allowed on one of the rides in the park. Helen Clark is 50 inches tall. Use 1 inch = 2.54 cm to show that she will not be allowed on this ride. Answer(e) [1]

9 marks

Mark scheme: Qu. Answers Mark Part Mark 1 (a) 342.63 2 M1 for 500 ÷ 1.4593 (b) 280 3 M1 for 2 × 62 + 3 × 52 B1 for 124 or 156 seen (c) 71.4 or 71.42 to 71.43 1ft (d) 4.12 2 B1 for 6 × 0.98 seen B1 for 5.88 or 4 + 6 × 0.02 (e) correct working 1 50 × 2.54 = 127 oe or 130 ÷ 2.54 = 51.2 or better

This question in 0580/31 May/June 2011

1 Falla buys 3000 square metres of land for a house and garden. For The garden is divided into areas for flowers, vegetables and grass. Examiner's Use He divides the land in the following ratio. house : flowers : vegetables : grass = 4 : 7 : 8 : 5 (a) (i) Show that the area of land used for flowers is 875 m2. Answer(a)(i) [2] (ii) Calculate the area of land used for the house. Answer(a)(ii) m2 [2] (b) Write down the fraction of land used for vegetables. Give your answer in its simplest form. Answer(b) [2] (c) During the first year Falla plants flowers in 64% of the 875 m2. For Examiner's Calculate the area he plants with flowers. Use Answer(c) m2 [2] (d) Falla sells some of the vegetables he grows. These vegetables cost $85 to grow. He sells them for $105. Calculate his percentage profit. Answer(d) % [3] (e) To buy the land Falla borrowed $5000 at a rate of 6.4% compound interest for 2 years. Calculate the total amount he pays back at the end of the 2 years. Give your answer correct to the nearest dollar. Answer(e) $ [3]

14 marks

Mark scheme: Qu. Answers Mark Part Marks 77 1 (a) (i) 3000 ÷ ( 4 + 7 + 8 + 5) 2 M2 for × 3000 24 and multiply by 7 M1 for 3000 ÷ (24 or their clear attempt at total) (ii) 500 www cao 2 M1 for 4 ÷ their 24 × 3000 oe or 74 × 875 1 8 4 2 2 (b) 2 B1 for or or oe seen or SC1 3 24 12 6 5 (c) 560 2 M1 for 64 ÷ 100 × 875 or 0.64 × 875 oe (d) 23.5 or 23.52 to 23.53 3 W1 for 105 − 85 implied by 20 M1dep for their (105 − 85) ÷ 85 × 100 (e) 5660 3 B2 for 5660.48 or 5660.5 or 660 4.6 4.6 If B0 then M1 for 5000 × 1( + ) × 1( + ) or 100 100 better

This question in 0580/32 May/June 2011

4 (a) Using the exchange rates For Examiner's $1 = 0.70 Euros and $1 = 90 Yen Use change (i) $100 to Euros, Answer(a)(i) Euros [1] (ii) 100 Yen to dollars. Answer(a)(ii) $ [2] (b) Tania went on holiday to Switzerland. The exchange rate was $1 = 1.04 Swiss francs (CHF). She changed $1500 to Swiss francs and paid 1% commission. (i) How much commission, in dollars, did she pay? Answer(b)(i) $ [1] (ii) Show that she received CHF 1544.40. Answer (b)(ii) [2] (c) Tania spent CHF 950 on her holiday. She converted the remaining Swiss francs back into dollars. She paid CHF 10 to make the exchange. Calculate the amount, in dollars, Tania received. Answer(c) $ [3]

9 marks

Mark scheme: 4 (a) (i) 70 cao 1 1 (ii) 1.11(11…) 2 B1 for 100 ÷ 90, 10 ÷ 9, 1 9 (b) (i) 15 cao 1 (ii) (1500 – 15) × 1.04 2 B1 for × 1.04, 1560, 15.60 (c) 561.92 3 M1 for 1544.40 – 950 – 10 (584.40) oe M1 indep for ÷ 1.04 4 rise

This question in 0580/31 Oct/Nov 2011

6 For E NOT TO Examiner's SCALE Use F 16 cm D C 24 cm A 30 cm B The diagram shows a wedge in the shape of a triangular prism. AB = 30 cm, AF = 16 cm and BC = 24 cm. Angle BAF = 90°. (a) Calculate (i) the area of triangle ABF, Answer(a)(i) cm2 [2] (ii) the volume of the wedge. Answer(a)(ii) cm3 [1] (b) (i) Calculate BF. Answer(b)(i) cm [2] (ii) 1.6 cm NOT TO SCALE A coin with diameter 1.6 cm is rolled down the sloping surface of the wedge. It travels in a straight line parallel to BF, starting on FE and ending on BC. Calculate the number of complete turns it makes. Answer(b)(ii) [3] (c) On the grid, complete the net of the wedge. For The base and one of the triangles have been drawn for you. Examiner's Use Each square on the grid represents a square of side 4 centimetres. [3] (d) Calculate the surface area of the wedge. Answer(d) cm2 [3]

14 marks

Mark scheme: 6 (a) (i) 240 2 M1 for 0.5 × 30 × 16 (ii) 5760 1ft ft is (a)(i) × 24 (b) (i) 34 2 M1 for (FB 2) = 16 2 + 30 2 (ii) 6 3 M1 for (circumference) = 1.6 × π M1 dep their (b)(i) ÷ their 1.6π (6.76 implies M1, M1) If 0 scored either SC1 for their (b)(i) ÷ 3.2 × π and then SC1 for truncating correctly If M1 or still 0 scored then SC1 for truncating correctly any number with at least 1 decimal place (c) 6 by 4 rectangle above 1 6 by their 8.5 rectangle below 1ft ft (b)(i) ÷ 4 Correct triangle on AB 1 1 1 (d) 2400 3cao M2 for × 30 × 16 + × 30 × 16 + 16 × 24 + 2 2 30 × 24 + their 34 × 24 (M1 for any 3 areas) If 0, SC2 for 150 or SC1 for 120 (3 rectangles) or SC1 for 30 (2 triangles)

This question in 0580/32 Oct/Nov 2011

9 On the scale drawing opposite, point A is a port. For B and C are two buoys in the sea and L is a lighthouse. Examiner's Use The scale is 1 cm = 3 km. (a) A boat leaves port A and follows a straight line course that bisects angle BAC. Using a straight edge and compasses only, construct the bisector of angle BAC on the scale drawing. [2] (b) When the boat reaches a point that is equidistant from B and from C, it changes course. It then follows a course that is equidistant from B and from C. (i) Using a straight edge and compasses only, construct the locus of points that are equidistant from B and from C. Mark the point P where the boat changes course. [2] (ii) Measure the distance AP in centimetres. Answer(b)(ii) cm [1] (iii) Work out the actual distance AP. Answer(b)(iii) km [1] (iv) Measure the obtuse angle between the directions of the two courses. Answer(b)(iv) [1] (c) Boats must be more than 9 kilometres from the lighthouse, L. (i) Construct the locus of points that are 9 kilometres from L. [2] (ii) Mark the point R where the course of the boat meets this locus. Work out the actual straight line distance, AR, in kilometres. Answer(c)(ii) km [1] For Examiner's Use L C B Scale: 1 cm = 3 km A Question 10 is printed on the next page.

10 marks

Mark scheme: 9 (a) Bisector of angle BAC with correct 2 Either B1 correct without arcs arcs or B1 for 2 pairs of accurate arcs seen (b) (i) Bisector of BC with 2 pairs of 2 Either B1 correct without arcs correct arcs or B1 for 2 pairs of accurate arcs seen (ii) 10.8 to 11.2 (cm) cao 1 (iii) 32.4 to 33.6 1ft Their (b)(ii) × 3 (iv) 155° to 165° cao 1 (c) (i) Circle centre L, radius 3cm 2 B1 circle centre L, incorrect radius or SC1 for part circle with correct radius (ii) 41km to 44km cao 1

This question in 0580/32 Oct/Nov 2011

1 (a) Vince and Wendy share $2000 in the ratio Vince : Wendy = 19 : 21. For Examiner's Calculate the amount of money that Vince receives. Use Answer(a) $ [2] (b) Wendy has $265 to spend on some chairs. The chairs cost $37 each. Work out the largest number of chairs she can buy. Answer(b) [2] (c) Wendy shares $200 between her three children Jake, Karl and Lana. 2 She gives 27% of the money to Jake and of the money to Karl. 5 Work out the amount of money she gives to Lana. Answer(c) $ [3] (d) Wendy invests $500 at a rate of 4% per year compound interest. Calculate the total amount of interest she receives at the end of 2 years. Give your answer correct to the nearest dollar. Answer(d) $ [4]

11 marks

Mark scheme: Qu. Answers Mark Part Mark 1 (a) 950 2 M1 for 2000 ÷ (19 + 21) 265 (b) 7 cao 2 M1 for seen oe e.g. adding up 37s 37 (c) 66 3 M1 for 54 seen M1 indep for 80 seen Or 33 67 M2 for × 200 or M1 for × 200 100 100 (d) 41 4 M1 for (500 × 1.04) × (1.04) oe A1 for 540.8 M1 dep for ‘their 540.8’ – 500 B1 ft for ‘their 40.8’ rounded to 41 Alt Method M1 for [500 + (500×0.04)] × 0.04 M1 dep ‘their 20’ + ‘their 20.8’ A1 for 40.8 B1 ft for ‘their 40.8’ rounded to 41

This question in 0580/31 May/June 2012

6 For y Examiner's Use B 6 4 2 A E C x –4 –2 0 2 4 6 8 10 12 –2 –4 –6 Triangle ABC is drawn on a 1cm2 grid. E is the point (0, 0). (a) Write down the gradient of the line AB. Answer(a) [2] (b) The gradient of BC is – 0.5 . Write down the equation of the line BC in the form y = mx + c. Answer(b) y = [2] (c) Write down the ratio AE : EC. For Give your answer in its simplest form. Examiner's Use Answer(c) : [2] (d) Measure angle ABE. Answer(d) Angle ABE = [1] (e) Triangle ABE is similar to triangle BCE. Explain what the word similar tells you about the triangles ABE and BCE. Answer(e) [2] (f) Calculate the area of triangle ABC. Answer(f) cm2 [3] (g) ABCD is a rectangle. (i) Mark point D on the grid. [1] (ii) Write down the co-ordinates of D. Answer(g)(ii) ( , ) [1]

14 marks

Mark scheme: (e) 6 × 10–3 4 M1 ‘50’ × ‘120’ figs seen in area calculation A1 for 6000 seen (implied by 0.006 later) M1 for dividing by 1000², 0.05 & 0.12 seen or ×10–6 oe somewhere B1 ft from ‘their 0.006’ provided SF power is –ve Or SC1 for 0.6 × 10–2 oe 9 (a) (i) 226 to 226.224 cm³ 3 M1 π × 3² × 8 B1 for units : cm³ (ii) 8 cao www 4 B1 1500 used M1ft 3 × their (a)(i) 4 their 1500 M1ft 3 × their (a)(i) 4 16 (b) 5.09 (5.092 to 5.10) 2 M1 π (c) 148 cm² 3 M2 for 2 × 4 × 5 + 2 × 4 × 6 + 2 × 5 × 6 SC1 for 2 × 4 × 5 oe or 4 × 5 + 4 × 6 + 5 × 6 implied by 40, 48, 60 or 74, or list of 20, 20, 24, 24, 30, 30 (d) (i) mv oe 1 (ii) msv oe 1ft Ft (d)(i) × s (iii) 1000 msv oe 1ft Ft (d)(ii) × 1000

This question in 0580/31 May/June 2012

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

2 (a) Find all the factors of 28 . For Examiner's Use Answer(a) [2] (b) Write down a multiple of 8 that is greater than 20 . Answer(b) [1] (c) Work out 183 . Answer(c) [1] (d) p and q are prime numbers. p3 × q2 = 200 Find the values of p and q. Answer(d) p = q = [2] (e) A town has two bus companies. Buses from Western Travel stop at the Town Hall every 8 minutes. Buses from Eastern Travel stop at the Town Hall every 14 minutes. (i) Write down the lowest common multiple of 8 and 14 . Answer(e)(i) [2] (ii) A bus from each company stops at the Town Hall at 08 00. When is the next time that a bus from each company stop together at the Town Hall? Answer(e)(ii) [1] (iii) The cost of an adult ticket on Western Travel is $a and the cost of a child’s ticket is $c. One day 84 adult tickets and 36 child tickets are sold. Write an expression, in terms of a and c, for the total cost of these tickets. Answer(e)(iii) $ [2]

11 marks

Mark scheme: 2 (a) 1, 2, 4, 7, 14, 28 2 1 for four or five correct or 1 × 28 and 2 × 14 and 4 × 7 (b) 24 1 (c) 5832 1 (d) (p =) 2 1 (q =) 5 1 (e) (i) 56 2 M1 for a method to achieve this such as prime factors, 8 = 23 and 14 = 2 × 7 or another multiple of 56, or two trials (ii) 08 56 1ft accept 8 56 (am) (iii) 84a + 36c final answer 2 B1 for either 84a or 36c IGCSE – May/June 2012 0580 33

This question in 0580/33 May/June 2012

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

2 (a) Luka earns $475 each week. For Examiner's Use (i) He works for 38 hours each week. How much does he earn for each hour he works? Answer(a)(i) $ [1] (ii) Luka pays $175 in rent each week. Write the amount he pays in rent as a fraction of his weekly earnings. Give your answer in its lowest terms. Answer(a)(ii) [2] 7 (iii) He spends of his weekly earnings on bills. 20 How much money does he have left after paying rent and bills? Answer(a)(iii) $ [2] (b) Luka’s weekly earnings of $475 are increased by 6%. Calculate his new weekly earnings. Answer(b) $ [2] (c) Luka has saved $350. He invests this for 2 years at a rate of 4% per year compound interest. How much interest does he receive after 2 years? Answer(c) $ [3]

10 marks

Mark scheme: 2 (a) (i) 12.5(0) 1 7 175 (ii) 2 B1 for oe seen 19 475 7 (iii) 133.75 2 M1 for × 475 20 (b) 503.5(0) 2 M1 for 106 ÷ 100 × 475 Or 475 + (6 ÷ 100 × 475) (c) 28.56 3 M1 for 350 × 1.042 oe dep M1 for ‘their 378.56’ – 350 Or M1 for (350 × 0.04) (imp by 14) and (350 + ‘their 14’) × 0.04 (imp by 14.56) dep M1 ‘their 14’ + ‘their 14.56’ IGCSE – October/November 2012 0580 31

This question in 0580/31 Oct/Nov 2012

5 For B 20 m C Examiner's Use NOT TO SCALE 15 m A 32 m D The diagram shows a plot of land, ABCD, in the shape of a trapezium. (a) Show that CD = 19.2 m, correct to 1 decimal place. Answer(a) [2] (b) A fence is built around the perimeter of the plot of land. The cost of the fence is $35 for each metre. Calculate the total cost of the fence. Answer(b) $ [2] (c) Calculate the area of the plot of land. Give your answer in square metres. Answer(c) m2 [2] (d) A house is built on the plot of land. For The area of the plot is divided in the ratio house : grounds = 3 : 7 . Examiner's Use Calculate the area of the grounds. Answer(d) m2 [2] (e) (i) In the space below, make a scale drawing of the plot of land. Use a scale of 1 centimetre to represent 4 metres. The side AB has been drawn for you. B A [2] (ii) Measure angle ADC. Answer(e)(ii) Angle ADC = [1] (iii) Use your diagram to find the actual length BD in metres. Answer(e)(iii) BD = m [1]

12 marks

Mark scheme: 5 (a) (CD2 =) (32 – 20)2 + 152 oe M1 (CD =) 369 = 19.20 to 19.21 A1 A0 for 19.2 alone. 2 M1 for 20 + 15 + 32 + 19.2(1) [implied by (b) 3017 86.2(1)] Or M1 for (20 × 35) + (15 × 35) + (32 × 35) + (19.2(1) × 35) 2 M1 for (20 + 32) × 15 ÷ 2 oe (c) 390 2ft M1 for ‘their (c)’ × 7 ÷ 10 (d) 273 2 B1 for C or D correctly positioned (e) (i) trapezium constructed BC = 5 cm, AD = 8 cm Both 90o to AB 1ft (ii) 49 – 53° 1ft (iii) 34.4 – 36.4 m

This question in 0580/31 Oct/Nov 2012

1 An area of 94 500 m2 in a city is developed. For Examiner's Use (a) The area is divided into housing, shops and a park in the ratio housing : shops : park = 7 : 6 : 5 . (i) Show that the area of the park is 26 250 m2. Answer(a)(i) [2] (ii) Calculate the area for housing. Answer(a)(ii) m2 [1] (b) The diagram shows the children’s playground in the park. 76 m NOT TO SCALE 45 m 100 m (i) Calculate the area of the playground. Answer(b)(i) m2 [2] (ii) What fraction of the area of the park does the playground occupy? Answer(b)(ii) [1] (c) Buildings occupy 30 625 m2 of the area for housing. For Examiner's Use Calculate the percentage of the area for housing occupied by buildings. Answer(c) % [1] 5 3 (d) Of the buildings, are bungalows and are houses. 12 8 The rest of the buildings are apartments. (i) Complete these equivalent fractions. 5 3 = = [2] 12 24 8 24 5 (ii) Show that of the buildings are apartments. 24 Answer(d)(ii) [1] (iii) There are 120 buildings altogether. Work out the number of houses. Answer(d)(iii) [1]

11 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) (i) 94 500 ÷ (7 + 6 + 5) or M1 94 500 ÷ 18 Multiply by 5 M1dep dependent on first mark (ii) 36 750 1 (b) (i) 3960 2 M1 for 0.5 × (76 + 100) × 45 oe 3960 1ft their(b)(i) (ii) oe Ft for 26250 26250 provided answer is integer/integer and less than 1 (c) 83.3(3...) 1ft 30625 Ft for × 100 their (a)(ii) (d) (i) 10 9 1, 1 10 9 (ii) 1 − − M1ft Accept 1 – 19/24 24 24 (iii) 45 1

This question in 0580/32 Oct/Nov 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

3 Mrs Ali sold her house for $600 000. For Examiner's Use 2 (a) She gives of the money to her son. 5 Work out how much her son receives. Answer(a)$ [1] (b) Mrs Ali gives $2400 to her grandchildren Elize, Sam and Juan in the ratio Elize : Sam : Juan = 8 : 3 : 5 . Calculate how much they each receive. Answer(b) Elize $ Sam $ Juan $ [3] (c) Mrs Ali invests $200 000 for 3 years at a rate of 4% per year compound interest. Calculate the total amount of money she will have at the end of the 3 years. Give your answer correct to the nearest dollar. Answer(c) $ [3] (d) Mrs Ali spends a total of $9000 on the following items. For Examiner's Use Amount spent ($) Angle in pie chart Holiday 4050 162° Television 90° Clothes 1800 72° Computer (i) Complete the table. [3] (ii) Complete the pie chart. Label each of your sectors. Holiday [2]

12 marks

Mark scheme: 3 (a) 240000 1 (b) 1200, 450, 750 3 SC2 for all three correct in wrong order seen SC1 for 2400 ÷ 16 implied by 150 (c) 224973 3 M2 224972.8 or 200000 × 1.043 or 224793.0(0) if M0 M1 200000 × 1.042 or 216320 SC1 for their answer correctly rounded to nearest dollar (d) (i) 2250 1,1,1 If first B0,B0 then SC1 for adding to 3150 900 36 (ii) 2 correct sectors 1 correct labels 1 Must only be 4 sectors in total

This question in 0580/33 Oct/Nov 2012

8 Ben and Ruth own a company. For Examiner′s Use (a) The company’s profi ts of $43 680 are shared in the ratio Ben : Ruth = 2 : 5 . Calculate Ruth’s share of the profi ts. Answer(a) $ … [2] (b) Ruth invests $15 000 at a rate of 4% per year simple interest. Calculate how much her investment is worth at the end of 3 years. Answer(b) $ … [3] (c) The company employs 450 people. 14% of these people work in sales. Calculate the number of people who work in sales. Answer(c) … [2] (d) Every year Ben travels 32 000 km on business. For Examiner′s Use (i) Car-rent Cost ($) = 600 + 0.35d where d is the distance travelled in kilometres Calculate the cost of hiring a car from Car-rent to travel 32 000 km. Answer(d)(i) $ … [2] (ii) Drive-easy Cost = $100 plus $4 for every 10 km travelled Calculate the cost of hiring a car from Drive-easy to travel 32 000 km. Answer(d)(ii) $ … [2] _____________________________________________________________________________________

11 marks

Mark scheme: 8 (a) 31 200 2 M1 for (43 680 ÷ 7) × 5 or 6240 × 5 (b) 16 800 3 M2 for 15 000 + 15 000 × 0.04 × 3 oe or M1 for 15 000 × 0.04 × 3 oe, imp by 1800 (c) 63 2 M1 for 450 × [0].14 oe (d) (i) 11 800 2 M1 for 600 + 0.35 × 32 000 or better (ii) 12 900 2 M1 for 100 + 4 × 32 000 ÷ 10 or better IGCSE – May/June 2013 0580 31

This question in 0580/31 May/June 2013

10 (a) In 2001 Arnold was x years old. For Examiner′s Ken is 34 years younger than Arnold. Use (i) Complete the table, in terms of x, for Arnold’s and Ken’s ages. 2001 2013 Arnold’s age x Ken’s age [3] (ii) In 2013 Arnold is three times as old as Ken. Write down an equation in x and solve it. Answer(a)(ii) x = … [4] (b) Solve the simultaneous equations. For Examiner′s Use 3x + 2y = 18 2x – y = 19 Answer(b) x = … y = … [3] _____________________________________________________________________________________ Question 11 is printed on the next page.

