Classifying statistical data — Paper 3 · IGCSE Mathematics 0580

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 Marie counts the number of people in each of 60 cars one morning. For Examiner's (a) She records the first 40 results as shown below. Use Number of people in a car Tally Number of cars 1 2 3 4 5 6 The remaining 20 results are 2, 2, 5, 2, 2, 4, 2, 6, 5, 3, 4, 5, 4, 6, 2, 5, 3, 2, 1, 6. (i) Use these results to complete the frequency table above. [2] (ii) On the grid below, draw a bar chart to show the information for the 60 cars. 20 18 16 14 12 Number 10 of cars 8 6 4 2 0 1 2 3 4 5 6 Number of people in a car [1] (iii) Write down the mode. For Examiner's Answer(a)(iii) [1] Use (iv) Find the median. Answer(a)(iv) [1] (v) Work out the mean. Answer(a)(v) [3] (b) Manuel uses Marie’s results to draw a pie chart. Work out the sector angle for the number of cars with 5 people. Answer(b) [2]

10 marks

Mark scheme: 3 (a) (i) 6,17,8,9,11,9 B2 B1 for 4 or 5 correct or for all tallies correct (ii) correct bar chart B1ft ft from their frequency table or tallies (iii) 2 B1ft from their table or chart (iv) 3 B1ft from their table or chart B3cao M1 for clear indication of 1x6 + 2x17 + 3x8 + 4x9 + (v) 3.48 5x11 + 6x9 ft imp by 209 M1 dep for ÷ 60 (b) 66º B2ft M1 for "11" ÷ 60 x 360 or "11" x 6 [10] IGCSE – May/June 2008 0580/0581 03

This question in 0580/31 May/June 2008

8 The table below shows the age and price of 20 used cars in a showroom. For Examiner's Use Age (years) 6 5 4 5 4 5 1 6 3 8 Price ($) 1800 7600 9500 2500 4100 3100 5600 4700 4800 7900 Age (years) 1 2 9 10 3 7 1 8 2 3 Price ($) 6500 7000 1000 3800 1900 5200 3400 2100 4300 8200 (a) Use this information to complete the following table. Age of cars (years) Number of cars Angle in a pie chart 1 to 3 8 144° 4 to 6 7 7 or more [3] (b) (i) Complete the frequency table for the price, $x, of the cars. Price ($) 0 Y x < 2000 2000 Y x < 4000 4000 Y x < 6000 6000 Y x < 8000 8000 Y x < 10 000 Frequency [2] (ii) Draw a histogram to show this information. 6 Frequency 5 4 3 2 1 0 2000 4000 6000 8000 10 000 Price of car ($) [2] (c) (i) On the grid below complete the scatter diagram showing the age and price of each car. For Examiner's The first 10 points from the original table have been plotted. Use 10 000 9000 8000 7000 6000 Price of car 5000 ($) 4000 3000 2000 1000 0 1 2 3 4 5 6 7 8 9 10 Age of car (years) [3] (ii) What correlation is there between the price of a car and its age? Answer(c)(ii) [1] (iii) A car is chosen at random. Using your scatter diagram, find the probability that the car is more than 4 years old and the price is more than $5000. Answer(c)(iii) [2] Question 9 is on the next page

13 marks

Mark scheme: 8 (a) 5, 1 126, 90 1, 1 SC1 for both angles incorrect but totalling 216°. W1 for 3 or 4 correct or left as tallies and all (b) (i) 3, 5, 6, 4, 2 2 correct. W1 for only 1 incorrect (ii) Blocks ‘correct’ heights 2ft SC1 All correct but small gaps between or full No gaps. horizontal lines only (c) (i) 10 points plotted correctly 3 W2 for 8 or 9 correct W1 for 6 or 7 correct On vertical age line (±1 mm) and between (or on) correct horizontal lines. (ii) Zero oe 1 (allow weak (slight) negative) (iii) 3 oe or 0.15 or 15% 2ft Ft numerator only 20 W1 for their3 k ≥ 3 k

