Averages and range — Paper 3 · IGCSE Mathematics 0580

8 (a) The list shows the rainfall in millimetres in Prestbury for the 12 months of 2002. For Examiner's 61 146 22 54 67 94 141 22 37 167 87 170 Use (i) Write down the mode. Answer(a)(i) mm [1] (ii) Find the median. Answer(a)(ii) mm [2] (iii) Calculate the mean. Answer(a)(iii) mm [2] (b) During the years 1996 - 2000 the total rainfall in Prestbury was 5400 millimetres. The pie chart shows how this was spread over the five years. 1996 2000 1997 1999 1998 (i) Measure the angles of the sectors for 1998, 1999 and 2000. For Write your answers in the table below. [3] Examiner's Use (ii) Work out the annual rainfall, in millimetres, for each of the years 1998, 1999 and 2000. Write your answers in the table below. [3] Answers (b)(i) and (ii) Year Angle (degrees) Rainfall (mm) 1996 54 810 1997 60 900 1998 1999 2000 Total 360 5400 (iii) What do you notice about the trend in the rainfall from 1996 to 2000? Answer(b)(iii) [1]

12 marks

Mark scheme: 8 a) i) 22 1 ii) 67 + 87 2 M1 for evidence of 77 or 2 ranking seen anywhere. e.g. 67,87 iii) 89 2 ∑x M1 for their 12 IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 3 b) i) 72 ± 1 1 80 ± 1 1 94 ± 1 1 ii) 1080 ± 5 1√ strict f.t.s for their angle x 15 ± 5 1200 ± 5 1√ 1410 ± 5 1√ iii) appropriate observation 1 12

This question in 0580/31 Oct/Nov 2004

5 For Examiner's 6 Use 1 5 2 4 3 (a) Asif tests a six-sided spinner. The results of 60 spins are shown below. 3 3 6 5 6 1 2 6 5 2 3 4 4 4 3 4 6 5 2 1 6 3 6 4 1 5 3 6 2 6 6 6 3 6 1 6 6 5 1 6 1 6 2 5 3 6 4 2 3 5 1 4 4 1 5 4 6 6 2 3 (i) Use these results to complete the frequency table. Number Frequency 1 2 3 4 5 6 [3] (ii) Write down the mode. Answer(a)(ii) [1] (iii) Find the median. Answer(a)(iii) [2] (iv) Calculate the mean. For Give your answer correct to one decimal place. Examiner's Use Answer(a)(iv) [3] (b) Asif tests a different six-sided spinner. He draws a bar chart to show the results. 14 12 10 8 Frequency 6 4 2 0 1 2 3 4 5 6 Number (i) How many times did he spin this spinner? Answer(b)(i) [2] (ii) Calculate the mean score for this spinner. Answer(b)(ii) [3]

14 marks

Mark scheme: 5 (a) (i) 8 7 10 9 8 18 3 2 for 4 or 5 correct, 1 for 2 or 3 correct accept tallies if in 5’s, accept 8/60, 7/60 etc. (ii) 6 1 c.a.o (iii) 4 2 c.a.o M1 for evidence of ranking (cum. freq.) IGCSE – JUNE 2005 0580/0581 3 (iv) 3.9 3 c.a.o M1 (f.t.) for 8 x 1 + 7 x 2 + 10 x 3 or 8 +14 +30 (min 3) M1 (f.t.) dep. for /60 [both M marks may be by the table] answer of 3.93(3333) is M2 implied 39.3(33...) is M1 implied (b) (i) 60 2 M1 for 10 + 7 + 10 + 7 + 14 + 12 (min 3) (ii) 3.7(3333 ) 3 M1 (f.t.) for 10 x 1 + 7 x 2 + 10 x 3 … or 10 +14 + 30 … (min 3) M1 (f.t.) dep. for /(b)(i) 14

This question in 0580/31 May/June 2005

4 Jane records the number of telephone calls she receives each day for two weeks. For Examiner's 5 6 10 0 15 6 12 2 13 16 0 16 6 10 Use (a) Calculate the mean. Answer(a) [3] (b) Find the median. Answer(b) [2] (c) Write down the mode. Answer(c) [1] (d) Complete the frequency table below. Number of calls 0 − 4 5 − 9 10 − 14 15 − 19 Frequency [2] (e) Find the probability that Jane receives (i) ten or more calls, Answer(e)(i) [1] (ii) less than five calls. Answer(e)(ii) [1] (f) Estimate the number of days in the next six weeks that Jane can expect to receive 10 − 14 calls. Answer(f) days [2]

12 marks

Mark scheme: 4 (a) 8.36 3 M1 for addition of at least 10 numbers M1 for divide by 14 (b) 8 www 2 M1 for ranking list seen or SC1 for (6 + 10)/2 seen (c) 6 1 (d) 3 4 4 3 2 1 for 2 or 3 correct (e) (i) 7/14 oe √1 ft for their (4 +3)/their 14, correct or ft correct (ii) 3/14 √1 (f) 12 √2 M1 for their (10 – 14) x 3 [12]

This question in 0580/31 Oct/Nov 2005

8 (a) Naomi records the sizes of the 34 pairs of shoes that her shop sells in one day. For Examiner's Use 4 10 5 6 4 8 6 4 7 3 9 7 4 7 3 5 4 6 5 10 7 5 5 6 4 7 7 6 6 5 5 3 5 6 (i) Using the list above complete the frequency table. Shoe size 3 4 5 6 7 8 9 10 Frequency [3] (ii) Calculate the mean of these shoe sizes. Answer(a) (ii) [3] (iii) Find the range of these sizes. Answer(a) (iii) [1] (iv) Find the mode of these sizes. Answer(a) (iv) [1] (v) Work out the median shoe size. Answer(a) (v) [2] (vi) Calculate the percentage of all the pairs of shoes that are size 7. Answer(a) (vi) %. [2] (vii) Naomi orders 306 pairs of shoes to sell in her shop. Estimate how many of these pairs of shoes should be size 7. Answer(a) (vii) [2] (b) Findlay draws a bar chart to show how many pairs of shoes he has sold in his shop in one week. For Examiner's Use 15 10 Frequency 5 3 4 5 6 7 8 9 10 Shoe size (i) Use the information in the bar chart to complete the frequency table below. Shoe size 3 and 4 5 and 6 7 and 8 9 and 10 Frequency [2] (ii) Which is the modal class in the frequency table? Answer(b) (ii) [1]

17 marks

Mark scheme: 8 (a) (i) 3 6 8 7 6 1 1 2 3 2 for 6 or 7 correct –1 if tally marks 1 for 4 or 5 correct (ii) 5.71 art 3 M1 for evidence of size x frequency calculated for the sizes. M1dep for sum of at least 5 ÷ 34 (iii) 7 cao 1 (iv) 5 cao 1 (v) 5.5 2 M1 for evidence of finding the middle shoe size. (Not just an answer of 5 or 6) (vi) 17.6 art 2ft M1 for their 6 ÷ 34 × 100 or 17.65 (vii) 54 or 53 2ft M1 for their 6 ÷ 34 × 306 or ‘53.8….’. or 53.9 (b) (i) 12 25 19 2 2 1 mark for 2 or 3 correct or all correct but not added (ii) 5 and 6 1ft Their class with the highest frequency. –1 for tally marks 17 IGCSE - OCT/NOV 2006 0580, 0581 3

This question in 0580/31 Oct/Nov 2006

1 Margarita keeps a record of all her marks for science experiments, as shown in the table below. For Examiner's Mark 5 6 7 8 9 10 Use Frequency 1 5 10 9 7 3 (a) (i) How many science experiments did Margarita do? Answer(a)(i) [1] (ii) Write down the mode. Answer(a)(ii) [1] (iii) Find the median. Answer(a)(iii) [1] (iv) Calculate the mean. Answer(a)(iv) [3] (b) Margarita draws a pie chart to show this information. The sectors for her marks of 5, 6, 7 and 8 have already been drawn. 5 6 7 8 (i) Calculate the angle of the sector for her mark of 9. Answer(b)(i) [2] (ii) Complete the pie chart accurately. [1]

9 marks

Mark scheme: 1 (a) (i) 35 B1 cao (ii) 7 B1 cao (iii) 8 B1 cao (iv) 7.71 art B3 ft M1 for 1x5 + 5x6 + 10x7 + 9x8 + 7x9 + 3x10 attempted M1 for ÷ 35 (ft from (a)(i) but not for 6) SC2 for 7.7 (b) (i) 72 2 M1 for 7/35 x 360 (ft but not for 6) oe (ii) line drawn B1 final line (ft) drawn accurately, 1° accuracy [9]

This question in 0580/31 Oct/Nov 2007

3 The table below shows the average daily sunshine, s, and the total monthly rainfall, r, for a city For during one year. Examiner's Use Month Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec s (hours) 6 7 7 9 10 12 12 12 9 8 6 5 r (mm) 70 52 72 41 20 6 1 4 16 52 65 67 (a) For s, find (i) the mode Answer(a)(i) hours [1] (ii) the range, Answer(a)(ii) hours [1] (iii) the median. Answer(a)(iii) hours [2] (b) On the grid below, plot the 10 points for March to December to complete the scatter diagram. r 70 60 50 Total 40 Monthly Rainfall (mm) 30 20 10 0 s 5 6 7 8 9 10 11 12 Average Daily Sunshine (hours) [3] (c) (i) Calculate the mean of s. For Examiner's Use Answer(c)(i) hours [2] (ii) The mean of r is 38.8 millimetres. On the grid, plot the point representing these means. Label this point M. [1] (d) (i) Draw a line of best fit on the grid. [1] (ii) What type of correlation does your scatter diagram show? Answer(d)(ii) [1]

12 marks

Mark scheme: 3 (a) (i) 12 W1 (ii) 7 W1 (iii) 8.5 W2 M1 for Attempt at ordering the data. (b) 10 points correctly plotted W3 W2 for 8 or 9 points correctly plotted W1 for 6 or 7 points correctly plotted IGCSE – October/November 2008 0580 and 0581 03

This question in 0580/31 Oct/Nov 2008

3 Twelve students each answer 30 questions in a quiz. Examiner's Use The time taken and the number of correct answers for each student is given in the table. Time taken in 9 4 5 10 3 2 8 8 4 5 6 7 minutes Number of correct 19 28 26 17 30 26 25 20 23 21 24 22 answers (a) Complete the scatter diagram below to show this information. The first six points have been plotted for you. 31 30 29 28 27 26 25 24 Number of correct 23 answers 22 21 20 19 18 17 16 15 0 1 2 3 4 5 6 7 8 9 10 11 Time taken in minutes [3] For (b) What type of correlation does the scatter diagram show? Examiner's Use Answer(b) [1] (c) (i) Find the range of the time taken. Answer(c)(i) min [1] (ii) Calculate the mean time taken. Answer(c)(ii) min [3] (d) (i) Find the mode for the number of correct answers. Answer(d)(i) [1] (ii) Find the median for the number of correct answers. Answer(d)(ii) [1] (e) One of the 12 students is selected at random. Write down the probability that the student (i) took more than 8 minutes to answer the quiz, Answer(e)(i) [1] (ii) took less than 5 minutes and had more than 24 correct answers. Answer(e)(ii) [2]

13 marks

Mark scheme: 3 (a) 6 points correctly plotted 3 P2 for 4 or 5 points, P1 for 2 or 3 points (b) negative cao 1 (c) (i) 8 cao 1 (ii) art 5.92 3 M1 for attempt to add the 12 values (for time) implied by 71 M1 dep for division by 12 SC1 for 23.4 (d) (i) 26 cao 1 (ii) 23.5 cao 1 2 (e) (i) oe 1 0.166 or 0.167 or 16.6% or 16.7% 12 3 (ii) oe 2 0.25 or 25% 12 SC1 for (4,28) (2,26) (3,30) listed or ringed on diagram or table

This question in 0580/31 May/June 2010

3 For Examiner's Month Total rainfall (mm) Average daily sunshine (hours) Use January 79 6 February 84 7 March 62 4.5 April 46 1.5 May 53 3.5 June 54 1.5 The table shows some data about rainfall and sunshine. (a) For the rainfall, calculate (i) the mean, Answer(a)(i) mm [2] (ii) the range. Answer(a)(ii) mm [1] (b) For the sunshine, find (i) the mode, Answer(b)(i) h [1] (ii) the median. Answer(b)(ii) h [2] (c) Dinesh draws a pie chart to display the rainfall data. Calculate the sector angle for February. Answer(c) [2] (d) Amalia draws a pictogram to display the sunshine data for January and February. For Examiner's Use January February March (i) Complete the key for the pictogram. represents [1] (ii) Complete the pictogram for March. [1] (e) Priya draws a scatter diagram to find the correlation between rainfall and sunshine for January to June. (i) Complete the scatter diagram below. January and February are plotted for you. 90 80 70 Total rainfall (mm) 60 50 40 0 1 2 3 4 5 6 7 Average daily sunshine (hours) [2] (ii) What type of correlation does the scatter diagram show? Answer(e)(ii) [1]

13 marks

Mark scheme: 3 (a) (i) 63 2 M1 for their “378” ÷ 6 or SC1 for 333 seen (ii) 38 cao 1 (b) (i) 1.5 cao 1 (ii) 4 2 B1 for attempt to order the numbers (c) 80° 2 M1 for 84 ÷ their total × 360 (d) (i) 1 hour 1 (ii) 4 and a half more suns drawn 1 Condone size, shape of suns (e) (i) 4 correct plots 2 B1 for 3 or 2 correct (ii) Positive 1 IGCSE – October/November 2010 0580 31

This question in 0580/31 Oct/Nov 2010

1 For 10 Examiner's Use 9 8 7 6 Frequency 5 4 3 2 1 0 0 1 2 3 4 5 6 Number of children The number of children in each of 40 families was recorded. The bar chart shows the results. (a) Complete the frequency table. Number of children 0 1 2 3 4 5 6 Frequency 4 6 [3] (b) Find (i) the mode, Answer(b)(i) [1] (ii) the median, Answer(b)(ii) [2] (iii) the mean. For Examiner's Use Answer(b)(iii) [3] (c) A pie chart showing the information has been started. (i) Calculate the angles of the sectors for 3 and 4 children. Answer(c)(i) , [3] (ii) Complete the pie chart accurately. 1 child 2 children 0 children 6 children 5 children [1]

