Rates — Paper 1 · IGCSE Mathematics 0580

6 Write as a 3-figure bearing the direction For Examiner's (a) West, Use Answer(a) [1] (b) North-East. Answer(b) [1]

2 marks

Mark scheme: 6 (a) 270 1 (b) (0)45 1

This question in 0580/11 Oct/Nov 2004

19 In New Zealand, a bus leaves New Plymouth at 8.10 am and arrives in Wellington at 2.55 pm. For Examiner's (a) How long, in hours and minutes, does the journey take? Use Answer(a) h min [1] (b) The distance from New Plymouth to Wellington is 355 kilometres. Calculate, in kilometres per hour, the average speed for the journey. Answer(b) km/h [3]

4 marks

Mark scheme: 19 (a) 6 (hours) 45 (minutes) 1 16 (b) rounds to 52.6 or 52 3f.t. 3 27 B1 for 6.75 or 6 oe used or 4 his time correctly converted to hours. M1 for 355 ÷ his time. (any form) (55.0…or 0.87….ww implies M1) A1 f.t. provided his (a) correctly converted to hours.

This question in 0580/11 Oct/Nov 2004

11 Yasmeen is setting up a business. For She borrows $5000 from a loan company. Examiner's The loan company charges 6% per year simple interest. Use How much interest will Yasmeen pay after 3 years? Answer $ [2]

2 marks

Mark scheme: 11 900 2 M1 for (5000 x 3 x 6) ÷ 100 oe or B1 for 300 seen SC1 for 5900

This question in 0580/11 May/June 2005

22 For Examiner's DISTANCE 15 Use FROM HOME (km) 14 13 School 12 11 10 9 8 7 6 Friend's House 5 4 3 2 1 Home 0 7 30 8 00 8 30 9 00 TIME (am) Ricardo rode to his friend’s house. He waited for his friend to get ready. Then they cycled together to school. Ricardo’s journey is shown on the grid. (a) Work out the speed at which Ricardo cycled to his friend’s house. Answer (a) km/h [2] (b) How long did he wait for his friend? Answer (b) min [1] (c) Ricardo’s brother left home at 8 00 am. For He cycled directly to school at a constant speed of 15 kilometres per hour. Examiner's Draw his journey on the grid opposite. Use [1] (d) How many minutes earlier than Ricardo did his brother arrive at school? Answer (d) min [1]

5 marks

Mark scheme: 22 (a) 10 2 M1 for use of distance ÷ time with figures. 5/0.5, 5/30, 5/6, 5/0.30 only. Not 5/8.00, 5/0.3 (b) 20 1 (c) on the graph 1 ruled single line from 8.00 am home continued to school, 12 km line. Ignore beyond 12 km line must cross within square (d) 12 1ft ft their intended single ‘straight’ line (need not be (allow 10 < time < 15) ruled) and within a square, not on the boundary (allow 12 from unless actually on a boundary calculation)

This question in 0580/11 May/June 2005

19 Joseph buys 45 kilograms of potatoes from a supplier for $0.65 per kilogram. (a) How much does he pay for the potatoes? Answer(a) $ [1] (b) He then puts the potatoes into bags which each hold 2.5 kilograms. How many bags can he fill with the potatoes? Answer(b) bags [1] (c) At the market he sells the bags of potatoes for $2.20 per bag. Calculate the smallest number of complete bags he needs to sell in order to make a profit. Answer(c) bags [2]

4 marks

Mark scheme: 19 (a) 29.25 or 29.2 or 29.3 1 (b) 18 1 (c) Their (a) ÷ 2.20 M1 Implied by 13.3 or 13.2 (...) seen 14 A [16]

This question in 0580/11 Oct/Nov 2005

21 The graph below shows the amount a plumber charges for up to 6 hours work. For Examiner's Use 120 100 80 Charge ($) 60 40 20 0 1 2 3 4 5 6 Time (hours) (a) How much does he charge for 3 1 hours work? 2 Answer(a) $ [1] (b) The plumber charged $50. How many hours did he work? Answer(b) hours [1] (c) Another plumber charges $16 per hour. (i) Draw a line on the grid above to show his charges. Start your line at (0,0). [2] (ii) Write down the number of hours for which the two plumbers charge the same amount. Answer(c)(ii) hours [1]

5 marks

Mark scheme: 21 (a) 62 1 (b) 1 1 2 2 (c) (i) Ruled line through (0, 0) and (1, 16) B1 Through and further than (5, 80) B1 Dependent (ii) 5 1f.t. Intersection of their line with the given line. [10]

This question in 0580/11 Oct/Nov 2005

20 There are 565 sheets of paper in a book. (a) How many sheets of paper are there in 2000 of these books? Give your answer in standard form. Answer(a) [2] (b) A pile of 565 sheets of paper is 25 millimetres high. Calculate the thickness of 1 sheet of paper. Give your answer in standard form. Answer(b) mm [3]

5 marks

Mark scheme: 20 (a) 1.13 x 106 2 M1 for 2000 x 565 seen or B1 for figs 113 (b) 4.42(….) x 10–2 3 M1 for 25 ÷ 565 soi and B1 for figs 442(….) 10 Total 56

This question in 0580/11 May/June 2006

15 A truck uses 2.5 litres of fuel to travel 8 kilometres. (a) How far will the truck travel on 1 litre of fuel? Answer(a) km [1] (b) How far will the truck travel on 120 litres of fuel? Answer(b) km [1]

2 marks

Mark scheme: 15 (a) 3.2 1 (b) 384 1 ft their (a) × 120.