This question in 0580/31 May/June 2009

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

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

3 (a) A shop has maps arranged in bookcases. For Examiner′s Use (i) The length of one wall in the shop is 7.35 m. Each bookcase is 120 cm wide. Work out the maximum number of bookcases that will fi t along this wall. Answer(a)(i) … [2] (ii) Each bookcase weighs 45 kg correct to the nearest 5 kg. Write down the upper bound for the weight of a bookcase. Answer(a)(ii) … kg [1] (b) During July and August the shop sells a total of 160 maps. Some of these maps are driving maps and the rest are walking maps. (i) Complete the table below. Driving maps Walking maps Total July 15 August 65 Total 40 160 [2] (ii) Write down the fraction of the total number of walking maps that are sold in July. Give your answer in its simplest form. Answer(b)(ii) … [2] (c) The shopkeeper buys each map for $5.50 . For Examiner′s He sells each map for $6.60 . Use (i) Calculate his percentage profi t. Answer(c)(i) … % [3] (ii) Each map has a price in dollars ($) and euros (€). The price is $6.60 or €3.52 . Work out the exchange rate for €1 . Answer(c)(ii) €1 = $ … [2] (d) The shop is open for 312 days each year. The shopkeeper pays 3 employees $47.66 each per day. The total annual wage bill for the three employees is given by 3 × 312 × 47.66 . (i) Rewrite this calculation so that each number is rounded to 1 signifi cant fi gure. 3 × … × … [1] (ii) Use your answer to part (d)(i) to work out an estimate for the total annual wage bill. Answer(d)(ii) $ … [1] _____________________________________________________________________________________

14 marks

Mark scheme: 3 (a) (i) 6 cao 2 M1 for 735/120 oe implied by 6.125 or SC1 for figs ‘61 … ’ (ii) 47.5 1 (b) (i) 55 ---- 70 2 M1 for 3 or 4 correct numbers ---- 25 90 120 ---- --- 3 15 3 (ii) cao 2 B1 for or seen 8 40 8 20 (c) (i) 3 B1 for 6.6 - 5.5 or better M1 for ‘their 1.1’ / 5.5 OR (an alternative method) M1 for 6.6/5.5 M1 for ‘their 1.2’ –1 oe 1.875 cao (ii) 2 M1 for 6.60/3.52, imp by 1.87 or 1.88 300, 50 (d) (i) 1 45000 (ii) 1 SC1 43200

This question in 0580/32 May/June 2013

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

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 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

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

1 (a) 120 children take part in an athletics competition. (i) Complete the table to show the number of children in each group. Girls Boys Total Age 15 65 Age 16 44 Total 70 120 [2] (ii) One child is selected at random. Find the probability that it is a girl aged 16. Give your answer as a fraction in its lowest terms. Answer(a)(ii) … [2] (iii) Write down the ratio number of girls aged 15 : number of boys aged 15. Give your answer in its simplest form. Answer(a)(iii) … : … [2] (b) Here are the distances, in metres, recorded in the boys’ shot putt. 9.23 6.21 9.86 8.64 7.15 7.72 9.01 7.34 6.53 6.89 (i) Find the median. Answer(b)(i) … m [2] (ii) Find the range. Answer(b)(ii) … m [1] (iii) Another boy was a late entry to the competition. After his attempt, the range increased by 20 cm. Work out the two possible distances of his attempt. Answer(b)(iii) … m or … m [2] __________________________________________________________________________________________

11 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 2 B1 for 3 or 4 correct 26 39 65 44 11 55 70 50 120 (ii) 11 cao 2 B1 for 44 or 22 30 120 60 (iii) 2 : 3 cao 2 B1FT for 2k : 3k where k is an integer or their 26 : their 39 or better with integer values (b) (i) 7.53 2 M1 for attempt at ordered list, or 7.34 and 7.72 identified (ii) 3.65 1 (iii) 10.06 6.01 2 B1 for 1 correct