10 marks

Mark scheme: 10 (a) (i) x +12 in each part allow correct unsimplified x – 34 x − 22 1,1,1 terms (ii) x +12 = 3(x – 22) 1ft accept x +12 = 3x – 66 or (x+12) / 3 = x – 22 39 cao 3 M1 for their 3x – 66 seen M1 for correctly collecting terms from ax + b = cx + d a,b,c,d ≠ 0 (e) 8 3 M1 for correct method to eliminate one − 3 variable. A1 for x or y correct. 2

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

1 (a) Kasem earns $900 each month. For Examiner′s 14% of this amount is deducted for tax and insurance. Use Show that he receives $774 each month. Answer(a) [2] 2 (b) He pays of the $774 in rent. 9 Calculate the amount of rent he pays. Answer(b) $ … [1] (c) Kasem spends $480 each month on food, entertainment and clothes. He shares this in the ratio food : entertainment : clothes = 9 : 3 : 4. Calculate how much he spends on food each month. Answer(c) $ … [2] (d) Kasem saves the rest of his money. Work out the amount he saves as a percentage of $774. Answer(d) … % [2] _____________________________________________________________________________________

7 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 900 × 86 ÷ 100 = 74 2 M1 for 900 × 14 ÷ 100 A1 for 900 – 126 = 774 (b) [$] 172 1 (c) [$] 270 2 M1 for 480 ÷ (9 + 3 + 4) (d) 15.8 or 15.76(...) 2ft B1 for 774 – their (b) – 480 B1 Or 294 – their (b) SC1 for 38 or 37.9

This question in 0580/33 May/June 2013

6 For Examiner′s 30 m A B Use NOT TO SCALE HOUSE 17 m D C The rectangle ABCD shows Mr Liu’s garden. (a) Mr Liu puts a fence around three sides of his garden, AB, BC and CD. The fence costs $3.28 per metre. Calculate the cost of the fence. Answer(a) $ … [2] (b) (i) Calculate the area of Mr Liu’s garden. Answer(b)(i) … m2 [2] (ii) Mr Liu uses an area of 408 m2 in his garden for a lawn, fl owers and vegetables. He divides this area into three parts, in the ratio lawn : fl owers : vegetables = 5 : 3 : 4 . Calculate the area used for each part. Answer(b)(ii) Lawn … m2 Flowers … m2 Vegetables … m2 [3] (c) Mr Liu walks in a straight line across his garden from A to C. For Examiner′s Use Calculate the distance Mr Liu walks. Answer(c) … m [3] (d) Mr Liu has a circular pond, radius 4.5 m, in his garden. (i) Calculate the area of the pond. Answer(d)(i) … m2 [2] (ii) The pond is fi lled with water to a depth of 2 metres. Calculate the volume of water in the pond. Answer(d)(ii) … m3 [1] _____________________________________________________________________________________

13 marks

Mark scheme: 6 (a) 252.56 2 M1 for (30 + 30 + 17) × 3.28 or better oe (b) (i) 510 2 M1 for 30 × 17 (ii) 170 3 M2 for 2 correct areas clearly identified 102 or M1 for 408 ÷ (5 + 3 + 4) soi by 34 or 136 one correct area clearly identified SC2 for three correct answers in incorrect places (c) 34.5 3 M2 for 30 2 + 17 2 soi by 1189 or M1 for 302 + 172 soi by 1189 (d) (i) 63.6 or 63.61 – 63.63 2 M1 for 4.52 × π or 20.25 π (ii) 127 or 127.2… 1FT FT for their (d)(i) × 2 IGCSE – October/November 2013 0580 31

This question in 0580/31 Oct/Nov 2013

2 Ravi sells cars. For Examiner′s Use (a) He has a total of 144 cars for sale. (i) 64 of these cars are 3 or more years old. What fraction of the cars are less than 3 years old? Give your answer in its simplest form. Answer(a)(i) … [2] (ii) Some of the 144 cars use petrol, some use diesel and some are electric cars. The ratio of petrol to diesel to electric cars is 6 : 5 : 1 . Work out the number of these cars that use diesel. Answer(a)(ii) … [2] (b) Lola buys a car from Ravi. There are two ways she can pay for the car. Option 1: one payment of $5200 . 2 Option 2: a payment of of $5200 plus 24 monthly payments, each of $175 . 5 Work out how much more Lola pays using Option 2 than Option 1. Answer(b) $ … [3] (c) For one week, Ravi reduces all his car prices by 15%. The price of a car was $3450. Show that the reduced price of the car is $2932.50 . Answer(c) [2] (d) Ravi buys a car for $2500 . He sells it for $3300 . Calculate his percentage profi t. Answer(d) … % [3] _____________________________________________________________________________________

12 marks

Mark scheme: 5 80 2 (a) (i) 2 B1 for or better or 0.556 or 0.555… or 9 144 4 answer 9 (ii) 60 2 M1 for 144 ÷ (6+5+1) or 144÷12 (b) 1080 3 M1 for 2 ÷ 5 × 5200 soi by 2080 And M1 for their 2080 + 24×175 – 5200 or better (c) 0.85 × 3450 2 B1 for 0.85 or for 0.15 × 3450 Or 3450 – 0.15 × 3450 3300 − 2500 (d) 32 3 M2 for × 100 oe 2500 3300 or ( – 1 ) × 100 oe 2500 Or 3300 − 2500 3300 B1 for 800 or or or 2500 2500 1.32 or 132 or 0.32

This question in 0580/32 Oct/Nov 2013

1 Adam owns a farm. For Examiner′s Use (a) He plans to keep twenty hens. He works out what he thinks this will cost. Complete the following table. Item Cost ($) Equipment 500 20 hens costing $12 each 3 years supply of feed costing $25 per month TOTAL [3] (b) The equipment actually costs $600. The ratio of costs is equipment : hens : feed = 5 : 3 : 9 . (i) Show that the total cost is now $2040. Answer(b)(i) [2] (ii) Adam actually buys more than 20 hens, each costing $12. How many hens does he buy? Answer(b)(ii) … [2] (c) Adam makes $2920 from selling his hens’ eggs. For Examiner′s Use Calculate his percentage profi t on the $2040. Answer(c) … % [2] (d) Adam borrows $1500 for 3 years at a rate of 5.5% per year compound interest. Calculate the interest he will pay, correct to the nearest cent. Answer(d) $ … [3] _____________________________________________________________________________________

12 marks

Mark scheme: Qu. Part Answers Mark Part Marks 1 (a) 240 900 1,1 [Total] 1640 1FT 500 + their 2 costs (b) (i) 600 ÷ 5 × 17 M2 M1 for 600 ÷ 5 or 17 ÷ 5 (ii) 30 2 M1 for 2040 ÷ 17 × 3 Or 120 × 3, soi by 360 2920 − 2040 (c) 43.1 2 M1 for × 100 oe 2040 2920 or ( − )1 × 100 oe 2040 2920 or × 100 − 100 oe 2040 (d) 261.36 cao 3 M1 for 1500 × 1.0553 oe M1FT for their 1761.36 – 1500 If only 1 scored SC1 for correctly rounding to 2 decimal places from at least 3 decimal places SC2 if only 1761.36 seen

This question in 0580/33 Oct/Nov 2013

1 (a) The angles in a triangle are in the ratio 3 : 4 : 8 . (i) Show that the smallest angle of the triangle is 36°. Answer(a)(i) [2] (ii) Work out the other two angles of the triangle. Answer(a)(ii) … and … [2] (b) Another triangle ABC has angle BAC = 35° and angle ABC = 65°. (i) Using a protractor and straight edge complete an accurate drawing of the triangle ABC. The side AB has been drawn for you. A B [2] (ii) Measure the length, in centimetres, of the shortest side of your triangle. Answer(b)(ii) … cm [1] (c) A different triangle has base 7.0 cm and height 5.6 cm. Calculate the area of this triangle, giving the units of your answer. Answer(c) … … [3] __________________________________________________________________________________________

10 marks

Mark scheme: Question Answers Mark Part Marks 1 (a) (i) 3 180 or M1 3 + 4 + 8 3 + 4 + 8 180 × 3 3 ÷ (15) × 180 or (= 36) M1 15 (ii) 48 [and] 96 1,1 One mark for each. If zero, SC1 for sum of both angles = 144. (b) (i) Angle BAC = 35 (±2º) B1 Angle ABC = 65 (±2º) and triangle completed B1 If zero SC1 for AC and BC reversed and triangle completed (ii) 4.45cm to 4.85cm 1 FT FT for their shortest side (c) 19.6 cao 2 M1 for 0.5 × 7 × 5.6 cm2 oe 1

This question in 0580/31 May/June 2014

8 (a) Write down an expression for the total mass of c cricket balls, each weighing 160 grams, and f footballs, each weighing 400 grams. Answer(a) … grams [2] (b) Expand and simplify. 3(2x – 5y) – 4(x – 2y) Answer(b) … [2] (c) Factorise completely. 5x2y – 20x Answer(c) … [2] (d) Solve the simultaneous equations. 3x + 4y = 7 4x – 3y = 26 Answer(d) x = … y = … [4] __________________________________________________________________________________________

10 marks

Mark scheme: 8 (a) 160c + 400f final answer 2 B1 for 160c or 400f seen (b) 2x – 7y final answer www 2 B1 for 2 x or –7y or 6x – 15y or –4x + 8y www (c) 5x(xy – 4) final answer 2 B1 for 5( x 2 y − 4 x ) or x ( 5 xy − 20 ) IGCSE – May/June 2014 0580 31 (d) [x=] 5 [y=] – 2 4 M1 for correctly equating one set of coefficients M1 for correct method to eliminate one variable A1 for correct x or y If zero scored SC1 for 2 values satisfying one of the original equations Alternative method M1 for correct rearrangement of one equation x = (7 – 4y) ÷ 3 or y = (7 – 3x) ÷ 4 or x = (26 + 3y) ÷ 4 or y = (4x – 26) ÷ 3 M1 for correct substitution in other equation 4(7 – 4y) ÷ 3 – 3y = 26 4x – 3(7 – 3x) ÷ 4 = 26 3(26 + 3y) ÷ 4 + 4y = 7 3x + 4(4x – 26) ÷ 3 = 7 (7 – 4y) ÷ 3 = (26 + 3y) ÷ 4 (7 – 3x) ÷ 4 = (4x – 26) ÷ 3 A1 for correct x or y If zero scored SC1 for 2 values satisfying one of the original equations

This question in 0580/31 May/June 2014

3 The Wong family spend the day at the zoo. (a) The Wong family has 2 adults and 3 children aged 2, 5 and 11 years old. Admission Adults $8.50 Children 11-16 years $6.00 Children 3-10 years $4.50 Children under 3 years FREE Mr Wong pays for his family to go into the zoo using a $50 note. Work out the change he receives. Answer(a) $ … [3] (b) The dolphin show fi nishes at 11 05. It lasts for 1 hour and 20 minutes. Write down the time the dolphin show starts. Answer(b) … [1] (c) Torty the tortoise was born on 27 December 1898. Work out how many years old she was on 3 January 2003. Answer(c) … years [1] (d) Last year, the ratio snakes : lizards = 3 : 5 . There were 45 lizards. (i) Work out how many snakes there were last year. Answer(d)(i) … [2] (ii) This year, there are 3 more snakes and the same number of lizards. Write down the new ratio snakes : lizards. Give your answer in its simplest form. Answer(d)(ii) … : … [2] (e) Mr Wong hires a vehicle to drive around the zoo. The cost is $25 for the fi rst hour and $7.50 for every extra half hour. He pays $85 altogether. For how long does he hire the vehicle? Answer(e) … hours [3] (f) Mrs Wong wants to buy some food for the giraffes. Small Bag Medium Bag Large Bag 225g 250g 325g 60 cents 70 cents 90 cents Work out which bag is the best value for money. Show how you decide. Answer(f) … [3] (g) The diagram shows a map of the zoo. The scale is 1 centimetre represents 50 metres. North Entrance Scale: 1 cm to 50 m Flamingos North Exit (i) Measure the bearing of the fl amingos from the entrance. Answer(g)(i) … [1] (ii) Xanthe looks after all the animals within 200 m of the exit. Draw accurately the locus of points inside the zoo which are 200 m from the exit. [2] (iii) A shop, S, is on a bearing of 212° from the entrance and a bearing of 293° from the exit. Mark the point S on the map. [3] __________________________________________________________________________________________

21 marks

Mark scheme: 3 (a) 22.5[0] 3 M1 for (2 × 8.5 + 6 + 4.50) M1 for 50 – their total (b) [0]9 45 1 (c) 104 1 45 (d) (i) 27 2 M1 for × 3 5 (ii) 2 : 3 cao 2 M1 for (their 27 + 3) : 45 or better If zero SC1 for 3 : 2 85− 25 (e) 5 3 M1 for soi by 8 7.50 their 8 M1 for + 1 2 (f) 3.75, 3.57... 3.61... [g / c] 3 M1 for 1 correct division, not evaluated small [bag] M1 for 2 further consistent correct divisions, not evaluated (g) (i) 105 1 (ii) correct locus drawn 2 M1 for any arc centre exit (iii) S marked correctly 3 B1 for indication of bearing of 212° B1 for indication of bearing of 293°

This question in 0580/33 May/June 2014

1 A carton of fruit juice contains apple, orange, pineapple and tropical juices. (a) They are mixed in the ratio apple : orange : pineapple : tropical = 9 : 7 : 4 : 5. The carton contains 540 millilitres of apple juice. (i) Show that the total amount of fruit juice in the carton is 1.5 litres. Answer(a)(i) [3] (ii) Calculate the amount of tropical juice in the carton. Give your answer in millilitres. Answer(a)(ii) … ml [2] (iii) 70% of the tropical juice is mango. Calculate the amount of mango juice in the carton. Answer(a)(iii) … ml [2] (b) A shopkeeper pays $36 for 16 cartons. (i) How much does he pay for one carton? Answer(b)(i) $ … [1] 7 (ii) He sells of the 16 cartons for $3.40 each and the rest for $2.50 each. 8 Calculate the total amount he receives from selling the cartons. Answer(b)(ii) $ … [2] (iii) Calculate his percentage profi t. Answer(b)(iii) … % [3] __________________________________________________________________________________________

13 marks

Mark scheme: Qu. Answers Mark Part Marks Alternative method 1 (a) (i) 540 ÷ 9 M1 M1 540 ÷ 1000 their 60 × (9 + 7 + 4 + 5) M1FT M1FT their 0.54 ÷ 9 A1 A1 0.06 × (9 + 7 + 4 + 5) 1500 ÷ 1000 If 0 scored SC1 for 0.54 + 0.42 + 0.24 + 0.3 (ii) 2 M1 for 5 ÷ (9 + 7 + 4 + 5) × 1500 300 or (540/9) × 5 or 60 × 5 (iii) 2FT M1 for 70 ÷ 100 × their (a)(ii) oe 210 (b) (i) 1 2.25 (ii) 52.6[0] 2 B1 for 14 or (7/8) × 16 × 3.4[0] (iii) 46.1 3FT M2 for (their (b)(ii) – 36) ÷ 36 × 100 or M1 for their (b)(ii) – 36 M2 for their (b)(ii) ÷ 36 × 100 – 100 M1 for their (b)(ii) ÷ 36 [× 100]

This question in 0580/31 Oct/Nov 2014

7 The scale drawing represents the positions of 3 towns, A, B and C. The scale is 1 centimetre represents 4 kilometres. North A B C Scale: 1 cm to 4 km (a) Measure the bearing of B from A. Answer(a) … [1] (b) A transmitter is placed near to the 3 towns. (i) The transmitter is equidistant from A and B. Using a straight edge and compasses only, construct the locus of points equidistant from A and B. [2] (ii) The transmitter is also on the bisector of angle ABC. Using a straight edge and compasses only, construct the bisector of angle ABC. [2] (iii) Mark the position, T, of the transmitter on the scale drawing. [1] (c) Work out the actual distance, in kilometres, of town A from T. Answer(c) … km [2] (d) The signal from the transmitter has a range of 30 kilometres in all directions. On the scale drawing, construct the locus of points 30 kilometres from T. [2] (e) Would the signal from the transmitter reach town C ? Give a reason for your answer. Answer(e) … because … … [1] __________________________________________________________________________________________

11 marks

Mark scheme: 7 (a) 106 to 110 1 (b) (i) Correct bisector of AB constructed with 2 2 B1 for correct bisector pairs of arcs. (ii) Correct bisector of angle ABC with arcs 2 B1 for correct bisector without arcs (iii) T marked at intersection of their bisectors 1FT (c) 24.4[km] to 26.0[km] 2FT FT their AT B1 for their AT correctly measured. (d) Circle, radius 7.5(±0.2)cm centre T. 2FT FT their intersection SC1 for circle centre T, incorrect radius. (e) No It is outside the circle. oe 1FT FT their circle.

This question in 0580/31 Oct/Nov 2014

1 A building company buys 4 square kilometres of land. On the land the company builds houses, shops and a school. (a) Show that 4 square kilometres is equivalent to 4 000 000 square metres. Answer(a) [1] (b) The company uses 5% of the land for roads and paths. Show that the remaining area of land is 3 800 000 m2. Answer(b) [1] (c) The 3 800 000 m2 of land is divided in the ratio houses : shops : school = 11 : 5 : 3. (i) Show that the area for the school is 600 000 m2. Answer(c)(i) [2] (ii) Calculate the area for houses. Answer(c)(ii) … m2 [1] (iii) 140 m2 is needed for each house. Calculate, correct to the nearest 10, the number of houses that can be built. Answer(c)(iii) … [2] 3 1 (d) of the school area is for classrooms and is for other rooms. 5 8 The remainder is for sporting facilities. (i) Without using a calculator, and showing all your working, fi nd the fraction of the school area for sporting facilities. Answer(d)(i) … [3] (ii) The school has an area of 600 000 m2. Work out the area for sporting facilities. Answer(d)(ii) … m2 [1] (e) To pay for materials, the building company borrows $250 000 from a bank for 3 years. The bank charges compound interest at a rate of 4% per year. Calculate the total amount the company must pay back at the end of 3 years. Answer(e) $ … [3] __________________________________________________________________________________________

14 marks

Mark scheme: 1 (a) 4 × 1000 × 1000 or 4 × 10002 1 (b) 0.95 × 4 000 000 oe 1 (c) (i) 3 ÷ 19 × 3 800 000 2 M1 for 3 ÷ (11 + 5 + 3) or 3 800 000 ÷ (11 + 5 + 3) (ii) 2 200 000 1 (iii) 15 710 2FT M1FT for their 2 200 000 ÷ 140  24 5  24 5 3 × 8 1 × 5 (d) (i) 1 −  +  M2 M1 for or or or  40 40  40 40 5 × 8 8 × 5 11 11 k or final answer A1 If zero scored, 40 40 k 275 SC3 for 1 – (0.6 + 0.125) = 0.275 = = 1000 11 11 k [ or ] 40 40 k or 275 SC2 for 1 – (0.6 + 0.125) = 0.275 = 1000 followed by incorrect fraction 11 11 k SC1 for or final answer 40 40 k (ii) 165 000 1FT FT their (d)(i) × 600 000 (e) 281 216 cao 3 M2 for 250 000 × 1.043 oe or M1 for 250 000 × 1.042 oe If zero scored, SC1 for 31 216

This question in 0580/32 Oct/Nov 2014

6 (a) The grid shows part of the net of a cuboid. Complete the net. [2] (b) The volume of another cuboid is 60 cm3. Each side is a whole number of centimetres long. Write down a possible set of dimensions for the cuboid. Answer(b) Length … cm Width … cm Height … cm [2] (c) Each side of a cube has length 2 cm. Work out the total surface area of the cube. Give the units of your answer. Answer(c) … … [3] (d) Change 9 cm2 into mm2. Answer(d) … mm2 [1] (e) The diagram shows a triangle. B NOT TO SCALE 11 m A 8 m C (i) Calculate the length AB. Answer(e)(i) AB = … m [3] (ii) Use trigonometry to calculate angle ACB. Answer(e)(ii) Angle ACB = … [2] (f) NOT TO SCALE The diameter of the large circle is 13 cm. The radius of the small circle is 2 cm. Calculate the shaded area. Answer(f) … cm2 [4] __________________________________________________________________________________________

17 marks

Mark scheme: 6 (a) correct net drawn 2 B1 for 2 correct faces seen added to correct edges of net (b) 60,1,1 or 30,2,1 or 20,3,1 or 2 SC1 for 3 numbers with a product of 60 but 15,4,1 or 15,2,2 or 12,5,1 or including non-integer values 10,6,1 or 10,3,2 or 6,5,2 or 5,4,3 (c) 24 2 M1 for 2 × 2 × 6 oe cm2 1 (d) 900 1 (e) (i) 7.55 or 7.549 … 3 M2 for (11 2 − 8 2 ) or M1 for AB2 + 82 = 112 8 (ii) 43.3 or 43.34 2 M1 for cos [C] = or better 11 (f) 120 or 120.16 to 120.2 4 B1 for 6.5 seen M2 for their 6.52π – their 22π (must be using πr2) or M1 for 6.52π or 22π seen If M0 scored, SC1 for 165π or 518(.3) to 518.43 or 41.25π or 129.59 … to 129.6075

This question in 0580/32 Feb/March 2015

3 Sonia works in a toy shop. (a) (i) One week she works for 30 hours and is paid $180. Calculate the amount she is paid per hour. Answer(a)(i) $ … [1] (ii) The next week Sonia works for 38 hours and is paid $220. Find the difference in her pay per hour for these two weeks. Answer(a)(ii) $ … [2] (b) The shop sells bags of 40 marbles. One bag has marbles in the ratio red : blue : green = 1 : 3 : 4. (i) Calculate the number of marbles of each colour. Answer(b)(i) Red = … , blue = … , green = … [2] (ii) A second bag of 40 marbles contains 11 red marbles, 9 blue marbles and 20 green marbles. All the marbles from the two bags are mixed together. Write down the ratio of marbles red : blue : green. Give your answer in its simplest form. Answer(b)(ii) … : … : … [2] (c) Thilo and Toby buy some boats and trains from the toy shop. The cost of one boat is b cents and the cost of one train is t cents. (i) Toby buys 3 boats and 4 trains for $5.70 . Complete this equation. 3b + 4t = … [1] (ii) Thilo buys 1 boat and 2 trains for $2.40 . Write this information as an equation. … = … [2] (iii) Solve your two equations to find the cost of a boat and the cost of a train. You must show all your working. Answer(c)(iii) Cost of a boat = … cents Cost of a train = … cents [3] (d) Train track costs 99 cents per 20 cm. Calculate the cost of buying 3.4 metres of train track. Answer(d) $ … [3] __________________________________________________________________________________________