This question in 0580/11 Oct/Nov 2006

17 (a) Alex invests $200 for 2 years at 4.05% per year simple interest. Calculate how much interest Alex receives. Answer(a) $ [2] (b) Bobbie invests $200 for 2 years at 4% per year compound interest. Calculate how much interest Bobbie receives. Give your answer to 2 decimal places. Answer(b) $ [2]

4 marks

Mark scheme: 17 (a) ($) 16.2(0) 2 M1 for (200 × 4.05 × 2)/100 SC1 for 216.2(0) (b) ($) 16.3(2) or 16.3(0) 2 M1 for 200(1.04) 2 − 200oe SC1 for 216.3(2). SC1 for both 8.(00) and 8.3(2) seen

This question in 0580/11 Oct/Nov 2007

3 How many glasses, each holding 200 cm3, can be filled completely from a full 4.5 litre bottle of water? Answer [2]

2 marks

Mark scheme: 3 22 2 M1 for 4500 ÷ 200 or 4.5 ÷ 0.2

This question in 0580/11 May/June 2009

4 North NOT TO SCALE North B 72° A The diagram shows the position of two airports, A and B. The bearing of B from A is 072°. Work out the bearing of A from B. Answer [2]

2 marks

Mark scheme: 4 252 2 W1 for 108 or 72 correctly shown on the diagram at B. Or M1 for 180 + 72 or 360 − (180 − 72) soi

This question in 0580/11 Oct/Nov 2009

9 A train sets off at 11 53 on a journey to Mumbai. The journey takes 2 hours 30 minutes. (a) Write down the time when the train arrives in Mumbai. Answer(a) [1] (b) The distance to Mumbai is 235 kilometres. Calculate the average speed of the train. Answer(b) km/h [2]

3 marks

Mark scheme: 9 (a) 14 23 isw or 2.23 pm isw. 1 Not 02 23 or 2 23 alone. Not 14h(ours)23 (b) 94 2cao M1 for 235 ÷ 2.5 (or 2h 30min or 150) Method mark is for formula with values.

This question in 0580/11 Oct/Nov 2009

16 As the earth rotates, a point on the equator moves round at a speed of 1669.8 kilometres/hour. For Examiner's (a) Write down this number in standard form, correct to 3 significant figures. Use Answer(a) [2] (b) Change 1669.8 kilometres/hour into metres/second. Answer(b) m/s [2]

4 marks

Mark scheme: 16 (a) 1.67 × 103 2 W1 for 1.67 × 10n (n ≠ 0) or 1.(…..) × 103 as answer If zero SC1 for figs 167 in answer. (b) 464 or 463.8(3…..) 2 M1 for 1669.8 × 1000 ÷ 3600

This question in 0580/11 Oct/Nov 2009

9 A train sets off at 10 48 on a journey to Mumbai. The journey takes 4 hours 30 minutes. (a) Write down the time when the train arrives in Mumbai. Answer(a) [1] (b) The distance to Mumbai is 441 kilometres. Calculate the average speed of the train. Answer(b) km/h [2]

3 marks

Mark scheme: 9 (a) 15 18 isw or 3.18 pm isw. 1 Not 03 18 or 3 18 alone. Not 15h(ours)18 (b) 98 2cao M1 for 441 ÷ 4.5 (or 4h 30min or 270) Method mark is for formula with values.

This question in 0580/12 Oct/Nov 2009

16 As the earth rotates, a point on the equator moves round at a speed of 1669.8 kilometres/hour. ForFor Examiner'sExaminer's (a) Write down this number in standard form, correct to 3 significant figures. UseUse Answer(a) [2] (b) Change 1669.8 kilometres/hour into metres/second. Answer(b) m/s [2]

4 marks

Mark scheme: 16 (a) 1.67 × 103 2 W1 for 1.67 × 10n (n ≠ 0) or 1.(…..) × 103 as answer If zero SC1 for figs 167 in answer. (b) 464 or 463.8(3…..) 2 M1 for 1669.8 × 1000 ÷ 3600

This question in 0580/12 Oct/Nov 2009

17 City 3 2 Distance (kilometres) 1 Port 0 0 15 30 45 60 Time (minutes) (a) The travel graph shows the journey of a bus from a port to a city. Calculate the average speed of the bus (i) in kilometres per minute, Answer(a)(i) km/min [1] (ii) in kilometres per hour. Answer(a)(ii) km/h [1] (b) The bus waits in the city for 20 minutes and then returns to the port at an average speed of 12 km/h. Complete the travel graph. [2] Questions 18 and 19 are printed on the next page.