This question in 0580/31 Oct/Nov 2015

6 (a) Natalia has 16 reels of cotton. 6 reels are blue, 4 are white, 3 are red, 2 are black and 1 is green. Natalia picks a reel at random. (i) Write down the colour she is most likely to pick. Answer(a)(i) … [1] (ii) Find the probability that she picks a black reel. Answer(a)(ii) … [1] (b) Natalia is making a circular tablecloth of radius 1.5 m using blue and white material. The diagram shows this tablecloth. White NOT TO SCALE 0.9 m 1.5 m Blue (i) The radius of the blue circle is 0.9 m. Work out the area of the white material shown in the diagram. Answer(b)(i) … m2 [3] (ii) Natalia puts ribbon around the edge of the tablecloth. Calculate the length of ribbon used. Answer(b)(ii) … m [2] (iii) Natalia buys 12 m of ribbon costing $1.45 per metre. Calculate the amount of change she receives from a $20 note. Answer(b)(iii) $ … [2] __________________________________________________________________________________________

9 marks

Mark scheme: 6 (a) (i) Blue 1 2 (ii) oe 1 16 (b) (i) 4.52 or 4.523 to 4.524… 3 M2 for 1.52π – 0.92π or better or M1 for either 1.52π or 0.92π or better (ii) 9.42 or 9.43 or 9.424 to 9.426 2 M1 for 2 ×1.5π or better (iii) 2.6[0] 2 M1 for 20 – (12 × 1.45)

This question in 0580/33 Oct/Nov 2015

1 (a) A group of 20 children were asked to choose their favourite type of fruit juice. The results are listed below. Orange Apple Apple Pineapple Mango Tropical Orange Mango Apple Mango Pineapple Apple Apple Mango Orange Apple Mango Pineapple Orange Apple (i) Complete the frequency table for the results. You may use the tally column to help you. Type of juice Tally Frequency Orange Apple Pineapple Mango Tropical [2] (ii) Draw a bar chart to show these results. Remember to mark the scale on the frequency axis. Frequency Orange Apple Pineapple Mango Tropical [3] (iii) Sarah has a pack of 20 cartons of juice. 5 are orange, 5 are apple, 5 are pineapple and 5 are mango. She would like to give each child their favourite type of juice. How many children will not get their favourite type of juice? … [1] (b) One litre of a mixed fruit drink contains 550 millilitres of apple juice. Write down the fraction of the drink that is apple juice. Give your answer in its simplest form. … [2] (c) Amir wants to buy a bottle of fruit juice. There are three sizes of bottle. 0.9 litres 1.25 litres 1.35 litres $2.40 $3.15 $3.50 Work out which size of bottle gives the best value. Show how you decide. … [3] (d) The amount of juice in a glass, j millilitres, is 150 millilitres correct to the nearest 10 millilitres. Complete this statement about the value of j. … G j 1 … [2]

13 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) Frequencies 4, 7, 3, 5, 1 2 B1 for 3 or 4 correct in frequency column or for fully correct tally in tally column or for 4, 7, 3, 5, 1 in tally column (ii) Correct bar chart 3FT B1 for linear vertical scale B2FT for all bars correct height and equal width, with equal gaps or no gaps or B1FT for all bars correct height with unequal widths and/or gaps or at least four bars correct height and equal width, with equal gaps or no gaps (iii) 3 1 11 550 (b) final answer 2 M1 for oe seen 20 1000 (c) Three correct evaluated, to at least 3 M2 M2 implied by 2.67 or 2.66… and 2.52 and significant figures, consistent divisions 2.59… or M1 for one correct evaluated division soi, implied by one of 2.67 or 2.66…, 2.52, 2.59… [$/litre] or one of 2.40/0.9 = 2.7, 3.15/1.25 = 2.5, 3.50/1.35 = 2.6 1.25 litre bottle indicated A1 Dependent on M2 (d) 145 155 1, 1 B1 for both correct in reverse order