16 marks

Mark scheme: 3 (a) (i) 6 1 220 (ii) 0.21 2 M1 for or better 38 (b) (i) 5, 15, 20 2 B1 for 1 correct answer in the right place or M1 for 40 ÷ (1 + 3 + 4) [×k] soi where k is 1 or 3 or 4 (ii) 2 : 3 : 5 2 M1 for (16,24,40) or better or M1FT for ‘their (5,15,20)’ + (11,9,20) or better (c) (i) 570 1 (ii) b + 2t = 240 2 B1 for b + 2t seen (iii) [b] 90 3 M1FT for correct elimination of one [t] 75 variable Working must be shown A1 for b = 90 A1 for t = 75 If zero is scored SC1 for 2 values satisfying one of their equations (ft) SC1 if no working shown, but 2 correct answers given (d) 16.83 3 B1 for 340 or 0.2 or 5 seen M1 for figs 340 ÷ figs 20 × figs 99 or figs 340 × figs 5 × figs 99

This question in 0580/31 May/June 2015

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

5 Indira makes a playground for children. (a) She borrows $40 000 for 5 years at a rate of 3.6% per year simple interest. Calculate the total amount she will owe at the end of 5 years. Answer(a) $ … [3] (b) Bandhura works at the playground for 28 hours. She is paid $15.85 per hour. Calculate the total amount Bandhura is paid. Answer(b) $ … [1] (c) To visit the playground each adult pays $1.25 and each child pays $3.50 . One day 24 adults and 32 children visit the playground. Calculate how much they pay altogether. Answer(c) $ … [3] (d) On another day 180 people visit the playground. These people are in the ratio adults : boys : girls = 3 : 2 : 7. Calculate the numbers of adults, boys and girls. Answer(d) Adults = … Boys = … Girls = … [3] (e) The opening hours for the playground are shown below. Monday Closed Tuesday 08 30 to 17 15 Wednesday 08 30 to 17 15 Thursday 08 30 to 17 15 Friday 08 30 to 18 00 Saturday 08 30 to 17 15 Sunday 09 00 to 17 00 Calculate the total number of hours that the playground is open in the week. Answer(e) … hours [2] (f) Indira introduces a family ticket for $7.95 . 21 families buy this ticket. By rounding both numbers to 1 significant figure, estimate how much Indira receives. Show clearly how you worked out your estimate. Answer(f) $ … [2]

14 marks

Mark scheme: 40 000 × 6.3 × 5 5 (a) 47 200 3 M2 for 40 000 + 100 40 000 × 6.3 × 5 or M1 for or 7200 100 (b) 443.8[0] cao 1 (c) 142 3 M2 for 24 × 1.25 + 32 × 3.5 or 30 + 112 or M1 for either 24 × 1.25 or 32 × 3.5 or 30 or 112 (d) 45 3 180 M2 for 3 (or 2 or 7) × or better 30 3 + 2 + 7 105 180 or M1 for or better 3 + 2 + 7 If zero scored SC2 for the correct answers in the incorrect places (e) 52.5 2 M1 for 2 of 8[h] 45[m], 9[h] 30[m] and 8[h] oe (f) 8 × 20 = 160 2 B1 for 8 or 20 seen

This question in 0580/33 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

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

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 (a) Goat food is sold in 20 kg bags. One goat eats 25 of a bag of food each week. (i) Work out how many kilograms of food this goat eats in one week. Answer(a)(i) … kg [1] (ii) How many bags of food will the goat eat in 15 weeks? Answer(a)(ii) … [2] (b) This scale drawing shows a field. The scale is 1 centimetre represents 2 metres. A B C (i) Find the actual length of AB. Answer(b)(i) … m [1] (ii) There are two goats in the field. One goat is on a 14 m lead fastened at point B. The other goat is on a 12 m lead fastened at point C. There is a water trough positioned so that both goats can reach it. Shade the area where the trough can be positioned. [3] (iii) The trough holds 6.5 litres of water. How many millilitres is this? Answer(b)(iii) … ml [1] __________________________________________________________________________________________

8 marks

Mark scheme: 7 (a) (i) 8 1 their 8× 15 2 (ii) 6 2FT M1 for or × 15 oe 20 5 (b) (i) 30 or 29.6 to 30.4 1 (ii) Arc 7 cm from B 1 Arcs must be continuous lines and fit for purpose (intersect twice) Arc 6 cm from C 1 If 0, 0 scored then SC1 for two correct arcs that intersect once Correct area shaded 1 dep Dependent on an attempt at 2 arcs (iii) 6500 1

This question in 0580/33 Oct/Nov 2015

4 (a) A farmer has 45 horses and 20 cows. (i) Write this as a ratio horses : cows. Give your answer in its simplest form. … : … [1] (ii) The farmer wants the ratio horses : cows to equal 5 : 3. He keeps his 45 horses but buys some more cows. Work out the number of cows he must buy. … [2] (b) Three years ago the farmer invested $3750 at a rate of 4% per year compound interest. (i) Calculate the total value of his investment after the 3 years. $ … [3] (ii) The farmer wants to spend his investment on buying goats. Goats cost $126 each. Work out the maximum number of goats he can buy and how much money is left over. Number of goats … Amount of money left over $ … [4] (c) The farmer grows carrots. In 2014 the selling price for carrots was $96 per tonne. In 2015 this selling price increased by 18%. Work out the increase in the selling price from 2014 to 2015. $ … [1] (d) The farmer has 20 female sheep. Each sheep has 0, 1, 2 or 3 lambs. The table shows this information. Number Number of of lambs sheep 0 1 1 4 2 12 3 3 (i) Calculate the mean number of lambs per sheep. … [3] (ii) The farmer takes 1 lamb away from each of the sheep with 3 lambs. These lambs are given to 3 of the 4 sheep that have 1 lamb. Complete the table after the farmer has done this. Number Number of of lambs sheep 0 1 2 3 0 [2] (iii) Explain why the mean number of lambs per sheep does not change. … [1]

17 marks

Mark scheme: 4 (a) (i) 9 : 4 1 3 (ii) 7 2 M1 for 5× 45 or 45 : 3 × 9 (b) (i) 4218.24 cao 3 M2 for 3750 × 1.043 oe or M1 for 3750 × 1.042 oe If zero scored SC2 for 468.24 4218.24 (ii) 33 2FT M1FT for their 126 60.24 2FT M1FT for their 4218.24 – 126 × their 33 4218.24 or (their – their33)×126 126 (c) 17.28 1 (d) (i) 1.85 3 M1 for 0 × 1 + 1 × 4 + 2 × 12 + 3 × 3 their 37 M1dep for 20 (ii) 1 2 B1 for 1 answer correct and total number of 1 sheep = 20 18 or 18 [0] (iii) Same total number of sheep and 1 same total number of lambs oe

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

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

1 A wildlife park covers an area of 18 hectares. (a) The 18 hectares is divided between enclosures, paths and buildings in the ratio enclosures : paths : buildings = 11 : 14 : 5. (i) Show that the area for enclosures is 6.6 hectares. [1] (ii) Calculate the area for paths and the area for buildings. Paths … hectares Buildings … hectares [2] 7 (b) Of the 6.6 hectares for enclosures, 11 is for mammals and 30% is for reptiles. Calculate the area for mammals and the area for reptiles. Mammals … hectares Reptiles … hectares [2] (c) The table shows the opening times of the wildlife park. Days Opening times Monday to Friday 09 30 to 17 15 Saturday and Sunday 10 00 to 18 30 (i) Work out how long, in hours and minutes, the wildlife park is open on a Wednesday. … h … min [1] (ii) Calculate the total time, in hours and minutes, that the wildlife park is open in one week. … h … min [2] (d) This table shows the ticket prices for the wildlife park. Adult $11.00 Senior (age 65 and over) $9.25 Child (age 4 to 16) $7.50 Child (age 3 and under) Free Mr Lu visits the wildlife park with his wife, their children (aged 6 and 2) and his parents (both aged 67). (i) Work out the total cost of the tickets for this visit. $ … [2] (ii) Mr Lu has a voucher for the wildlife park that reduces the total cost of the tickets to $42. Calculate the percentage saving. … % [3]

13 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 11 ÷ (11 + 14 + 5) × 18 1 (ii) [paths] 8.4 1 [buildings] 3[.0] 1 (b) [Mammals] 4.2 1 [Reptiles] 1.98 1 (c) (i) 7 [h] 45 [min] 1 (ii) 55 [h] 45 [min] 2FT B1 for 55.75 seen or 38 [h] 45 [min] or 17 [h] soi or M1FT for 5 × their (c)(i) + 2 × 8 [h] 30 [min] or better (d) (i) [$] 48[.00] 2 M1 for 2 × 11 + 2 × 9.25 + 7.50 or better If M0 then SC1 for 55.50 (ii) 12.5 3FT M2 for their ( d )(i ) − 42[×100] or their ( d )(i )  42   100 − ( × 100)   their ( d )(i )  or 42 M1 for or figs 875 their ( d )(i ) or B1 for their (d)(i) – 42 or their 6 seen

This question in 0580/33 May/June 2016

1 (a) Juan and his family fly from London to Rio de Janeiro. (i) The plane departs at 10 20 and arrives in Rio de Janeiro 11 hours 40 minutes later. The local time in Rio de Janeiro is 5 hours behind the local time in London. Work out the time in Rio de Janeiro when the plane arrives. … [2] (ii) The total cost of the plane tickets is 3500 pounds (£). The exchange rate is £1 = 4.45 Brazilian Real. Calculate the cost of the tickets in Brazilian Real. … Real [1] (b) (i) Juan and his family go to a soccer match. He buys 2 adult tickets and 2 child tickets. The price of an adult ticket is 660 Brazilian Real. 2 The price of a child ticket is 3 of the price of an adult ticket. Calculate the total cost of the tickets. … Real [2] (ii) The length, x metres, of the soccer pitch is 105 m, correct to the nearest metre. Complete the statement about the value of x. … G x 1 … [2] (c) The table shows how Juan and his family spent their time in Rio de Janeiro. Sector angle in a Activity Percentage of time pie chart Watching soccer 10 36° Sleeping 108° Shopping Beach 25 90° Other 15 54° (i) Complete the table. [3] (ii) Complete the pie chart. Watching soccer Other Beach [1]

11 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 1700 or 5pm 2 B1 for 2200 or [0]5 20 or 10pm or 5:20am or 6h 40 (ii) 15 575 1 (b) (i) 2200 2 B1 for 440 10 or M1 for 660 × 2 + their 440 × 2 or × 660 3 or better (ii) 104.5 1 SC1 for both correct but reversed 105.5 1 (c) (i) 30 1 20 72 1 1 (ii) Correct pie chart 1 160 + 58 + 45 + 82 + 125 470

This question in 0580/31 Oct/Nov 2016

5 (a) This graph shows Gianna’s journey to work. 20 Work 15 Distance from home 10 (km) 5 Home 0 07 00 07 30 08 00 08 30 09 00 Time (i) How far did Gianna travel to work? … km [1] (ii) Explain what happened at 07 10. … [1] (iii) Calculate the average speed for Gianna’s journey to work. … km/h [2] (b) Gianna earns $1320 each month. She divides her money in the ratio Bills : Leisure : Other = 12 : 5 : 7. Work out how much she spends on each. Bills = $ … Leisure = $ … Other = $ … [3] (c) Gianna invests $5000 for 3 years at a rate of 2.1% per year compound interest. Calculate the amount she will have at the end of the 3 years. Give your answer correct to 2 decimal places. $ … [4]

11 marks

Mark scheme: 5 (a) (i) 17.5 1 (ii) She stopped oe 1 (iii) 8.75 2 M1FT for their (a)(i) ÷ 2 soi (b) 660 3 M2 for one correct value in correct place 275 1320 385 or × k where k is 5, 12 or 7 ( 5 + 12 + 7 ) or better in working 1320 or M1 for or better ( 5 + 12 + 7 ) If zero scored, SC1 for all correct answers in incorrect order (c) 5321.66 cao 4 M2 for 5000 × 1.0213 oe or M1 for 5000 × 1.021 × 1.021 oe A1 for 5321.661….. B1 indep for their answer corrected to 2 d.p. if their unrounded answer is shown to at least 3 d.p.

This question in 0580/31 Oct/Nov 2016

9 (a) The area of Cuba, in square kilometres, is one hundred and five thousand eight hundred and six. Write this number in figures. … [1] (b) The population of an island is 103 000. Write this number in standard form. … [1] (c) The table shows some populations in 2014. Population Puerto Rico 3.68 × 106 St Maarten 4.61 × 104 Haiti 1.05 × 107 US Virgin Islands 1.07 × 105 (i) Write the population of St Maarten as an ordinary number. … [1] (ii) Complete the statement. The population of Haiti is approximately … times the population of the US Virgin Islands. [1] (iii) Find the difference between the population of Haiti and the population of Puerto Rico. Give your answer in standard form. … [2] (d) In 2013 the population of a town was 30 405. In 2014 the population was 30 851. Calculate the percentage increase in the population. … % [3]

9 marks

Mark scheme: 9 (a) 105 806 1 (b) 1.03 × 105 1 (c) (i) 46 100 1 (ii) 100 1 (iii) 6.82 × 106 2 B1 for figs 682  30 851  (d) 1.47 or 1.466 to 1.467 3 M2 for  − 1  [×100] oe soi by 0.0146….  30 405  or 0.0147  30 851 or  × 100 [–100] oe soi by 101.46….  30 405  or 101.47  30 851  or M1 for   soi by 1.0146……. or 1.0147  30 405  Alternative method 30 851 − 30 405 M2 for [× 100 ] oe soi by 0.0146…. 30 405 or 0.0147 or B1 for 30 851 – 30 405 soi by 446

This question in 0580/31 Oct/Nov 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

7 (a) Mei is paid $15.25 for each hour she works. (i) Work out how much she is paid when she works for 8 hours. $ … [1] (ii) Mei gets a pay increase. She is paid 8% more for each hour she works. Mei works for 38 hours each week. Work out how much Mei earns each week after the pay increase. $ … [3] (b) Xia works in France. She is paid 425 euros each week. The exchange rate between euros (€) and dollars is €1 = $1.45 . Work out who earns more each week, Mei or Xia, and by how much. Give your answer in dollars. … earns more by $ … [3] (c) Mei invests $500 in a bank at a rate of 3.5% per year compound interest. Calculate the total amount of money she will receive at the end of 3 years. $ … [3]

10 marks

Mark scheme: 7 (a) (i) 122 1 (ii) 625.86 cao 3 M2 for 15.25 × 1.08 × 38 oe soi by 626 or 625.9 or M1 for 15.25 × 1.08 soi by 16.47 or for 15.25 × 38 soi by 579.5 If zero scored, SC1 for 131.76 or 5006.88 (b) Mei 9.61 cao 3 M1 for 425 × 1.45 M1FT for ±(their 625.86 – their 616.25) If zero scored, SC1 for [€] 6.62 to 6.63 (c) 554.36 3 M2 for 500 ×1.0353 oe or M1 for 500 × 1.035k , k ≠ 1, 3 If zero scored, SC1 for answer of 54.36 or 54.35 or 54.4 or 54.358… 54.359

This question in 0580/32 Oct/Nov 2016

1 (a) Juan takes his car to a garage for repairs. Complete his bill. Item Price ($) Service 475.00 3 tyres at $86 each … 4.5 litres of oil at $5.68 per litre … __________________________ Total … [3] (b) Juan buys a van costing $4400. He pays a deposit of $3740. (i) Work out $3740 as a percentage of $4400. … % [1] (ii) He borrows the rest of the money for one year at a rate of 12% per year simple interest. Work out how much he pays back at the end of one year. $ … [3] (c) Juan pays $321 for insurance. He makes 12 equal payments. Work out each payment. $ … [1] (d) Juan’s car travels 12.4 km and uses 1 litre of fuel. His van travels 1 km and uses 0.0792 litres of fuel. Using 1 litre of fuel, which vehicle travels further? Explain how you decide. … travels further because … … [2] (e) In 2015 the total cost of repairs and fuel for his van was $4200. These costs are in the ratio repairs : fuel = 1 : 2. Find the cost of the fuel. $ … [2]

12 marks

Mark scheme: Question Answer Mark Part marks 1 (a) 258[.00] 1 25.56 1 758.56 1FT FT 475 + their two previous answers (b) (i) 85 1 (ii) 739.2[0] 3 M1 for 4400 – 3740 or soi by 660 M1 for their 660 × 1.12 oe (c) 26.75 cao 1 (d) Van and 12.6 > 12.4 oe 2 B1 for 12.6[…] or 0.0806[…] or 0.982[…] or 0.0792 < 0.0806 or 0.982 < 1 (e) 2800 2 M1 for [2×] 4200 ÷ (1 + 2) oe or soi by 1400

This question in 0580/33 Oct/Nov 2016

6 (a) A regular hexagon has side length h. Write down an expression, in terms of h, for the perimeter of the hexagon. … [1] (b) A square has side length x. Write down an expression, in terms of x, for (i) the perimeter of the square, … [1] (ii) the area of the square. … [1] (c) In this part, all measurements are in centimetres. (2x + 1) NOT TO (x + 3) SCALE A rectangle has length (2x + 1) and width (x + 3 ) . The perimeter of the rectangle is 53. Work out the value of x. x = … [5] (d) Simplify. 5a + 4b - 2a - b + 3a - 2b … [2] (e) Multiply out the brackets. (i) 5 (x - 4) … [1] (ii) x (x 2 + 3) … [2] (f) Factorise completely. 8x 2 - 4x … [2]

15 marks

Mark scheme: 6 (a) 6h oe 1 (b) (i) 4x oe 1 (ii) x2 oe 1 (c) 7.5 5 M1 for 2x + 1 + x + 3 + 2x + 1 + x + 3 oe M1 for 6x + 8 or their expression simplified correctly M1 for their 6x + 8 = 53 M1 for a correct first step in solving their linear equation (d) 6a + b final answer 2 B1 for 6a or [+] b (e) (i) 5x – 20 final answer 1 (ii) x3 + 3x final answer 2 B1 for x3 or [+] 3x (f) 4x(2x – 1) final answer 2 B1 for x(8x – 4) or 4(2x2 – x) or 2(4x2 – 2x) or 2x(4x – 2)

This question in 0580/33 Oct/Nov 2016

9 (a) Here is a list of ingredients to make 18 chocolate chip biscuits. butter 130 g sugar 60 g flour 180 g chocolate chips 30 g Work out how much of each ingredient you need to make 45 biscuits. butter … g sugar … g flour … g chocolate chips … g [3] (b) In a recipe for bread, 58 of the mass of bread mixture is flour. Paul uses 395 g of flour. (i) What mass of bread mixture does he make? … g [2] (ii) Write your answer to part(b)(i) in kilograms. … kg [1]

6 marks

Mark scheme: 9 (a) 325 3 B2 for 3 correct 150 or B1 for 1 or 2 correct 450 or M1 for 45 ÷ 18 soi by 2.5 75 (b) (i) 632 2 M1 for (395 × 8) ÷ 5 oe (ii) 0.632 1FT FT their (b)(i) ÷ 1000

This question in 0580/33 Oct/Nov 2016

3 Mrs Singh and Mr Patel are teachers. They take their two classes to the theatre to see a play. (a) (i) Mrs Singh has 20 girls in her class. The ratio of girls : boys = 5 : 3. Show that Mrs Singh has 32 students in her class. [2] (ii) Mr Patel has 40 students in his class. The ratio of girls : boys = 3 : 2. For the 72 students in the two classes, work out the ratio of total number of girls : total number of boys. Give your answer in its simplest form. … : … [4] (b) Ticket price Student $5.75 Teacher $8.25 For every 25 students, one teacher receives a free ticket. Four teachers go to the theatre with the 72 students. Calculate the total cost of the tickets. $ … [3] (c) The play is in three parts. Each part lasts for 45 minutes. There is a 20 minute interval between each part. The first part starts at 13 30. Work out the time that the play ends. … [2] (d) Mr Patel pays $3.60 for a programme. Last year, the price of a programme was $3.20 . Calculate the percentage increase in the price of a programme. … % [3] (e) The probability that a student loses their theatre ticket is 181 . (i) Write down the probability that a student does not lose their ticket. … [1] (ii) Work out how many of the 72 students you would expect to lose their ticket. … [1]

16 marks

Mark scheme: 20 20 203 (a) (i) × ( 5 + 3 ) or × 8 M2 M1 for 5 5 5 (ii) 11 : 7 4 B2 for [girls=]24 and [boys=]16 or B1 for 24 or 16 40 or M1 for 5 B1FT for 44:28 or their24+ 20: their16+ their (32–20) Only FT provided total is 72 before simplifying (b) 430.5[0] 3 M2 for 72 × 5.75 + 2 × 8.25 oe or M1 for 72 × 5.75 or 2 × 8.25 (c) 16 25 or 4.25pm 2 M1 for 45 × 3 + 2 × 20 3.6 − 3.2 (d) 12.5 3 M2 for × [100 ] oe 3.2 3.6 or M1 for 3.6 − 3.2 or [×100] or better 3.2 17 (e) (i) oe 1 18 (ii) 4 1