4 marks

Mark scheme: 17 (a) (i) 0.3 oe 1 (ii) 18 1 Follow through their (a)(i) × 60 (b) horizontal line to (30,3) 1 line from (30,3) to (45,0) 1ft OR from their (x,3) to (their x + 15, 0)

This question in 0580/11 May/June 2010

20 Examiner's Use 100 Garage 90 80 70 Distance (kilometres) 60 50 Café 40 30 20 10 Factory 0 0 1 2 3 4 5 6 7 8 9 Time (hours) The travel graph shows part of the journey of a truck driver. The driver leaves a factory to deliver tyres to a garage. After unloading the tyres, the driver returns to the factory, but stops at a café for 1 hour. He then completes the journey at an average speed of 80 km/h. (a) Calculate the average speed of the truck on its journey from the factory to the garage. Answer(a) km/h [1] (b) Write down the length of time the truck stays at the garage. Answer(b) hours [1] (c) Complete the travel graph. [2]

4 marks

Mark scheme: 20 (a) 45 1 (b) 1.5 o.e. 1 Allow 1 h(our) 30(min) or 1:30 (c) horizontal line from 1 (5.5, 40) to (6.5, 40) diagonal line from their 1ft Independent (x, 40) to (x + ½ , 0) √ 2 2 √

This question in 0580/13 May/June 2010

5 Sophie invests $450 at a rate of 1.5% per year simple interest. For Examiner's Calculate the interest she earns after 8 years. Use Answer $ [2]

2 marks

Mark scheme: 450 × 8 × 5.1 5 54(.00) final answer 2 M1 for oe 100 or SC1 for 504(.00)

This question in 0580/11 Oct/Nov 2010

22 School NOT TO SCALE Distance Shop (kilometres) Home 08 00 08 05 08 10 08 15 08 20 08 25 08 30 Time Rob walks to school each morning. One day, he leaves home at 08 00. He stops at a shop at 08 10 and stays there for 5 minutes. He then continues to school and arrives at 08 30. (a) Draw the travel graph for Rob’s journey from home to school. [3] (b) Rob’s average speed for the whole journey from home to school is 3.3 km/h. Calculate the distance from Rob’s home to school. Answer(b) km [2]

5 marks

Mark scheme: 22 (a) Lines connecting 3 (08 00, home) to (08 10, shop) B1 home to shop (their 08 10, shop) to B1ft horizontal and 5 minute period (their 08 15, shop) (their 08 15, shop) to B1ft for line to 08 30 and school (08 30, school) (b) 1.65 2 M1 for use of speed × time SC1 for 1.375 or 1.376 to 1.38

This question in 0580/13 Oct/Nov 2010

14 A train leaves Barcelona at 21 28 and takes 10 hours and 33 minutes to reach Paris. (a) Calculate the time the next day when the train arrives in Paris. Answer(a) [1] (b) The distance from Barcelona to Paris is 827 km. Calculate the average speed of the train in kilometres per hour. Answer(b) km/h [3]

4 marks

Mark scheme: 14 (a) (0)8(.)01(am) 1 Not 8.01 pm (b) 78.4 or 78.38 to 78.39 3 M2 for 827 ÷ 10.55 or M1 for figs 827 ÷ their time

This question in 0580/11 May/June 2011

19 (a) The travel graph on the opposite page shows Joel’s journey to his school. For He walks to the bus stop and waits for the bus, which takes him to the school. Examiner's Use (i) How long did Joel wait for the bus? Answer(a)(i) min [1] (ii) Find the distance from the bus stop to the school. Answer(a)(ii) km [1] (b) Joel’s sister, Samantha, leaves home 14 minutes later than Joel to cycle to the same school. She cycles at a constant speed and arrives at the school at 08 16. (i) On the grid, show her journey. [1] (ii) At what time did the bus pass Samantha? Answer(b)(ii) [1] (iii) How far from the school was she when the bus passed her? Answer(b)(iii) km [1] (iv) How many minutes after Joel did Samantha arrive at the school? Answer(b)(iv) min [1] 10 For Examiner's Use School 9 8 7 6 Distance 5 (km) 4 3 2 1 Home 0 07 00 07 10 07 20 07 30 07 40 07 50 08 00 08 10 08 20 Time

6 marks

Mark scheme: 19 (a) (i) 8 (min) 1 (ii) 7.8 (km) 1 (b) (i) Ruled line from 1 Ignore line continued above school. (07 20, 0) to (08 16, 9.4) (ii) (0)7 38 to (0)7 40 1ft Follow through their graph (iii) 5.8 (km) to 6.4 (km) 1ft Follow through their graph. (iv) 17 to 19 (min) 1ft Follow through their graph

This question in 0580/12 May/June 2011

20 For School 900 Examiner's Use 800 700 600 500 Distance (metres) 400 300 Friend’s house 200 100 Home 0 08 00 08 05 08 10 08 15 08 20 08 25 08 30 Time The graph shows part of Ali’s journey from home to his school. The school is 900 m from his home. He walks 200 m to his friend’s house and waits there. He then takes 20 minutes to walk with his friend to their school. (a) Complete the travel graph showing Ali’s journey. [1] (b) How long does he wait at his friend’s house? Answer(b) min [1] (c) Calculate the average speed for Ali’s complete journey from home to his school. Give your answer in kilometres per hour. Answer(c) km/h [4]

6 marks

Mark scheme: 20 (a) Straight ruled line from 1 (08 10, 200) to (08 30, 900) (b) 5 1 (c) 1.8 4 M1 for total distance ÷ total time M1 for converting time to hours M1 for converting metres to km

This question in 0580/13 May/June 2011

18 (a) Lucinda invests $500 at a rate of 5% per year simple interest. For Examiner's Calculate the interest Lucinda has after 3 years. Use Answer(a) $ [2] (b) Andy invests $500 at a rate of 5% per year compound interest. Calculate how much more interest Andy has than Lucinda after 3 years. Answer(b) $ [4]

