Ordering — Paper 3 · IGCSE Mathematics 0580

2 5 (a) –4 –16 0.12 7 144 7 2 For 3 Examiner's Use From this list of numbers, write down (i) the smallest number, Answer(a)(i) [1] (ii) a natural number, Answer(a)(ii) [1] (iii) a square number, Answer(a)(iii) [1] (iv) an irrational number. Answer(a)(iv) [1] (b) Write down 40 as a product of prime numbers. (1 is not a prime number.) Answer(b) 40 = [2] (c) Three pairs of prime numbers have a sum of 40. One pair is 3 and 37. Find the other two pairs. Answer(c) and and [2]

8 marks

Mark scheme: 5 (a) (i) –16 B1 cao (ii) 7 or 144 or both B1 (iii) 144 B1 cao (iv) √7 B1 cao (b) 2 x 2 x 2 x 5 B2 B1 for 8x5, 2x20, 4x10, 2x4x5, or list 2, 2, 2, 5 (c) 11, 29 B1 cao 17, 23 B1 cao [8] IGCSE – October/November 2007 0580 and 0581 3

This question in 0580/31 Oct/Nov 2007

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

7 marks

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

This question in 0580/33 May/June 2012

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

14 marks

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

This question in 0580/31 Oct/Nov 2013

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

12 marks

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

This question in 0580/31 Oct/Nov 2014

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

11 marks

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

This question in 0580/31 May/June 2016

1 (a) Write down the temperature shown by each arrow. (i) Temperature (°C) 0 10 20 … °C [1] (ii) Temperature (°C) –20 0 20 … °C [1] (b) The table shows the daily temperature in Hayville for one week in January. Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday Temperature –4 2 –1 0 1 –6 –2 (°C) (i) Which was the coldest day? … [1] (ii) Find the difference between the temperature on Sunday and the temperature on Monday. … °C [1] (c) In Grassington, the temperature recorded at 07 35 was −3 °C. (i) The temperature was recorded again 8 12 hours later. At what time was this temperature recorded? … [1] (ii) By this time, the temperature had risen by 7 °C. Find this temperature. … °C [1]

6 marks

Mark scheme: Question Answer Marks Partial marks 1(a)(i) 16 1 1(a)(ii) –15 1 1(b)(i) Friday 1 1(b)(ii) 6 1 1(c)(i) 16 05 or 4 05 pm 1 1(c)(ii) 4 1

This question in 0580/31 Oct/Nov 2017

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

17 marks

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

This question in 0580/33 May/June 2018

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

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

13 marks

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

This question in 0580/31 Oct/Nov 2020

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

15 marks

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

This question in 0580/32 Feb/March 2024

10 3 0.41 17 42% 7 41 Write these numbers in order, starting with the smallest. … < … < … < … [2] smallest

2 marks

Mark scheme: 10 17 3 2 B1 for three in the correct order 0.41 42% or M1 for conversion to common 41 7 format e.g. 0.428…or 0.429 [0.41] 0.414…or 0.415 0.42 42.8…% or 42.9% 41% 41.4…% or 41.5% [42%]

This question in 0580/31 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