13 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 10, 9, 5, 5, 1 3 B2 for 4 correct, B1 for 3 correct (b) (i) 2 1 (ii) 2.5 2 M1 for evidence of finding mid-value of 20 pieces of data (iii) 2.6 3 M1 for evidence of ∑fx then M1dep for ÷ 40 (c) (i) 81 or 45 2ft ft their 9 or their 5 M1 for their 9 or their 5 ÷ 40 × 360 45 or 81 1ft Correct or ft 126 – their first angle (ii) Correct angles of 81° and 45° 1ft ft only if add up to 126

This question in 0580/33 Oct/Nov 2010

3 The colours of 30 cars in a car park are shown in the frequency table. For Examiner's Use Colour Frequency Red 5 Silver 15 Black 6 White 4 (a) Complete the bar chart to represent this information. Frequency Red Silver Black White Colour [3] (b) Write down the mode. Answer(b) [1]

4 marks

Mark scheme: 3 (a) Scale shown on axis in 2s or 4s or 5s 1 Bars correct for their linear scale 2ft B1 for 3 bars correct or B1 for 4 correct tops only shown, B0 for line graph allow consistent gaps between bars (b) Silver 1

This question in 0580/32 May/June 2011

6 The number of ice-creams sold in a shop each month is shown in the table. For Examiner's Use Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Number of ice-creams 1300 1200 1700 1800 2300 2500 2800 2600 1500 1600 1100 1900 sold (a) (i) Find the range. Answer(a)(i) [1] (ii) Calculate the mean. Answer(a)(ii) [2] (iii) Find the median. Answer(a)(iii) [2] (b) The numbers of chocolate, strawberry and vanilla ice-creams sold are shown in the table. Flavour Number of ice-creams Pie chart sector angle Chocolate 4200 140° Strawberry 3600 Vanilla 3000 (i) Complete the table by working out the sector angles for strawberry and vanilla. [3] (ii) Complete the pie chart below and label the sectors. [2] (c) The table shows the average temperature and the number of ice-creams sold each month. For Examiner's Use Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Temperature 5.6 5.7 7.0 11.4 16.0 23.3 23.4 20.0 15.5 11.5 8.0 14.0 (°C) Number of ice-creams 1300 1200 1700 1800 2300 2500 2800 2600 1500 1600 1100 1900 sold (i) Complete the scatter diagram for the months August to December. The points for January to July are plotted for you. 3000 2500 Number of 2000 ice-creams sold 1500 1000 5 10 15 20 25 Average temperature (°C) [2] (ii) What type of correlation does the scatter diagram show? Answer(c)(ii) [1] (iii) Write down a statement connecting the number of ice-creams sold to the average monthly temperature. Answer(c)(iii) [1]

14 marks

Mark scheme: 6 (a) (i) 1700 1 (ii) 1858(.3…) or 1860 2 M1 for attempt at sum divided by 12 or SC1 for 20558.3 (iii) 1750 2 M1 for clear attempt to find the middle (b) (i) (Strawberry) 120 3 B2 if only one is correct (Vanilla) 100 B1 for Strawberry + Vanilla = 220 and/or M1 for (Strawberry) 3600 ÷ (4200 + 3600 +3000) × 360 or 140 ÷ 4200 × 3600 or better or (Vanilla) 3000 ÷ (4200 + 3600 +3000) × 360 or 140 ÷ 4200 × 3000 or better (ii) Angles correct 1ft Independent. Labelling with names 1ft Consistent with angles in their table. (c) (i) 5 points correctly plotted 2 B1 for 3 or 4 correct (ii) Positive 1 (iii) Hotter weather more sales 1 Or any equivalent statement IGCSE – May/June 2011 0580 32 7 (a) (i) −1, −3, 3 2 B1 for any 2 correct

This question in 0580/32 May/June 2011

8 The table shows the average temperature and rainfall each month at Wellington airport. For Examiner's Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Use Temperature 18 18 17 14 12 10 9 10 11 13 15 16 (°C) Rainfall 67 48 76 87 99 113 111 106 82 81 74 74 (mm) (a) Complete the bar chart to show the temperature each month. 20 18 16 14 12 Temperature 10 (°C) 8 6 4 2 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month [2] (b) For the rainfall calculate (i) the mean, Answer(b)(i) mm [2] (ii) the median. Answer(b)(ii) mm [2] (c) In the scatter diagram the rainfall for January to April is plotted against temperature. For Examiner's Use 120 115 110 105 100 95 90 85 Rainfall 80 (mm) 75 70 65 60 55 50 45 40 8 9 10 11 12 13 14 15 16 17 18 19 20 Temperature (°C) (i) Complete the scatter diagram by plotting the values for the months May to December. [3] (ii) Draw the line of best fit on the scatter diagram. [1] (iii) What type of correlation does the scatter diagram show? Answer(c)(iii) [1]

11 marks

Mark scheme: 8 (a) heights 11, 13, 15, 16 2 B1 for 3 correct (b) (i) 84.8(3…) 2 M1 addition of 12 rainfall values (ii) 81.5 2 Either M1 for evidence of ordering values or substantial part of list (at least first 7 or last 7) or M1 for answers of 81 and 82 (c) (i) 8 values correctly plotted P3 P2 for 6 or 7 correct P1 for 4 or 5 correct (ii) Line of best fit 1 Must be continuous and straight (iii) Negative 1 IGCSE – October/November 2011 0580 32

This question in 0580/32 Oct/Nov 2011

2 James takes 12 science tests during one school term. For These are his marks. Examiner's Use 18 11 20 15 15 12 15 9 11 15 14 13 (a) Find (i) the range, Answer(a)(i) [1] (ii) the mode, Answer(a)(ii) [1] (iii) the median, Answer(a)(iii) [2] (iv) the mean. Answer(a)(iv) [2] (b) James sorts his marks into three levels. For The levels are Satisfactory (less than 12), Good (12 to 16) and Excellent (more than 16). Examiner's Use (i) Complete the frequency table to show this information. Level Satisfactory Good Excellent Frequency 7 [1] (ii) Complete the pie chart accurately and label each sector. Good [2] (c) What fraction of the marks were Satisfactory or Good? Give your answer in its lowest terms. Answer(c) [2]

11 marks

Mark scheme: 2 (a) (i) 11 1 (ii) 15 1 (iii) 14.5 2 M1 for ordering list or substantial part of list or 14 & 15 (iv) 14 2 M1 for (9 + 11 + 11 + 12 + 13 + 14 + 15 + 15 + 15 + 15 + 18 + 20) (b) (i) 3, …, 2 1 (ii) Angles of 90° and 60° 1ft ft only if total equals 12 Correct labels 1 (Dependent) 5 10 their 3 + 7 (c) cao 2 M1 for or from table 6 12 their 12

This question in 0580/33 Oct/Nov 2011

7 For 8 Examiner's Use 7 6 5 Frequency 4 3 2 1 0 3 3 12 4 4 12 5 5 12 6 6 12 Shoe size The bar chart shows the frequencies of the shoe sizes for a group of students. (a) Use the information in the bar chart to complete the frequency table. 1 1 1 1 Shoe size 3 3 4 4 2 5 5 2 6 6 2 2 Frequency 4 1 [2] (b) How many students are in the group? Answer(b) [1] (c) Calculate the mean shoe size. Answer(c) [3]

6 marks

Mark scheme: 7 (a) …, 5, 8, 7, 6, 4, 5, … 2 B1 for 4 or 5 correct (b) 40 1ft (c) 4.5375 or 4.537 or 4.538 or 4.54 3 M1 for 4 × 3 + 5 × 3.5 + 8 × 4 + 7 × 4.5 + 6 × 5 www3 + 4 × 5.5 + 5 × 6 + 1 × 6.5 Allow 4.5 but only with working M1 dependent for dividing their 181.5 by their 40 (M1 + M1 implied by 175(.1625)) IGCSE – October/November 2011 0580 33

This question in 0580/33 Oct/Nov 2011

3 (a) Jon spins this 6-sided spinner. For 2 Examiner's 2 10 Use 4 8 6 The probability that the spinner lands on any of the six sides is equally likely. Write down the probability that the spinner lands on (i) the number 6, Answer(a)(i) [1] (ii) a prime number, Answer(a)(ii) [1] (iii) a number less than 11. Answer(a)(iii) [1] (b) Felix has a 12-sided spinner with the numbers 2, 4, 5, 7 and 9 written on it. It is equally likely to land on any side. The table shows the probability of the spinner landing on each number. Number on spinner 2 4 5 7 9 1 1 1 1 1 Probability 4 3 6 6 12 The diagram of the spinner has been completed for the number 2. Complete the diagram for the numbers 4, 5, 7 and 9. 2 2 2 [3] (c) Felix says that his spinner is more likely to land on a 2 than Jon’s spinner. Explain why he is wrong. Answer(c) [1] (d) Felix spins his 12-sided spinner 60 times and records the results. For Examiner's Use Number on spinner Frequency Pie chart sector angle 2 15 90° 4 20 120° 5 5 30° 7 12 9 8 (i) Complete the table by working out the sector angles for the numbers 7 and 9 . [3] (ii) Complete the pie chart. 2 4 [2] (iii) Write down the mode. Answer(d)(iii) [1] (iv) Calculate the mean. Answer(d)(iv) [3]

16 marks

Mark scheme: 1 3 (a) (i) oe 1 Accept 0.167 or 16.7% or better 6 2 1 (ii) oe 1 Accept or 0.333 or 33.3% or better 6 3 (iii) 1 1 Accept “one” or 100% (b) (2,2,2), 4,4,4,4,5,5,7,7,9 seen on 3 B1 for 4,4,4,4 seen spinner B1 for 5,5 AND 7,7 seen B1 for ONE 9 seen. 3 (c) Felix’s probability is which is 1 Accept equivalent reasoning 12 2 less than Jon’s probability (of ) 6 4 which is oe 12 360 (d) (i) (90°, 120°, 30°), 72°, 48° 3 M1 for × f for one ‘Number’ correct 60 A1 for 1 correct answer If zero scored SC1 for their two answers totalling 120° (ii) 30° angle correct 1 72°, 48° 1ft (iii) 4 1 (iv) 4.85 3 M1 2 × 15 + 4 × 20 + 5 × 5 + 7 × 12 + 9 × 8 (allow 1 error) Σfx M1 dep for their 60

This question in 0580/31 May/June 2012

6 The total distance, to the nearest kilometre, travelled by a taxi each day for 24 days is shown below. For Examiner's Use 100 98 95 98 97 99 96 98 97 98 97 99 100 96 97 99 100 250 97 99 98 95 97 96 (a) (i) Complete the frequency table. You may use the tally column to help you. Distance travelled (km) Tally Number of days 95 96 97 98 99 100 250 [2] (ii) Write down the mode. For Examiner's Use Answer(a)(ii) km [1] (iii) Find the median. Answer(a)(iii) km [2] (iv) Calculate the mean. Answer(a)(iv) km [3] (v) Which of the mean or the median best represents the average distance the taxi travels each day? Give a reason for your answer. Answer(a)(v) because [1] (b) Find the probability that, on a day chosen at random, the taxi travels 98 km or more. Answer(b) [2]

11 marks

Mark scheme: 6 (a) (i) 2, 3, 6, 5, 4, 3, 1 2 B1 for 4 correct or a fully correct tally (ii) 97 1ft Ft their table (iii) 98 2ft M1 for clear recognition of 12th / 13th value used IGCSE – May/June 2012 0580 32 (iv) 104 3 M1 for clear attempt at finding total hours (implied by 2496) M1 independent for division by 24 7 835 24 but not nor nor 24 24 24 (v) Median, extreme value 1 Any correct statement referring to the size of the 250 value

This question in 0580/32 May/June 2012

7 The table shows the marks for ten students in their Chemistry papers for Unit A and Unit B. For Examiner's Use Unit A 32 78 45 63 36 73 58 41 68 54 Unit B 43 81 49 58 40 74 60 50 72 59 (a) On the grid, complete the scatter diagram for these results. The first six points have been plotted for you. 90 80 70 Unit B 60 50 40 30 30 40 50 60 70 80 90 Unit A [2] (b) What type of correlation does the scatter diagram show? Answer(b) [1] (c) (i) Calculate the mean of the marks for Unit A. For Examiner's Use Answer(c)(i) [2] (ii) Work out the range of the marks for Unit A. Answer(c)(ii) [1] (iii) The mean for Unit B is 58.6 . Which unit did the students find more difficult? Give a reason for your answer. Answer(c)(iii) Unit because [1] (d) (i) Draw a line of best fit on the grid. [1] (ii) Lee scored 48 on Unit A but she was absent for Unit B. Use your line of best fit to estimate her score on Unit B. Answer(d)(ii) [1] (e) Find how many students scored more than 65 marks on both units. Answer(e) [1]

10 marks

Mark scheme: 7 (a) four points correctly plotted 2 M1 for three points correctly plotted (b) positive 1 ignore extras like ‘strong’ (c) (i) 54.8 2 M1 for their sum (548) ÷ 10 (ii) 46 1 (iii) A and it has a lower mean 1ft allow any correct reason using appropriate information from the table and ft their mean (d) (i) correct ruled line 1 at A = 40 allow 44–48 at A = 70 allow 70–78 (ii) correct reading from their line 1ft read from their ruled line (e) 3 1ft

This question in 0580/33 May/June 2012

3 (a) Amir asked 15 friends how many hours they spent playing sport last weekend. For His results are shown in the table below. Examiner's Use Number of hours 0 1 2 3 4 5 Frequency 6 2 3 1 2 1 (i) Write down the mode. Answer(a)(i) hours [1] (ii) Find the median. Answer(a)(ii) hours [1] (iii) Calculate the mean. Answer(a)(iii) hours [3] (iv) On the grid, draw a bar chart to show the information given in the table. Frequency Number of hours [4] (b) Amir also asked these 15 friends which was their favourite sport. For His results are shown in the table below. Examiner's Use Football 4 Cricket 5 Basketball 2 Badminton 4 Amir picks one of these friends at random. Write down the probability that his friend’s favourite sport is (i) cricket, Answer(b)(i) [1] (ii) not football, Answer(b)(ii) [1] (iii) basketball or badminton. Answer(b)(iii) [1]