This question in 0580/32 Feb/March 2017

1 Camilla joins a soccer club. The total cost of joining is made up of membership, kit and travel. (a) The ratio membership : kit : travel = 3 : 5 : 6. The cost of membership is $78. (i) Show that the total cost of joining is $364. [1] (ii) Calculate the cost of the kit and the cost of the travel. Kit = $ … Travel = $ … [3] 10 (b) Camilla’s father pays of the $364. 13 Camilla pays the rest. Calculate how much she pays. $ … [2] (c) Camilla’s brother joins the soccer club. He receives a 12% discount on the $364 because he is younger than Camilla. Calculate the total cost of joining for him. $ … [2] (d) During the year, Camilla’s team played 24 matches. The table gives some information about the results of these matches. Played Won Drawn Lost 24 W 6 L (i) Write down an equation, in terms of W and L, for the number of matches played. … [1] (ii) Points are given when a team wins or draws a match. The points are Match won 3 points Match drawn 1 point Match lost 0 points. The team has a total of 54 points. Write down an equation, in terms of W, for the total points given. … [1] (iii) Work out the value of W and the value of L. W = … L = … [3]

13 marks

Mark scheme: Question Answer Marks Part marks 1(a)(i) 78 ÷ 3 × (3 + 5 + 6) [= 364] 1 1(a)(ii) [kit] 130 3 M1 for 364 ÷ (3 + 5 + 6) × 5 (or × 6 if travel first) [travel] 156 or 78 ÷ 3 × 5 (or × 6 if travel first) A1 for one of kit or travel correct If zero scored, SC1 for kit + travel = 286 1(b) 84 2 M1 for 3 ÷ 13[ × 364] or 364 – (10 ÷ 13 × 364) or B1 for 280 1(c) 320.32 final answer 2 M1 for (100 – 12) ÷ 100 [× 364] or B1 for 43.68 1(d)(i) W + 6 + L = 24 oe 1 1(d)(ii) 3W + 6 = 54 isw 1 1(d)(iii) [W=] 16 2 M1 for 3W = 54 – 6 or W + 2 = 18 or better or correct first step from an equation in W only [L=] 2 1FT FT is 18 – their W If zero scored, SC1 for both correct but reversed

This question in 0580/31 May/June 2017

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

3 The McVay family go to the cinema. (a) The cinema has 510 seats. (i) The first 6 rows each have 18 seats. The next 8 rows each have 20 seats. All the other rows each have 22 seats. Work out the total number of rows of seats in the cinema. … [3] (ii) 70% of the 510 seats are occupied. Work out how many seats are occupied. … [1] (b) The McVay family has 2 adults and 2 children. Ticket Prices Adult $7.95 Child $5.95 Family Ticket (2 Adults and 2 Children) $24 Work out how much they save by buying a family ticket rather than a ticket for each person. $ … [2] (c) The film starts at 14 15 and lasts for 116 minutes. Work out the time that the film ends. … [2] (d) Popcorn is sold in tubs. Large Medium Small 135g 100g 70g $3.15 $2.30 $1.60 Work out which tub of popcorn is the best value for money. You must show your working. … [3]

11 marks

Mark scheme: 3(a)(i) 25 3 510 − ( 6 × 18 + 8 × 20 ) M2 for soi 22 or M1 for 6 × 18 + 8 × 20 soi 3(a)(ii) 357 1 3(b) 3.8[0] 2 M1 for 2 × 7.95 + 2 × 5.95 or better 3(c) 16 11 or 4.11 pm 2 M1 for conversion to 1 hour and 56 mins or a complete correct method 3(d) Complete correct method M2 M2 for 2.28… or 2.29, 2.3, 2.33… [c/g] oe or 43.75, 43.47… or 43.48, 42.85… or 42.86 [g/$] oe or M1 for one correct calculation small A1

This question in 0580/33 May/June 2017

5 Simone makes a fruit cake. (a) (i) The recipe needs 175 g sugar, 200 g butter and 225 g flour. Write the ratio sugar : butter : flour in its simplest form. … : … : … [2] (ii) The recipe needs a total of 600 g of fruit. The ratio sultanas : currants : raisins = 4 : 3 : 1. Work out the mass of each type of fruit. Sultanas = … g Currants = … g Raisins = … g [3] (b) The cake can be made in either a cylindrical tin or a square-based tin. (i) The cylindrical tin has radius 10 cm. NOT TO In this tin the cake is 5 cm high. SCALE Show that the volume of the cake is 1600 cm3, correct to 2 significant figures. [2] (ii) In the square-based tin, the cake is 4 cm high. NOT TO The volume of the cake is 1600 cm3. SCALE Work out the length of a side of the base of this tin. … cm [2] (c) The mass, m grams, of the cake is 1340 g, correct to the nearest 20 g. Complete the statement about the value of m. … G m < … [2] (d) The number of kilocalories (kcal) in one quarter of the cake is 1290 kcal. The whole cake is cut into 12 equal pieces. (i) Calculate the number of kilocalories in one piece of cake. … kcal [2] (ii) The daily recommended number of kilocalories for Simone is 2000 kcal. Work out the number of kilocalories in one piece of cake as a percentage of 2000 kcal. … % [1]

14 marks

Mark scheme: 5(a)(i) 7 : 8 : 9 2 M1 for 35 : 40 : 45 oe If zero scored, SC1 for 7,8,9 in wrong order 5(a)(ii) 300 3 600 M1 for or better 225 ( 4 + 3 + 1) 75 and A1 for one correct answer in the correct place or for two correct answers not in the correct place 5(b)(i) π ×102 × 5 M1 1570 to 1571 A1 5(b)(ii) 20 2 M1 for 1600 = 4 ×l 2 or better 5(c) 1330 1 1350 1 SC1 for correct but answers reversed 5(d)(i) 430 2 M1 for 1290 × 4 or for recognising that 1290 is 3 pieces 5(d)(ii) 21.5 1FT their ( d )( i ) 1FT is × 100 2000

This question in 0580/33 May/June 2017

2 (a) Write the number 8045 in words. … [1] (b) Write down a number between 60 and 70 that is (i) a square number, … [1] (ii) a prime number, … [1] (iii) a common multiple of 4 and 17. … [1] (c) (i) Write 98 as a product of its prime factors. … [2] (ii) Find the highest common factor (HCF) of 98 and 182. … [2] (d) Find the value of (i) 64, … [1] (ii) 3 24 389 , … [1] (iii) 141, … [1] (iv) 5−3. … [1]

12 marks

Mark scheme: 2(a) Eight thousand [and] forty-five 1 2(b)(i) 64 1 2(b)(ii) 61 or 67 1 2(b)(iii) 68 1 2(c)(i) 2 × 72 or 2 × 7 × 7 2 M1 for 2, 7, 7 or 2, 72 or 1 × 2 × 7 × 7 or 1 × 2 × 72 2(c)(ii) 2 M1 for (182 = ) 2 × 7 × 13 or 2, 7, 13 14 or B1 for 2 or 7 or 2 × 7 as final answer 2(d)(i) 1296 1 2(d)(ii) 29 1 2(d)(iii) 14 1 2(d)(iv) 1 1 0.008 or 125

This question in 0580/32 Oct/Nov 2017

4 Leo, Kim and Priya own a shop. (a) (i) Pens cost $1.45 each. Andre has a $10 note. Find the greatest number of pens that he can buy and how much change he receives. Number of pens = … Change = $ … [3] (ii) The price of a pack of printer paper is $5.60 . In a sale this price is reduced by 15%. Calculate the sale price. $ … [2] (b) Each day, Kim records the number of people who buy a pen. The results for 10 days are shown below. 40 7 19 25 18 19 32 57 12 47 Find the median. … [2] (c) The shop makes a profit of $7000. The profit is shared in the ratio Leo : Kim : Priya = 6 : 3 : 5. Calculate the amount they each receive. Leo = $ … Kim = $ … Priya = $ … [3] (d) Leo changed $1400 into pounds (£). The exchange rate was £1 = $1.54 . Work out how many pounds Leo received. £ … [2] (e) Priya invested $2000 for 3 years at a rate of 2.6% per year compound interest. Calculate the value of her investment at the end of the 3 years. $ … [3]

15 marks

Mark scheme: 4(a)(i) 6 pens and 1.3[0] 3 10 M1 for 1.45 M1 for k × 1.45 where k is an integer 4(a)(ii) 4.76 2 15 M1 for 5.60 × ( 1 − ) oe 100 4(b) 22 2 M1 for ordered list of first 6 or last 6 or B1 for 19 and 25 both identified 4(c) 3000 3 7000 M2 for × k or better, where k is 6 or 3 1500 6 + 3 + 5 2500 or 5 7000 or M1 for or better implied by 500 6 + 3 + 5 If no working M2 implied by one correct answer in correct place If zero scored, M1 for all correct answers in wrong order 4(d) 909.09 or 909.1[0] or 909.0 or 909 2 1400 M1 for 1.54 4(e) 2160.09 or 2160.1[0] or 2160.0 or 3 2.6 M2 for 2000 ( 1 + )3 oe 2160 100 2.6 or M1 for 2000 ( 1 + )2 soi by 2105.35 100

This question in 0580/32 Oct/Nov 2017

8 (a) Simplify. (i) 8p + 2r + 4p − 9r … [2] (ii) 4x3 × 6x2 … [1] (b) Write down an expression, in terms of x and y, for the total cost of x cakes at 90 cents each and y drinks at 75 cents each. … cents [2] (c) Factorise completely. 12p2 − 8p … [2] (d) Solve. 4(7r − 3) = 128 r = … [3] (e) Solve the simultaneous equations. You must show all your working. 4x + 3y = 43 6x + 7y = 92 x = … y = … [4] Question 9 is printed on the next page.

14 marks

Mark scheme: 8(a)(i) 12p – 7r final answer 2 B1 for 12p + jr or kp –7r j, k can be 0 or 12p + –7r 8(a)(ii) 24x5 final answer 1 8(b) 90x + 75y final answer 2 B1 for 90x + jy or kx +75y j, k can be 0 or 0.9x + 0.75y 8(c) 4p(3p – 2) final answer 2 B1 for 4(3p2 – 2p) or p (12p – 8) or 2(6p2 – 4p) or 2p(6p – 4) 8(d) 5 3 M1 for first correct step M1FT for second correct step 8(e) Correctly equating one set of M1 coefficients Correct method to eliminate one M1 Dependent on the coefficients being the same for variable one of the variables. Correct consistent use of addition or subtraction using their equations. [x = ] 2.5 A1 [y = ] 11 A1 If zero scored, SC1 if no working shown, but 2 correct answers given or SC1 for 2 values satisfying one of the original equations

This question in 0580/32 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

3 Three boys each have $600. (a) Victor spends 40% of his $600. He spends the money in the ratio clothes : books : music = 10 : 2 : 3. (i) Work out how much he spends on music. $ … [3] (ii) Work out how much more he spends on clothes than books. $ … [2] (b) Walter invests his $600 for 3 years at a rate of 4.5% per year compound interest. Calculate the interest Walter receives at the end of the 3 years. $ … [3] (c) Xavier goes on holiday to Europe and changes his $600 into euros (€). He spends €325 whilst he is on holiday. When he gets home he changes the euros he has left back into dollars. The exchange rate is $1 = €0.864 . Work out how many dollars he has left after his holiday. Give your answer correct to the nearest cent. $ … [3]

11 marks

Mark scheme: 3(a)(i) 48 3 B1 for 240 [ their 240 M1 for ][× 3] soi by 16 10 + 2 + 3 3(a)(ii) 128 2 k M1 for × their 240 oe where k = 2, 10 or 8 15 or for their (a)(i) ÷3 ×k oe where k = 2, 10 or 8 3(b) 84.7[0] or 84.69 to 84.7 3 3  4.5  M2 for 600 ×  1 +  oe  100   4.5  2 or M1 for 600 ×  1 +  oe  100  3(c) 223.84 3 600 × 0.864 − 325 M2 for oe or better 0.864 or 325 M1 for 600×0.864 or 0.864

This question in 0580/31 May/June 2018

7 The scale drawing shows the positions of Annika’s house, A, and Bernhard’s house, B, on a map. The scale is 1 centimetre represents 300 metres. North A North B Scale: 1 cm to 300 m (a) Work out the actual distance, in metres, between Annika’s house and Bernhard’s house. … m [2] (b) Measure the bearing of Bernhard’s house from Annika’s house. … [1] (c) (i) Using a straight edge and compasses only, construct the perpendicular bisector of AB. Show all your construction arcs. [2] (ii) Cordelia’s house is • the same distance from Annika’s house and Bernhard’s house and • due south of Annika’s house. Mark on the map the position of Cordelia’s house. Label this point C. [2] (d) Dougie’s house is • on a bearing of 320° from Bernhard’s house and • 1650 m from Annika’s house. Mark on the map the two possible positions of Dougie’s house. Label each of these points D. [4]

11 marks

Mark scheme: 7(a) 3300 2 B1 for 11 cm seen 7(b) 117 1 7(c)(i) Correct ruled perpendicular bisector 2 B1 for correct bisector drawn without arcs or with 2 pairs of arcs for two pairs of correct arcs 7(c)(ii) C marked correctly 2 M1 for clear attempt at a line south from A 7(d) D marked correctly twice with 4 B1 for line indicating correct bearing of 320 correct arc(s) and line seen measured B2 for an arc radius 5.5, centre A, [meeting their bearing line at least once], or B1 for an arc any radius, centre A, with D marked on it [meeting their bearing line at least once], or B1 for a complete circle centre A of any radius, or M1 for 1650 ÷ 300 If 0 scored SC2 for D marked correctly within tolerance at least once with incorrect/no arc(s) and incorrect/no line seen

This question in 0580/31 May/June 2018

3 A car company has three sales people, Anna, Mustapha and Joshua. (a) During March, Anna sold 21 cars, Mustapha sold 12 cars and Joshua sold 15 cars. Write down and simplify the ratio of the number of cars they sold during March. Anna : Mustapha : Joshua = … : … : … [2] (b) Each month, they receive a bonus which is proportional to the number of cars they sell. The total bonus in March is $1248. (i) Show that Anna receives a bonus of $546. [1] (ii) Calculate the bonuses received by Mustapha and Joshua. Mustapha $ … Joshua $ … [2] 3 (c) The total bonus of $1248 is of the total profit in March. 7 Calculate the total profit in March. $ … [2] (d) Ella wants to buy a car with a price of $13 500. The company reduces this price by 16%. Ella then pays a deposit of $500. Show that the amount left for her to pay is $10 840. [2] (e) Ella borrows $10 840 from a bank. She pays this back over 3 years at a rate of $340 per month. (i) Show that the total amount she pays back during the 3 years is $12 240. [1] (ii) Calculate the percentage increase from $10 840 to $12 240. … % [3]

13 marks

Mark scheme: 3(a) 7 : 4 : 5 2 B1 for any correct ratio other than 21 : 12 : 15, not in simplest form 3(b)(i) 7 B1 oe × 1248 16 3(b)(ii) [Mustapha] 312 2 B1 for each [Joshua] 390 or 1248 M1 for × k where k = 12 or 15 21 + 12 + 15 1248 or × k oe where their 7 + their 4 + their 5 k = their 4 or their 5 3(c) 2912 2 M1 for 1248 ÷ 3 [× 7] 3(d) 13 500 – 0.16 × 13 500 − 500 M2 M1 for 0.16 × 13 500 or 0.84 × 13 500 seen or 0.84 × 13 500 − 500 3(e)(i) 3 × 12 × 340 B1 3(e)(ii) 12.9 or 12.91 to 12.92 3 12240 − 10840 M2 for [× 100 ] 10840 12240 or × 100 [ − 100 ] or 10840  12240   − 1  [× 100 ]  10840  12240 or M1 for 12240 – 10840 or oe 10840

This question in 0580/32 May/June 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

2 (a) Write down the fraction of the rectangle that is shaded. Give your answer in its simplest form. … [2] 7 (b) Write down a fraction that is equivalent to . 12 … [1] (c) Write down a fraction that completes this calculation. 13 … # = 1 11 … [1] (d) Find a fraction that makes this statement true. 7 … 8 1 1 9 9 … [1] (e) Write these numbers in order, starting with the smallest. -1 4 .57 # 10 .033 57.2% 7 … 1 … 1 … 1 … [2] smallest

7 marks

Mark scheme: 2(a) 4 2 8 cao M1 for 15 30 2(b) 7 k 1 k ≠ 1 12 k 2(c) 11k 1 13k 2(d) Any correct fraction 1 2(e) 1 4 2 B1 for 3 in correct order 5.7 × 10− , , 57.2% , 0.33 M1 for 3 of 0.57, 0.571[….], 0.574[….], 7 0.572

This question in 0580/32 Feb/March 2019

3 (a) Maia shares $3000 between her three children. She gives the eldest child $1200, the second eldest child $1000 and the rest to the youngest child. Write this information as a ratio in its simplest form. … : … : … [2] eldest youngest (b) Yani’s house is for sale. She decides to reduce the selling price of $240 000 by 15%. Calculate the new selling price. $ … [2] (c) Hawa invests $750 at a rate of 3.5% per year compound interest. Calculate the value of his investment at the end of 3 years. $ … [3]

7 marks

Mark scheme: 3(a) 6 : 5 : 4 2 M1 for 1200 : 1000 : 800 or better 3(b) 204 000 2  15  M1 for 240000 ×  1 −  oe  100  3(c) 832 or 831.5 or 831.53 or 831.54 or 3 3  3.5  831.538… M2 for 750×  1 +  oe  100   3.5  2 or M1 for 750×  1 +  oe  100 

This question in 0580/32 Feb/March 2019

4 A car park has 880 parking spaces. (a) Some of the spaces are reserved. The ratio of reserved spaces : not reserved spaces = 1 : 10. Work out the number of spaces that are not reserved. … [2] (b) 25% of the 880 spaces are on the top floor. Work out the number of spaces that are on the top floor. … [1] (c) At 06 00 one morning, 401 of the 880 spaces are filled. By 06 30, no cars have left the car park but another 15 of the 880 spaces are filled. Work out the fraction of the 880 spaces that are empty at 06 30. … [3] (d) The cost of each visit to the car park is shown in the table. Length of visit Cost ($) Up to 20 minutes Free More than 20 minutes and up to 2 hours 2.50 More than 2 hours and up to 4 hours 4.50 More than 4 hours and up to 8 hours 8.50 More than 8 hours and up to 24 hours 12.00 (i) Samarth arrives at 11 40 and leaves at 15 30. Find the cost of his visit. $ … [1] (ii) Radhika leaves the car park at 17 50 and pays $8.50 . (a) Work out the earliest time she could have arrived at the car park. … [1] (b) Work out the change she receives from a $20 note. $ … [1] (iii) Dhruv bought a weekly car park ticket for $26. That week, he visited the car park four times. These are the lengths of time he parked his car for. 17 minutes 6 12 hours 11 hours 9 14 hours Work out how much he saved by buying a weekly ticket. $ … [3]

12 marks

Mark scheme: 4(a) 800 2 10 880 M1 for [× 880 ] or [× 10 ] oe 10 + 1 10 + 1 4(b) 220 1 4(c) 31 3  1 1  or equivalent fraction M2 for 1 −  +  oe 40  40 5  1 1 or M1 for + oe 40 5 OR B2 for 682 1 or M1 for × 880 soi by 22 40 1 or × 880 soi by 176 5 4(d)(i) 4.5[0] 1 4(d)(ii)(a) 09 50 1 4(d)(ii)(b) 11.5[0] 1 4(d)(iii) 6.5[0] 3 B2 for 32.5 or M2 for ([0] + 8.5 + 12 + 12) – 26 or M1 for [0] + 8.5 + 12 + 12

This question in 0580/32 Feb/March 2019

9 The diagram shows a rectangle and two semicircles with diameters AC and BD. This diagram is a scale drawing of a running track. AC = BD = 60 m AB = CD = 120 m A B 60 m C 120 m D (a) (i) Complete the statement. 1 centimetre represents … metres. [2] (ii) Work out the total length of the running track in metres. … m [3] (iii) Shreva walks at 1.4 m/s. Work out how long it will take her to walk once around the track. Give your answer in minutes and seconds, correct to the nearest second. … minutes … seconds [3] (b) Talan completes one lap of the track every 80 seconds. (i) Work out how many laps he can complete in one hour. … [2] (ii) Naima completes one lap of the track every 88 seconds. Talan and Naima start running from point A on the track at the same time. They each complete a number of laps of the track. Work out the smallest number of laps they each complete before they are both at point A again at the same time. Talan completes … laps and Naima completes … laps. [3]

13 marks

Mark scheme: 9(a)(i) 15 2 B1 for 4 cm or 8 cm 9(a)(ii) 428 or 429 or 428.4 or 428.5 3 M2 for 120 × 2 + 60π or 428.49 to 428.52 or M1 for 60π If 0 scored SC1 for 28.6 or 28.56 to 28.57 9(a)(iii) 5 minutes 6 seconds 3 FT their (a)(ii) their (a)(ii) M1 for 1.4 M1dep for ÷ 60 9(b)(i) 45 2 60 × 60 M1 for oe 80 9(b)(ii) 11, 10 3 B2 for 880 or 8 × 10 × 11 oe or B1 for 880k, k > 1 or M1 for 80, 160, 240.. and 88, 176, 264,… or 8 × 10 and 8 × 11 seen

This question in 0580/32 Feb/March 2019

10 (a) Using a straight edge and compasses only, construct the equilateral triangle ABC. The base AB has been drawn for you. A B [2] (b) 16 m NOT TO SCALE 14 m 24 m Calculate the area of this trapezium. … m2 [2] (c) Each interior angle of a regular polygon is 162°. Calculate the number of sides of the polygon. … [3] (d) NOT TO SCALE h cm 6h cm The area of this triangle is 363 cm2. Calculate the value of h. h = … [3] (e) NOT TO SCALE This shape is drawn using two semicircles that have the same centre. The large semicircle has radius 7 cm. The small semicircle has radius 3 cm. Calculate the area of the shape. … cm2 [3]

13 marks

Mark scheme: 10(a) correct triangle drawn with arcs 2 B1 for correct triangle without arcs or for correct arcs 10(b) 280 2 1 M1 for ( 24 + 16 ) × 14 oe 2 10(c) 20 3 360 M2 for or better 180 − 162 or M1 for 180 − 162 or ( n − 2 ) × 180 = 162 n or better 10(d) 11 3 2 363 M2 for h = or better 3 1 or M1 for × h × 6 h = 363 oe 2 10(e) 62.8 or 62.83 to 62.84 3 1 2 1 2 M2 for π × 7 − π × 3 oe 2 2  1  2  1  2 or M1 for × π × 7 or × π × 3      2   2 