6 marks

Mark scheme: 500 × 5 × 3 18 (a) 75 2 M1 for oe 100 or SC1 for answer of 575 (b) 3.81(25) 4 M2 for 500 × 1.05 × 1.05 × 1.05 or M1 for 500 × 1.05 × 1.05 A1 for 578.81(25) or 78.81(25) seen and A1ft for value of 500(1.05)3 – 500 – their (a)

This question in 0580/11 Oct/Nov 2011

15 A cruise ship travels at 22 knots. [1 knot is 1.852 kilometres per hour.] Convert this speed into metres per second. Answer m/s [3]

3 marks

Mark scheme: 15 11.3 3 M2 22 × 1.852 × 1000/3600 oe or M1 22 × figs 1852 or 22 × 1000/3600

This question in 0580/12 Oct/Nov 2011

6 Hans invests $750 for 8 years at a rate of 2% per year simple interest. Calculate the interest Hans receives. Answer $ [2]

2 marks

Mark scheme: 750 × 2 × 8 6 120 2 M1 for 100 oe seen or SC1 870 as final answer

This question in 0580/13 May/June 2012

6 On a mountain, the temperature decreases by 6.5 °C for every 1000 metres increase in height. At 2000 metres the temperature is 10 °C. Find the temperature at 6000 metres. Answer °C [2]

2 marks

Mark scheme: 6 –16 2 M1 for 4 × 6.5

This question in 0580/11 Oct/Nov 2012

20 For Distance from Examiner's Lola’s house (km) Use 14 Sarah’s house 12 10 8 6 4 2 Lola’s house 0 14 00 14 30 15 00 15 30 16 00 16 30 17 00 17 30 Time The travel graph shows Lola’s journey from her house to Sarah’s house. (a) Lola stopped at a shop on the way to Sarah’s house. For how many minutes did she stop? Answer(a) min [1] (b) Write down the time she arrived at Sarah’s house. Answer(b) [1] (c) Calculate Lola’s average speed from leaving the shop to arriving at Sarah’s house. Give your answer in kilometres per hour. Answer(c) km/h [2] (d) Lola stayed at Sarah’s house for 1 hour 20 minutes. She then cycled home without stopping. Her journey took 50 minutes. Complete the travel graph. [2]

6 marks

Mark scheme: 20 (a) 10 1 (b) 15 10 1 2 (c) 9 [km/h] 2 M1 for 6 ÷ or 6 ÷ 40 or better 3 (d) horizontal line from (15 10, 12) 1 ‘their 16 30’ + 50 minutes to (16 30, 12) line from (16 30, 12) to (17 20, 0) 1 ft

This question in 0580/11 Oct/Nov 2012

11 An athlete runs 1500 metres in 4 minutes. For Examiner's Use Calculate her average speed in (a) metres per minute, Answer(a) m/min [1] (b) kilometres per hour. Answer(b) km/h [2]

3 marks

Mark scheme: 11 (a) 375 1 (b) 22.5 2 ft M1 for their (a) ÷ 1000 × 60 or 1500 × 15 ÷ 1000 If zero SC1 for answer figs 225

This question in 0580/12 Oct/Nov 2012

22 The travel graph shows Natasha’s visit to her friend’s house. For Examiner′s She starts by walking and then runs. Use She stays at her friend’s house until 11 10 before returning home. 2000 1800 Friend’s 1600 house 1400 Distance 1200 from home (metres) 1000 800 600 400 200 Home 0 10 30 10 40 10 50 11 00 11 10 11 20 11 30 11 40 Time (a) (i) How far does Natasha walk on the journey to her friend’s house? Answer(a)(i) … m [1] (ii) Find Natasha’s average speed, in metres per minute, on the journey to her friend’s house. Answer(a)(ii) … m/min [2] (iii) How long does Natasha stay at her friend’s house? Answer(a)(iii) … min [1] (b) Natasha returns home at a constant speed of 64 metres per minute. For Examiner′s Use (i) Complete the travel graph. [2] (ii) Write down the time she arrives home. Answer(b)(ii) … [1] _____________________________________________________________________________________

7 marks

Mark scheme: 22 (a) (i) 1000 [m] 1 (ii) 80 [m/min] 2 M1 for 1600 ÷ 20 (iii) 20 [min] 1 (b) (i) Ruled line from (11 10, 1600) to (11 35, 0) 2 M1 for 1600 ÷ 64 soi (ii) 11 35 1FT their line at the axis if on the grid and not before 11 10.