12 marks

Mark scheme: 3 (a) (i) 0 1 (ii) 1 1 (iii) 1.6 3 M1 for (0 × 6) + 1 × 2 + 2 × 3 + 3 × 1 + 4 × 2 + 5 × 1 or better dep M1 for ‘their 24’ ÷ 15 (iv) Bar chart with 4 – horizontal axis correctly labelled B1 for horizontal axis labelled correctly – and vertical axis correctly scaled B1 for linear vertical scale to at least 5 – and bars of correct height and B2 for all bars correct height and equal width equal width, with equal or no gaps – and with equal gaps or no gaps Or B1 for unequal widths or at least four bars correct height and equal width 5 1 (b) (i) or 15 3 1 11 (ii) 1 15 6 2 (iii) or 1 15 5

This question in 0580/31 Oct/Nov 2012

4 The table shows a summary of the types of employment for 90 people. For Examiner′s Use Employment Frequency Pie chart sector angle Retail 18 72° Leisure industry 12 48° Public service 35 Other 25 (a) (i) Complete the table. [2] (ii) Complete the pie chart and label the sectors. Retail Leisure industry [2] (b) Here are the ages of the people working in the leisure industry. For Examiner′s Use 16 17 19 23 23 24 27 31 33 40 45 56 (i) Work out the range. Answer(b)(i) … years [1] (ii) Calculate the mean. Answer(b)(ii) … years [2] (iii) Sabrina wants to interview someone working in the leisure industry. She chooses one person at random. Write down the probability that the person chosen is under 30 years old. Answer(b)(iii) … [1] _____________________________________________________________________________________

8 marks

Mark scheme: 4 (a) (i) 140 1 if 0 scored SC1 for their total = 240 100 1 (ii) correct labelled pie chart 2ft B1 ft for correct sectors drawn B1 for correct labelling consistent with table (b) (i) 40 1 (ii) 29.5 2 M1 for (attempt to add ) ÷ 12 (iii) 7 1 isw oe 12

This question in 0580/31 May/June 2013

1 (a) For Examiner′s 3 5 8 10 10 Use For the numbers above, fi nd (i) the mean, Answer(a)(i) … [2] (ii) the mode, Answer(a)(ii) … [1] (iii) the median, Answer(a)(iii) … [1] (iv) the range. Answer(a)(iv) … [1] (v) A sixth number, 11, is added to the list. Write down which one of the mean, the mode, the median and the range will stay the same. Answer(a)(v) … [1] (b) The table shows the results of asking 24 children their favourite colour. Colour Red Blue Yellow Green Pink Number of children 4 8 2 3 7 Write down the probability, as a fraction, that the favourite colour of a child chosen at random is (i) blue, Answer(b)(i) … [1] (ii) not pink. Answer(b)(ii) … [1] (c) The information in part (b) is to be shown in a pie chart. Work out the sector angle for green. Do not draw the pie chart. Answer(c) … [2] _____________________________________________________________________________________

10 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) (i) 7.2 oe 2 M1 for (3 + 5 + 8 + 10 + 10)/5 or 36/5 (ii) 10 1 (iii) 8 1 (iv) 7 1 (v) Mode 1 8 (b) (i) oe 1 Must be a fraction 24 (ii) 17 1 SC1 for bi and bii both given as 24 decimals only i.e. 0.333(…..) and 0.708(….) (c) 45° 2 M1 for 360 × 3/24 or better seen

This question in 0580/32 May/June 2013

6 For Examiner′s Use Felix rolls two fair dice, each numbered from 1 to 6, and adds the numbers shown. He repeats the experiment 70 times and records the results in a frequency table. The fi rst 60 results are shown in the tally column of the table. The last 10 results are 6, 8, 9, 2, 6, 4, 7, 9, 6, 10 . Total Tally Frequency 2 3 4 5 6 7 8 9 10 11 12 (a) (i) Complete the frequency table to show all his results. [2] (ii) Write down the relative frequency of a total of 5. Answer(a)(ii) … [1] (b) (i) Write down the mode. For Examiner′s Use Answer(b)(i) … [1] (ii) Write down the range. Answer(b)(ii) … [1] (iii) Work out the median. Answer(b)(iii) … [2] (iv) Calculate the mean. Answer(b)(iv) … [3] (c) (i) Complete this table showing how different totals can be made when rolling two dice. Dice 1 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 3 Dice 2 4 7 5 7 9 6 12 [1] (ii) Explain why 7 is the most likely total. Answer(c)(ii) … [1] _____________________________________________________________________________________

12 marks

Mark scheme: 6 (a) (i) Frequency table completed 2 M1 for 8 correct frequencies SC1 for all correct tallies if no frequencies. OR SC1 for all correct frequencies in tally column (ii) 3 1 ft ft their table oe 70 (b) (i) 6 1 (ii) 10 1 (iii) 6 2 M1 for clear recognition of mid values used (iv) 6.43 to 3sf 3 M1 for total of freq × their result M1 dep for division by their 70 (c) (i) All totals filled in 1 Allow 1 error or omission (ii) More ways of getting 7 1 Any equivalent explanation

This question in 0580/33 May/June 2013

1 Pedro is on a cruise ship. For Examiner′s Use (a) The ship has a climbing wall. These are the number of attempts that each of 30 people made at climbing the wall. 29 27 11 3 12 4 29 9 16 17 30 29 38 36 18 2 15 24 36 3 33 26 21 9 38 4 28 23 19 27 (i) Find the range. Answer(a)(i) … [1] (ii) Complete the frequency table. You may use the tally column to help you. Number of attempts Tally Frequency 1 – 5 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30 31 – 35 36 – 40 [2] (iii) Draw a bar chart to show this information. Complete the scale on the frequency axis. Frequency 1 – 5 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30 31 – 35 36 – 40 Number of attempts [3] (iv) Write down the modal group. For Examiner′s Use Answer(a)(iv) … [1] (b) Pedro left the ship in Cadiz at 08 45. He returned to the ship at 16 10. Find how long Pedro was in Cadiz. Answer(b) … hours … minutes [1] (c) Exchange Rate $1 = €1.428 (i) Pedro changed $167 into euros (€). Calculate how many euros Pedro received. Give your answer correct to 2 decimal places. Answer(c)(i) € … [2] (ii) Later, Pedro changed €107.10 back into dollars ($) using the same exchange rate. Calculate how many dollars Pedro received. Answer(c)(ii) $ … [2] _____________________________________________________________________________________

12 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) (i) 36 cao 1 (ii) 5, 2, 3, 4, 3, 8, 1, 4 2 B1 for 6 or 7 frequencies correct or 8 correct tallies if frequency column blank or 8 correct frequencies in tally column (iii) fully correct bar chart 3FT B1 for a correct linear scaled frequency axis B2FT for correct height and equal width of bars or B1FT for correct height of at least 5 bars or all bars correct height but unequal widths or gaps SC2 for a fully correct bar chart but linear scale not marked (iv) 26 – 30 cao 1 (b) 7 (hours) 25 ( minutes) cao 1 (c) (i) 238.48 2 M1 for 167 × 1.428 soi by 238.47(6) or 238.5 or 238 (ii) 75 2 M1 for 107.1 ÷ 1.428

This question in 0580/31 Oct/Nov 2013

7 12 people each solved the same puzzle. For Examiner′s The table shows their ages and the time they each took to solve the puzzle. Use Age (years) 19 24 28 16 25 20 15 22 32 30 68 16 Time (seconds) 36 38 42 36 45 42 32 40 40 46 56 38 (a) Find the median age. Answer(a) … years [2] (b) For these 12 people, explain why the mean age may not be an appropriate average. Answer(b) … … [1] (c) Calculate the mean time taken. Answer(c) … seconds [2] (d) (i) Complete the scatter diagram. For Examiner′s The fi rst six points have been plotted for you. Use 70 60 50 40 Time (seconds) 30 20 10 0 10 20 30 40 50 60 70 Age (years) [2] (ii) What type of correlation does the scatter diagram show? Answer(d)(ii) … [1] (iii) Draw a line of best fi t on the scatter diagram. [1] (iv) Would it be sensible to use your line of best fi t to estimate the time taken by a child aged 8 to solve the puzzle? Explain your answer. Answer(d)(iv) … because … … [1] _____________________________________________________________________________________

10 marks

Mark scheme: 7 (a) 23 2 M1 for clear attempt to find middle If zero scored then SC1 for 40 (b) [Affected by an] extreme value oe 1 (c) 40.9 2 M1 for (36+38+42+36+45+42+32+40+40+46+56+38) ÷ 12 implied by 491 ÷ 12 If zero scored then SC1 for 26.25 or 26.3 (d) (i) 6 points correctly plotted P2 P1 for 4 or 5 correctly plotted (ii) positive 1 (iii) line of best fit ruled and 1 dep on at least 11 points on graph continuous (iv) No, [estimate unreliable as] 1 outside range [of data] IGCSE – October/November 2013 0580 32

This question in 0580/32 Oct/Nov 2013

6 Alison scored the following number of runs in 15 cricket matches. For Examiner′s Use 12 3 27 35 0 7 52 4 18 30 18 7 94 61 7 (a) For these scores, (i) work out the median, Answer(a)(i) … [2] (ii) write down the mode, Answer(a)(ii) … [1] (iii) calculate the mean. Answer(a)(iii) … [2] (b) These are the averages for the number of runs scored by Bethan in the 15 matches. Median = 21 Mode = 13 Mean = 20 Alison says that her scores are better than Bethan’s scores. Bethan says that her scores are better than Alison’s scores. Explain how they could both be correct. Answer(b) … … … [2] (c) Alison puts her 15 scores into 4 groups and shows them in a pie chart. For Examiner′s Use (i) Complete the table. Score Frequency Sector Angle 0 to 25 9 216° 26 to 50 51 to 75 76 to 100 [3] (ii) Complete the pie chart and label the sectors. 0 to 25 [3] (d) Estimate the probability that in the next match Alison will score more than 25 runs. Give your answer as a fraction in its simplest form. Answer(d) … [2] _____________________________________________________________________________________

15 marks

Mark scheme: 6 (a) (i) 18 2 M1 for evidence of ordering (ii) 7 1 (iii) 25 2 M1 for sum of 15 items ÷ 15 soi (b) Alison with reference to [higher] mean 1FT Strict FT and Bethan with reference to [higher] median 1FT Strict FT (c) (i) [Frequencies] 3, 2, 1 1 [Angles] 72°, 48°, 24° 2 B1 for 1 correct or M1 for one frequency ÷ 15 × 360 or × 24 (ii) Two correct sectors on pie chart 2FT B1FT for 1 correct sector Only ft if (c)(i) angles total 144 3 ‘correct’ labels 1 Independent 2 6 (d) 2 B1 for 0.4 or 40% or or any equivalent 5 15 fraction

This question in 0580/33 Oct/Nov 2013

4 Denzil grows tomatoes. He selects a random sample of 25 tomatoes. The mass of each tomato, to the nearest 5 grams, is shown below. 55 65 50 75 65 80 70 70 55 60 70 60 65 50 75 65 70 75 80 70 55 65 70 80 55 (a) (i) Complete the frequency table. You may use the tally column to help you. Mass Tally Frequency (grams) 50 55 60 65 70 75 80 [2] (ii) Write down the mode. Answer(a)(ii) … g [1] (iii) Find the range. Answer(a)(iii) … g [1] (iv) Show that the mean mass is 66 g. Answer(a)(iv) [2] (b) Denzil picks 800 tomatoes. 4% of the 800 tomatoes are damaged. How many of these tomatoes are not damaged? Answer(b) … [2] (c) Denzil sells 750 of his tomatoes. (i) The mean mass of a tomato is 66 g. Calculate the mass of the 750 tomatoes in kilograms. Answer(c)(i) … kg [3] (ii) Denzil sells his tomatoes at $1.40 per kilogram. Calculate the total amount he receives from selling all the 750 tomatoes. Answer(c)(ii) $ … [1] (iii) The cost of growing these tomatoes was $33. Calculate his percentage profi t. Answer(c)(iii) … % [3] __________________________________________________________________________________________

15 marks

Mark scheme: 4 (a) (i) 2, 4, 2, 5, 6, 3, 3 2 B1 for 5 or 6 correct Or 7 correct tallies if frequency column blank Or 7 correct frequencies in tally column (ii) 70 1FT (iii) 30 1 (iv) ∑(Frequency, f × mass, w) M1 7 items attempted and added or sum of 25 masses 1650 ÷ 25 B1 (b) 768 2 M1 for 0.96 × 800 oe IGCSE – May/June 2014 0580 31 (c) (i) 49.5 cao 3 M1 for figs 66 × 750 soi M1 for ÷ 1000 (ii) 69.3[0] 1 FT Their (c)(i) × 1.40 (iii) 110 3 their ( c )(ii ) − 33 M2 for × 100 33 or M1 for their (c)(ii) − 33 Alternative method their ( c )(ii ) M2 for × 100 – 100 33 their ( c )(ii ) Or M1 for 33

This question in 0580/31 May/June 2014

4 Paolo’s football team played 46 games. The pictogram shows some information about the number of goals scored by Paolo’s football team. They did not score any goals in fi ve games. Number Number of games of goals 0 1 2 3 4 5 6 Key: = … games (a) (i) Complete the key. [1] (ii) Paolo’s team scored 2 goals in each of nine games. Complete the pictogram. [1] (b) (i) Write down the modal number of goals. Answer(b)(i) … [1] (ii) Find the median number of goals. Answer(b)(ii) … [1] (iii) Find the range. Answer(b)(iii) … [1] (iv) One of the 46 games is chosen at random. Work out the probability that Paolo’s team scored at least 4 goals. Answer(b)(iv) … [2] (c) The table shows the total goals scored and the total points gained by 10 teams. Team A B C D E F G H I J Goals 31 40 46 50 43 92 60 84 68 87 Points 36 35 52 56 72 78 59 70 61 75 (i) Complete the scatter diagram. The fi rst six points have been plotted for you. [2] 80 70 60 Points 50 40 30 30 40 50 60 70 80 90 100 Goals (ii) Draw the line of best fi t. [1] (iii) What type of correlation is shown? Answer(c)(iii) … [1] (iv) Use your line of best fi t to estimate the total points gained by a team scoring 75 goals. Answer(c)(iv) … [1] (v) Which team only scores a few goals but gains a lot of points? Answer(c)(v) … [1] __________________________________________________________________________________________