This question in 0580/32 May/June 2016

3 (a) The table shows the results of a survey in a village. It shows the number of males and females who are left-handed, right-handed or ambidextrous. Left-handed Right-handed Ambidextrous Total Male 17 5 84 Female 21 102 3 126 Total 38 164 8 210 (i) Complete the table by finding the number of males in the survey who are right-handed. [1] (ii) Using these results, write down the probability that (a) a male chosen at random is left-handed, … [1] (b) a left-handed person chosen at random is female, … [1] (c) a person chosen at random is right-handed. … [1] (iii) Here are the ages of the people who are ambidextrous. 27 79 31 16 60 45 42 52 Find the median age of these people. … [2] (b) This table shows the results of another survey. It shows the number of people in each of 50 households. Number of people Frequency 1 5 2 8 3 12 4 14 5 7 6 4 Work out the mean number of people in each household. … [3] (c) Some students in the village school were given a multiplication test and a spelling test. The scores are shown in the table. Spelling test 14 16 33 22 26 17 36 25 10 30 55 38 42 48 score Multiplication 11 15 19 18 15 21 27 21 35 26 34 23 28 31 test score 40 30 Multiplication test score 20 10 0 0 10 20 30 40 50 60 Spelling test score (i) Complete the scatter diagram. The first ten points have been plotted for you. [2] (ii) One student has a high score in the multiplication test and a low score in the spelling test. On the scatter diagram, put a ring around this point. [1] (iii) What type of correlation is shown in this scatter diagram? … [1] (iv) On the scatter diagram, draw a line of best fit. [1] (v) Another student, Kim, scored 45 in the spelling test but was absent for the multiplication test. Use your line of best fit to estimate a score for Kim in the multiplication test. … [1]

15 marks

Mark scheme: 3(a)(i) 62 1 3(a)(ii)(a) 17 1 oe isw 84 3(a)(ii)(b) 21 1 oe isw 38 3(a)(ii)(c) 164 1 oe isw 210 3(a)(iii) 43.5 oe 2 M1 for an ordered list giving at least the first 5 or the last 5 numbers in order or 42 and 45 identified 3(b) 3.44 3 M2 for (1 × 5 + 2×8 + 3 × 12 + 4 × 14 + 5 × 7 + 6 × 4) ÷ 50 implied by 172 ÷ 50 or M1 for (1 × 5) + (2 × 8) + (3 × 12) + (4 × 14) + (5 × 7) + (6 × 4) or 172 3(c)(i) 4 points plotted within tolerance 2 B1 for 2 or 3 points plotted within tolerance 3(c)(ii) (10, 35) indicated 1 3(c)(iii) Positive 1 3(c)(iv) Correct ruled line 1 3(c)(v) 28 to 32 1 If zero scored, FT their line of best fit if positive

This question in 0580/32 May/June 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

6 The 262 students at a college each study one of the languages shown in the table. French German Spanish Italian Japanese Total Boys 27 48 19 123 Girls 32 54 12 Total 53 30 262 (a) Complete the table. [3] (b) Find the probability that (i) a girl, chosen at random, studies Spanish, … [1] (ii) a boy, chosen at random, studies French or Italian, … [1] (iii) a student, chosen at random, does not study German. … [1] (c) 72 students each study one of the sciences shown in the table. The results are to be shown in a pie chart. Science Number of students Pie chart sector angle Biology 25 125° Chemistry 16 Physics 31 (i) Complete the table. [2] (ii) Complete the pie chart. [2]

10 marks

Mark scheme: 6(a) 3 B2 for 6 or 7 correct F G S I J Tot B 21 8 or B1 for 3, 4 or 5 correct G 30 11 139 Tot 57 102 20 6(b)(i) 54 1 FT their table oe isw their139 6(b)(ii) 46 1 oe isw 123 6(b)(iii) 209 1 oe isw 262 6(c)(i) [Chemistry] 80° 2 B1 for each [Physics] 155° or if 0 scored M1 for 125 ÷ 25 or 360 ÷ 72 or 5 If 0 scored SC1 for the two angles adding to 235° 6(c)(ii) Two correct lines on the pie chart 2 2FT only if (c)(i) angles total 235° B1 for a correct sector of 125° or 80° or 155°

This question in 0580/32 May/June 2018

1 Lena owns a café. (a) One day, Lena records the drinks she sells in one hour. Tea Tea Coffee Juice Milkshake Milkshake Coffee Coffee Milkshake Coffee Tea Juice Tea Coffee Tea Juice Milkshake Tea Milkshake Tea Coffee Tea Milkshake Coffee (i) Complete the frequency table. You may use the tally column to help you. Drink Tally Frequency Coffee Juice Milkshake Tea Total 24 [2] (ii) Draw a bar chart to show this information. Complete the scale on the frequency axis. Frequency 0 Coffee Juice Milkshake Tea [3] (b) This table shows the opening hours of the café. Day Opening hours Monday to Thursday 08 30 to 17 00 Friday and Saturday 08 30 to 19 00 Sunday 09 00 to 18 00 (i) Work out the total number of hours the café is open in one week. … hours [2] (ii) Lena is in the café for 40 hours each week. Ron is in the café when Lena is not there. Calculate the percentage of the total opening hours that Ron is in the café each week. … % [2] (c) Saddak buys 3 cups of tea and 2 cookies for $6.95 . A cup of tea costs $1.75 . Work out the cost of one cookie. $ … [2] (d) The price of a cake is $2.60 . At the end of the day, Lena reduces the price of each cake by 35%. Calculate the reduced price of a cake. $ … [2]