This question in 0580/13 Oct/Nov 2013

13 The graph can be used to convert between miles and kilometres. 80 70 60 50 Kilometres 40 30 20 10 0 10 20 30 40 50 Miles A train travels 24 miles in 20 minutes. Find its average speed in kilometres per hour. Answer … km/h [2] __________________________________________________________________________________________

2 marks

Mark scheme: 13 114 to 117 2 B1 for 38 to 39 seen or 72 [mph]

This question in 0580/11 May/June 2014

17 A plane is travelling at 180 metres per second. How many minutes will it take the plane to travel 800 km? Give your answer correct to the nearest minute. Answer … min [4] __________________________________________________________________________________________

4 marks

Mark scheme: 17 74 4 M1 for 800 × 1000 or 180 ÷ 1000 soi and M1 for figs 8 ÷ figs 18 and M1 for converting (secs) to mins 74.1 or 74.07… implies M3

This question in 0580/12 May/June 2014

25 William Toby Town 4 3 Distance 2 (km) 1 Home 0 10 00 10 04 10 08 10 12 10 16 10 20 10 24 10 28 10 32 Time Toby and William cycled into town. Their journeys are shown on the travel graph. (a) For how many minutes did Toby stop on his journey into town? Answer(a) … min [1] (b) Explain what happened at 10 20. Answer(b) … [1] (c) Work out how long William took to cycle into town. Answer(c) … min [1] (d) Calculate William’s speed in km/h. Answer(d) … km/h [2] __________________________________________________________________________________________

5 marks

Mark scheme: 25 (a) 6 1 (b) They are at the same place at the same time 1 (c) 16 1 (d) 15 cao 2 M1 FT for 4 × 60 oe their ( c ) IGCSE – May/June 2014 0580 13

This question in 0580/13 May/June 2014

14 A train takes 65 minutes to travel 52 km. Calculate the average speed of the train in kilometres per hour. Answer … km/h [2] __________________________________________________________________________________________

2 marks

Mark scheme: 14 48 2 M1 for 52 ÷ 65 [× 60] oe implied by 0.8

This question in 0580/13 Oct/Nov 2014

20 Ravi cycles from home to the bank. It takes him 15 minutes, cycling at a constant speed of 14 km/h. (a) Work out how far Ravi cycles from home to the bank. Answer(a) … km [1] (b) Ravi stays at the bank for 18 minutes. He then cycles home at a constant speed for 12 minutes. Draw the travel graph to show Ravi’s journey since he left home. 4.5 4 3.5 3 Distance 2.5 (km) 2 1.5 1 0.5 Ravi’s home 0 5 10 15 20 25 30 35 40 45 50 Time (minutes) [3] __________________________________________________________________________________________ Question 21 is printed on the next page.

4 marks

Mark scheme: 20 (a) 3.5 1 (b) straight line from (0,0) to (15,their 3.5) 1FT FT from (a) horiz line from (their 15, their 3.5) to 1FT FT is horizontal line length 18 mins (their 33, their 3.5) 1FT FT is from (their x, their y) to straight line from (their 33, their 3.5) to (their x + 12, 0) (their 33 + 12, 0)

This question in 0580/12 Feb/March 2015

4 The total mass of 38 spoons is 1824 g. Work out the mass of 53 spoons. Answer … g [2] __________________________________________________________________________________________

2 marks

Mark scheme: 4 2544 2 M1 for 1824 ÷ 38 [×53] oe 3000 × 5 × 4

This question in 0580/11 May/June 2015

14 Six donkeys are each given two 5 ml spoons of medicine three times each day. Calculate the number of whole days a 2 litre bottle of medicine will last. Answer … days [3] __________________________________________________________________________________________

3 marks

Mark scheme: 14 11 3 B1 for 2000[ml] or 0.005[litres] soi M1 for figs 2 ÷ (6 × 2 × 5 × 3) or better or figs 111…. seen

This question in 0580/11 May/June 2015

21 (a) Sara works for 28 hours each week. She earns $12.45 per hour. Calculate how much she earns in one week. Answer(a) $ … [1] (b) Sara invests $750 for 3 years at a rate of 2.4% per year compound interest. Calculate the total amount she will have at the end of the 3 years. Answer(b) $ … [3] __________________________________________________________________________________________

4 marks

Mark scheme: 21 (a) 348.6[0] cao final answer 1 (b) 805.31 3 M2 for 750 × 1.0243 oe or M1 for 750 × 1.024 × 1.024 oe If zero scored, SC2 for answer of 55.31 or 55. 30[...], i.e. total interest

This question in 0580/11 Oct/Nov 2015

6 $2600 is invested for 5 years at a rate of 4% per year simple interest. Calculate the total interest at the end of the 5 years. Answer $ … [2]

2 marks

Mark scheme: 4 6 520 final answer 2 M1 for 2600 × 5 × oe 100

This question in 0580/12 Oct/Nov 2015

2 Apples cost $1.12 for each kilogram. Calculate the cost of 4.5 kilograms of apples. $ … [1]

1 marks

Mark scheme: 2 5.04 1

This question in 0580/12 Feb/March 2016

23 10 Sports 8 centre 6 Distance (km) 4 2 Home 0 15 30 15 45 16 00 16 15 16 30 16 45 17 00 17 15 17 30 17 45 Time Sonali cycles from home to the sports centre. The travel graph shows her journey. (a) At what time does she arrive at the sports centre? … [1] (b) Work out Sonali’s cycling speed in kilometres per hour. … km/h [2] (c) Sonali stays at the sports centre for 45 minutes. She then takes 30 minutes to cycle home. Complete the travel graph. [2]

5 marks

Mark scheme: 23 (a) 16 10 or 4 10 pm 1 (b) 12 2 M1 for 8 ÷ 40 or better (c) Line from (16 10, 8) to (16 55, 8) 1 Line from (16 55, 8) to (17 25, 0) 1FT FT line from their (16 55, 8) to ((their 16 55 + 30 mins), 0)