This question in 0580/32 Feb/March 2019

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

10 The scale drawing shows a rectangle ABCD. The scale is 1 centimetre represents 20 metres. A B D C Scale: 1 cm to 20 m (a) Using a straight edge and compasses only, construct the bisector of angle ADC. Show all your construction arcs. [2] (b) Shade the region inside the rectangle that is • nearer to DA than to DC and • less than 210 m from C. [3]

5 marks

Mark scheme: 10(a) Correct angle bisector with two 2 B1 for correct angle bisector with pairs of correct arcs no/incorrect arcs or two pairs of correct arcs with no line 10(b) Correct arc with radius 10.5 cm 3 B2 for correct arc centre C or B1 for any arc centre C or 10.5 seen and correct region shaded B1dep for shading correct region dep on at least (a) B1(b) B1

This question in 0580/31 May/June 2019

1 (a) (i) Write 26% as a decimal. … [1] (ii) Write 0.48 as a fraction. … [1] (b) Write down 5 (i) a fraction that is equivalent to , 9 … [1] (ii) the 7th odd positive number, … [1] (iii) a decimal number that is larger than 0.0467 but smaller than 0.0468 . … [1] (c) Find the value of (i) 3 512 , … [1] 6 8 (ii) 6 , 2 … [1] (iii) 70. … [1] (d) Find the first even multiple of seven that is greater than 100. … [2] - 1 - 3 7 (e) 6 10 .897 # 10 64 5 From the list, write down the irrational number. … [1]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 0.26 cao 1 1(a)(ii) 48 1 or equivalent fraction 100 1(b)(i) 5k 1 where k ≠ 1 9k 1(b)(ii) 13 1 1(b)(iii) Any decimal between 0.0467 and 1 0.0468 1(c)(i) 8 1 1(c)(ii) 26 244 1 1(c)(iii) 1 1 1(d) 112 2 B1 for any multiple of 7 greater than 100 seen 1(e) 10 1

This question in 0580/32 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

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

3 The music teacher at a school forms an orchestra. The instruments in the orchestra are 36 string, 15 woodwind and 12 brass. (a) Write the ratio string : woodwind : brass in its simplest form. … : … : … [2] (b) The 36 string instruments are violins, cellos and double basses in the ratio violins : cellos : double basses = 9 : 2 : 1. (i) Show that the number of violins is 27. [1] (ii) Work out the number of cellos and the number of double basses. Cellos … Double basses … [2] (c) The 15 woodwind instruments are oboes, flutes and clarinets. 20% of these instruments are oboes. There are twice as many flutes as clarinets. Find the number of flutes. … [2] 1 (d) Of the 12 brass instruments, are trumpets, 3 are trombones and the remainder are horns. 3 Find the number of horns. … [2] (e) The music teacher needs to buy all the instruments for the orchestra. Number of Price of each Cost ($) instruments instrument ($) String 36 131 4716 Woodwind 15 217 Brass 12 221 (i) Complete the table. [1] (ii) Find the total cost of all the instruments. $ … [1] (f) The school is given 65% of the total cost of all the instruments. Find how much more money is needed. $ … [2]

13 marks

Mark scheme: 3(a) 12 : 5 : 4 2 B1 for 36 : 15 : 12 oe 3(b)(i) 9 1 × 36 (9 + 2 + 1) 3(b)(ii) [Cellos] 6 2 B1 for each [Double basses] 3 3(c) 8 2 B1 for 3 [oboes] seen 3(d) 5 2 B1 for 4 [trumpets] seen 3(e)(i) [Woodwind] 3255 1 [Brass] 2652 3(e)(ii) 10 623 1 FT their (e)(i) 3(f) 3718.05 2 M1 for (1 – 0.65) × their (e)(ii) oe

This question in 0580/33 May/June 2019

5 The scale drawing shows a play area, ABCDE. The scale is 1 centimetre represents 3 metres. D h E C A B Scale: 1 cm to 3 m (a) Find the actual distance h in metres. h = … m [2] (b) Find the actual area of triangle CDE. … m2 [3] (c) A straight path crosses the play area from C to AB. It is equidistant from CB and CD. Using a straight edge and compasses only, construct the path. Show all your construction arcs. [2] (d) There is a circular pool in the play area. The pool has a diameter of 8 m. Calculate (i) the circumference of the pool, … m [2] (ii) the area of the pool. … m2 [2]

11 marks

Mark scheme: 5(a) 10.8 to 12 2 B1 for 3.6 cm to 4.0 cm measured 5(b) 191 to 220 3 B1 for 11.8 to 12.2 measured or 35.4 to 36.6 M1 for 0.5 × their (a) × their actual EC oe 5(c) Correct ruled bisector of angle BCD 2 B1 for correct angle bisector with with correct arcs no/incorrect arcs, or two pairs of supporting arcs or correct line short of AB with or without arcs 5(d)(i) 25.1 or 25.13 to 25.14 2 M1 for 8 × π oe 5(d)(ii) 50.3 or 50.26 to 50.272 2 M1 for π (0.5 × 8)2 oe

This question in 0580/33 May/June 2019

9 Mr Razif travels by bus from Singapore to Kuala Lumpur with his wife and his four children. (a) Ticket Price Adult $32.40 Child $24.40 Family (2 adults and 3 children) $115.00 Work out how much Mr Razif saves if he buys a family ticket and one child ticket rather than six individual tickets. $ … [4] (b) The bus leaves Singapore at 12 40 and arrives in Kuala Lumpur at 17 35. Work out, in hours and minutes, the time this journey takes. … h … min [1] (c) Mr Razif changes some dollars into Malaysian ringgits. He receives 318 ringgits when the exchange rate is $1 = 4.24 ringgits. Work out how many dollars he changes. $ … [2]

7 marks

Mark scheme: 9(a) 23 4 M3 for 2 × 32.4 + 4 × 24.4 – 115 – 24.4 oe OR B2 for 162.4[0] or 2 × 32.4 + 4 × 24.4 oe or M1 for 2 × 32.4 or 4 × 24.4 B1 for 139.4[0] 9(b) 4 [h] 55[min] 1 9(c) 75 2 M1 for 318 ÷ 4.24

This question in 0580/33 May/June 2019

11 (a) Write as a decimal. 4 … [1] 36 (b) Write as a fraction in its lowest terms. 124 … [1] 5 (c) Work out of 128. 8 … [1] (d) Write down all the factors of 24. … [2] (e) Find the highest common factor (HCF) of 24 and 108. … [2] (f) Write down an irrational number between 3 and 9. … [1] (g) Write down the value of 250. … [1] (h) $8400 is invested for 2 years at a rate of 3.5% per year compound interest. Work out the total amount of interest earned by the end of the 2 years. $ … [3] 1 4(i) Without using a calculator, work out 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) [0].25 1 1(b) 9 1 cao 13 1(c) 80 1 1(d) 1, 2, 3, 4, 6, 8, 12, 24 2 B1 for 6 or 7 correct factors and no extras or 8 correct factors and at most one extra 1(e) 12 2 B1 for 2, 3, 4 or 6 as final answer or 2 × 2 × 3 or for 2 × 2 × 2 × 3 and 2 × 2 × 3 × 3 × 3 1(f) Accept any irrational number between 1 3 and 9 1(g) 1 1 1(h) 598.29 cao 3 2  3.5  M2 for 8400 × 1 + oe    100  OR  3.5  2 M1 for 8400 ×  1 +  oe  100  A1 for 8998.29 1(i) 5 12 35 B1 allow denominators with multiples of 15 or or 35k 5 k 15 15 15 e.g. , 15k 15 k 5 12 35 12 M1 allow other common denominators [ 2 ] [+] or [+] 15 15 15 15 [2]17 or 47 leading to 2 cao A1 with no errors or omissions seen 15 15 315

This question in 0580/33 Oct/Nov 2019

4 (a) A plane leaves Karachi at 15 30 to fly to Bangkok. The distance is 3840 km. The plane flies at an average speed of 720 km/h. The local time in Bangkok is 2 hours ahead of the local time in Karachi. Find the local time in Bangkok when the plane arrives. … [4] (b) In Bangkok a watch costs 2610 baht. The exchange rate is $1 = 34.8 baht. Find the cost of the watch in dollars. $ … [2] (c) The price of another watch increases from $18 to $19.17 . Find the percentage increase in the price of this watch. … % [3] (d) Raoul makes a profit when he sells his watch for $36. The ratio of the price Raoul paid for the watch and the profit he makes is price paid : profit = 7 : 2. Work out the profit that Raoul makes. $ … [2]

11 marks

Mark scheme: 4(a) 22 50 4 M1 for 3840 ÷ 720 A1 for 5[h] 20[m] M1dep for 15 30 + their 5[h] 20[m] [+2] or 17 30 + their 5[h] 20[m] 4(b) 75 2 M1 for 2610 ÷ 34.8 4(c) 6.5 3 19.17 − 18 M2 for [× 100] oe 18  19.17  or  − 1  [× 100] oe  18  19.17 or × 100 [– 100] oe 18 19.17 or M1 for or 19.17 – 18 18 4(d) 8 2 36 M1 for 2 + 7

This question in 0580/33 Oct/Nov 2019

4 Alexa, Ben and Chloe own a restaurant. (a) Alexa records some temperatures. Fridge 4 °C Cool box -3 °C Freezer -19 °C (i) Find the difference in temperature between the fridge and the cool box. … °C [1] (ii) Find the difference in temperature between the cool box and the freezer. … °C [1] (iii) The temperature in the cold room is 5 °C lower than the fridge. Find the temperature in the cold room. … °C [1] (b) Alexa, Ben and Chloe share the profits from their restaurant in the ratio 2 : 6 : 7. One year the restaurant makes a profit of $60 000. Work out how much each receives. Alexa = $ … Ben = $ … Chloe = $ … [3] (c) They invest $12 000 at a rate of n% per year simple interest. At the end of 3 years the value of the investment is $12 900. Find the value of n. n = … [3]

9 marks

Mark scheme: 4(a)(i) 7 1 4(a)(ii) 16 1 4(a)(iii) −1 1 4(b) 8000 3 B2 for one correct 24 000 60000 or M2 for × k 28 000 2 + 6 + 7 60000 or M1 for 2 + 6 + 7 4(c) 2.5 3 12900 − 12000 M1 for 3 their 300 M1dep for [× 100] 12000

This question in 0580/32 May/June 2020

11 (a) (i) Write down a fraction equivalent to . 15 … [1] 1 2 (ii) Find a fraction that is greater than but less than . 15 15 … [1] (b) (i) Write 15% as a decimal. … [1] (ii) Shade 15% of this grid. [1] (c) Write down all the factors of 15. … [2] (d) Find the value of 15. Give your answer correct to 3 decimal places. … [2] (e) (i) Write down the reciprocal of 15. … [1] (ii) Write down the value of 150. … [1] (iii) Write 0.015 in standard form. … [1]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) k 1 cao 15k 1(a)(ii) a 1 a 2 1 , where < < b 15 b 15 1(b)(i) 0.15 cao 1 1(b)(ii) 6 squares shaded 1 1(c) 1, 3, 5, 15 2 B1 for 3 correct and no extras or 4 correct and one extra 1(d) 3.873 cao 2 B1 for 3.87 or 3.872... 1(e)(i) 1 1 15 1(e)(ii) 1 1 1(e)(iii) 1.5 × 10−2 cao 1

This question in 0580/33 May/June 2020

3 (a) NOT TO SCALE 6 m 8 m The diagram shows a rectangular patio with sides 6 m and 8 m. (i) Work out the perimeter of the patio. … m [1] (ii) Henri covers the patio floor with square tiles. The tiles are 0.5 m by 0.5 m. Work out the number of tiles he needs. … [2] (b) The diagram shows the net of a solid on a 1 cm2 grid. (i) Write down the mathematical name for the solid. … [1] (ii) Work out the volume of the solid. … cm3 [2] (c) A square has perimeter 12x. Find an expression, in terms of x, for the area of the square. Give your answer in its simplest form. … [3] (d) B NOT TO SCALE A C 10 cm The diagram shows a semicircle with diameter AC. B is a point on the circumference and AB = BC. Work out the area of triangle ABC. … cm2 [3]

12 marks

Mark scheme: 3(a)(i) 28 1 3(a)(ii) 192 2 8 6 M1 for × oe 0.5 0.5 or B1 for 16 and 12 or 4 tiles = 1 m2 soi 3(b)(i) Cuboid 1 3(b)(ii) 10 2 M1 for 5 × 2 [× 1] 3(c) 9x 2 3  12 x  2 M2 for   oe  4  12 x or M1 for oe 4 If 0 scored, SC1 for final answer kx 2 3(d) 25 3 B1 for height is 5 [cm] 1 M1 for × 10 × 5 oe 2

This question in 0580/33 May/June 2020

4 349 West side East side 347 348 346 NOT TO 7 SCALE 5 6 3 4 1 2 A road has 349 houses on it numbered from 1 to 349. The diagram shows some of these houses. The houses on the West side of the road have odd numbers. The houses on the East side have even numbers. (a) Put a ring around the numbers in this list that are on the West side. 25 87 126 178 252 329 [1] (b) On the East side, how many houses are there between the house numbered 168 and the house numbered 184? … [1] (c) How many houses on the road have a house number that is a multiple of 39? … [2] (d) Tomaz delivers a leaflet to every house on the West side of the road. He starts at house number 1 and then delivers to each house in order. (i) Find an expression, in terms of n, for the house number of the nth house he delivers to. … [2] (ii) Work out the house number of the 40th house he delivers to. … [1] (iii) Work out how many houses are on the West side of the road. … [2] (e) Alicia delivers a leaflet to every house on the East side of the road. She starts at house number 348 and then delivers to each house in order. (i) Find an expression, in terms of n, for the house number of the nth house she delivers to. … [2] (ii) What is the largest value of n that can be used in your expression? Give a reason for your answer. The largest value of n is … because … … [2]

13 marks

Mark scheme: 4(a) 25, 87, 329 circled 1 4(b) 7 1 4(c) 8 2 349 M1 for 39 or B1 for at least four of 39, 78, 117, 156, 195, 234, 273, 312 4(d)(i) 2n – 1 oe 2 B1 for 2n + c or kn – 1, k ≠ 0 4(d)(ii) 79 1 FT their (d)(i) if linear 4(d)(iii) 175 2 M1 for their ( 2 n − 1) = 349 348 350 or + 1 or 2 2 4(e)(i) 350 – 2n oe 2 B1 for −2n + c or kn + 350, k ≠ 0 4(e)(ii) 174 2 B1 for each n ⩾ 175 gives house numbers that are If 0 scored, SC1 for 175 zero/negative

This question in 0580/33 May/June 2020

7 (a) The diagram shows a regular polygon. (i) Write down the mathematical name for this shape. … [1] (ii) Write down the order of rotational symmetry of this shape. … [1] (b) The diagram shows part of a different regular polygon. NOT TO SCALE i e i e e is an exterior angle. i is an interior angle. The ratio e : i = 2 : 13 . (i) Work out angle e. … [3] (ii) Work out the number of sides of this regular polygon. … [1] (c) Using a straight edge and compasses only, construct the equilateral triangle ABC. Side AB has been drawn for you. A B [2] (d) In this part, all angles are in degrees. 2x NOT TO SCALE x + 23 2x - 13 (i) Use the information in the triangle to write down an equation in terms of x. … [1] (ii) Solve this equation to find the value of x. x = … [3] (iii) Work out the size of the smallest angle in the triangle. … [2]

14 marks

Mark scheme: 7(a)(i) Hexagon 1 7(a)(ii) 6 1 7(b)(i) 24 3 180 M2 for × k where k = 1, 2 or 13 2 + 13 or B1 for e + i = 180 soi 7(b)(ii) 15 1 360 FT if is an integer their (b)(i) 7(c) Correct ruled triangle with arcs 2 M1 for correct triangle without arcs or for correct arcs and no lines 7(d)(i) 2x + x + 23 + 2x – 13 = 180 oe 1 7(d)(ii) 34 3 M1 for correctly collecting their like terms in form ax + b = k M1 for correctly isolating their x k − b x = a 7(d)(iii) 55 2 M1 for evaluating 2x – 13 and x + 23 with their x

This question in 0580/33 May/June 2020

1 Sean is the manager of a museum. (a) He buys a Chinese pot costing 1200 yuan. The exchange rate is $1 = 6.4 yuan. Work out the cost of this pot in dollars. $ … [1] (b) Sean records the maximum and minimum temperatures, in °C, at the museum. Some of the results for one week are shown in the table. Day Mon Tue Wed Thu Fri Sat Sun Maximum 8 12 15 14 11 7 4 temperature (°C) Minimum - 5 - 2 - 4 - 1 3 temperature (°C) (i) Find the difference between the maximum temperature and the minimum temperature on Wednesday. … °C [1] (ii) The minimum temperature on Saturday was 2 °C higher than the minimum temperature on Monday. Find the minimum temperature on Saturday. … °C [1] (iii) In this week the range of temperatures was 23 °C. Find the minimum temperature on Sunday. … °C [1] (c) These are the opening times for the museum. Monday to Friday 09 00 to 17 00 Saturday and Sunday 10 00 to 16 00 During opening hours the museum has 4 security guards working. Each guard works a maximum of 30 hours each week. Work out the smallest number of guards needed each week. … [4] (d) The entry price to the museum is $18. This price is increased by 28%. Find the increased entry price. $ … [2]

10 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 187.5[0] 1 1(b)(i) 19 1 1(b)(ii) −3 1 1(b)(iii) −8 1 1(c) 7 nfww 4 M1 for 8 × 5 + 6 × 2 oe and M2 for their 52 × 4 ÷ 30 oe or M1 for their 52 × 4 oe or their 52 ÷ 30 oe 1(d) 23.04 2 28 M1 for 18 × (1 + ) oe 100 or B1 for 5.04

This question in 0580/31 Oct/Nov 2020

1 George, Louis and Beatriz have a café. (a) George records the number of each type of meal sold. He draws a pictogram to show his results. All rows are complete except for Salad. Type of meal Number of meals Meat curry Pasta Vegetarian Salad Fish Sandwich Key: = 8 meals (i) Six salads were sold. Complete the pictogram. [1] (ii) Write down which type of meal was sold most. … [1] (iii) Find the number of meals sold altogether. … [1] (b) The café also sells drinks. Drinks Cup of tea $2.20 Cup of coffee $2.80 Bottle of juice $1.50 Bottle of water $1.35 Johan buys 2 cups of tea, 1 bottle of juice and 1 bottle of water. Calculate the change he receives from a $10 note. $ … [2] (c) These are the opening times of the café. Monday to Friday 8 am to 6 pm Saturday 9.30 am to 3 pm Sunday Closed Work out the total number of hours the café is open in one week. … hours [2] (d) One week the café makes a profit of $1027. George, Louis and Beatriz share this profit in the ratio George : Louis : Beatriz = 7 : 4 : 2. Calculate the amount of money they each receive. George $ … Louis $ … Beatriz $ … [3] (e) In 2019 the rent for the café was $7275. In 2020 the rent is $7566. Calculate the percentage increase in the rent. … % [2] (f) George drives 315 km from the café to the airport. The journey takes 3 hours 30 minutes. Calculate his average speed. … km/h [1]

13 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 3 1 of rectangle marked on diagram 4 1(a)(ii) Pasta 1 1(a)(iii) 68 1 1(b) 2.75 2 M1 for [10 –] (2.20 + 2.20 + 1.50 + 1.35) oe 1(c) 55.5 oe 2 M1 for (10 × 5 + 5.5) oe 1(d) 553 3 M2 for 1027 ÷ (7 + 4 + 2) × k or better 316 where k is 7, 4 or 2 158 M1 for 1027 ÷ (7 + 4 + 2) oe 1(e) 4 nfww 2 7566 − 7275 M1 for [× 100] 7275  7566  or  − 1  [× 100]  7275  7566 or × 100 [ −100] 7275 1(f) 90 1

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

7 Prakash buys 45 flowers from a shop. (a) Special offer Buy 3 bunches of flowers for the price of 2 bunches. Each bunch has 5 flowers. The price of one bunch of flowers is $2.68 . Using the special offer, work out how much Prakash pays for the 45 flowers. $ … [3] (b) 15 of the flowers are red. 18 of the flowers are orange. The rest of the flowers are yellow. Write down the ratio of the number of red flowers : orange flowers : yellow flowers. Give your answer in its simplest form. … : … : … [2] (c) Prakash gives the 45 flowers to his family. He gives his grandmother x flowers. He gives his mother 8 more flowers than his grandmother. He gives his cousin 6 fewer flowers than his grandmother. He gives his sister twice as many flowers as he gives his cousin. (i) Use this information to show that 5x - 10 = 45 . [3] (ii) Solve the equation 5x - 10 = 45 . x = … [2] (iii) Find the number of flowers that Prakash gives to his cousin. … [1]

11 marks

Mark scheme: 7(a) 16.08 3 45 2 M2 for × × 2.68 oe 5 3 45 2 45 or M1 for × or × 2.68 oe 5 3 5 7(b) 5 : 6 : 4 2 B1 for 15 : 18 : (45−18−15) or better 7(c)(i) x + x + 8 + x − 6 + 2 ( x − 6 ) = 45 M3 M2 for x + x + 8 + x − 6 + 2 ( x − 6 ) = 45 or M1 for two of x + 8, x − 6, 2 ( x − 6 ) leading to 5 x − 10 = 45 with no errors seen 7(c)(ii) 11 2 M1 for x − 2 = 9 or 5 x = 55 7(c)(iii) 5 1 FT their(c)(ii) −6