13 marks

Mark scheme: 4 (a) (i) 2 1 (ii) 4 and a half circles 1FT FT is 9 / their a(i) if their a(i) is an integer (b) (i) 1 1FT (ii) 2 cao 1 (iii) 6 cao 1 (iv) 13 oe isw 2 M1 for 13 seen or (6 + 5 + 2) / 46 or 6 1 / 23 46 2 (c) (i) 2 M1 for 3 points correctly plotted four points correctly plotted (ii) 1 dependent on at least 9 points on graph continuous ruled line of best fit (iii) 1 positive (iv) 1FT 65 to 70 (v) E 1 FT their continuous ruled line of best fit if positive

This question in 0580/32 May/June 2014

4 The ages of 15 children who go to a swimming club are shown below. 10 11 10 12 12 13 11 12 12 12 12 10 11 11 11 (a) Complete the frequency table. You may use the tally column to help you. Age Tally Frequency 10 11 12 13 [2] (b) For the ages of the 15 children, fi nd (i) the range, Answer(b)(i) … [1] (ii) the mode, Answer(b)(ii) … [1] (iii) the median, Answer(b)(iii) … [1] (iv) the mean. Answer(b)(iv) … [2] (c) One child is chosen at random from the group. Write down the probability that the child’s age is (i) 10, Answer(c)(i) … [1] (ii) more than 13. Answer(c)(ii) … [1] __________________________________________________________________________________________

9 marks

Mark scheme: 4 (a) Frequencies 3, 5, 6, 1 2 B1 for 4 frequencies adding to 15 and at least two correct values or B1 for three correct values SC1 for fully correct tallies and nothing in frequency column. (b) (i) 3 1 (ii) 12 1 (iii) 11 1 (iv) 11.3 (…) 2 M1 for (10 × their 3 +11 × their 5 + 12 × their 6 +13 × their 1)÷15 3 1 (c) (i) or or 0.2 1FT isw 15 5 (ii) 0 1 IGCSE – May/June 2014 0580 33

This question in 0580/33 May/June 2014

8 (a) One day a survey is taken of the ages of 120 children at a fairground. The results are shown in the frequency table. Age in completed years Number of children 1 to 3 12 4 to 6 19 7 to 9 32 10 to 12 41 13 to 15 9 16 to 18 7 (i) On the grid, draw a bar chart for this data. Complete the scale on the frequency axis. Frequency 1 to 3 4 to 6 7 to 9 10 to 12 13 to 15 16 to 18 Age in completed years [3] (ii) What is the modal age group? Answer(a)(ii) … [1] (iii) One of the 120 children is chosen at random. Write down the probability that the child is aged 4 to 6. Answer(a)(iii) … [1] (b) Lalia says the probability of taking a yellow bead from a bag containing yellow beads and black 7 beads is . 5 7 Explain why cannot be a correct probability. 5 Answer(b) … [1] (c) Another bag contains 9 green marbles and 11 red marbles. A marble is taken at random. Write down the probability that the marble is (i) green, Answer(c)(i) … [1] (ii) blue. Answer(c)(ii) … [1] __________________________________________________________________________________________ Question 9 is printed on the next page.

8 marks

Mark scheme: 8 (a) (i) Correct diagram with scale 3 B1 scale correct. B1 for all widths the same B1 for all 6 heights correct (ii) 10 to 12 cao 1 19 (iii) or 0.158[3 … ] or 15.8[3 … ]% 1 120 (b) Probability must be between 0 and 1 oe 1 9 (c) (i) or 0.45 or 45% 1 20 (ii) 0 oe 1

This question in 0580/31 Oct/Nov 2014

7 (a) 21 11 7 29 3 20 24 8 18 14 For these numbers (i) calculate the mean, Answer(a)(i) … [2] (ii) fi nd the median, Answer(a)(ii) … [2] (iii) fi nd the range. Answer(a)(iii) … [1] (b) The table shows the number of births for each month of 2013 in a hospital. Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 319 299 336 309 334 336 348 363 351 347 331 335 (i) On the grid opposite, complete the bar chart. The fi rst 6 months have been drawn for you. [2] (ii) Write down the modal month. Answer(b)(ii) … [1] (iii) A month is chosen at random. Find the probability that the number of births in that month is greater than 340. Answer(b)(iii) … [1] 370 360 350 340 Number of births 330 320 310 300 290 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month __________________________________________________________________________________________

9 marks

Mark scheme: 7 (a) (i) 15.5 2 M1 Sum of the 10 items of data ÷ 10 (ii) 16 2 M1 for ordering at least first or last 6 items or for 14 and 18 indicated (iii) 26 1 (b) (i) 6 correct bars 2 B1 for 4 or 5 correct bars or 6 correct heights (ii) Aug[ust] 1 (iii) 1 4 oe 12

This question in 0580/32 Oct/Nov 2014

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

14 marks

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

This question in 0580/32 Feb/March 2015

7 A machine produces nails. (a) A random sample of 100 nails is taken from the machine. The lengths are measured and recorded in the table. Length (mm) 62 63 64 65 66 67 68 Number of nails 0 12 30 35 8 0 (i) Complete the table. [1] (ii) Write down the modal length. Answer(a)(ii) … mm [1] (iii) Write down the range of the lengths. Answer(a)(iii) … mm [1] (iv) Calculate the mean length. Answer(a)(iv) … mm [3] (v) Nails that have length 64 mm, 65 mm or 66 mm are accepted. Other nails are rejected. Number of nails accepted 80 Number of nails rejected 20 Complete the pie chart to show the proportion of nails that are accepted and rejected. [3] (b) One nail from the machine measures 65 mm, correct to the nearest millimetre. Complete the statement about the length, n mm, of this nail. Answer(b) … G n 1 … [2] __________________________________________________________________________________________

11 marks

Mark scheme: 7 (a) (i) 15 1 (ii) 65 1 (iii) 4 1 (iv) 64.77 or 64.8 3 M1FT for 63 × 12 + 64 × 30 + 65 × 35 + 66 × their 15 + 67 × 8 M1FT dep for their total ÷ 100 (v) Line at 72° to the given line 3 M2 for 288° or 72° or 80 20 M1 for × 360 or × 360 100 100 (b) 64.5 65.5 1, 1 If zero scored, SC1 for correct but wrong way round

This question in 0580/32 May/June 2015

1 (a) The number of trains stopping each day, for 20 days, at Pherlak Station is recorded below. 15 14 16 14 13 13 12 15 16 15 14 13 14 13 13 12 11 12 10 10 (i) Complete the table to show the frequency of the number of trains stopping each day. Number of trains stopping each day Tally Frequency 10 11 12 13 14 15 16 [2] (ii) Write down the modal number of trains stopping each day. Answer(a)(ii) … [1] (iii) Work out the mean number of trains stopping each day. Answer(a)(iii) … [2] (iv) The time of the last train to leave one night is shown on this clock. 12 11 1 10 2 9 3 8 4 7 5 6 Write down this time using the 24-hour clock. Answer(a)(iv) … [1] (b) This bar chart shows the number of trains stopping each day, for 20 days, at Sparke Station. 7 6 5 4 Frequency 3 2 1 0 10 11 12 13 14 15 16 Number of trains (i) Write down the modal number of trains stopping each day at Sparke Station. Answer(b)(i) … [1] (ii) Write down the range of the number of trains stopping each day at Sparke Station. Answer(b)(ii) … [1] (iii) Write one comment comparing the number of trains stopping each day at Pherlak Station to those stopping at Sparke Station. Answer(b)(iii) … … … [1]

9 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 2, 1, 3, 5, 4, 3, 2 2 M1 for 4 correct frequencies or all tallies correct and frequency column blank or for all frequencies correct in tally column (ii) 13 1 (iii) 13.25 2 M1FT for attempt at their Σ(xf ) ÷ 20 (iv) 23 50 cao 1 (b) (i) 16 1 (ii) 6 1 (iii) one correct comment 1 examples; Mode for Sparke(16) greater than mode for Pherlak(13) ; the range is the same for both; the mean is the same for both [13.25]; the total [number of trains] is the same [265]; median for Sparke(13.5) greater than median for Pherlak(13)

This question in 0580/33 May/June 2015

5 (a) The table shows the age and the total distance travelled for 10 cars. Car A B C D E F G H I J Age (years) 5 9 12 3 7 4 10 11 5 9 Total distance (thousand km) 86 126 156 48 148 60 70 150 105 138 (i) Find the mean age of the cars. … years [2] (ii) Complete the scatter diagram. The first six points have been plotted for you. 160 140 120 100 Total distance 80(thousand km) 60 40 20 0 2 4 6 8 10 12 14 Age (years) [2] (iii) What type of correlation does the scatter diagram show? … [1] (iv) Draw the line of best fit on the scatter diagram. [1] (v) Use your line of best fit to estimate the total distance travelled by a car that is 6 years old. … thousand km [1] (vi) Car G travelled less than the average number of kilometres per year. Explain how you know this from your scatter diagram. … [1] (b) Juan is a car salesman. (i) Last year, Juan sold 75 small cars, 45 medium cars and 30 large cars. Find the ratio small cars : medium cars : large cars in its simplest form. … : … : … [2] (ii) Ana wants to buy a car with a price of $2550. Juan reduces the price by 12%. Calculate the amount Ana pays for this car. $ … [2] (iii) Juan advertises a car for sale. Plan A Cash price $4500 OR Plan B 15% of the cash price plus 36 monthly payments of $120 Work out how much more it costs to buy the car using Plan B than using Plan A. $ … [3]

15 marks

Mark scheme: 5 (a) (i) 7.5 2 M1 for (5+9+12+3+7+4+10+11+5+9) ÷ 10 or better (ii) 4 points correct 2 B1 for 3 correct (iii) Positive 1 (iv) Ruled line of best fit 1 (v) 84 to 96 1FT FT their positive line of best fit (vi) (Point) below /lower than/right of/under 1 line (of best fit) (b) (i) 5 : 3 : 2 2 M1 for 75 : 45 : 30 or better (ii) 2244 2 M1 for [ 2550 × ] 0.88 oe (iii) 495 3 M2 for 36 × 120 + 0.15 × 4500 soi or M1 for 36 × 120 or 0.15 × 4500 soi

This question in 0580/32 May/June 2016

4 A garage sells second-hand cars. The table shows the number of cars sold and the year they were made. Year 2010 2011 2012 2013 2014 2015 Frequency 14 13 4 8 0 11 (a) Complete the bar chart to show this information. 16 14 12 10 Frequency 8 6 4 2 0 2010 2011 2012 2013 2014 2015 Year [2] (b) For these cars, write down the modal year. … [1] (c) The garage sold 6 cars last week. The selling prices, in dollars, are listed below. 920 1070 3100 2240 2650 1840 (i) Work out the range. $ … [1] (ii) Work out the median. $ … [2] (iii) Calculate the mean. $ … [2]

8 marks

Mark scheme: 4 (a) 5 bars correct heights and equal 2 B1 for 4 bars correct height and equal widths widths or 5 bars of correct height (b) 2010 1 (c) (i) 2180 1 (ii) 2040 2 B1 for ordering at least 4 or identifying the middle two (iii) 1970 2 M1 for (920 + 1070 + 3100 + 2240 + 2650 + 1840) ÷ 6 or 11820 ÷ 6

This question in 0580/33 May/June 2016

2 Javier went to a carnival with his friends. (a) He played five games of darts. These are his scores. 160 58 45 82 125 (i) Work out his mean score. … [2] (ii) Find the range. … [1] (b) The 5000 tickets for the carnival are different colours. The table shows the number of tickets of each colour. Colour of ticket Red Green Blue Pink White Number of tickets 370 560 1800 1320 950 A ticket is picked at random. Find the probability that this ticket is Blue. … [1] (c) Five different types of food are sold at the carnival. Javier chooses one of these types of food. The table shows the probability that he chooses each type of food. Type of food Curry Fries Pasta Burger Salad Probability 0.15 0.23 0.4 0.07 Complete the table. [2] (d) Javier hires a four-seater bike. The hire cost is $8.50 for the first hour and then $7.75 for each extra hour. Calculate the cost of hiring the bike for 5 hours. $ … [2] (e) The table shows the number of drinks sold by one stall at the carnival. Drink Number sold Tea 70 Orange 60 Water 120 Coffee 180 Smoothie 40 Draw a bar chart to show this information. Complete the scale on the frequency axis. Frequency Tea Orange Water Coffee Smoothie [3]

11 marks

Mark scheme: 160 + 58 + 45 + 82 + 125 470 2 (a) (i) 94 2 M1 for or 5 5 (ii) 115 1 1800 (b) oe isw 1 5000 (c) [0].15 oe 2 M1 for 1 – ( 0.15 + 0.23 + 0.4 + 0.07) or 1 – 0.85 (d) 39.5[0] 2 M1 for [8.50 +] (7.75 × 4) soi by 31 If zero scored, SC1 for 47.25 (e) Correct bar chart 3 B1 for any correct linear scale starting at zero soi B2 for all bars correct height and equal width, with equal gaps or no gaps or B1 for all bars correct height with unequal widths and/or gaps or at least three bars correct height with equal width, with equal gaps or no gaps