13 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 7, 3, 6, 8 2 B1 for 3 correct in frequency column or for 2 correct if they all sum to 24 or for all correct tallies if frequency column blank or for 7, 3, 6, 8 seen in tally column with frequency column blank or incorrect. 1(a)(ii) Correct bar chart with scaled 3 B1 for correctly scaled frequency axis frequency axis B1FT all heights correct B1 equal width bars and gaps 1(b)(i) 64 2 B1 for two from 8.5, 10.5 and 9 soi 1(b)(ii) 37.5 2 their ( b )( i ) − 40 M1 for oe their ( b )( i ) If 0 scored, SC1 for answer 62.5 1(c) [0].85 2 M1 for 6.95 – 3 × 1.75 oe 1(d) 1.69 2  35  M1 for 2.6 ×  1 −  oe  100 

This question in 0580/31 Oct/Nov 2018

3 (a) The table gives some information about the numbers of visitors at a leisure centre one day. Adult Child Total Male 144 240 Female 129 260 Total 225 275 500 (i) Complete the table. [1] (ii) Work out how many more child visitors than adult visitors there are. … [1] (iii) Write down the fraction of visitors that are adults. Give your answer in its lowest terms. … [2] (iv) Write the ratio number of males : number of females. Give your answer in its simplest form. … : … [2] (v) One of these visitors is selected at random. Find the probability that this visitor is a male child. … [1] (b) The number of people in each of 150 cars entering the leisure centre car park is recorded. The table shows the results. Number of people 1 2 3 4 5 Frequency 44 43 30 25 8 (i) Write down the mode. … [1] (ii) Calculate the mean. … [3] (c) In a survey of 50 visitors to the leisure centre, 18 used the gym. One day, 1500 people visited the leisure centre. Calculate an estimate for the number of people who used the gym on this day. … [2]

13 marks

Mark scheme: 3(a)(i) 96 144 240 1 both correct 129 131 260 225 275 500 3(a)(ii) 50 1 3(a)(iii) 9 2 225 45 B1 for or or 0.45 20 500 100 3(a)(iv) 12 : 13 2 B1 for 240 : 260 oe If 0 scored, SC1 for answer 13 : 12 3(a)(v) 144 1 oe 500 3(b)(i) 1 1 3(b)(ii) 2.4 3 M1 for 44 × 1 + 43 × 2 + 30 × 3 + 25 × 4 + 5 × 8 M1dep for their 360 ÷ 150 3(c) 540 2 18 1500 M1 for [× 1500 ] or [× 18] 50 50

This question in 0580/31 Oct/Nov 2018

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

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

8 (a) COMMONWEALTH Lindon picks a letter at random from this word. 1 Explain why the probability that he picks a letter M is not . 10 … [1] (b) Tickets for athletics or swimming or hockey or diving are placed in a box. A ticket is picked at random from the box. Sport Athletics Swimming Hockey Diving Probability 0.12 0.09 0.4 Complete the table. [2] (c) In a group of 40 students, • 24 students like football • 19 students like cricket • 10 students like football but not cricket. Football Cricket Complete the Venn diagram. [3] (d)  = {x : x is a positive integer less than 20} A = {x : x is an even number} B = {x : x is a multiple of 3} A B 2 4 3 6 8 10 9 12 14 15 18 16 1 5 7 11 13 17 19 (i) Write down n ( A ) . … [1] (ii) List the elements of set B. B = { … } [2] (iii) One of these 19 numbers is picked at random. Work out the probability that this number is (a) not in set A and not in set B, … [1] (b) in A , B . … [1] (iv) Complete the statement. A + B = {x : x is … } [1]