This question in 0580/32 Feb/March 2021

8 (a) A baker puts some cakes in the oven at 5.50 pm. The cakes take 20 minutes to bake. 12 11 1 10 2 9 3 8 4 7 5 6 Complete the clock diagram to show the time when the cakes are baked. [1] (b) A recipe uses 550 g of flour to make 8 cakes. Work out the amount of flour needed to make 360 cakes. Give your answer in kilograms. … kg [3] (c) NOT TO Bag A Bag B Bag C SCALE 850 g 950 g 1250 g 55 cents 60 cents 80 cents Work out which bag of flour is the best value. Show all your working. Bag … [3] (d) One cake costs 24 cents to make. The baker sells each cake for 65 cents. Calculate the percentage profit the baker makes on each cake. … % [2] (e) The baker asks some customers if they like lemon cake (L) and if they like chocolate cake (C). The Venn diagram shows the results. L C Kab Bel Yesa Jai Haji Var Rea Nera Esh Ada Chir Taj (i) Complete the statement. n() = … [1] (ii) Work out the fraction of the customers who like lemon cake or chocolate cake but not both. … [1] (iii) Use set notation to complete the statement. {Jai, Nera} = … [1] (iv) What does the Venn diagram show about Taj? … [1]

13 marks

Mark scheme: 8(a) 10 past 6 shown on clock face 1 diagram 8(b) 24.75 3 550 × 360 M2 for oe 8 × 1000 550 × 360 or M1 for oe 8 or B1 for figs 2475 or figs 248 8(c) B 3 M2 for 3 correct divisions shown but either With correct comparisons made of not evaluated to enough accuracy or wrong the 3 bags with suitable accuracy bag selected shown or M1 for 2 correct divisions shown for 2 bags 8(d) 171 or 170.8… 2 65 − 24 M1 for [×100] 24 65 or × 100 [−100] 24 65 or −[×100]1 24 8(e)(i) 12 1 8(e)(ii) 3 1 or equivalent fraction 4 8(e)(iii) L ∩ C 1 8(e)(iv) Correct statement 1

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

5 y 88 66 44 22 x –– 88 –– 66 –– 44 –– 22 0 22 44 66 88 –– 22 –– 44 –– 66 –– 88 k The diagram shows the graph of y = for 1 G x G 8 . x (a) Use the graph to find the value of x when y = 4 . x = … [1] (b) (i) Show that k = 8 . [1] (ii) Calculate the value of y when x = 250 . y = … [1] 8 (c) (i) Complete this table of values for y = . x x - 8 - 4 - 2 - 1 y [2] 8 (ii) On the grid, draw the graph of y = for - 8 G x G - 1. [3] x (d) Write down the equation of each line of symmetry of the graph. … and … [2]

10 marks

Mark scheme: 5(a) 2 1 5(b)(i) k 1 accept use of any correct co-ordinates e.g. 4 = 2 leading to k = 8 5(b)(ii) 0.032 oe 1 5(c)(i) −−−−1, 2, 4, 8 2 B1 for 2 correct 5(c)(ii) Correct curve 3 B2FT for 3 or 4 correct plots B1FT for 1 or 2 correct plots 5(d) y = x oe y = − x oe 2 B1 for each

This question in 0580/31 May/June 2021

1 Alex is building a house. The materials cost 1 12 times the cost of the land. The wages cost 1 14 times the cost of the land. (a) Show that the ratio of costs, in its simplest form, is land : materials : wages = 4 : 6 : 5. [2] (b) The wages cost $47 500. Show that the total cost of land, materials and wages is $142 500. [2] (c) Work out the cost of (i) the land, $ … [2] (ii) the materials. $ … [1] (d) Alex borrows $28 000 for 6 years at a rate of 5.5% per year compound interest. Calculate the amount he repays at the end of the 6 years. Give your answer correct to the nearest dollar. $ … [3] (e) When Alex sells the house, he makes a profit of 27% on the $142 500. Calculate the selling price of the house. $ … [2]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1 1 B1 1 : 1.5 : 1.25 or 1 : 1 :1 2 4 Working shown leading to 4 : 6 : 5 M1 1(b) 47 500 ÷ 5 × (4 + 6 + 5) M2 M1 for 47 500 ÷ 5 1(c)(i) 38 000 2 M1 for 142 500 ÷ 15 [× 4] or 47 500 ÷ 5 [× 4] oe soi 1(c)(ii) 57 000 1 FT for 95 000 – their (c)(i) 1(d) 38 608 cao 3 6  5.5  M1 for 28 000 ×  1 +  oe  100  A1 for 38 607.5… or 38 607.6 or 38 607 or 38 610 or 38 600 B1 for their correctly rounded answer 1(e) 180 975 2  27  M1 for 142 500 ×  1 +  oe  100  or B1 for 38 475

This question in 0580/32 May/June 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

2 (a) In one year, a theatre sells four hundred and ninety-six thousand and fifty tickets. Write this number in figures. … [1] (b) The theatre is used for performances of operas, plays, concerts and musicals. The pie chart shows information about the number of each type of performance. Operas 27° Musicals Plays Concerts (i) Complete these statements. The type of performance shown the most is … . The sector angle for this type of performance is … degrees. [2] (ii) Write down the percentage of performances that are plays. … % [1] (iii) The theatre is used for 320 performances in the year. Calculate the number of opera performances. … [2] (iv) The number of concert performances is in the ratio classical music : popular music = 7 : 5. There are 56 classical music concerts. Find the number of popular music concerts. … [2] (c) The table shows the prices of a child ticket and a senior ticket for a play. Adult Child Senior $ … $15.50 $35 Alex buys tickets for 2 adults, 3 children and 1 senior. He pays a total of $159.50 . Complete the table. [2] (d) Last week the cost of a ticket for a musical was $65. This week the same ticket costs $55.90 . Find the percentage reduction in the cost of this ticket. … % [2]

12 marks

Mark scheme: 2(a) 496 050 1 2(b)(i) Musicals 2 B1 for each 135 2(b)(ii) 25 1 2(b)(iii) 24 2 27 320 M1 for [× 320 ] oe or [× 27 ] oe 360 360 2(b)(iv) 40 2 56 M1 for [×k ] oe where k = 5 or 12 7 2(c) 39 2 M1 for 159.50 −×3 15.5 − 35 or better 2(d) 14 2 65 − 55.9 [ 0 ] M1 for [× 100] oe 65  55.9 [ 0 ]  or  1 −  [× 100 ] oe  65  55.9 [ 0 ] or [100 –] × 100 oe 65

This question in 0580/31 Oct/Nov 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

2 (a) The bar chart shows the number of cars sold by a garage in each of six months. 16 14 12 10Number of cars sold 8 6 4 2 0 Jan Feb Mar Apr May Jun Jul Month (i) In July, 11 cars were sold. Complete the bar chart. [1] (ii) How many more cars were sold in March than in May? … [1] (b) These are the opening times of the garage. Monday to Friday 8.30 am to 5.30 pm Saturday 8.30 am to 1.00 pm Sunday Closed Work out how many hours the garage is open in one week. … h [2] (c) Mohammed works at the garage. He works for 36 hours from Monday to Friday and for 2 hours on Saturday. He is paid $10.50 per hour from Monday to Friday. On Saturday he is paid 1 12 times this rate. Calculate how much Mohammed is paid for this week. $ … [3] (d) Viktor is saving to buy a car. He invests $8000 for 5 years at a rate of 2.4% per year compound interest. Calculate the value of Viktor’s investment at the end of the 5 years. Give your answer correct to the nearest dollar. $ … [3] (e) At the garage, Pierre, Luigi and Freda sell cars. They share a bonus of $12 000 in the ratio Pierre : Luigi : Freda = 8 : 4 : 3. Calculate the amount they each receive. Pierre $ … Luigi $ … Freda $ … [3]

13 marks

Mark scheme: 2(a)(i) Bar at height 11 1 2(a)(ii) 9 1 2(b) 49.5 2 M1 for 5 × 9 + 4.5 oe 2(c) 409.5[0] cao 3 M2 for 36 × 10.5 + 10.5 × 1.5 × 2 oe or M1 for 36 × 10.5 or 10.5 × 1.5 × 2 or 36 + 1.5 × 2 oe 2(d) 9007 cao nfww 3 B2 for 9007.[...] 2.4 or M1 for 8000 × (1 + )5 oe 100 If M0 or M1 scored, SC1 for their decimal answer correctly rounded to the nearest dollar 2(e) 6400 3 B2 for one correct answer in the correct 3200 place 2400 or M1 for 12 000 ÷ (8+4+3) [× k] where k is 8, 4, 3 or 1

This question in 0580/33 Oct/Nov 2021

7 (a) 1 mile = 1.609344 kilometres Change 6 miles into metres. Give your answer correct to the nearest metre. … m [3] (b) (i) The bearing of a boat from a harbour is 322°. Work out the bearing of the harbour from the boat. … [2] (ii) The boat is 12 km from the harbour. At 2.30 pm the boat starts to sail to the harbour. The speed of the boat is 5 km/h. Work out the time the boat arrives at the harbour. … [3] (c) The scale drawing shows the positions of Shakti’s house, S, and Mairi’s house, M, on a map. The scale is 1 cm represents 4 km. North S North M Scale: 1 cm to 4 km (i) Measure the bearing of M from S. … [1] (ii) North S Scale: 1 cm to 5 km This scale drawing shows another map with Shakti’s house, S, marked on it. The scale of this map is 1 cm represents 5 km. Mark the position of Mairi’s house, M, on this map. [4]

13 marks

Mark scheme: 7(a) 9656 cao 3 M2 for 6 × 1.609344 × 1000 or M1 for 6 × 1.609344 or B1 for final answer figs 9654 to 9660 If 0 scored, SC1 for their decimal answer correctly rounded to nearest integer 7(b)(i) 142 2 M1 for 322 −180 oe or a clear diagram with both 322 or 38 marked and the reverse bearing to be found 7(b)(ii) 4.54 pm or 16 54 3 12 M1 for soi 5 A1 for 2 h 24 [mins] 7(c)(i) 107 1 7(c)(ii) The position of M correctly marked 4 B1 for SM = 9[cm] soi on the diagram  1  M1 for their SM × 4 ×    5  B1 for 7.2[cm] soi or for bearing of M drawn at 107°

This question in 0580/32 Feb/March 2022

2 (a) Write down the number of sides of a hexagon. … [1] (b) B A C In triangle ABC, AB = AC. (i) Write down the mathematical name for this type of triangle. … [1] (ii) Measure angle CAB. Angle CAB = … [1] (iii) Write down the mathematical name for angle CAB. … [1] (c) Show that the interior angle of a regular pentagon is 108°. [2] (d) B C NOT TO SCALE D A 248° ABCD is a parallelogram. The reflex angle at D is 248°. Find angle DCB. Angle DCB = … [2] (e) The angles of a triangle are in the ratio 3 : 5 : 7. Find the size of the largest angle in this triangle. … [3]

11 marks

Mark scheme: 2(a) 6 1 2(b)(i) Isosceles 1 2(b)(ii) 124 1 2(b)(iii) Obtuse 1 2(c) 360 M2 360 180 − [= 108] M1 for or (5 – 2)  180 5 5 (5  2)  180 or [= 108 ] 5 2(d) 68 2 360 2 (360  248) M1 for 248 – 180 or 2 or 180 – (360 – 248) or B1 for ADC = 112 2(e) 84 3 180 M2 for  j or better 3  5  7 where j = 1, 3, 5 or 7 7 or B1 for 180 or k 15

This question in 0580/31 May/June 2022

6 (a) A football team has w wins and d draws. The team scores 3 points for each win and 1 point for each draw. Write an expression, in terms of w and d, for the total number of points scored by the team. … [2] (b) Athletic, Rovers and United are three football teams. Athletic have a point score of x. Rovers have 12 points more than Athletic’s point score. United have 3 points fewer than twice Athletic’s point score. The total point score of all three teams is 121. Use this information to write down an equation in terms of x. Solve your equation to work out the point score for each team. Athletic … points Rovers … points United … points [5] (c) Simplify. (i) 4a - 3b + 5a + 6b … [2] (ii) 6 ( 2x + 1) - 5 ( x - 2) … [2] (d) Solve the simultaneous equations. You must show all your working. 3x + 5y = 11 2x - 3y = 20 x = … y = … [4]

15 marks

Mark scheme: 6(a) 3w + [1]d final answer 2 B1 for 3w or [1]d in final answer 6(b) 28 5 M2 for x + x + 12 + 2x – 3 = 121 or better 40 or B1 for x + 12 or 2x – 3 or 4x + 9 53 M1 for 4x + 9 = 121 or better or for simplifying their equation to ax + b = 121or better M1 for solving their linear equation if 0 scored then SC1 for 3 numbers adding to 121 6(c)(i) 9a + 3b final answer 2 B1 for 9a or 3b in final answer or 9a + 3b seen and spoilt 6(c)(ii) 7x + 16 final answer 2 B1 for 12x + 6 or −5x + 10 or 5x – 10 or for 7x or 16 in the final answer 6(d) Correctly equating one set of coefficients M1 correct method to eliminate one variable M1 [x =] 7 A1 [y =] −2 A1 If M0 scored, SC1 for 2 values satisfying one of the original equations or no working shown but 2 correct answers given

This question in 0580/31 May/June 2022

1 Antonio has a shop near the beach. (a) (i) He makes a tally of the number of ice creams he sells on Friday. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Work out the number of ice creams he sells on Friday. … [1] (ii) 15 of the ice creams he sells on Friday are vanilla. Work out the fraction of ice creams he sells on Friday that are vanilla. Give your answer in its simplest form. … [1] (iii) He buys tubs of ice cream for his shop in the ratio vanilla : chocolate = 11 : 7. He buys 28 tubs of chocolate ice cream. Work out how many tubs of vanilla ice cream he buys. … [2] (b) Antonio records the number of chairs his shop hires out on each day for a week. 123 98 116 45 67 165 156 (i) Work out the range. … [1] (ii) Find the median. … [2] (iii) Calculate the mean. … [2] (c) (i) Antonio buys beach balls for $2.50 each and sells them for $4.20 each. Work out the percentage profit he makes on each beach ball. … % [2] (ii) A beach ball is a sphere with radius 15 cm. Calculate the volume of the beach ball. Give the units of your answer. 4 3 [The volume, V, of a sphere with radius r is V = rr .] 3 … … [3] (d) The shop sells sun cream in bottles A, B and C. NOT TO SCALE Bottle A Bottle B Bottle C 160 ml 200 ml 240 ml $3.75 $4.75 $6.50 Work out which bottle is the best value. You must show all your working. Bottle … [3]

17 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 48 1 1(a)(ii) 5 1 FT their (a)(i) provided simplification required and cao answer given in its simplest form 16 1(a)(iii) 44 nfww 2 28 M1 for  11 oe 7 1(b)(i) 120 1 1(b)(ii) 116 2 M1 for at least first four or last four correctly ordered 1(b)(iii) 110 2 123  98  116  45  67  165  156 M1 for oe 7 1(c)(i) 68 2 4.2  2.5 M1 for  100  oe 2.5 4.2 or  100   100  oe 2.5  4.2  oe or   1   100   2.5  1(c)(ii) 14 100 or 14 140 2 4 3 M1 for  π  15 oe or 14 137 to 14 139 3 cm3 1 1(d) A 3 M2 for 3 correct comparable values, or for a correct With correct comparisons method to compare 3 bottles shown but not evaluated to made of the 3 bottles with enough accuracy suitable accuracy shown or M1 for 2 correct comparable values or for a correct method to compare 3 bottles but not evaluated

This question in 0580/32 May/June 2022

3 Mr Zhang, his wife and three children go on a holiday from Shanghai to Auckland. (a) The flight for an adult costs $630. 5 The cost for a child is of the adult cost. 8 Show that the total cost of the flight for the family is $2441, correct to the nearest dollar. [3] (b) The plane leaves Shanghai at 20 05 local time on 13th November. The plane stops for 2 hours 30 minutes in Sydney. The plane lands in Auckland at 17 25 local time on 14th November. The local time in Auckland is 5 hours ahead of the local time in Shanghai. (i) Work out how long the plane is flying, in hours and minutes. … h … min [3] (ii) Write your answer to part (b)(i) in hours, correct to 3 decimal places. … h [1] (iii) The flight distance from Shanghai to Sydney is 7882 km. The flight distance from Sydney to Auckland is 2156 km. Find the total distance the plane flies. … km [1] (iv) Calculate the average speed of the plane when it is flying. … km/h [2] (c) The holiday expenses are in the ratio hotel : car hire : food = 8 : 5 : 6. The cost of the hotel is $2400. Show that the total of the holiday expenses is $5700. [2]

12 marks

Mark scheme: 3(a) 5 M2 5 2 × 630 + 3 ×  630 M1 for [3 ×]  630 8 8 2441.25 A1 3(b)(i) 13 [h] 50 [min] 3 B2 for 16[h] 20[min] or 18[h] 50[min] as final answer or 13[h] 50[min] not as final answer or 16[h] 20[min] with – 2[h] 30[min] attempted or 18[h] 50[min] with – 5[h] attempted or B1 for 21[h] 20[min] seen or 16[h] 20[min] or 18[h]50 [min] seen or 23[h] 50[min] as final answer or an attempt made to find a time of flight 3(b)(ii) 13.833 cao 1 FT their time correct to 3 decimal places 3(b)(iii) 10 038 1 3(b)(iv) 726 or 725.6 to 725.7 2 FT their (b)(iii) ÷ their (b)(ii) correctly evaluated M1 for their (b)(iii) ÷ their (b)(ii) 3(c) 2400 ÷ 8 × ( 8 + 5 + 6 ) [=5700] M2 M1 for 2400 ÷ 8

This question in 0580/33 May/June 2022

5 (a) Work out the number of days in seven weeks. … days [1] (b) The summit of Mount Everest is 8848 metres above sea level. Ayding Lake is 154 metres below sea level. Work out the difference in height between these places. … m [1] (c) Find two integers that have a sum of - 12 and a product of 32. … and … [1] 3 (d) Write as 8 (i) a decimal, … [1] (ii) a percentage. … % [1] (e) Write down the reciprocal of 1. 9 … [1] (f) Find the value of (i) 45, … [1] (ii) 3 512 . … [1] (g) (i) Write 587 000 in standard form. … [1] (ii) Calculate 4.9 # 10 - 3 + 8.1 # 10 - 4 . Give your answer in standard form. … [1] (h) The height, h metres, of a fence post is 2.43 m, correct to the nearest centimetre. Complete the statement about the value of h. … G h 1 … [2]

12 marks

Mark scheme: 5(a) 49 1 5(b) 9002 1 5(c) −8 and −4 1 5(d)(i) [0].375 1 5(d)(ii) 37.5 1 5(e) 9 1 5(f)(i) 1024 1 5(f)(ii) 8 1 5(g)(i) 5.87 × 105 cao 1 5(g)(ii) 5.71 × 10−3 cao 1 5(h) 2.425 2.435 2 B1 for each If zero scored, SC1 for 242.5 ⩽ h < 243.5 or for both correct but reversed

This question in 0580/33 May/June 2022

9 Ahmed owns a company. (a) (i) Each year he earns $56 000 plus 3% of the year’s profit. Calculate the amount he earns in a year when the profit is $320 600. $ … [2] (ii) In the following year the profit is $347 851. Calculate the percentage increase in the profit. … % [2] (b) Ahmed employs three people, Budi, Citra and Dian. Budi earns $17 000, Citra earns $13 600 and Dian earns $6800. Find the ratio of their earnings in its simplest form. Budi : Citra : Dian = … : … : … [2] (c) Ahmed buys materials from China costing 7560 yuan. Work out the cost of the materials in dollars when the exchange rate is $1 = 7.06 yuan. Give your answer correct to the nearest dollar. $ … [2] (d) Ahmed borrows $8 000 for 3 years at a rate of 5% per year compound interest. Calculate the amount of interest he will pay at the end of the 3 years. $ … [3]

11 marks

Mark scheme: 9(a)(i) 65 618 2 3 M1 for × 320 600 oe 100 9(a)(ii) 8.5 2 347851  320600[ 100] M1 for 320600 347851 or 1[ 100] 320600 347851 or  100 [− 100] 320600 9(b) 5 : 4 : 2 2 B1 for any correct partial simplification of the ratio 9(c) 1071 cao 2 M1 for 7560 ÷ 7.06 If zero scored, SC1 for their decimal answer correctly rounded to the nearest dollar 9(d) 1261 cao 3 B2 for 9261 as final answer or  5  3 M2 for 8000  1   8000 oe    100  or  5  3 M1 for 8000  1  oe    100 

This question in 0580/33 May/June 2022

1 Helga buys some items to do some knitting. (a) Complete Helga’s bill from one shop. Item Cost ($) 2 pairs of knitting needles at $4.95 a pair 6 buttons at $0.65 each 1 knitting pattern at $3.60 3.60 Total [3] (b) Helga also buys 8 balls of wool from another shop. Each ball costs $3.12 . Helga pays with a $50 note. Work out the amount of change she receives. $ … [2] (c) Helga knits some squares. Each square is either white, pink or blue. The number of squares are in the ratio white : pink : blue = 5 : 3 : 2. 30 squares are blue. Show that Helga knits 150 squares. [2] (d) Helga uses some of the squares to make a rectangular blanket. The blanket is 6 squares long and 4 squares wide. (i) Calculate the percentage of the 150 squares she uses to make this blanket. … % [2] (ii) Each square has side length 15 cm. Work out the perimeter of this blanket. Give your answer in metres. … m [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 9.9[0] 2 B1 for each 3.9[0] 17.4[0] 1 FT their table 1(b) 25.04 2 M1 for 50 – (8  3.12) or B1 for 24.96 1(c) 30 2 30 5 + 3 + 2  (5 + 3 + 2) M1 for or 2 2 2 1(d)(i) 16 2 M1 for 6  4 soi by 24 1(d)(ii) 3 3 M2 for 2(6  15 + 4  15) oe or 2(6  0.15 + 4  0.15) oe or M1 for 6  15 or 4  15 oe or 6  0.15 or 4  0.15 oe or 2  (6 + 4) oe