This question in 0580/31 Oct/Nov 2016

2 Eight athletes compete in both the 200 metre race and the long jump. Their results are shown in the table. Time for 200 m 23.85 23.91 23.92 23.96 24.02 24.15 24.23 24.30 (seconds) Distance in the 6.42 6.32 6.24 6.18 6.05 5.97 5.90 5.84 long jump (metres) (a) (i) Work out the range of the times for the 200 metre race. … s [1] (ii) Work out the mean of the distances in the long jump. … m [2] (b) (i) Complete the scatter diagram. The first four points have been plotted for you. 6.5 6.4 6.3 6.2 6.1 Distance in the 6.0 long jump (m) 5.9 5.8 5.7 5.6 5.5 23.8 23.9 24.0 24.1 24.2 24.3 Time for 200 m (s) [2] (ii) What type of correlation is shown on the scatter diagram? … [1] (iii) Joe says that the scatter diagram shows that the faster an athlete runs the 200 metre race the shorter their distance in the long jump. Is he correct? Explain your answer. … because … … [1] (iv) Draw a line of best fit on the scatter diagram. [1] (v) Jessica’s time for the 200 metre race is 24.05 s. Use your line of best fit to estimate her distance in the long jump. … m [1]

9 marks

Mark scheme: 2 (a) (i) [0].45 1 (ii) 6.115 or 6.12 2 M1 for adding the lengths (soi by 48.92) ÷ 8 (b) (i) 4 correct points 2 B1 for 2 or 3 correct points (ii) Negative 1 (iii) No [because] the faster an 1 Accept any correct statement athlete runs the further they jump oe (iv) Correct ruled line of best fit 1 (v) Correct distance from their line 1FT Strict 1FT from straight line with negative of best fit gradient

This question in 0580/33 Oct/Nov 2016

3 Francis asks 30 families how many children they have. The table shows the results. Number of children in each family 0 1 2 3 4 5 Number of families 4 6 6 2 9 3 (a) (i) Write down the mode. … [1] (ii) Find the median. … [1] (iii) Calculate the mean. … [3] (iv) Complete the bar chart, including the vertical scale. Number of families 0 1 2 3 4 5 Number of children in each family [3] (b) Francis also recorded the age group and gender of the children aged 12 or less. The information is shown in the table. Age 4 and Age 5 to 8 Age 9 to 12 Total younger Male 9 Female 11 36 Total 30 20 75 Complete the table. [2] (c) Francis displays the results for the totals of each age group on a pie chart. The sector angle for the group ‘Age 4 and younger’ is 120°. Calculate the sector angle for (i) age 5 to 8, … [2] (ii) age 9 to 12. … [1] (d) Complete the pie chart. Age 4 and younger [1]

14 marks

Mark scheme: 3(a)(i) 4 1 3(a)(ii) 2 1 3(a)(iii) 2.5 3 M1 for [(0 × 4)+] (1 × 6) + (2 × 6) + (3 × 2) + (4 × 9) + (5 × 3) oe M1 dep their total ÷ 30 soi 3(a)(iv) 4 bars correct height, correct 2 B1 for 2 bars correct heights and widths, or 4 correct width and correct gaps heights Correct vertical scale shown 1 3(b) 6 values correctly placed 2 B1 for 3, 4 or 5 correctly placed 14 16 [9] 39 [11] 14 11 [36] 25 [30] [20] [75] 3(c)(i) 144 2 M1 for 30 ÷ 75 [× 360] oe 3(c)(ii) 96 1FT FT 240 – their (c)(i) 3(d) Correct line from centre to 1FT FT their angles provided they sum to 240° circumference, angles 144° and 96°

This question in 0580/31 May/June 2017

1 Some children chose their favourite ice-cream flavour from chocolate, vanilla, strawberry and banana. Some of the results are shown in the pie chart below. Chocolate 72° 126° Vanilla (a) 8 children chose chocolate. Work out the total number of children. … [2] (b) Work out how many children chose vanilla. … [2] (c) The rest of the children chose strawberry or banana. Twice as many children chose strawberry as chose banana. Use this information to complete the pie chart. [2] (d) Write down the flavour of ice-cream that is the mode. … [1]

7 marks

Mark scheme: Question Answer Marks Part marks 1(a) 40 2 360 M1 for × 8 oe 72 1(b) 14 2 126 126 M1 for × 8 oe or ×their 40 oe 72 360 1(c) Correct ruled line drawn 2 162 162 M1 for [ = 54 ] or × 2 [ = 108 ] 3 3 72 or (their 40 −−8 their 14) ÷ 3 × [ × 2 ] 8 1(d) Vanilla 1FT FT from their pie chart

This question in 0580/33 May/June 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

6 (a) Luca records the total distance, in kilometres, he walks each day for 10 days. Here are his results. 4.7 2.4 10.3 3.6 2.3 4.3 5.1 2.6 6.9 9.6 (i) Find the median. … km [2] (ii) Find the range. … km [1] (iii) Calculate the mean. … km [2] (b) (i) On another day, Luca walks 9 km. He starts walking at 14 20 and he walks at an average speed of 6 km/h. Work out the time he finishes. … [2] (ii) Convert 6 km/h to metres per minute. … m/min [2] (c) For another 10 days, Luca records the distance he walks each day and the time it takes. The scatter diagram shows this information. 70 60 50 40 Time (minutes) 30 20 10 0 0 1 2 3 4 5 6 Distance (km) (i) What type of correlation is shown on the scatter diagram? … [1] (ii) On one of these days, Luca’s average speed was much slower than on all of the other days. Draw a ring around this point on the scatter diagram. [1]

11 marks

Mark scheme: 6(a)(i) 4.5 2 M1 for ordered list of at least 6 values or B1 for 4.3 and 4.7 both identified 6(a)(ii) 8 1 6(a)(iii) 5.18 2 M1 for sum of 10 distances ÷ 10 6(b)(i) 15 50 or 3.50 pm 2 M1 for 9 ÷ 6 or 1.5 hours oe seen 6(b)(ii) 100 2 M1 for 6 × 1000 or 6 ÷ 60 soi 6(c)(i) Positive 1 6(c)(ii) Point (4, 68) indicated 1

This question in 0580/33 Oct/Nov 2017

1 Mr Marr asks his mathematics class to complete a statistics project about books. (a) Olga counts the number of letters in each of the last 50 words in the book she is reading. She has only counted the letters in 43 words so far. Her results for these 43 words are shown in the table below. Number of letters Tally Frequency in each word 1 2 3 4 5 6 7 8 9 The last seven words in the book that Olga needs to add to the table are ………. and they all lived happily ever after. (i) Complete the tally and frequency columns in the table. [2] (ii) Find the range. … [1] (iii) Find the median. … [1] (b) Billie asks 60 students in his school what their favourite type of book is. He has started to draw a pictogram to show his results. Type of book Frequency Comedy Science fiction 10 Poetry Music Romance 8 Detective 14 Key: represents … books. The science fiction row in the pictogram is complete. (i) Complete the key. [1] (ii) Complete the pictogram. [2] (iii) Write down the mode. … [1] (iv) Work out how many more students choose detective books than music books. … [1] (v) Work out the fraction of students who did not choose romance books. … [2]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Tally for 3, 4, 5 increased by two. 2 M1 for all four tallies correct Tally for 7 increased by one. or B1 for correct frequency column Frequencies If 0 scored SC1 for correct frequency for 3, 5, 14, 10, 11, 3, 3, 0, 1 their tallies 1(a)(ii) 8 1 1(a)(iii) 4 1 1(b)(i) 4 1 1(b)(ii) 2 and 3.5 boxes drawn 2 B1 16, 3 and 9 frequencies B1 1(b)(iii) Comedy 1 1(b)(iv) 5 1 FT 14 − their music frequency 1(b)(v) 52 2 8 or equivalent fraction B1 for oe or 52 or 0.866 to 0.867 60 60

This question in 0580/31 May/June 2018

5 (a) Geoff keeps a record of the number of goals scored in the first eight games played by his football team. 3 1 8 5 7 2 1 6 Find (i) the mode, … [1] (ii) the range, … [1] (iii) the median. … [2] (b) The table shows the number of goals scored by Geoff’s team in each game during one season. Number of 0 1 2 3 4 5 6 7 8 goals Number of 5 7 8 10 6 4 5 3 2 games (i) How many games did the team play? … [1] (ii) Work out the mean number of goals scored per game. … [3] (c) Geoff asks some supporters to choose a new colour for the team’s shirts. The results are to be shown in a pie chart. The table shows some of this information. Pie chart sector Colour Frequency angle Red 41 123° Blue 69° Green Other 18 54° (i) Complete the table. [3] (ii) Complete the pie chart. Red Blue [1]

12 marks

Mark scheme: 5(a)(i) 1 1 5(a)(ii) 7 1 5(a)(iii) 4 nfww 2 M1 for 1 1 2 3 5 … or … 3 5 6 7 8 or 3 and 5 selected 5(b)(i) 50 1 5(b)(ii) 3.28 3 M1 for [0 × 5] + 1 × 7 + 2 × 8 + 3 × 10 + 4 × 6 + 5 × 4 + 6 × 5 + 7 × 3 + 8 × 2 oe implied by 164 M1dep for their 164 ÷ their(b)(i) 5(c)(i) 23 3 B1 for each 38 114 or if 0 scored M1 for 123 ÷ 41 or 54 ÷ 18 or 3 5(c)(ii) correct line 1

This question in 0580/33 May/June 2018

6 (a) 70 people each attempt a driving test. Each person repeats the test until they pass. The results are shown in the table. Number of Number of attempts people 1 19 2 17 3 8 4 12 5 9 6 5 (i) Write down the mode. … [1] (ii) Calculate the mean. … [3] (iii) Jules says that the median is 3.5 . Show that he is wrong. … … [1] (b) The number of attempts at a driving test and the number of driving lessons for each of 17 people are shown in the scatter diagram. 10 9 8 7 6 Number of 5 attempts 4 3 2 1 0 0 5 10 15 20 25 30 Number of lessons (i) What type of correlation is shown in the scatter diagram? … [1] (ii) One of these people is picked at random. Work out the probability that this person had 5 or more attempts. … [1] (iii) Draw a line of best fit on the scatter diagram. [1] (iv) Another person had 15 lessons. Estimate their number of attempts. … [1]

9 marks

Mark scheme: 6(a)(i) 1 1 6(a)(ii) 6 3 M1 for 2.86 or 2.857 … or 2 1 × 19 + 2 × 17 + 3 × 8 + 4 × 12 + 5 × 9 + 6 × 5 7 or 200 M1dep for their 200 ÷ 70 6(a)(iii) Any correct reason 1 e.g. 44 are below and 26 are above or it is 2 or the median is 2 or the 35th and 36th values shown 2 + 2 or = 2 2 or the 35.5th (value) is 2 or the 35.5th (value) is not 3.5 6(b)(i) Negative 1 6(b)(ii) 10 1 oe 17 6(b)(iii) Correct ruled line of best fit 1 6(b)(iv) 5 or 6 1 must be an integer

This question in 0580/32 Oct/Nov 2018

5 (a) Stef buys 3.5 kilograms of bananas. (i) Bananas cost $1.24 per kilogram. Stef pays with a $5 note. Work out how much change she receives. $ … [2] (ii) Write 3.5 kilograms in grams. … g [1] (b) Oranges cost 85 cents each. Leo has a $10 note. Work out the maximum number of oranges he can buy. … [2] (c) 87% of the mass of a pineapple is water. A pineapple has a mass of 700 g. Work out the mass of water in this pineapple. … g [2] (d) The number of melons sold in a shop each day for 7 days is shown below. 18 5 23 40 28 19 17 Work out the mean number of melons sold. … [2] (e) Rio and Chi go to a fruit shop. Rio buys 4 apples and 2 plums for $1.96 . Chi buys 7 apples and 3 plums for $3.24 . Write down a pair of simultaneous equations and solve them to find the cost of 1 apple and the cost of 1 plum. You must show all your working. Apple $ … Plum $ … [6]

15 marks

Mark scheme: 5(a)(i) [0].66 2 M1 for 1.24 × 3.5 5(a)(ii) 3500 1 5(b) 11 2 M1 for 10 ÷ [0].85 oe soi by 11.7[6]... 5(c) 609 2 M1 for [0].87 × 700 oe 5(d) 21.4 or 21.42 to 21.43 2 18 + 5 + 23 + 40 + 28 + 19 + 17 M1 for 7 or 150 ÷ 7 5(e) 2 correct simultaneous equations B2 Allow equations working in cents or e.g. dollars 4a + 2p = 1.96 and 7a + 3p = 3.24 B1 for one correct equation Correctly equating one set of coefficients M1 FT their equations Correct method to eliminate one variable M1 FT their equations Dependent on the coefficients being the same for one of the variables. Correct consistent use of addition or subtraction using their equations [apple =] 0.3[0] A1 [plum =] 0.38 A1 If M0M0 scored SC1 for 2 correct answers given or SC1 for 2 values satisfying one of their two original equations.