12 marks

Mark scheme: 8(a) There are 2 M’s or 12 letters 1 8(b) 0.39 oe 2 M1 for 1– (0.12 + 0.09 + 0.4) oe 8(c) Football Cricket 3 B1 for 10 B1FT for 14 and 5 10 14 5 or their 10 + their 14 = 24 and their 14 + their 5 = 19 11 B1FT for 11 or 40 – (their 10 + their 14 + their 5) 8(d)(i) 9 cao 1 8(d)(ii) 3 6 9 12 15 18 2 B1 for 4 or 5 correct and no extras 8(d)(iii)(a) 7 1 oe 19 8(d)(iii)(b) 12 1 oe 19 8(d)(iv) Even and a multiple of 3 1 or a multiple of 6 oe

This question in 0580/32 Oct/Nov 2020

8 (a) 15 people take a test. These are the test scores. 29 27 12 32 42 26 7 23 22 31 40 9 18 35 8 (i) Complete the frequency table. You may use the tally column to help you. Score Tally Frequency 0 to 10 11 to 20 21 to 30 31 to 40 41 to 50 [2] (ii) Use your table to complete the bar chart. 8 7 6 5 Frequency 4 3 2 1 0 0 to 10 11 to 20 21 to 30 31 to 40 41 to 50 Score [2] (b) On Monday and Tuesday, the probability that a train is late is 0.2 . Monday Tuesday Late 0.2 Late 0.2 Not late … Late 0.2 … Not late Not late … (i) Complete the tree diagram. [1] (ii) Use the tree diagram to find the probability that a train is (a) late on both days, … [2] (b) not late on Monday and late on Tuesday. … [2]

9 marks

Mark scheme: 8(a)(i) 3 2 5 4 1 2 B1 for 3 or 4 correct or all tallies correct if no frequencies are given or for 3 2 5 4 1 in tally column 8(a)(ii) Correct bar chart 2 FT their table B1FT for correct bar chart with one height incorrect or all heights correct but with inconsistent widths or gaps 8(b)(i) [0].8 in the three correct places 1 8(b)(ii)(a) [0].04 oe 2 M1 for [0].2 × [0].2 8(b)(ii)(b) [0].16 oe 2 FT their diagram M1 for their [0].8 × [0].2

This question in 0580/33 May/June 2021

3 360 people go on a school trip to one of four places. Some of the information is shown in the table. Adventure Botanic Wildlife Red castle Total park gardens centre Boys 65 12 36 Girls 9 62 163 Staff 15 3 37 Total 144 24 121 71 360 (a) Complete the table. [3] (b) Find the probability that (i) a girl, picked at random, visits the Wildlife centre, … [1] (ii) a person, picked at random from those visiting the Botanic gardens, is a girl, … [1] (iii) a person, picked at random, visits the Adventure park or the Botanic gardens. … [1] (c) The people who visit the Adventure park travel by coach. Each coach has 52 seats for passengers. Complete this statement. The least number of coaches needed for the trip to the Adventure park is … and there will be a total of … empty seats. [2] (d) The school hires one coach from each of two different companies for the trip to Red castle. A coach from Fast Track coaches costs $600 plus $0.72 per kilometre travelled. The total cost, in dollars, for travelling x kilometres is 600 + 0.72x . (i) A coach from Rapid coaches costs $550 plus $1.12 per kilometre travelled. Write an expression for the total cost, in dollars, for travelling x kilometres. … [1] (ii) Both companies charge the same amount for the trip. Write down an equation and solve it to find the distance travelled. … km [3] (e) The length, l km, of the journey to the Wildlife centre is 53 km, correct to the nearest kilometre. Complete this statement about the value of l. … G l 1 … [2] (f) Samira takes $31.50 to spend in the Botanic gardens. 2 (i) She spends of this money on food. 7 Work out how much Samira spends on food. $ … [1] (ii) At the end of the visit to the Botanic gardens, Samira has $4.50 left. What fraction of her money does Samira spend? Give your answer in its simplest form. … [2]