This question in 0580/31 Oct/Nov 2022

3 Miguel works in an office. (a) It takes Miguel 40 minutes to drive to work. (i) He leaves home at 07 45. What time does he arrive at work? … [1] (ii) Miguel drives to work at an average speed of 57 km/h. Show that he drives 38 km. [2] (b) White paper costs w cents per sheet and pink paper costs p cents per sheet. Miguel uses 56 sheets of white paper and 21 sheets of pink paper. Write down an expression, in terms of w and p, for the total cost, in cents, of the paper he uses. … cents [2] (c) Miguel has a closed box of pens. The box is in the shape of a cuboid measuring 20 cm by 12 cm by 7 cm. Calculate the surface area of the box. … cm2 [3] (d) Miguel records the length of time of each telephone call he receives, correct to the nearest minute. 7 15 6 28 8 21 17 19 20 12 11 19 12 3 20 23 14 9 4 18 (i) Complete the frequency table. You may use the tally column to help you. Time (minutes) Tally Frequency 0 - 5 6 - 10 11 - 15 16 - 20 21 - 25 26 - 30 [2] (ii) Draw a bar chart to show this information. Complete the scale on the frequency axis. Frequency 0 0 – 5 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30 Time (minutes) [3] (iii) Use the bar chart to write down the modal group. … — … [1]

14 marks

Mark scheme: 3(a)(i) 08 25 1 3(a)(ii) 40 2 40 57  [= 38] M1 for or 57  40 60 60 3(b) 56w + 21p final answer 2 B1 for 56w or 21p in final answer or for 56w + 21p seen then spoilt 3(c) 928 3 M2 for [2 ](20  12 + 20  7 + 12  7) oe or M1 for (20  12) or (20  7) or (12  7) 3(d)(i) 2 4 5 6 2 1 2 B1 for 4 or 5 correct frequencies If 0 scored SC1 for correct tallies if frequency column blank or all frequencies correct but not in the frequency column 3(d)(ii) Suitable scales on y-axis 1 Bars at correct height 1 FT their frequency Bars equal width 1 3(d)(iii) 16 – 20 1 FT their bar chart

This question in 0580/31 Oct/Nov 2022

4 Mr and Mrs Perez and their 3 children go on holiday to Tokyo. (a) The holiday costs $3800 for an adult and $2400 for a child. 8% tax is then added to the cost of the holiday. Find the total cost of the holiday, including tax, for the Perez family. $ … [4] (b) The plane takes 11 hours 40 minutes to fly from Los Angeles to Tokyo. The plane leaves on Wednesday at 10 35 local time. The local time in Tokyo is 17 hours ahead of the local time in Los Angeles. (i) Find the day and local time in Tokyo when the plane arrives. Day … Time … [3] (ii) The distance the plane flies is 8820 km. Calculate the average speed of the plane. … km/h [2] (c) The diagram shows a conversion graph between dollars and Japanese yen. 4500 4000 3500 3000 2500 Yen 2000 1500 1000 500 0 0 5 10 15 20 25 30 35 40 Dollars A watch costs $100. Find the cost of this watch in yen. … yen [2] (d) The family go to a restaurant. The total cost of the food and drinks is $154. The ratio cost of food : cost of drinks = 21 : 4. Work out the cost of drinks. $ … [2]

13 marks

Mark scheme: 4(a) 15 984 cao 4 8 M3 for (2×3800 + 3×2400) × (1+ ) oe 100 8 or M2 for [2×]3800 × (1+ ) oe 100 8 or [3×]2400 × (1+ ) oe 100 8 or (2 × 3800 + 3 × 2400) × oe 100 or M1 for 2 × 3800 + 3 × 2400 oe 8 or [k×]3800 × oe 100 8 or [k×]2400 × oe 100 where k is any integer 8 If 0 scored, SC1 for j × (1+ ) 100 where j is any value 4(b)(i) Thursday and 15 15 or 3 15 pm 3 B1 for Thursday as final answer B2 for 15 15 as final answer or B1 for 22 15, [0]3 35, 28h 40, 39 15 If 0 scored, SC1 for 10 35 + 11 40 + 17 4(b)(ii) 756 2 M1 for 8820 ÷ their time 4(c) 11 000 or 10 875 to 11 125 2 B1 for 10 000 to 12 000 as answer or M1 for 110 × 100 or for a valid method e.g. look up ‘40’ × 2.5 4(d) 24.64 cao 2 154 M1 for × k where k is 1, 4 or 21 oe 21 + 4

This question in 0580/32 Oct/Nov 2022

3 (a) A recipe for making 20 biscuits uses 150 g flour, 125 g butter and 50 g sugar. (i) Write the ratio flour : butter : sugar in its simplest form. flour : butter : sugar = … : … : … [2] (ii) Work out the amount of flour, butter and sugar needed to make 50 biscuits. flour … g butter … g sugar … g [3] (b) (i) A recipe for making one loaf of bread uses 600 g of flour. A sack of flour contains 16 kg of flour. Complete the statements. One sack of flour makes a maximum of … loaves of bread. The amount of flour left over is … g. [4] (ii) The amount of flour in a sack decreases from 16 kg to 15 kg. Work out the percentage decrease of flour in the sack. … % [2]

11 marks

Mark scheme: 3(a)(i) 6 : 5 : 2 2 B1 for 150 : 125 : 50 or any correct ratio 6k : 5k : 2k 3(a)(ii) 375, 312.5, 125 3 B2 for one correct in the correct place 50 or M1 for k oe where k = 1, 20 150, 125 or 50 3(b)(i) 26, 400 4 B1 for 16 000 or 0.6 seen figs16 M1 for figs6 A1 for 26 If B0, M1, A0 scored, figs16 SC1 for their seen and figs6 rounded down to nearest positive integer 3(b)(ii) 6.25 2 16 − 15 M1 for  100  oe 16 15 or (1 − )[×100] oe 16 15 or [ 100−]16 ×100 oe

This question in 0580/32 Feb/March 2023

7 The scale drawing shows the positions of three towns, R, S and T, on a map. RS and ST are straight roads between the towns. The scale is 1 centimetre represents 8 kilometres. North North T R North S Scale: 1 cm to 8 km (a) Work out the actual distance between R and S. … km [2] (b) Another town, V, is on a bearing of 163° from R and on a bearing of 215° from T. Mark the position of V on the map. [2] (c) A man cycles at a constant speed of 24 km/h along the straight road from S to T. After 1 hour and 50 minutes he stops at a café, C. Mark the position of C on the map. You must show all your working. [3] (d) A hotel, H, is on a bearing of 321° from R. Work out the bearing of R from H. … [2] (e) Write the scale 1 cm to 8 km in the form 1 : n. 1 : … [1]

10 marks

Mark scheme: 7(a) 48 2 B1 for 6 cm or M1 for their 6  8 7(b) The position of V correctly marked on the 2 B1 for V on bearing 163° from R diagram B1 for V on bearing 215° from T 7(c) The position of C correctly marked on the 3 B2 for 5.5 seen diagram with correct working seen 24 their time or M2 for oe 8 or M1 for 24 their time oe If 0 scored, SC1 for C correctly marked on diagram with no working 7(d) 141 2 M1 for 321 −180 or a clear diagram with both 321 marked and the reverse bearing to be found shown 7(e) 800 000 1

This question in 0580/32 Feb/March 2023

5 Antonio buys a restaurant for $240 000. 5 This is of the amount he has available to spend. 8 (a) Show that he has $144 000 left after buying the restaurant. [2] (b) Some of the $144 000 is spent on expenses. Expenses are wages, equipment and supplies in the ratio wages : equipment : supplies = 9 : 5 : 8. The amount spent on wages is $45 000. (i) Find the amount spent on (a) equipment $ … [2] (b) supplies. $ … [1] (ii) Work out the amount Antonio has left now. $ … [2] (c) Antonio borrows $25 400 for 6 years at a rate of 5% per year simple interest. Calculate the total amount he repays at the end of the 6 years. $ … [3] (d) In one week, the number of customers in the restaurant was 560. In the next week, the number of customers in the restaurant was 656. Calculate the percentage increase. … % [2]

12 marks

Mark scheme: 5(a) 240 000 ÷ 5 × 8 – 240 000 M2 M1 for 240 000 ÷ 5 × 8 3 or 240 000 × 5 5(b)(i)(a) 25 000 2 M1 for 45 000 ÷ 9 oe 5(b)(i)(b) 40 000 1 5(b)(ii) 34 000 2 FT 99 000 – (their 25 000 + their 40 000) M1 for 144 000 – 45 000 – (their 25 000 + their 40 000) oe 5(c) 33 020 3 B2 for 7620 or M2 for 25400 5 6 25 400 + oe 100 25400 5 6 or M1 for oe 100 5(d) 17.1 or 17.1[4…] 2 656 560 M1 for  100  oe 560  656  100  oe or   100     560   656  100  oe or  1    560 

This question in 0580/31 May/June 2023

3 (a) 50 Australian dollars = 540 South African rands 600 550 500 450 400 350 South African 300 rand 250 200 150 100 50 0 0 5 10 15 20 25 30 35 40 45 50 Australian dollar (i) On the grid, draw a conversion graph between Australian dollars and South African rands. [2] (ii) A watch costs 1350 South African rands. Find the cost of this watch in Australian dollars. … Australian dollars [2] (b) (i) A plane leaves Sydney at 21 48 local time to fly to Johannesburg. The flight takes 14 hours 15 minutes. The local time in Sydney is 8 hours ahead of the local time in Johannesburg. Find the local time in Johannesburg when the plane arrives. … [3] (ii) On the plane there are 315 people. The ratio of children : adults = 7 : 8. Work out the number of adults on the plane. … [2] (iii) Another plane has 420 seats. 90% of the seats are occupied. Work out the number of seats that are occupied. … [2]

11 marks

Mark scheme: 3(a)(i) Ruled line joining (0, 0) to 2 B1 for plotting point (50, 540) or for a ruled (50, 540) line from (0, 0) to their point (50, 520 – 560) 3(a)(ii) 125 or 123 to 127 2 B1 for 108 to 135 as answer 50 or M1 for 1350  oe 540 or for a valid method e.g. look up ‘50’ × 27 3(b)(i) 04 03 3 B2 for 28 03 or B1 for 36 03 or 12 03[pm] or 6h 15(m) or 13 48 or 1 48pm or 20 03 or 8 03pm seen or M1 for their arrival time – 8 hours 3(b)(ii) 168 2 315 M1 for × k where k = 1,7 or 8 oe 7  8 3(b)(iii) 378 2 90 M1 for 420 × oe 100

This question in 0580/32 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

9 (a) Pure gold costs $42 per gram. The fraction of pure gold in an object is measured in carats. 1 One carat means of the mass of an object is pure gold. 24 Henry buys a 9-carat gold bracelet weighing 16 g. The price of the bracelet is $204. Is the price of the bracelet more or less than the cost of the pure gold in it? You must show your working. [4] (b) A clock made of metals has a mass of 1080 g. The mass of each metal in the clock is in the ratio copper : zinc : other metals = 21 : 14 : 1. Calculate the mass of copper in this clock. … g [2] (c) There are 110 people in a group. G = { people who own gold jewellery } S = { people who own silver jewellery } 18 people own both gold jewellery and silver jewellery. 46 people own gold jewellery. 11 people own no gold jewellery and no silver jewellery. G S (i) Complete the Venn diagram. [2] (ii) Write down n ( G + S ) . … [1] (iii) One of the 110 people is chosen at random. Write down the probability that this person owns gold jewellery but not silver jewellery. … [1] (d) E F Use set notation to describe the shaded region. … [1]

11 marks

Mark scheme: 9(a) Less 4 1 M3 for  9  16  42 oe with working leading to 252 24 or M2 for three of these multiplied or M1 for any two of these multiplied 9(b) 630 2 1080 M1 for [ k] oe 21 + 14 + 1 where k =1,14 or 21 oe 9(c)(i) 2 B1 for two or three in the correct places 9(c)(ii) 18 1 FT their diagram 9(c)(iii) 28 1 FT their 28 from their diagram oe 110 9(d) E F cao 1

This question in 0580/31 Oct/Nov 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

7 Elize, Lily and Marco start a business. (a) Elize invests $5000. Lily invests $8000. Marco invests $3000. After one year they make a profit of $40 000. They share this profit in the ratio of their investments. Work out how much they each receive. Elize $ … Lily $ … Marco $ … [3] (b) (i) Lily buys 20 rolls of ribbon. 8 are red, 6 are blue, 4 are yellow and 2 are pink. A roll of ribbon is chosen at random. On the probability scale, draw an arrow ( ) to show the probability that this roll is (a) yellow 0 0.5 1 [1] (b) not red 0 0.5 1 [1] (c) green. 0 0.5 1 [1] (ii) The length, l m, of a roll of ribbon is 120 m, correct to the nearest metre. Complete this statement about the value of l. … G l 1 … [2] (c) Elize buys some picture frames. The frames cost $5.80 each in New York and 4.50 euros each in Paris. The exchange rate is 1 euro = $1.37 . Calculate the difference in the cost in euros. Give your answer correct to 2 decimal places. … euros [3] (d) Elize buys a framed picture. (i) 18 cm NOT TO SCALE 18 cm The picture is a circle with diameter 18 cm. The frame is a square of side length 18 cm. Calculate the shaded area. … cm2 [3] (ii) Elize buys the framed picture for $12.50 . She sells the framed picture for $20.25 . Calculate the percentage profit. … % [2]

16 marks

Mark scheme: 7(a) 12 500, 20 000, 7500 3 B2 for 12 500 or 7500 in correct place 40000 or M1 for  k where k = 1, 5, 8 or 3 5 + 8 + 3 7(b)(i)(a) Arrow at 0.2 1 7(b)(i)(b) Arrow at 0.6 1 7(b)(i)(c) Arrow at 0 1 7(b)(ii) 119.5 120.5 2 B1 for each or both correct but reversed 7(c) 0.27 3 B2 for 0.266… or 5.80 5.80 M2 for 4.50 – oe or −4.50 oe 1.37 1.37 5.80 or M1 for soi by 4.23… 1.37 If 0 or 1 scored, SC1 for correct rounding to 2dp from their more accurate answer 7(d)(i) 69.5 or 69.49 to 69.531 3 M2 for 182 – 92  π oe or M1 for 92  π oe 7(d)(ii) 62 2 20.25 − 12.50 M1 for [ 100] oe 12.50 20.25 or  100 [– 100] oe 12.50  20.25  or  –1  [ 100] oe  12.50 

This question in 0580/32 Oct/Nov 2023

13 (a) Aneel has 80 tea bags, kg of sugar and 1 litre of milk. 2 To make a cup of tea he uses: • 1 tea bag • 8 grams of sugar • 40 millilitres of milk. (i) In the morning, Aneel makes 15 cups of tea. Work out (a) the fraction of the tea bags he uses, in its simplest form … [2] (b) the mass of sugar, in grams, he has left. … g [2] (ii) During the day, Aneel uses all of the milk to make cups of tea. Work out the total number of cups of tea Aneel makes. … [1] (b) Bobby, Carl and Davood share $6875 in the ratio Bobby : Carl : Davood = 6 : 8 : 11. Calculate the amount of money they each receive. Bobby $ … Carl $ … Davood $ … [3] 3 2 # 3 4(c) (i) Write 6 as a power of 3. 3 … [1] (ii) Write the value of 2 - 4 as a decimal. … [1] (d) Simplify. (i) ( b5 ) 3 … [1] 4 - 2 (ii) b m l … [1] (e) 30 = 2 # 3 # 5 84 = 2 2 # 3 # 7 Use this information to find the lowest common multiple (LCM) of 30 and 84. … [2] 2 5(f) 7 16 23 9 4 Put a ring around the irrational number in this list. [1]

15 marks

Mark scheme: 3(a)(i)(a) 3 2 15 cao M1 for oe 16 80 3(a)(i)(b) 380 2 B1 for 500[g] or 120[g] 3(a)(ii) 25 1 3(b) 1650 3 B2 for one correct answer in the correct 2200 place 3025 6875 or M1 for k oe where k is 1, 6 + 8 + 11 6, 8 or 11 3(c)(i) 30 final answer 1 3(c)(ii) 0.0625 cao 1 3(d)(i) b15 1 3(d)(ii) m 2 1 16 3(e) 420 2 B1 for 22 × 3 × 5 × 7 or 2 × 2 × 3 × 5 × 7 or for 2,2,3,5,7 as final answer 3(f) √7 1

This question in 0580/33 Oct/Nov 2023

4 (a) A company makes glass using silica, soda, lime and magnesia. The table gives information about the proportions used. Percentage of total mass Pie chart sector angle Silica 75 270° Soda 15 Lime and magnesia 10 (i) Complete the table. [2] (ii) Complete the pie chart to show this information. 270° Silica [1] (iii) The masses of lime and magnesia used are in the ratio lime : magnesia = 3 : 2. Find the percentage of the total mass of glass that is magnesia. … % [1] (iv) The company uses 8.25 kg of soda to make some glass. Work out how many kilograms of silica they use. … kg [2] (b) The company uses the formula M = 2 .5 # A # T to find the mass of a sheet of glass. M is the mass in kilograms. A is the area in square metres. T is the thickness in millimetres. Use the formula to calculate the mass of a rectangular sheet of glass that is 1.9 m long, 0.6 m wide and 8 mm thick. … kg [2] (c) In one year, 130 000 000 tonnes of glass were produced worldwide. Write this number in standard form. … [1] (d) The company sets targets to recycle its waste materials. The bar chart shows the target rate and the actual rate for some of its recycling. Key: Metal Target rate Actual rate Paper & cardboard Glass Plastic Wood 0 10 20 30 40 50 60 70 80 90 100 Percentage recycling rate (i) The target rate for recycling glass was 55%. The actual rate for recycling glass was 70%. Complete the bar chart. [2] (ii) Which materials did the company recycle at more than double their target rate? … [2]

13 marks

Mark scheme: 4(a)(i) 54 2 B1 for each 36 360 270 If 0 scored M1 for or or 3.6 100 75 4(a)(ii) Correct pie chart 1 FT dep on their 54and their 36 adding to 90 4(a)(iii) 4 1 4(a)(iv) 41.25 2 8.25  75 M1 for oe 15 4(b) 22.8 2 M1 for 1.9 × 0.6 [× 2.5] [× 8] oe soi or B1 for figs 228 as answer 4(c) 1.3 × 108 1 4(d)(i) Correct bars drawn 2 B1 for shaded bar 55% or unshaded bar 70% or both bars of correct length 4(d)(ii) Plastic 2 B1 for 1 correct and none incorrect or 2 Wood correct and 1 incorrect

This question in 0580/33 Oct/Nov 2023

4 (a) A shop sells 58 televisions in one week. The bar chart shows the number of televisions that the shop sells on five of the days. 16 14 12 10 Number of 8 televisions 6 4 2 0 Monday Tuesday Wednesday Thursday Friday Saturday Sunday (i) Write down the number of televisions that the shop sells on Monday. … [1] (ii) Find the fraction of the televisions that the shop sells on Sunday. … [1] (iii) The number of televisions that the shop sells on the other two days is in the ratio Wednesday : Friday = 2 : 3. Complete the bar chart. [4] (iv) Write down the mode. … [1] (b) A television has a price of $550. This price is reduced by 4%. Calculate the new price of this television. $ … [2] (c) The scatter diagram shows the prices of different sized televisions. Price Television size Write down the type of correlation shown in the scatter diagram. … [1] (d) Hemang buys two televisions. The probability that a television is faulty is 0.02 . 1st television 2nd television faulty … faulty 0.02 not faulty … faulty … … not faulty not faulty … (i) Complete the tree diagram. [2] (ii) Find the probability that Hemang buys two faulty televisions. … [2] (iii) The shop sells 4150 televisions in one year. Calculate the expected number of faulty televisions. … [1]

15 marks

Mark scheme: 4(a)(i) 3 1 4(a)(ii) 11 1 cao 58 4(a)(iii) Completely correct bar chart 4 B3 for a bar height 8 drawn for Wednesday or a bar height 12 drawn for Friday. or 58 −−3 4 − 4 − 16 − 11 M2 for  k , 2 + 3 k = 1,2 or 3 or M1 for 58 −−−−3 4 4 16 − 11 oe If 0 scored SC1 for 2 bars drawn correctly from their identified values in working 4(a)(iv) Saturday 1 4(b) 528 2  4  M1 for 550   1 −  oe  100  or B1 for 22 4(c) Positive 1 4(d)(i) 0.02 2 B1 for 0.98 correctly placed once on tree 0.98 or for 0.02 correctly placed twice on tree. 0.98 0.02 0.98 oe 4(d)(ii) 0.0004 oe 2 M1 for 0.02 × 0.02 4(d)(iii) 83 1

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) Chen asks some people if they prefer a beach, cruise, lake or mountain holiday. The pie chart shows the results. Mountain Beach 120° 135° 75° 30° Lake Cruise (i) Find the fraction of people who prefer a mountain holiday. Give your answer in its simplest form. … [2] (ii) Find the percentage of people who prefer a beach holiday. … % [1] (iii) Find the ratio of people who prefer each type of holiday in the form beach : cruise : lake : mountain. Give your answer in its simplest form. … : … : … : … [2] (iv) One person is chosen at random. Find the probability that this person prefers a cruise or a lake holiday. … [2] (v) 675 people prefer a beach holiday. Show that the total number of people Chen asks is 1800. [1] (vi) (a) Complete the table. Type of holiday Pie chart sector angle Frequency Beach 135° 675 Cruise 30° 150 Lake 75° Mountain 120° [2] (b) Complete the bar chart, including the scale on the frequency axis. Frequency 0 Beach Cruise Lake Mountain [3] (b) Mr Gibb pays $2208 for a holiday. Mr Shah pays 2050 euros for the same holiday. The exchange rate is 1 euro = $1 .15 . Work out how much more, in euros, Mr Shah pays for the holiday than Mr Gibb. … euros [2]

15 marks

Mark scheme: 2(a)(i) 1 2 120 cao M1 for oe 3 360 2(a)(ii) 37.5 1 2(a)(iii) 9 : 2 : 5 : 8 cao 2 B1 for 135 : 30 : 75 : 120 or better 2(a)(iv) 105 2 75  30 oe M1 for oe 360 360 2(a)(v) 675  360 1   1800  135 2(a)(vi)(a) 375 2 B1 for each 600 2(a)(vi)(b) A correct bar chart drawn with 3 B1 for an appropriate linear scale written linear scale labelled. with at least 2 more numbers. AND B2FT their table for 4 bars drawn correctly or B1FT their table for two or three bars drawn correctly 2(b) 130 2 2208 2050  1.15  2208 M1 for oe or oe 1.15 1.15

This question in 0580/31 May/June 2024

7 (a) The scale drawing shows the position of a castle, C. The scale is 1 centimetre represents 2 kilometres. North C Scale: 1 cm to 2 km Micah walks at 4.8 km/h for 3 hours on a bearing of 236° from C, to his house, H. Mark the position of H on the scale drawing. [3] (b) A restaurant, R, is on a bearing of 083° from C. (i) Work out the bearing of C from R. … [2] (ii) The distance, d km, from R to C is 5 km, correct to the nearest kilometre. Complete this statement about the value of d. … G d 1 … [2] (c) A model of the castle is made. On the model, the length of one of the castle walls is 5 centimetres. The actual length of the wall is 90 metres. Find the scale of the model in the form 1| n . 1| … [2] (d) The castle has two kitchens with rectangular floors. F G B C NOT TO SCALE 5.6 m 9.2 m A 8.4 m D E x m H Rectangle ABCD is mathematically similar to rectangle EFGH. Calculate the value of x. x = … [2] (e) The castle has a cylindrical tower. The tower has a radius of 2.4 m and a height of 25 m. Calculate the curved surface area of the tower. Give the units of your answer. … … [3] Question 8 is printed on the next page.