This question in 0580/33 Oct/Nov 2018

3 (a) On Monday, Main Street station sells 40 tickets. There are four types of ticket; infant, child, adult and senior. The bar chart shows the number of infant, child and adult tickets sold. 20 18 16 14 12 Frequency 10 8 6 4 2 0 Infant Child Adult Senior Type of ticket (i) Complete the bar chart. [3] (ii) Find how many more adult tickets were sold than child tickets. … [1] (iii) Write down the modal type of ticket. … [1] (iv) One of these 40 people is chosen at random. Find the probability that this person is a child. … [1] (b) At Donville station the number of tickets sold each day is recorded for seven days. 104 18 72 31 27 45 60 Find (i) the range, … [1] (ii) the median, … [2] (iii) the mean. … [2]

11 marks

Mark scheme: 3(a)(i) Correct bar 3 M1 for 5, 12, 17 or 34 M1 for 40 – their34 3(a)(ii) 5 1 3(a)(iii) Adult 1 FT 3(a)(iv) 12 40 oe 1 3(b)(i) 86 1 3(b)(ii) 45 2 M1 for 18, 27, 31, 45, or 45, 60, 72, 104 3(b)(iii) 51 2 M1 for (104 + 18 + 72 + 31 + 27 + 45 + 60) ÷ 7 soi 357 7

This question in 0580/31 May/June 2019

2 80 students each record the name of their mathematics teacher. The number of these students taught by Mr House and by Miss Patel are shown in the bar chart. 24 20 16 Frequency 12 8 4 0 Mr Mrs Mr Miss Mr Jones Brown House Patel Smith (a) How many more students are taught by Miss Patel than by Mr House? … [1] (b) 15 students are taught by Mr Smith. Twice as many students are taught by Mrs Brown than by Mr Jones. Use this information to complete the bar chart. [4] (c) Write down the mode. … [1] (d) One of these students is chosen at random. Work out the probability that this student (i) is taught by Mr House, … [1] (ii) is not taught by either Mr House or Miss Patel. … [2] (e) This information is also to be shown in a pie chart. Work out the sector angle for Miss Patel. … [2]

11 marks

Mark scheme: 2(a) 4 1 2(b) 3 correct bars drawn on bar chart 4 B1 for Mr Smith bar drawn height 15 M2 for their ( 80 − (18 + 14 + 15 ) ) ÷ 3 [× 2 ] or M1 for 80 − (18 + 14 + 15 ) oe 2(c) Mrs Brown 1 FT their bar chart provided 5 bars drawn 2(d)(i) 14 1 oe 80 2(d)(ii) 48 2 FT their bar chart oe 80 18 + 14 M1 for 80 − (18 + 14 ) or oe 80 OR M1FT for adding heights of bars for (Mr Jones, Mrs Brown and Mr Smith) 2(e) 81 2 360 18 M1 for [× 18 ] or [× 360 ] 80 80

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

8 (a) Kyung records the number of people in each of 24 cars on Wednesday. His results are shown below. 1 3 6 1 2 2 4 5 3 4 1 5 3 2 4 1 1 1 2 4 4 1 2 1 (i) Complete the frequency table. You may use the tally column to help you. Number in a car Tally Frequency 1 2 3 4 5 6 [2] (ii) Write down the mode. … [1] (iii) Work out the range. … [1] (iv) Work out the median. … [1] (v) Calculate the mean. … [3] (vi) One of these cars is chosen at random. Find the probability that the number of people in this car is 4. … [1] (b) Kyung also records the number of people in each of 24 cars on Saturday. The table shows the results. Number in a car 1 2 3 4 5 6 Frequency 1 2 5 13 2 1 On the grid, complete the bar chart to show these results. 14 12 10 8 Frequency 6 4 2 0 1 2 3 4 5 6 Number in a car [2] (c) Write down one comparison between the frequency tables in part (a)(i) and part (b). … … [1] Question 9 is printed on the next page.

12 marks

Mark scheme: 8(a)(i) Correct frequencies 2 B1 for 1 frequency incorrect 8 5 3 5 2 1 or 2 incorrect but total still 24 or 8 5 3 5 2 1 in tally column If 0 scored, B1 for completely correct tallies 8(a)(ii) 1 1 8(a)(iii) 5 1 8(a)(iv) 2 1 8(a)(v) 2.625 3 M1 for ∑fx 1 × 8 + 2 × 5 + 3 × 3 + 4 × 5 + 5 × 2 + 6 × 1 M1 dep for their ∑fx ÷ 24 8(a)(vi) 5 1 FT their table oe 24 8(b) Correct bar chart 2 B1 for 2 or 3 correct bars or for all 4 heights correct 8(c) Correct generalised comparison 1

This question in 0580/33 May/June 2019

4 (a) 50 students each record the number of glasses of water they drink in one day. The results for 10 of the students are shown below. 2 5 1 3 2 1 0 0 1 1 (i) The results for the remaining 40 students are recorded in the table. Complete the table to show the results for all 50 students. Number of glasses of water Tally Frequency 0 | | | | | 1 | | 2 | | | | | | | 3 | | | | | | | | | 4 | | | | | | | 5 | | | | Total 50 [2] (ii) Write down the range. … [1] (iii) Find the median. … [2] (iv) Find the percentage of the 50 students who drink 4 glasses of water. … % [1] (v) One of the 50 students is chosen at random. Find the probability that this student drinks fewer than 2 glasses of water in one day. Give your answer as a fraction in its lowest terms. … [2] (b) Musa has a glass that holds 250 ml of water. He drinks 5 of these glasses of water. He fills his glass from a 2-litre bottle of water. Work out how much water is left in the bottle. Give your answer in millilitres. … ml [2] (c) The amount of water, w litres, in a jug is 1.5 litres, correct to the nearest 0.1 litre. Complete this statement about the value of w. … G w 1 … [2] (d) NOT TO 15 cm SCALE 7 cm Another glass is in the shape of a cylinder. The cylinder has height 15 cm and diameter 7 cm. Calculate the volume of the glass. … cm3 [3]

15 marks

Mark scheme: 4(a)(i) Table completed correctly 2 B1 for tallies correct or frequencies correct 0 ̸ ̸ ̸ 8 If 0 scored, SC1 for correct frequency for 1 ̸ ̸ 6 their tallies 2 ̸ ̸ ̸ ̸ 10 3 ̸ ̸ ̸ ̸ ̸ 12 4 ̸ ̸ ̸ 8 5 ̸ ̸ 6 4(a)(ii) 5 1 4(a)(iii) 3 2 B1 for 25[th] and 26[th] seen or these values identified 4(a)(iv) 16 1 FT their table (their 8 × 2) 4(a)(v) 7 2 their 8 + their 6 final answer B1FT for oe seen 25 50 4(b) 750 2 B1 for 0.75[litres] 2000 [ml] or 0.25 [litres] or 1250 [ml] or 1.25 [litres] soi 4(c) 1.45 , 1.55 2 B1 for one value correct or for both values correct but reversed 4(d) 577 or 577.2 to 577.3… 3 2  7  M2 for π ×   × 15  2   7  2 or M1 for π ×    2  If 0 scored, SC1 for π × 72 × 15

This question in 0580/32 Oct/Nov 2019

2 (a) Emma records the number of letters in each word in a sentence. 7 1 5 4 2 4 5 3 3 1 2 4 Find (i) the median, … [2] (ii) the mode, … [1] (iii) the range. … [1] (b) Jack records the number of letters in 25 words. Number of Number of letters in a word words 1 3 2 1 3 5 4 8 5 6 6 2 (i) Calculate the mean. … [3] (ii) Priti picks one of Jack’s words at random. Find the probability that this word has 4 or more letters. … [2] (c) The table shows information about the first 90 words in a book. (i) Complete the table. Length of word Frequency Pie chart angle Very short 6 24° Short 34 Medium 41 Long 9 [2] (ii) Complete the pie chart to show this information. Very short [2]

13 marks

Mark scheme: 2(a)(i) 3.5 2 B1 for 1, 1, 2, 2, 3, 3, 4 or 3, 4, 4, 4, 5, 5, 7 or 3 and 4 identified 2(a)(ii) 4 1 2(a)(iii) 6 1 2(b)(i) 3.76 3 M2 for (1 × 3 + 2 × 1 + 3 × 5 + 4 × 8 + 5 × 6 + 6 × 2) ÷ 25 or M1 for 1 × 3 + 2 × 1 + 3 × 5 + 4 × 8 + 5 × 6 + 6 × 2 or 94 2(b)(ii) 16 2 B1 for 16 oe 25 2(c)(i) 136 2 B1 for one correct 164 36 2(c)(ii) Correct pie chart 2 FT for 1 or 2 marks provided their 3 angles add to 336° B1 for one correct sector

This question in 0580/33 Oct/Nov 2019

2 (a) 66 football players each take five penalties. The number of penalties that each player scores is recorded. The results are shown in the bar chart. 20 18 16 14 12 Frequency 10 8 6 4 2 0 0 1 2 3 4 5 Number of penalties scored (i) Write down the mode. … [1] (ii) Write down the range. … [1] (iii) Calculate the mean. … [3] (b) The attendance at a football match is 11 678. (i) Write 11 678 in words. … [1] (ii) Write 11 678 correct to the nearest 100. … [1] (c) In a football stadium there are 15 000 seats. 10 650 of these seats are occupied. Find the percentage of the 15 000 seats that are occupied. … % [1] (d) A ticket to a football match costs $20. Calculate the cost of the ticket in rupees when the exchange rate is 1 rupee = $0.016 . … rupees [2]

10 marks

Mark scheme: 2(a)(i) 1 1 2(a)(ii) 5 1 2(a)(iii) 1.62 or 1.621… 3 M1 for ([0 × 16] + 1 × 19 + 2 × 14 + 3 × 10 + 4 × 5 + 5 × 2) soi by 107 M1dep for their 107 ÷ 66 2(b)(i) Eleven thousand six hundred (and) 1 seventy-eight 2(b)(ii) 11 700 1 2(c) 71 1 2(d) 1250 2 20 M1 for 0.016

This question in 0580/32 Feb/March 2020

7 (a) 20 students from College A each run 5 km. The times, correct to the nearest minute, are recorded. 32 51 25 40 47 21 37 32 48 36 46 39 30 29 44 39 53 35 40 31 (i) Complete the stem-and-leaf diagram. 2 3 4 5 Key: 3 | 4 represents 34 minutes [2] (ii) Find the range of the times. … min [1] (iii) Find the median of the times. … min [1] (iv) Complete the bar chart for the times of the students. 10 9 8 7 6 Number of 5 students 4 3 2 1 0 20 to 29 30 to 39 40 to 49 50 to 59 Time (minutes) [2] (b) 20 students from College B each run 5 km. Their times, correct to the nearest minute, are recorded and the results are shown in the table. Time (minutes) Number of students Pie chart sector angle 30 to 39 5 90° 40 to 49 8 50 to 59 7 (i) Complete the table. [2] (ii) Complete the pie chart. [2] (c) Write down two comments comparing the times of students from College A with the times of students from College B. 1 … … 2 … … [2]

12 marks

Mark scheme: 7(a)(i) [2] 1 5 9 2 B1 for correct but not ordered [3] 0 1 2 2 5 6 7 9 9 or for 2 or 3 correct rows ordered [4] 0 0 4 6 7 8 [5] 1 3 7(a)(ii) 32 1 7(a)(iii) 38 1 7(a)(iv) Correct bar chart 2 FT their stem and leaf from (a)(i) B1 for two heights correct 7(b)(i) 144 2 B1 for each 126 If 0 scored, M1 for 90 ÷ 5 or 360 ÷ 20 or 18 7(b)(ii) Correct pie chart 2 FT their (b)(i) angles if they total 270 B1 for one correct sector 7(c) 2 correct expressions 2 B1 for one statistical comparison B1 for another comparison

This question in 0580/31 May/June 2020

1 (a) Paul has a set of 8 cards, each with a number written on it. The numbers on the cards are 1, 1, 2, 3, 3, 3, 4, 5. One card is taken at random. Write down the probability that the number on the card is (i) 1, … [1] (ii) an odd number, … [1] (iii) a prime number, … [1] (iv) a number less than 6. … [1] (b) Dina has a set of 12 cards. These are the numbers on the cards. 3 4 1 3 2 1 3 4 2 2 1 3 Work out (i) the median, … [2] (ii) the mode, … [1] (iii) the mean, … [2] (iv) the range. … [1] (c) Helena has a different set of cards. She takes one card at random and records the number shown. She does this 50 times. The results are shown in the table. Number on card Frequency 1 8 2 11 3 10 4 9 5 12 Calculate the mean of her results. … [3]

13 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 1 1 oe 4 1(a)(ii) 3 1 oe 4 1(a)(iii) 5 1 8 1(a)(iv) 1 1 1(b)(i) 2.5 2 M1 for ordering the numbers to the middle two e.g. 1 1 1 2 2 2 3 or 2 3 3 3 3 4 4 or B1 for 2 and 3 identified 1(b)(ii) 3 1 1(b)(iii) 5 2 M1 for (1 + 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 3 2.42 or 2.416 to 2.417 or + 4 + 4) ÷ 12 212 1(b)(iv) 3 1 1(c) 3.12 3 M1 for 1 × 8 + 2 × 11 + 3 × 10 + 4 × 9 + 5 × 12 soi 156 M1dep for their 156 ÷ 50

This question in 0580/32 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

5 (a) Here are the weekly wages, in dollars, of the ten workers in an office. 280 200 175 1180 95 182 238 256 194 250 (i) Find the median. $ … [2] (ii) Calculate the mean. $ … [2] (iii) For this office, explain why the mean is not a suitable average. … [1] (b) The stem-and-leaf diagram shows the ages of the workers in a factory. 1 6 7 7 9 2 2 3 4 6 8 3 0 2 3 6 9 4 1 4 4 8 5 0 1 6 6 6 9 6 1 5 8 Key : 2 3 represents 23 (i) Write down the mode. … [1] (ii) Work out the range. … [1]

7 marks

Mark scheme: 5(a)(i) 219 2 B1 for a list of at least first or last 6 correctly ordered or 200 and 238 identified 5(a)(ii) 305 2 M1 for (280 + 200 + 175 + 1180 + 95 + 182 + 238 + 256 + 194 + 250) ÷ 10 5(a)(iii) One extreme value makes it higher oe 1 5(b)(i) 56 1 5(b)(ii) 52 1

This question in 0580/32 Oct/Nov 2020

5 The table shows the maximum power, kW, and the time taken, in seconds, to accelerate from 0 to 100 km/h for each of 10 cars. Maximum 77 52 103 55 44 51 85 135 90 110 power (kW) Time 12.5 14.9 9.0 12.1 14.4 12.9 10.0 7.1 11.0 9.4 (seconds) (a) (i) Find the range of the times. … s [1] (ii) Find the median maximum power. … kW [2] (b) (i) Complete the scatter diagram. The first eight points have been plotted for you. 16 14 12 Time (s) 10 8 6 40 60 80 100 120 140 Maximum power (kW) [1] (ii) What type of correlation is shown on the scatter diagram? … [1] (iii) Describe the relationship between the maximum power of a car and the time taken to accelerate from 0 to 100 km/h. … … [1] (iv) Draw a line of best fit on the scatter diagram. [1] (v) Another car has a maximum power of 63 kW. Use your line of best fit to estimate the time taken for this car to accelerate from 0 to 100 km/h. … s [1] (c) Robert buys a car for $18 160. He pays a deposit of $6460. He pays the rest of the money in 24 equal monthly payments. Work out the amount of each monthly payment. $ … [3] (d) A fuel tank holds 52 litres when full. The tank is a quarter full. Jim fills the tank with fuel that costs $2.18 per litre. Work out how much Jim pays. $ … [3]