This question in 0580/12 May/June 2016

19 A D 93.5 m NOT TO SCALE B C 82.5 m The diagram shows a rectangular field, ABCD, with a straight path, BD. (a) Calculate the distance from C to D. … m [3] (b) Yan walks along the edge of the field from B to C and then from C to D. Lee walks along the straight path BD. Work out how much further Yan walks than Lee. … m [1]

4 marks

Mark scheme: 19 (a) 44 3 M2 for 93.52 − 82.5 2 or M1 for CD2 + 82.52 = 93.52 (b) 33 1FT FT 93.5 – (82.5 + their (a))

This question in 0580/13 May/June 2016

20 (a) Alice leaves home at 08 15 and walks at 80 metres per minute, arriving at her friend’s house half an hour later. (i) Work out the distance she walks, in metres, from her home to her friend’s house. … m [1] (ii) On the grid, show her journey from her home to her friend’s house. [1] 3000 2400 1800 Distance (m) 1200 600 Home 0 08 00 08 30 09 00 09 30 10 00 10 30 11 00 Time 1 (b) Alice stays at her friend’s house for 1 2 hours. She then jogs home, arriving 15 minutes later. (i) On the grid, complete the travel graph for her journey. [2] (ii) Calculate her average speed, in metres per minute, on her journey home. … m/min [2]

6 marks

Mark scheme: 20 (a) (i) 2400 1 (ii) Ruled line (08 15, 0) to 1FT Follow through their 2400 and 30 minute (08 45, their 2400) time period

This question in 0580/13 May/June 2016

9 30 28 26 24 22 DD 20 C 18 Distance (km) 16 B 14 12 10 8 A 6 4 2 0 0 10 20 30 40 50 60 70 80 90 Time (minutes) The diagram shows the distance-time graph for the first 65 minutes of a bicycle journey. (a) There are four different parts to the journey labelled A, B, C and D. Write down the part of the journey with the fastest speed. … [1] (b) After the first 65 minutes the bicycle travels at a constant speed of 20 km/h for 15 minutes. Draw this part of the journey on the diagram. [1]

2 marks

Mark scheme: 9 (a) A 1 (b) A ruled line joining (65, 23) to 1 (80, 28) 18 5 18 k 5 k

This question in 0580/13 Oct/Nov 2016

6 A taxi journey costs $4.50, plus 80 cents for each kilometre travelled. Julianna travels 7 km. Work out the cost of her journey. $ … [2]

2 marks

Mark scheme: 6 10.1[0] 2 M1 for [4.5 +] (7 × [0].8) or 450 + 7 × 80

This question in 0580/12 Oct/Nov 2017

3 Liz takes 65 seconds to run 400 m. Calculate her average speed. … m/s [1]

1 marks

Mark scheme: 3 2 1 6.15 or 6.153 to 6.154 or 6 13

This question in 0580/13 May/June 2018

14 Shohan cycles from home to the library. He stops at the post office on the way. The travel graph shows his journey. 10 Library 8 Distance 6 from home (km) 4 2 Home 0 10 00 10 15 10 30 10 45 11 00 11 15 11 30 11 45 12 00 Time (a) Write down the time Shohan arrives at the post office. … [1] (b) Shohan stays at the library for 25 minutes. He then cycles home at a constant speed of 18 km/h. Complete the travel graph. [2]

3 marks

Mark scheme: 14(a) 10 25 1 14(b) Graph completed correctly 2 B1 for line from (10 55, 9) to (11 20, 9) B1 FT for line from (their 11 20, 9) to (their 11 20 + 30 min, 0)

This question in 0580/11 Oct/Nov 2018

18 Jan invests $800 at a rate of 3% per year simple interest. Calculate the value of her investment at the end of 4 years. $ … [3]

3 marks

Mark scheme: 18 896 3 800 × 4 × 3 M2 for 800 + oe 100 800 × 4 × 3 or M1 for oe 100

This question in 0580/11 Oct/Nov 2018

24 A car travels at 108 km/h for 20 seconds. Calculate the distance the car travels. Give your answer in metres. … m [3]

3 marks

Mark scheme: 24 600 3 108 × 1000 × 20 M2 for oe 60 × 60 108 × 1000 or M1 for oe 60 × 60 or for figs108 × time oe

This question in 0580/13 Oct/Nov 2018

18 A car travels at a constant speed of 20 m/s. Work out the time it takes for the car to travel 10 km. Give your answer in minutes and seconds. … minutes … seconds [3]

3 marks

Mark scheme: 18 8 [min] 20 [sec] 3 10 M1 for [× 1000] soi 0.5 or 500 20 A1 for 500 [sec] or 8.33…[min] B1 for correctly converting their answer in seconds providing their answer is > 60 or decimal minutes to minutes and seconds

This question in 0580/11 May/June 2019

18 A machine always takes 5 minutes to paint an 80 metre white line on a road. (a) Work out the number of metres painted in 45 minutes. … m [1] (b) Work out the number of minutes taken to paint a 2.8 km line. … min [2]

3 marks

Mark scheme: 18(a) 720 1 18(b) 175 cao 2 2.8 × 1000[× 5] or 2.8 × 1000 × 45 M1 for 80 their (a) or B1 for figs 175