14 marks

Mark scheme: 7(a) H correctly marked 3 B2 for H 7.2 cm from C 7.2 cm from C on bearing 236° or M1 for 4.8×3 B1 for H on bearing 236 from C 7(b)(i) 263 2 M1 for 83  180 oe or indicates correct angle on diagram 7(b)(ii) 4.5 5.5 2 B1 for each If 0 scored SC1 for both correct but reversed 7(c) [1 : ] 1800 2 M1 for 5 : 9000 or 0.05:90 9000 90 or or 5 0.05 or B1 for answer figs 18 7(d) 13.8 2 9.2 5.6 M1 for  oe or better x 8.4 7(e) 377 or 376.9 to 377.04 2 M1 for 2 2.4  25 m2 1

This question in 0580/31 May/June 2024

7 The area of some land is in the ratio park : gardens : playground = 11 : 2 : 3. The park has an area of 4620 m 2. (a) Work out the area of the gardens and the area of the playground. Gardens … m2 Playground … m2 [3] (b) The park area of 4620 m 2 is made up of paths and grassland. 18% of the park area is paths. (i) Show that the grassland area is 3788.4 m 2. [1] (ii) Seed for the grassland is sold in bags. The seed in one bag covers an area of 280 m 2. The bags cost $72 each for the first 5 bags and then $58 each for any extra bags. Calculate the cost of the seed needed to cover the grassland. $ … [4] (c) The owners of the land buy new equipment for the playground. They borrow $8500 for 4 years at a rate of 6.5% per year compound interest. Calculate the amount they repay at the end of the 4 years. Give your answer correct to the nearest dollar. $ … [3] (d) The café in the park sells water in bottles A, B and C. NOT TO SCALE Bottle A Bottle B Bottle C 330 ml 500 ml 750 ml $1.98 $3.20 $5.10 Work out which bottle is the best value. You must show all your working. Bottle … [3]

14 marks

Mark scheme: 7(a) 840 3 B2 for 1 correct answer in correct place 1260 or answers reversed or M1 for 4620 ÷ 11 × k (k = 1, 2, or 3) 7(b)(i) (100  18) M1 18  4620 accept 4620 –  4620 100 100 18 or 4620 ( 1 – ) 100 7(b)(ii) [$]882 4 B3 for 854.74, 853, 824 OR M3 for 5 × 72 + (their 14 – 5) × 58 oe or B2 for 14 [bags] or M1 for 3788.4 ÷ 280 OR M3 for 5 × 72 + (their 9 ) × 58 oe or B2 for 9 [bags] or M1 for (3788.4 – 5  280) ÷ 280 oe OR if 0 scored SC2 for 1056 or SC1 for 1027 or 998 7(c) [$]10935 cao 3 4  6.5  M1 for 8500 × 1  oe    100  A1 for 10934.96…… If A0 scored SC1 for their answer correct to at least 1 decimal place correctly rounded to nearest whole number. 7(d) A 3 With correct comparisons made of the 3 M2 for 3 correct comparable values bottles with suitable accuracy shown or for a correct method to 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 incorrect or not evaluated.

This question in 0580/32 May/June 2024

2 (a) Here is part of the timetable for buses from the station to the city centre. All buses take the same time to travel from the station to the city centre. Station 09 24 11 06 City centre 10 03 … (i) Complete the timetable. [2] (ii) Beth walks 4 km from her home to the station at a speed of 6 km/h. She wants to travel on the 09 24 bus. Work out the latest time she can leave her home. … [3] (iii) 45 seats on the bus are occupied. 3 This is of the total number of seats on the bus. 5 Work out the total number of seats on the bus. … [2] (b) Beth buys 2.4 kg of onions costing $1.25 per kilogram and 4.5 kg of potatoes. The total cost is $11.64 . Find the cost of 1 kg of potatoes. $ … [3] (c) (i) One day 140 people enter a shop. The ratio adults : children = 3 : 2. Find the number of adults who enter the shop. … [2] (ii) The price of a television in this shop is $624. 37.5% of this price is profit. Calculate the profit on this television. $ … [1] (iii) The price of a phone in this shop is $420. This price increases by 12%. Calculate the new price. $ … [2]

15 marks

Mark scheme: 2(a)(i) 11 45 2 B1 for 39 [m] or 1 [h] 42 [m] or 102 [m] 2(a)(ii) 08 44 3 B2 for 40 [m] or M1 for 4 ÷ 6 [×60] oe 2(a)(iii) 75 2 45 M1 for [×5] oe 3 2(b) 1.92 3 M2 for (11.64 – 2.4 × 1.25) ÷ 4.5 oe or M1 for 2.4 × 1.25 oe 2(c)(i) 84 2 140 M1 for [× k] oe where k = 1, 2 or 3 2  3 2(c)(ii) 234 1 2(c)(iii) 470.40 cao 2  12  M1 for 420   1   oe  100  or B1 for 50.40

This question in 0580/33 May/June 2024

6 (a) This is a recipe to make ice cream for 6 people. 270 ml cream 270 ml milk 100 g sugar 4 egg yolks Tom makes ice cream for 10 people. (i) Work out how much milk he uses. … ml [2] (ii) The mass of all the ingredients Tom uses is 1100 g. After Tom heats the mixture, this mass reduces by 15%. Find the mass of the mixture after heating. … g [2] (iii) Tom lets the mixture cool to 5°C. He then puts it into a freezer to cool to -18°C. Find the difference in these temperatures. … °C [1] (b) (i) In a factory, a machine fills 25 920 tubs of ice cream in 8 hours. Work out the number of tubs the machine fills in 1 minute. … [1] (ii) A pack of ice cream contains 6 tubs. There are 120 packs on a tray. There are 24 trays on a truck. Work out how many tubs of ice cream are on the truck. … [1] (c) Mario sells ice creams in five flavours. The table shows the relative frequency of some of the ice cream flavours Mario sells. Vanilla Chocolate Strawberry Coconut Banana Relative 0.34 0.18 0.12 frequency Mario sells three times as many chocolate ice creams as banana ice creams. (i) Complete the table. [3] (ii) One week Mario sells 450 ice creams. Find how many strawberry ice creams Mario expects to sell. … [1] (iii) The probability that any customer is an adult is 0.7 . First customer Second customer Adult 0.7 Adult 0.7 … Child Adult 0.7 … Child … Child (a) Complete the tree diagram. [1] (b) Find the probability that the first two customers are adults. … [2]

14 marks

Mark scheme: 6(a)(i) 450 2 M1 for 270[10] oe 6 6(a)(ii) 935 2  15  M1 for 1100 ×  1 −  oe  100  or B1 for 165 6(a)(iii) 23 1 6(b)(i) 54 1 6(b)(ii) 17 280 1 6(c)(i) 0.27 oe 3 B2 for either 0.27 oe or 0.09 oe in any 0.09 oe position in the table or M1 for 1 – ( 0.34 + 0.18 + 0.12) oe or better 6(c)(ii) 81 1 6(c)(iii)(a) Correct complete tree diagram: 1 0.3 0.3 0.3 6(c)(iii)(b) [0].49 oe 2 M1 for [0].7 × [0].7 oe

This question in 0580/31 Oct/Nov 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

3 (a) A wedding invitation is in the shape of a rectangle. Draw the lines of symmetry on this rectangle. [2] (b) There are 98 adults and 56 children at the wedding. Find the fraction of people who are children. Give your fraction in its simplest form. … [2] (c) The wedding meal starts at 13 15 and lasts for 2 hours 50 minutes. Find the time the meal ends. … [1] (d) The probability that it will rain at the wedding is 0.12 . Find the probability that it will not rain. … [1] (e) (i) These are the ages of the staff at the wedding. 16 24 39 28 17 48 31 33 17 29 40 25 Complete the stem-and-leaf diagram. 1 2 3 4 Key: 1|6 represents 16 [2] (ii) Find the range. … [1]

9 marks

Mark scheme: 3(a) 2 correct lines only 2 B1 for one correct line with no extras or 2 correct and 1 extra 3(b) 4 2 M1 for 98 + 56 cao 11 3(c) 16 05 1 3(d) 0.88 1 3(e)(i) 1 6 7 7 2 B1 for two or three rows correct or a fully 2 4 5 8 9 correct unordered stem-and-leaf diagram 3 1 3 9 4 0 8 3(e)(ii) 32 1 FT their (e)(i) dep. on an ordered table

This question in 0580/33 Oct/Nov 2024

4 (a) n = 15 r + 20c Find the value of r when n = 180 and c = 3 . r = … [2] (b) Factorise completely. 20p 2 q - 5p … [2] (c) Apples cost 35 cents each and bananas cost 14 cents each. Write down an expression for the total cost, in cents, of x apples and y bananas. … cents [2] (d) Solve the simultaneous equations. You must show all your working. 8x + 3y = 59 5x + 7y = 83 x = … y = … [4]

10 marks

Mark scheme: 4(a) 8 2 M1 for 180 = 15r + 20 × 3 or better 4(b) 5p (4pq – 1) 2 B1 for 5 (4p2q – p) or p (20pq – 5) or 5p (4pq – 1) seen then spoilt 4(c) 35x + 14y 2 B1 for 35x or 14y in final answer or for 35x + 14y seen then spoilt 4(d) correctly equating one set of coefficients M1 correct method to eliminate one variable M1 x = 4 A1 y = 9 A1 If A0 scored SC1 for 2 values satisfying one of the original equations

This question in 0580/33 Oct/Nov 2024

5 (a) Kurt owns some toy cars of different colours. The pictogram shows the number of each colour. Colour Number of toy cars Red Yellow Green Blue White Other Key: = 8 cars (i) Write down the colour of toy car that Kurt owns most of. … [1] (ii) Find the number of yellow toy cars that Kurt owns. … [1] (iii) Find how many more red toy cars than white toy cars Kurt owns. … [1] (b) A toy car costs $12.40 in the USA and 11.50 euros in Spain. The exchange rate is 1 euro = $1.12 . Calculate the difference in the cost of the toy car in euros. Give your answer correct to 2 decimal places. … euros [3] (c) Leo owns some toy vehicles. He owns 57 cars, 12 bicycles and 42 trucks. Find the ratio of the number of cars : bicycles : trucks in its simplest form. … : … : … [2] (d) Leo keeps his toy vehicles on a shelf. (i) The shelf is in the shape of a right-angled triangle. NOT TO SCALE 0.75 m y m The area of the shelf is 0.3 m2. Calculate the value of y. y = … [2] (ii) The shelf is 1.35 metres from the floor. Change 1.35 metres into centimetres. … cm [1]

11 marks

Mark scheme: 5(a)(i) Blue 1 5(a)(ii) 18 1 5(a)(iii) 20 1 5(b) 0.43 cao 3 B2 for 0.429 or 0.428[5…] Or 12.4 M2 for 11.50 – oe 1.12 11.50 1.12 − 12.4 or oe 1.12 12.4 or M1 for soi by 11.07… 1.12 If 0 or M1 scored SC1 for correct rounding to 2dp from their more accurate answer 5(c) 19 : 4 : 14 cao 2 M1 for correct ratio not in its simplest form 5(d)(i) 0.8 2 1 M1 for y 0.75 = 0.3 or better 2 5(d)(ii) 135 1

This question in 0580/33 Oct/Nov 2024

6 (a) 8 m NOT TO SCALE 11 m 6 m 15 m The diagram shows a plan of Zak’s garden. Find the perimeter of the garden. … m [2] (b) Zak records the temperature in his garden each night for one week. Sunday Monday Tuesday Wednesday Thursday Friday Saturday 4 °C 1 °C -2 °C 2 °C -5 °C 3 °C -4 °C (i) Which night was coldest? … [1] (ii) Find the difference in temperature between Friday night and Saturday night. … °C [1] (c) Zak buys pea plants, bean plants and sunflower plants in the ratio peas : beans : sunflowers = 7 : 5 : 2. He buys 45 bean plants. Show that the total number of plants he buys is 126. [2] (d) Zak has a water barrel. On Monday the barrel contains 120 litres of water. On Friday the barrel contains 43.2 litres of water. Calculate the percentage decrease of the water in the barrel. … % [2] (e) Zak drives to a shop. 1 The journey takes 1 hours. 4 He drives at an average speed of 57 km/h. Calculate the distance he drives. … km [2] (f) Machine hire charges 1st day $22.60 Each additional day $11.80 Zak pays $69.80 to hire a machine. Calculate the number of days he hires it for. … days [3]

13 marks

Mark scheme: 6(a) 52 2 M1 for 15 – 8 and 11 – 6 or 2 × 11 + 2 × 15 oe or 11 + 8 + (11 − 6 ) + (15 − 8 ) + 6 + 15 oe 6(b)(i) Thursday 1 6(b)(ii) 7 1 6(c) 45 ÷ 5 × (7 + 5 + 2) [=126] M2 M1 for 45 ÷ 5 6(d) 64 2 120 − 43.2 M1 for [×100] 120 43.2 or [100−] ×100 120  43.2  or  1 −  [×100]  120  6(e) 71.25 2 M1 for their time × 57 oe 6(f) 5 nfww 3 69.80 – 22.60 M2 for oe 11.80 or M1 for 69.80 – 22.60 or 22.60 + 11.80 + 11.80 +. or better

This question in 0580/33 Oct/Nov 2024

5 (a) A farmer plants t trees each day. Write an expression for the number of trees he plants in d days. … [1] (b) A train has p passengers. x passengers get off the train and y passengers get on the train. Write an expression for the number of passengers on the train now. … [1]

2 marks

Mark scheme: 5(a) dt oe final answer 1 5(b) p − x + y oe final answer 1

This question in 0580/32 Feb/March 2025

13 Xie changes 2000 dollars into krona. 1 dollar = 0.615 euros 1 krona = 0.087 euros Use the exchange rates to calculate how many krona she receives. Give your answer correct to the nearest krona. … krona [3]

3 marks

Mark scheme: 13 14 138 cao 3 2000  0.615 M2 for oe 0.087 or M1 for 2000  0.615 oe If 0 or M1 scored SC1 for a decimal answer seen, correctly rounded to the nearest integer

This question in 0580/32 Feb/March 2025

16 (a) Chi shares $480 in the ratio 2 : 3 : 7. Calculate the value of the largest share. $ … [2] (b) Simplify these ratios. (i) 98 : 147 … : … [1] (ii) 2 450 : 2 452 … : … [1]

4 marks

Mark scheme: 16(a) 280 2 480 M1 for  k , k = 1,2,3 or 7 2 + 3 + 7 16(b)(i) 2:3 cao 1 16(b)(ii) 1:4 cao 1

This question in 0580/32 Feb/March 2025

14 Tom needs 225 g of flour to make 10 cakes. A shop sells flour in 500 g bags. Work out the number of bags of flour Tom needs to make 70 cakes. … [3]

3 marks

Mark scheme: 14 4 nfww 3 B2 for 3.15 OR 70 M1 for 225 × oe 10 M1 for their 1575 ÷ 500 oe If 0 or 1 scored SC1 for their decimal rounded up to an integer

This question in 0580/31 May/June 2025

22 (a) Anil invests $2000 and Baz invests $7500. Write the ratio money invested by Anil : money invested by Baz in its simplest form. … : … [1] (b) Kamil and Lavik share some money in the ratio Kamil : Lavik = 5 : 9. Lavik receives $72 more than Kamil. Calculate the total amount of money they share. $ … [2] (c) Vanisha invests $4000 for 5 years at a rate of 3.5% per year compound interest. Calculate the total interest earned during the 5 years. $ … [3]

6 marks

Mark scheme: 22(a) 4 : 15 cao 1 22(b) 252 cao 2 72 M1 for × k, k = 1, 5, 9 or 14 oe 9 − 5 22(c) 751 or 750.7… 3 B2 for 4750 or 4751 or 4750.7… 3.5 5 or M2 for 4000  (1 + 100) − 4000 oe 3.5 5 or M1 for 4000  (1 + ) oe 100

This question in 0580/31 May/June 2025

16 (a) Sam spends $187 on electricity and gas. The ratio electricity : gas = 8 : 3 . Work out how much Sam spends on electricity. $ … [2] (b) Jai spends $180 on electricity and $150 on gas. Write down the ratio electricity : gas in its simplest form. … : … [1] (c) Kat spends money on electricity and gas in the ratio electricity : gas = E : G. Write down an expression, in terms of E and G, for the fraction she spends on gas. … [1]

4 marks

Mark scheme: 16(a) 136 2 187 M1 for  k , where k = 1, 3 or 8 oe 3 + 8 16(b) 6 : 5 cao 1 16(c) G 1 E + G

This question in 0580/32 May/June 2025

13 In May a shop makes a profit of $542. In June the shop makes a profit of $600. (a) Calculate the percentage increase in the profit from May to June. … % [2] 2 (b) The shop gives of the profit from May to a charity. 5 Find the amount the shop gives to the charity. $ … [1] (c) The shop spends 38% of the profit from June on a fridge. Find the amount the shop spends on the fridge. $ … [1]

4 marks

Mark scheme: 13(a) 10.7 or 10.70… 2 600 − 542 M1 for 100  oe 542  600  or   100   −100  oe  542   600  or  − 1   100  oe  542  13(b) 216.8[0] 1 13(c) 228 1

This question in 0580/33 May/June 2025

16 The scale drawing shows a path from S to P. The scale is 1 cm represents 2.5 km. North P North S Scale: 1 cm to 2.5 km (a) Work out the actual distance between S and P. … km [2] (b) Measure the bearing of S from P. … [1] (c) E is 20 km from P on a bearing of 070°. On the scale drawing, mark the position of E. [2]

5 marks

Mark scheme: 16(a) 16.25 2 B1 for 6.5 or M1 for their 6.5 × 2.5 16(b) 142 1 16(c) E correctly placed 2 B1 for E on a bearing of 070 from P or for E 8 cm from P If 0 scored, SC1 for fully correct but from S not P

This question in 0580/33 May/June 2025

21 (a) These are the distances above the surface of the Earth of five satellites, A, B, C, D and E. Each distance is in kilometres. A B C D E 35 800 .78 # 102 .15 # 106 535 2 # 104 (i) Write these distances in order, starting with the shortest. … , … , … , … , … [2] shortest (ii) The radius of Earth is 6370 km. Satellite A is k times further from the centre of Earth than satellite D. Show that k = 6.11 correct to 2 decimal places. [2] (b) A satellite travels at a speed of 27 000 km/h. Find the distance the satellite travels in 95 minutes. … km [2] (c) A different satellite travels at a speed of 25 200 km/h. Convert this speed into m / s. … m / s [2]

8 marks

Mark scheme: 21(a)(i) 535, 7.8×102, 2×104, 35 800, 1.5×106 2 B1 for 4 in correct order or M1 for (B)780, (C)1 500 000 and (E)20 000 seen or for 3.58 × 104 and 5.35 × 102 seen 21(a)(ii) (35800 + 6370) ÷ (535 + 6370) M1 6.107…. A1 21(b) 42750 2 M1 for 27000 × their time 21(c) 7000 2 25200  1000 M1 for oe 60  60 or B1 for final answer figs 7

This question in 0580/33 May/June 2025

10 Anna and Bruno share some money in the ratio Anna : Bruno = 3 : 7. Bruno receives $36 more than Anna. Calculate the total amount of money they share. $ … [2]

2 marks

Mark scheme: 10 90 2 36 M1 for [ × k , where k = 1, 3, 7 or 10] oe 4

This question in 0580/31 Oct/Nov 2025

14 (a) Ada works from Monday to Friday. Her working hours each day are 08 00 to 12 30 and 13 30 to 17 00. Find the number of hours she works in 5 days. … hours [2] (b) Ada is paid $15.20 per hour. Work out her pay for these 5 days. $ … [1] 1 (c) On Saturday she is paid 1 times her normal hourly rate. 2 Work out her hourly rate of pay for Saturday. $ … [1] (d) Ada changes 370 euros into dollars. The exchange rate is $1 = 0.925 euros. Work out the amount she receives. $ … [1]

5 marks

Mark scheme: 14(a) 40 2 1 1 B1 for 8 or 22 or 17 2 2 if 0 scored SC1 for 45 as final answer 14(b) 608 1 FT their (a) × 15.20 correct to at least 3sf 14(c) 22.8[0] 1 14(d) 400 1

This question in 0580/32 Oct/Nov 2025

13 Divide $136 in the ratio 3 : 5. $ … , $ … [2]

2 marks

Mark scheme: 13 51 85 2 M1 for 136 ÷ (3 + 5) × k where k is 1, 3 or 5

This question in 0580/33 Oct/Nov 2025