14 marks

Mark scheme: 5(a)(i) 7.8 1 5(a)(ii) 81 2 M1 for an ordered list of at least the first 6 or last 6 values or B1 for 77 and 85 both identified 5(b)(i) Points plotted at (90, 11.0) and (110, 9.4) 1 5(b)(ii) Negative 1 5(b)(iii) [The] greater [the maximum] power the 1 less time [needed to accelerate from 0 to 100 km/h] oe 5(b)(iv) Correct ruled line 1 5(b)(v) 12.5 to 13.5 1 FT from their line provided negative gradient 5(c) 487.5[0] cao 3 18160 − 6460 M2 for or better 24 or M1 for 18 160 – 6460 5(d) 85.02 cao 3 M2 for 0.75 × 52 × 2.18 oe or M1 for 0.75 × 52 oe soi by 39 or for 52 × 2.18 soi by 113.36 If 0 scored, SC1 for 0.25 × 52 × 2.18 oe

This question in 0580/33 Oct/Nov 2020

1 20 students choose their favourite science subject. The results are shown in the bar chart. 12 10 8 Frequency 6 4 2 0 Biology Chemistry Physics (a) Work out how many more students choose biology than physics. … [1] (b) Write down the fraction of students whose favourite science subject is chemistry. … [1] (c) One of the 20 students is picked at random. Write down the probability that this student did not choose biology. … [2] (d) Only one of the averages, median, mode and mean can be found for these results. (i) Write down the average that can be found. … [1] (ii) Find this average for these results. … [1] (iii) Explain why the range cannot be found. … [1] (e) The results are to be shown in a pie chart. (i) Complete the table. Favourite Pie chart Frequency science sector angle Biology Chemistry Physics [3] (ii) Complete the pie chart. [2]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 5 1 1(b) 3 1 cao 20 1(c) 9 2 11 oe M1 for 1 − or 20 − 11 or 3 + 6 oe 20 20 1(d)(i) Mode 1 1(d)(ii) Biology 1 1(d)(iii) Correct reason 1 1(e)(i) 11 198 3 B2 for 2 correct angles 3 54 OR 6 108 B1 for 11, 3, 6 k M1 for × 360 seen, 20 k =1,11,3,6 or one of their frequencies 1(e)(ii) Correct pie chart drawn 2 B1FT for one correct sector drawn, provided sum of their 3 angles is 360

This question in 0580/32 Feb/March 2021

5 11 students record the time they spent on social media and watching television during one week. The table shows the time, in hours, for each student. Social media 2 9 18 6 28 14 7.5 27 22 19.5 13 (hours) Television 25 23 18.5 27.5 12 16 17 9 15 11 20 (hours) (a) Find the range of the times spent on social media. … hours [1] (b) (i) Complete the scatter diagram. The first nine points have been plotted for you. 30 25 20 Television 15 (hours) 10 5 0 5 10 15 20 25 30 Social media (hours) [1] (ii) What type of correlation is shown on the scatter diagram? … [1] (iii) Draw a line of best fit on the scatter diagram. [1] (iv) Another student spent 21 hours watching television. Use your line of best fit to estimate the number of hours this student spent on social media. … hours [1]

5 marks

Mark scheme: 5(a) 26 1 5(b)(i) Points plotted at (13, 20) and (19.5, 11) 1 5(b)(ii) Negative 1 5(b)(iii) Correct ruled line 1 5(b)(iv) 7.5 to 13.5 1 FT from their straight line provided negative gradient

This question in 0580/31 Oct/Nov 2021

3 (a) Simone completes one lap of a 400 metre running track in 79 seconds. Work out how long it will take her to run 6 km at the same rate. Give your answer in minutes and seconds. … minutes … seconds [4] (b) The probability that she does not win a race is 0.94 . Find the probability that she wins a race. … [1] (c) Each day she records the number of laps she runs. Here is her record for one week. 15 42 28 16 24 15 32 (i) Write down the mode. … [1] (ii) Find the median. … [2] (iii) Find the range. … [1] (d) Wilfred records his times, in seconds, for each of 5 laps. 59 74 69 63 65 After running a 6th lap his mean time is 67 seconds. Find his time for the 6th lap. … seconds [3]

12 marks

Mark scheme: 3(a) 19 [min] 45 [secs] 4 6000 79 M3 for × oe 400 60 or B2 for figs 1975 6000 or M2 for 79 × oe 400 or B1 for figs 1185 6000 400 79 79 or M1 for or or or 400 79 400 0.4 oe 3(b) 0.06 oe 1 3(c)(i) 15 1 3(c)(ii) 24 2 M1 for full list or 15 15 16 24 or 42 32 28 24 3(c)(iii) 27 1 3(d) 72 3 M2 for 6 × 67 – (59 + 74 + 69 + 63 + 65) oe or M1 for (59 + 74 + 69 + 63 + 65 + x) ÷ 6 = 67 or 6 × 67 oe

This question in 0580/32 Oct/Nov 2021

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

6 Maria owns a restaurant with 30 tables. One day she records the number of customers at each table at 7 pm. The bar chart shows the results. 12 10 8 Number of 6 tables 4 2 0 1 2 3 4 5 6 Number of customers at each table (a) (i) Write down the mode. … [1] (ii) Find the range. … [1] (iii) Calculate the mean. … [3] (b) On the same day she also recorded the number of customers at each table at 1 pm. The results are shown in the table. Number of customers at each 1 2 3 4 5 6 table Number of tables 8 13 5 4 0 0 Write down two comments comparing the results from 7 pm with the results from 1 pm. 1. … 2. … [2] (c) 270 meals are ordered one day at the restaurant. The table shows the number of each type of meal. Meal Number ordered Pie chart sector angle Meat 117 Fish 99 Vegetarian 54 72° (i) Complete the table. [2] (ii) Complete the pie chart. [2]

11 marks

Mark scheme: 6(a)(i) 4 1 6(a)(ii) 5 1 6(a)(iii) 3.7 3 M1 for 1 × 2 + 2 × 7 + 3 × 3 + 4 × 9 + 5 × 4 + 6 × 5 M1FTdep for their 111 ÷ 30 6(b) Two correct comments with 2 B1 for each different types of comment 6(c)(i) 156 132 2 B1 for each 360 72 If B0 scored, M1 for or for 270 54 6(c)(ii) Correct pie chart drawn 2 FT their table if angles add up to 360 B1FT for one correct sector drawn

This question in 0580/33 May/June 2022

5 (a) The table shows the number of items sold to each of 60 customers in a shop. Number of items Frequency sold 0 3 1 6 2 12 3 8 4 14 5 10 6 3 7 4 (i) Find the range. … [1] (ii) Calculate the mean. … [3] (iii) Find the probability that a customer picked at random buys more than 4 items. … [2] (b) Carlotta buys a bicycle. (i) The length, l cm, of the bicycle is 96 cm, correct to the nearest centimetre. Complete this statement about the value of l. … G l 1 … [2] (ii) The diameter of each bicycle wheel is 46 cm. Carlotta rides the bicycle a distance of 1.4 km. Calculate the number of complete revolutions that a wheel makes during this journey. … [5]

13 marks

Mark scheme: 5(a)(i) 7 nfww 1 5(a)(ii) 13 3 M1 for [0  3] + 1  6 + 2  12 + 3  8 + 3.43 or 330 4  14 + 5  10 + 6  3 + 7  4 M1 dep for their 206 ÷ 60 5(a)(iii) 17 2 10 + 3 + 4 M1 for 60 60 or B1 for 17 5(b)(i) 95.5 96.5 2 B1 for each If 0 scored, SC1 for both correct but reversed 5(b)(ii) 968 5 B4 for 969 or 968.6 to 968.8 as final answer OR 140000 M3 for oe 46π figs 1400 or M2 for oe figs 46  or M1 for figs 46 × π oe or 2  figs 23  π oe B1 for correctly truncating answer to integer

This question in 0580/31 Oct/Nov 2022

3 24 people own a car. (a) Ranjit asks each of these 24 people the colour of their car. The bar chart shows some of these results. 8 7 6 5 Frequency 4 3 2 1 0 Black Blue Red Green White Colour (i) Complete the bar chart by drawing the bar for the colour red. [2] (ii) Write down the mode. … [1] (iii) How many more people have a green car than have a blue car? … [1] (b) The table shows the size, in litres, of each of the 24 car engines. Engine size (litres) 0.8 1.2 1.5 1.8 2.4 Frequency 7 4 5 6 2 Calculate the mean. … litres [3] (c) Ranjit also asks each of the 24 people what type of car they have. The pie chart shows some of these results. Electric 60° 105° Hybrid (i) Work out the number of hybrid cars. … [2] (ii) The rest of the cars are either petrol or diesel. There are 8 petrol cars. Complete the pie chart to show this information. [2]

11 marks

Mark scheme: 3(a)(i) Bar at 6 with correct width 2 M1 for 24 – 6 – 2 – 7 – 3 oe 3(a)(ii) Green 1 FT their bar chart 3(a)(iii) 5 1 3(b) 1.4[0] or 1.395 to 1.396 3 M1 for 0.8×7 + 1.2×4 + 1.5×5 + 1.8×6 + 2.4×2 oe M1dep for their 33.5 ÷ 24 3(c)(i) 7 2 105 M1 for  24 oe 360 3(c)(ii) Correct sector with line at 120° 2 B1 for 120 soi

This question in 0580/32 Oct/Nov 2022

3 These are the test scores of 16 students. 15 26 9 45 36 20 41 39 40 23 32 18 41 34 37 31 (a) Complete the stem-and-leaf diagram. 0 1 2 3 4 Key: 1 5 represents 15 [2] (b) Find the mode. … [1] (c) Find the median. … [1] (d) Find the range. … [1] (e) Complete the bar chart for the test scores of the 16 students. 7 6 5 4 Number of students 3 2 1 0 0 to 9 10 to 19 20 to 29 30 to 39 40 to 49 Test score [2] (f) Work out the percentage of students with a test score of 40 or more. … % [1]

8 marks

Mark scheme: 3(a) 2 B1 for 3 fully correct rows 0 9 or for a fully correct unordered stem-and-leaf diagram 1 5 8 2 0 3 6 3 1 2 4 6 7 9 4 0 1 1 5 3(b) 41 1 3(c) 33 1 3(d) 36 1 3(e) Correct bar chart 2 FT their stem-and-leaf diagram B1FT for 3 correct or follow through heights 3(f) 25 1 their k FT × 100 from the bar 16 chart or from their stem-and-leaf diagram

This question in 0580/31 May/June 2023

2 (a) Mika counts the number of letters in each of the 61 words in a paragraph. Some of his results are shown in the table and bar chart. Number of letters 1 2 3 4 5 6 Frequency 7 12 15 5 15 14 13 12 11 10 9 Frequency 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 Number of letters (i) Complete the table and the bar chart. [3] (ii) Write down the mode. … [1] (b) Grace also counts the number of letters in each word of another paragraph. Her results are shown in the table. Number of letters 1 2 3 4 5 6 Frequency 10 18 9 6 5 2 (i) Work out the mean. … [3] (ii) She picks one of these words at random. Find the probability that it has more than three letters. … [2] (c) She counts the number of letters in each word in the next sentence. These are her results. 3 4 1 7 9 2 6 5 4 2 3 2 (i) Find the median. … [2] (ii) Find the range. … [1]

12 marks

Mark scheme: 2(a)(i) 14 8 3 B1 for frequency 14 Bars with heights 12 and 8 B1 for frequency 8 or 22 – their 14 B1FT for bars of heights 12 and their 8 2(a)(ii) 4 1 2(b)(i) 2.68 3 M1 for 1×10 + 2×18 + 3×9 + 4×6 + 5×5 + 6×2 oe their134 M1dep for oe 10  18  9  6  5  2 2(b)(ii) 13 2 M1 for 6 + 5 + 2 or better oe 50 2(c)(i) 3.5 cao 2 M1 for 1 2 2 2 3 3 4 or 3 4 4 5 6 7 9 or 3 and 4 identified 2(c)(ii) 8 1

This question in 0580/32 May/June 2023

1 (a) The bar chart shows the number of goals scored by a team in each of 5 months. 22 20 18 16 14 12 Frequency 10 8 6 4 2 0 Sept Oct Nov Dec Jan Feb Month (i) In February, 12 goals are scored. Complete the bar chart. [1] (ii) How many more goals were scored in January than in October? … [1] (b) Find the range of the number of goals scored. … [1] (c) (i) The team shop is open from 09 00 to 17 15 on Monday to Friday only. Work out how long the shop is open each week. Give your answer in hours and minutes. … h … min [3] (ii) Bruno buys a shirt for $36 and a scarf for $12.25 . He pays with a $50 note. Work out how much change he receives. $ … [2] (d) Ticket prices Adult $35 Child $20 Senior $25 (i) Calculate the cost of 150 adult tickets, 70 child tickets and 30 senior tickets. $ … [3] (ii) Calculate the percentage of these tickets that are senior tickets. … % [2] (e) A game starts at 15 00. The team plays for 90 minutes. There is also a break of 15 minutes. Find the time the game ends. … [2]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Bar to 12 1 1(a)(ii) 11 1 1(b) 14 1 1(c)(i) 41 [h] 15 [min] 3 1 B2 for 41.25 or 41 or 40 hr 75 [mins] 4 1 or B1 for 8.25 or 8 or 8 h 15 [min] or 4 495 [min] or M1 for 7.25  5 oe or 9.25  5 oe OR SC2 for 57 [h] 45 [min] 1(c)(ii) 1.75 2 M1 for 50 – (36 + 12.25) oe or B1 for 48.25 1(d)(i) 7400 3 M2 for 35  150 + 20  70 + 25  30 oe or M1 for two of 35  150, 20  70 or 25  30 oe 1(d)(ii) 12 2 30 M1 for  100 oe 150 + 70 + 30 1(e) 16 45 or 4.45 pm 2 M1 for 15 00 + 90 [min] + 15 [min] oe

