Graphs in practical situations — Paper 1 · IGCSE Mathematics 0580

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

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

18 100 B 80 60 Distance from A 40 (km) 20 A 10 00 11 00 12 00 13 00 14 00 15 00 Time of day (a) Carla drives from town A to a supermarket. At 11 00 she continues her journey to town B, driving at 80 km/h. The first part of the journey is shown on the grid above. (i) How many minutes is Carla at the supermarket? Answer(a) (i) min [1] (ii) Draw the rest of her journey to town B on the grid. [1] (b) Carla spends 1 hour in town B and then drives back to town A, at a constant speed, arriving at 14 30. Show this information on the grid. [2]

4 marks

Mark scheme: 18 (a)(i) 30 1 (ii) Straight line from (11 00, 20) to (11 45, 80) 1 Ignore all beyond (11 45, 80) (b) ‘Correct’ horizontal line 1 Horizontal line @ 80, 4 units long. ‘Correct’ return journey line 1 Line to (14 30, 0) 19 IGCSE - OCT/NOV 2006 0580, 0581 1

This question in 0580/11 Oct/Nov 2006

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

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

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 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

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

19 Alvin changes some money from dollars ($) to euros (€). When he changes $100 he receives €60. (a) On the grid, draw a conversion graph using this information. 160 140 120 100 Euros 80 (€) 60 40 20 0 0 20 40 60 80 100 120 140 160 180 200 220 240 Dollars ($) [2] (b) Use your graph to change (i) $140 to euros, € … [1] (ii) €20 to dollars. $ … [1]

4 marks

Mark scheme: 19(a) Ruled line through (0, 0) and (100, 60) 2 B1 for (100, 60) plotted 19(b)(i) 82 to 86 1 19(b)(ii) 31 to 35 1

This question in 0580/13 Oct/Nov 2017

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