This question in 0580/12 May/June 2019

20 Juan travels from his home to a shop. The travel graph shows his journey. 18 Shop 12 Distance (km) 6 Home 0 13 00 14 00 15 00 16 00 Time (a) Find the distance Juan travels to the shop. … km [1] (b) Write down what happens at 14 00. … [1] (c) Juan travels home at a constant speed of 15 km/h. He leaves the shop at 15 15. Complete the travel graph. [1]

3 marks

Mark scheme: 20(a) 15 1 20(b) He stopped or 1 arrived at the shop 20(c) Ruled line from 1 (15 15, 15) to (16 15, 0)

This question in 0580/11 Oct/Nov 2019

11 Kiran leaves home at 9.45 am. She drives 135 km to visit a friend. She arrives at her friend’s house at 11.15 am. Work out her average speed in km/h. … km/h [2]

2 marks

Mark scheme: 11 90 2 M1 for 135 ÷ their time

This question in 0580/12 Oct/Nov 2019

19 A car travels at a constant speed of 45 kilometres per hour for 5 minutes. Each wheel of the car has radius 25 centimetres. Calculate the number of complete revolutions that a wheel makes during the 5 minutes. … [5]

5 marks

Mark scheme: 19 2387 cao 5 7500 M4 for oe π 60 figs 45 ÷ 5 or M3 for 2 × π × figs 25 60 or M2 for 2 × π × figs 25 and figs 45 ÷ 5 or M1 for 2 × π × figs 25 60 or for figs 45 ÷ 5

This question in 0580/12 Feb/March 2020

6 (a) Diego flies from Madrid to Buenos Aires. His flight leaves at 20 55 and arrives at 03 50 local time. The local time in Buenos Aires is 5 hours behind the local time in Madrid. Work out, in hours and minutes, the time the flight takes. … h … min [2] (b) Diego changes 200 euros into Argentine Peso. The exchange rate is 1 euro = 24.8 pesos. Work out how many pesos he receives. … pesos [1] (c) The distance between Madrid and Buenos Aires is 10 050 km. Diego’s return flight takes 12 hours 30 minutes. Calculate the average speed, in km/h, for the return flight. … km/h [1]

4 marks

Mark scheme: 6(a) 11[h] 55[min] 2 B1 for 08 50 or 15 55 or 6[h] 55[min] seen 6(b) 4960 1 6(c) 804 1

This question in 0580/11 May/June 2020

7 Hua cycles from her home to the library. The travel graph shows this journey. Library 12 11 10 9 8 Distance from home 7 (km) 6 5 4 3 2 1 Home 0 10 00 10 30 11 00 11 30 12 00 Time (a) At what time does she start her journey? … [1] (b) (i) Find her distance from home when she stops for a rest. … km [1] (ii) How long does she stop for a rest? … min [1] (c) Hua stays at the library for 10 minutes. She then cycles home at a constant speed of 24 km/h. Complete the travel graph. [2]

5 marks

Mark scheme: 7(a) 10 10 [am] 1 7(b)(i) 8 1 7(b)(ii) 20 1 7(c) Line from 2 B1 for either line correct (11 10, 12) to (11 20, 12) and ruled line from (their11 20, 12) If zero scored, B1 for to (their11 20 + 30, 0) 30 [min] or half an hour or 0.5 [hours]

This question in 0580/11 Oct/Nov 2020

11 Rangan buys 3.6 kg of potatoes and 2.8 kg of leeks. The total cost is $13.72 . Leeks cost $2.65 per kilogram. Find the cost of 1 kg of potatoes. $ … [3]

3 marks

Mark scheme: 11 1.75 3 M2 for (13.72 – 2.8 × 2.65) ÷ 3.6 oe or M1 for 2.8 × 2.65

This question in 0580/11 Oct/Nov 2020

10 Ethan invests $6400 at a rate of 2.6% per year simple interest. Calculate the total value of his investment at the end of 3 years. $ … [3]

3 marks

Mark scheme: 10 6899.2[0] final answer 3 6400 × 2.6 × 3 M2 for + 6400 100 6400 × 2.6 × 3 or M1 for 100

This question in 0580/13 Oct/Nov 2020

18 Ramond walks 2460 metres in 33 minutes. Work out Ramond’s average speed in kilometres per hour. … km/h [3]

3 marks

Mark scheme: 18 4.47 or 4.472 to 4.473 3 2460 33 M2 for ÷ oe 1000 60 or B2 for figs 4472[7...] or 4473 or M1 for figs 246 ÷ their time or B1 for 2.46 or 0.55 seen

This question in 0580/13 Oct/Nov 2020

6 8 7 6 5 Distance (km) 4 3 2 1 0 12 00 13 00 14 00 15 00 16 00 Time The travel graph shows a student’s journey. (a) Explain what is happening between 14 20 and 14 40. … [1] (b) Complete the statement. The student is travelling fastest between the times … and … because … [2]

3 marks

Mark scheme: 6(a) Student is stationary oe 1 6(b) 13 00 13 20 2 B1 for both times correct or correct gradient is steepest reason

This question in 0580/11 May/June 2021

8 Nazaneen changes $6500 into 5798 euros at a bank. Work out the exchange rate the bank uses. $1 = … euros [1]

1 marks

Mark scheme: 8 0.892 1

This question in 0580/11 May/June 2021

22 There is a straight road between town A and town B of length 130 km. Maxi travels from town A to town B. Pippa travels from town B to town A. Both travel at a constant speed of 40 km/h. Maxi leaves 30 minutes before Pippa. Work out how far from town A they will be when they pass each other. … km [4]