This question in 0580/32 Oct/Nov 2023

5 Heidi records the colour of each of 500 cars crossing a bridge. The pie chart shows some of this information. Grey Red Other (a) How many cars are red? … [1] (b) 35 cars are grey. Show, by calculation, that the sector angle for grey is 25.2°. [1] (c) 175 cars are white and 150 cars are black. Complete the pie chart to show this information. [2] (d) Find the probability that a car chosen at random is not grey. Give your answer as a fraction in its simplest form. … [2] (e) Another 320 cars cross the bridge. How many of these 320 cars are expected to be white? … [2] (f) Heidi also records the number of people in each car crossing the bridge for one hour. Number of people Frequency 1 20 2 6 3 0 4 15 5 8 6 12 Calculate the mean. … [3]

11 marks

Mark scheme: 5(a) 125 1 5(b) 35 M1  360 500 5(c) Correct pie chart 2 B1 for 126º or 108º 5(d) 93 2 500 – 35 360 – 25.2 cao M1 for oe or oe 100 500 360 7 If 0 scored, then SC1 for final answer of 100 5(e) 112 2 175 126 M1 for  320 oe or  320 oe 500 360 5(f) 21 3 M1 for (1  20) + (2  6) + [3  0] + (4  15) + 3.34 or 3.344… or 3 61 (5  8) + (6  12) M1dep for their  fx  ( 20 + 6 + 0 + 15 + 8 +12 ) oe

This question in 0580/32 Oct/Nov 2023

5 (a) Zena records the number of letters she posts on each of 12 days. 3 7 3 8 7 1 0 6 5 1 7 2 (i) Write down the mode. … [1] (ii) Find the median. … [2] (b) Zena posts 6 parcels. • The lightest parcel has a mass of 4.6 kg. • The heaviest parcel has a mass of 6.2 kg. • The other 4 parcels have a mean mass of 5.01 kg. Calculate the mean mass of the 6 parcels. … kg [3] (c) Zena pays 105 euros to post a parcel. The exchange rate is $1 = 0.84 euros. Work out the cost in dollars to post the parcel. $ … [1] (d) The cost to post a box increases from $22.68 to $44. Work out the percentage increase in the cost. … % [2] (e) The diagram shows a parcel in the shape of a cuboid. NOT TO SCALE 3 cm 2 cm 6 cm (i) Complete the net of the parcel on the 1 cm 2 grid. Two faces have been drawn for you. [2] (ii) Find the volume of the parcel. … cm3 [1]

12 marks

Mark scheme: 5(a)(i) 7 1 5(a)(ii) 4 2 M1 for an ordered list of at least the first 7 or last 7 values or B1 for 3 and 5 both identified 5(b) 5.14 3 M2 for (4 × 5.01 + 4.6 + 6.2) ÷ 6 oe or M1 for 4 × 5.01 + 4.6 + 6.2 or B1 for 20.04 5(c) 125 1 5(d) 94 or 94.00… 2 44 − 22.68 M1 for [×100] 22.68  44  or  − 1  [×100]  22.68  44 or ×100 [– 100] 22.68 5(e)(i) Fully correct net 2 B1 for 2 or 3 correct extra faces in correct places 5(e)(ii) 36 nfww 1

This question in 0580/33 Oct/Nov 2023

2 (a) Fuel Fuel Garage A Garage B $1.41 per litre $1.50 per litre (i) Tiya buys 55 litres of fuel from garage A. Work out the change she receives from $100. $ … [2] (ii) Work out how much cheaper it is to buy 20 litres of fuel from garage A than from garage B. $ … [2] (iii) These are the amounts that 6 people spend on fuel at garage A. $63 $84.50 $72.23 $46 $54.10 $80 Calculate the mean number of litres that they buy. … litres [3] (iv) The cost of fuel at garage B increases from $1.50 to $1.53 . Calculate the percentage increase. … % [2] 2(b) The fuel tank of a car is full. 5 It takes 39 more litres of fuel to fill the tank. Work out the number of litres of fuel in a full tank. … litres [3] (c) (i) Use 1 litre = .022 gallons to complete this conversion graph. 30 25 20 Gallons 15 10 5 0 0 10 20 30 40 50 60 70 80 90 100 Litres [2] (ii) Use 1 litre = .022 gallons to complete this statement. 1 gallon = … litres. [1] (d) A cylindrical tank for storing fuel has radius 1.5 metres and height 8 metres. Calculate the volume of the tank in litres. … litres [3]

18 marks

Mark scheme: 2(a)(i) 22.45 2 M1 for 100 − 55 1.41 oe or B1 for 77.55 2(a)(ii) 1.8[0] 2 M1 for (1.50 − 1.41)  20 oe or B1 for 30 and 28.2[0] seen 2(a)(iii) 47.3 or 47.26… 3 M2 for 63 + 84.5 + 72.23 + 46 + 54.10 + 80 oe 6  1.41 or M1 for 63 + 84.5 + 72.23 + 46 + 54.10 + 80 oe 1.41 63 + 84.5 + 72.23 + 46 + 54.10 + 80 or oe 6 2(a)(iv) 2 2 1.53 − 1.50 M1 for  100  oe 1.50 1.53 or  100  −100 oe 1.50  1.53  or  − 1   100  oe  1.50  2(b) 65 3 5 M2 for 39  oe 3 3 or M1 for 39 is equivalent to or for 5 39 3 5 if 0 scored then SC1 for 39  oe 2 2(c)(i) A straight line through (0,0) and (100,22) 2 B1 for a straight line drawn through the origin or for 2 correct points plotted 2(c)(ii) 4.55 or 4.545… 1 2(d) 56500, 56600 or 56540 to 56560…. 3 M2 for  1.5 2 ×8×1000 oe or  150 2 ×800÷1000 oe or M1 for  1.5 2 ×8 oe or  150 2 ×800 oe or B1 for final answer figs 565 to 566 If 0 scored, SC1: for their volume in m3 1000 or for their volume in cm3 1000 or for stating clearly 1m3=1000l or 1000 cm3=1l

This question in 0580/32 Feb/March 2024

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

4 The stem-and-leaf diagram shows the ages of the 16 workers in a shop on 1st January 2022. 2 3 5 7 3 4 6 6 6 9 4 1 1 7 5 0 7 7 8 6 1 Key: 2 5 represents 25 (a) (i) Work out the range. … [1] (ii) Write down the mode. … [1] (iii) Work out the median. … [1] (iv) Work out the percentage of workers that are older than 40 but younger than 60. … % [2] (b) On 1st January 2023 the shop has the same 16 workers. Write down the range, the mode and the median on 1st January 2023. Range … Mode … Median … [2] (c) On 1st January 2024 the oldest worker leaves. His replacement is a new worker born on 12th November 1970. There are no other changes to the workers. Complete the stem-and-leaf diagram for 1st January 2024. 2 5 7 9 3 6 8 8 8 4 5 6 Key: 2 5 represents 25 [2] (d) The shop owner is x years old. x is a prime number. x + 2 is a square number. x - 2 is a multiple of 9. Find the value of x. x = … [2]

11 marks

Mark scheme: 4(a)(i) 38 1 4(a)(ii) 36 1 4(a)(iii) 40 1 4(a)(iv) 43.75 2 7 M1 for 16 their 7 or correctly converted to a %. 16 4(b) 38 2 FT their (a)(i), (a)(ii) + 1, (a)(iii) + 1 37 B1FT for one or two correct 41 4(c) 2 B1 for 53 seen 2 [5 7 9] or for stem and leaf with no more than 2 errors or omissions. 3 [6 8 8 8] 4 1 3 3 9 5 2 3 9 9 6 0 4(d) 47 2 B1 for a final answer satisfying 2 of the 3 conditions.

This question in 0580/31 May/June 2024

1 (a) 40 football players vote on the colour of new shirts. The results for red, yellow and green are shown in the bar chart. 12 11 10 9 8 7 Frequency 6 5 4 3 2 1 0 Red Yellow Green Blue Orange (i) Twice as many football players vote blue than vote orange. Complete the bar chart. [3] (ii) Write down the mode. … [1] (b) 40 hockey players vote on the colour of new shirts. The table shows the results. Colour Frequency White 21 Grey 12 Pink 7 (i) Complete the pie chart. [4] (ii) Work out the percentage of hockey players who vote grey. … % [1]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Correct bars at [blue] 10 and [orange] 5 3 M1 for 40 – their(11 + 6 + 8) oe M1 for their 15 ÷ (1 + 2) oe 1(a)(ii) Red 1 1(b)(i) Correct pie chart 4 B2 for correct angles 189, 108, 63 soi or B1 for 1 correct angle soi 360 or M1 for k where k is 1, 21, 12 or 40 7 AND B2FT for two correct FT sectors drawn provided the sum of their 3 stated angles is 360 or B1FT for one correct sector drawn or one correct FT sector drawn 1(b)(ii) 30 1

This question in 0580/33 May/June 2024

5 (a) Students solve a puzzle by making guesses. The table shows the number of guesses that each of 40 students make. Number of guesses 1 2 3 4 5 6 Frequency 2 4 8 7 12 7 (i) Find the mode. … [1] (ii) Calculate the mean. … [3] (b) In another puzzle each student gets a score. These are the scores for 12 students. 17 21 24 32 27 11 26 18 10 29 14 24 (i) Complete the stem-and-leaf diagram for these scores. 1 2 3 Key : 1 | 7 represents 17 [2] (ii) Find the median. … [1] (c) A different puzzle has three outcomes: win, draw or lose. The table shows the outcomes for 30 students. Outcome Frequency Win 9 Draw 14 Lose 7 Complete the pie chart to show this information. [4]

11 marks

Mark scheme: 5(a)(i) 5 1 5(a)(ii) 4.1 3 M1 for 1×2 + 2×4 + 3×8 + 4×7 + 5×12 + 6×7 M1dep for their 164 ÷ 40 5(b)(i) 2 B1 for correct unordered diagram or for ordered diagram with one error or omission 5(b)(ii) 22.5 1 FT their (b)(i) dep. on an ordered diagram 5(c) Correct pie chart 4 B3 for 2 or 3 of 108°, 168° and 84° seen and 1 correct sector drawn or B2 for 2 or 3 of 108°, 168° and 84° seen or 1 correct sector drawn or B1 for 1 of 108°, 168° and 84° seen or M1 for 36030 [× k] ( where k = 1, 7, 9 or 14) implied by 12 If 0 scored B2FT FT their angles for correct pie chart drawn if angles add to 360 or B1FT for one correct sector drawn

This question in 0580/32 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

10 The table shows an ordered stem-and-leaf diagram. A, B and C are missing numbers. 0 2 A 1 1 3 B 7 2 0 4 6 C Key : 1 | 3 represents 13 For the ten numbers • the range is 27 • the median is 16 • the mean is 16.5 . (a) Work out the values of A, B and C. A = … B = … C = … [5] (b) Complete this statement. There is no mode because … … [1]

6 marks

Mark scheme: 10(a) 8 5 9 5 B1 for [B=] 5 B1 for [C=] 9 If B0,B0 scored SC1 for B = 15 and C = 29 B3 for 8 , 15 , 29 or 8 , 5 , 29 or 8 , 15 , 9 or M2 for ( 2 + A + 11 + 13 + (10 + theirB) + 17 + 20 + 24 + 26 ++ (20 + theirC))10[=16.5] oe soi or better or M1 for 16.5×10 oe or better 10(b) All the numbers are different oe 1

This question in 0580/32 Feb/March 2025

19 A four-sided dice is numbered 1 to 4. Hrishi throws the dice 50 times. The results are shown in the table. Number Frequency 1 14 2 15 3 9 4 12 Calculate the mean. … [2]

2 marks

Mark scheme: 19 2.38 2 M1 for (1 × 14 + 2 × 15 + 3 × 9 + 4 × 12) ÷ 50 oe

This question in 0580/31 May/June 2025

12 Kai opens his restaurant from Tuesday to Saturday each week. He counts the number of customers each day for two weeks. The bar chart shows some of the results. 70 60 50 Number of 40 customers 30 20 10 0 Tue Wed Thur Fri Sat Day Key: = Week 1 = Week 2 (a) In week 1 there were 200 customers in total. Complete the bar chart. [2] (b) Write down the mode for week 2. … [1] (c) Find the mean number of customers for the 5 days in week 2. … [2]

5 marks

Mark scheme: 12(a) Bar drawn in correct position with height 2 M1 for 200 – (20 + 30 + 50 + 60) soi 40 12(b) 40 1 12(c) 48 2 30 + 40 + 40 + 70 + 60 M1 for oe 5

This question in 0580/33 May/June 2025

6 17 4 25 18 14 6 3 18 12 Find (a) the mode … [1] (b) the range. … [1]

2 marks

Mark scheme: 6(a) 18 1 6(b) 22 1

This question in 0580/31 Oct/Nov 2025

10 The bar chart shows the frequency of each score on a spinner. 10 9 8 7 6 Frequency 5 4 3 2 1 0 1 2 3 4 5 Score on spinner Calculate the mean score. … [3]

3 marks

Mark scheme: 10 3.06 or 3.057… 3 M1 for (1 × 7) + (2 × 5) + (3 × 8) + (4 × 9) + (5 × 6) M1dep for their  fx  ( 7 + 5 + 8 + 9 + 6 )

This question in 0580/32 Oct/Nov 2025

20 A town has two cinemas, Movie Scene and Flix. The table shows the mean and range of the audience numbers. Mean Range Movie Scene 83 52 Flix 105 25 (a) Which cinema has higher audience numbers on average? Give a reason for your choice. Cinema … because … … [1] (b) Which cinema has greater variation in its audience numbers? Give a reason for your choice. Cinema … because … … [1]

2 marks

Mark scheme: 20(a) Flix AND higher mean oe 1 20(b) Movie Scene AND higher range oe 1

This question in 0580/32 Oct/Nov 2025

10 (a) Jason records his score in each of 10 games of cricket. 16 7 21 8 20 9 11 7 14 3 (i) Find the mode. … [1] (ii) Work out the range. … [1] (b) Ed plays 5 games. His mean score is 28. After one more game his mean score is now 26. Work out his score in the sixth game. … [2]

4 marks

Mark scheme: 10(a)(i) 7 1 10(a)(ii) 18 1 10(b) 16 2 M1 for (26 × 6) and (28 × 5) oe

This question in 0580/33 Oct/Nov 2025