4 marks

Mark scheme: 22 75 4 B3 for 55 or B2 for 110 or B1 for 20 seen OR 30 M1 for × 40 or better seen 60 M1dep for 130−their 20 their110 M1dep for 2 OR M1 for 130 ÷ 40 or better seen M1 for their 3.25 – 0.50 2.75 M1 for their × 40 2

This question in 0580/11 May/June 2021

19 Angelique rents a room for a party. The cost of renting the room is $15.50 for the first hour and then $7.25 for each additional hour. She pays $95.25 in total. Work out the total number of hours she rents the room for. … hours [3]

3 marks

Mark scheme: 19 12 3 M2 for (95.25 – 15.5) ÷ 7.25 oe or (95.25 – (15.5 – 7.25)) ÷ 7.25 oe or M1 for 95.25 – 15.5 or B1 for 79.75

This question in 0580/12 Oct/Nov 2021

17 Sanjay invests $700 in an account paying simple interest at a rate of 2.5% per year. Calculate the value of his investment at the end of 6 years. $ … [3]

3 marks

Mark scheme: 17 805 3 B2 for 105 700 × 2.5 × 6 or M2 for + 700 oe 100 700 × 2.5 [× 6 ] or M1 for oe 100

This question in 0580/12 Feb/March 2022

19 Lin invests $16 000 at a rate of r % per year simple interest. At the end of 5 years, she has a total amount of $17 920. Find the value of r. r = … [3]

3 marks

Mark scheme: 19 2.4 3 B2 for 0.024 seen or M2 for oe or better r 17 920 – 16 000 = 5 16000 100  or 17 920 = 16 000 × (1 + 5r)[×100] or M1 for any of these, oe or better r 17 920 – 16 000 or 5 16000 100  their 1 920 or  100  or 16000 17920  100   1 00  16000 their 1920 or  100  or figs 384 5

This question in 0580/11 May/June 2022

22 The table shows the population and area of three countries in 2020. Country Population Area (km2) Nigeria .206 # 108 9.11 # 10 5 Comoros 8.70 # 10 5 1.86 # 10 3 Vietnam 9.73 # 10 7 3.10 # 10 5 (a) Calculate the difference in population between Nigeria and Vietnam. … [1] (b) Which of Comoros or Vietnam has the greater population density? You must show all your working. population Population density = 2 > area(km ) H … [3]

4 marks

Mark scheme: 22(a) 108 700 000 1 or 1.087 × 108 22(b) 8.70 × 105 ÷ 1.86 × 103 oe M1 9.73 × 107 ÷ 3.10 × 105 oe M1 Comoros A1 Dependent on M2

This question in 0580/11 May/June 2022

22 North B NOT TO SCALE A The bearing of B from A is 059°. Work out the bearing of A from B. … [2]

2 marks

Mark scheme: 22 239 2 M1 for 180  59 or 360  180  59  oe or indicates correct angle on diagram

This question in 0580/12 May/June 2022

19 The bearing of A from B is 137°. Find the bearing of B from A. … [2]

2 marks

Mark scheme: 19 317 2 M1 for 137 + 180 oe

This question in 0580/11 Oct/Nov 2022

15 Jenna buys 2.4 m of ribbon and 4.8 m of fabric. The total cost is $33.48 . Ribbon costs $0.85 per metre. Find the cost of 1 m of fabric. $ … [3]

3 marks

Mark scheme: 15 6.55 3 M2 for (33.48 – 2.4 × 0.85) oe or M1 for 2.4 × 0.85

This question in 0580/12 Oct/Nov 2022

9 Nerina invests $5400 at a rate of r% per year simple interest. At the end of 3 years, the total interest earned is $429.30 . Calculate the value of r. r = … [2]

2 marks

Mark scheme: 9 2.65 2 5400 3 r M1 for = 429.3[0] oe or better 100

This question in 0580/13 Oct/Nov 2022

10 The cost of hiring a bicycle, $C, for y hours is given by the formula C = 12 + 3.5y . Maria pays $36.50 to hire this bicycle. Work out the number of hours she hires the bicycle for. … hours [2]

2 marks

Mark scheme: 10 7 2 M1 for 36.5[0] – 12 = 3.5y or better

This question in 0580/11 May/June 2023

16 Filip invests $4000 for 3 years at a rate of 2.5% per year simple interest. Calculate the value of his investment at the end of the 3 years. $ … [3]

3 marks

Mark scheme: 16 4300 3 B2 for 300 4000  2.5  3 or M2 for 4000 + oe 100 4000  2.5  3 or M1 for oe 100

This question in 0580/12 Oct/Nov 2023

23 Change 9.6 km/h into m/s. … m/s [2]

2 marks

Mark scheme: 23 2 2 9.6  1000 2 or 2.67 M1 for oe 3 60  60 or 2.666 to 2.667

This question in 0580/11 May/June 2024

3 A piece of string has length 65.1 cm. The string is cut into 7 equal pieces. Find the length of each piece. … cm [1]

1 marks

Mark scheme: 3 9.3 1

This question in 0580/13 Oct/Nov 2024