17 marks

Mark scheme: 3(a) 3 B2 for 4 or 5 correct A B W R Tot or B1 for 2 or 3 correct B 47 160 G 64 28 S 12 7 Tot 3(b)(i) 62 1 oe 163 3(b)(ii) 3 1 oe 8 3(b)(iii) 7 1 oe 15 3(c) 3, 12 2 B1 for 3 (coaches) nfww or M1 for 144 ÷ 52 3(d)(i) 550 + 1.12x 1 3(d)(ii) 600 + 0.72x = 550 + 1.12x 1 FT 600 + 0.72x = their (d)(i) 125 2 M1FT for isolating x terms and constant terms or better for their linear equation DEP on their (d)(i) of the form ax + b (a ≠ 0) 3(e) 52.5, 53.5 2 B1 for each If zero scored, SC1 for both values correct but reversed 3f(i) 9 1 3(f)(ii) 6 2 31.5 [ 0 ] − 4.5 [ 0 ] cao M1 for oe 7 31.5 [ 0 ]

This question in 0580/31 Oct/Nov 2021

1 (a) One day, Mahika records the number of teachers and students who cycle to school. Tally Frequency Teachers | | | | Students | | | | | | | | | | | | | | | | | | | (i) Complete the frequency column in the table. [1] (ii) Work out the percentage of people who cycle that are students. … % [2] (b) Mahika records how 120 students from Year 1 and Year 2 travel to school. Each student walks, cycles or travels by bus. • 48 students are in Year 1. • 77 students walk. • 5 students in Year 2 cycle. • 36 students travel by bus. 4 • of the students who travel by bus are in Year 1. 9 (i) Complete the table. Walk Cycle Bus Total Year 1 Year 2 Total 120 [3] (ii) One of the 120 students is chosen at random. Work out the probability that this student does not travel by bus to school. … [2] (c) There have been 24 complaints about one of the buses. The complaints are: • The bus is late. • The price is too high. • The bus is crowded. (i) Complete the table. Pie chart Complaint Frequency sector angle Late 10 Price 6 Crowded 8 [2] (ii) Complete the pie chart. [2]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 5 23 1 1(a)(ii) 82.1 or 82.14… 2 FT their (a)(i) their 23 M1 for [× 100 ] soi their 5 + their 23 1(b)(i) 30 2 16 48 3 B2 for 9 or 10 correct 47 5 20 72 or B1 for 5, 6, 7 or 8 correct 77 7 36 [120] 1(b)(ii) 7 2 120 − 36 oe M1 for oe 10 120 or B1 for 84 or for their77 +their 7 1(c)(i) 150, 90, 120 2 B1 for one correct sector angle 360 or M1 for × k k =1, 6, 8 or 10 24 1(c)(ii) Correct pie chart drawn 2 FT their table if angles add up to 360 B1FT for one sector correctly drawn

This question in 0580/32 Feb/March 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

3 (a) Here is part of the timetable for trains from Hinton to Jarmouth. All trains take the same time to travel from Hinton to Jarmouth. Hinton 10 47 … Jarmouth 11 15 12 35 (i) Complete the timetable. [2] (ii) Marge arrives at Hinton station exactly 20 minutes before the 10 47 train leaves. 12 11 1 10 2 9 3 8 4 7 5 6 Complete the clock diagram to show the time she arrives at Hinton station. [1] (b) Each day, a bus leaves Texford to travel to Cranbrook every 45 minutes. The first bus leaves Texford at 07 10. The last bus leaves Texford at 22 10. Work out the number of buses that travel from Texford to Cranbrook each day. … [3] (c) The cost of a bus pass increases every year. On 1st January 2022 a bus pass costs $50. On 1st January 2023 the cost of the bus pass increases by 10%. On 1st January 2024 the cost of the bus pass increases by 5%. Calculate the cost of the bus pass on 1st January 2024. $ … [3] (d) The Venn diagram shows information about the number of workers in a hotel who travel to work by bus (B) and train (T). B T 31 9 85 107 (i) Work out the number of workers in the hotel. … [1] (ii) Work out n ( B , T ) . … [1] (iii) Explain in words what the number 85 in the Venn diagram represents. … [1] (iv) One of the workers is chosen at random. Find the probability that this worker travels to work by bus and train. … [1] (e) The hotel has single and double bedrooms in the ratio single | double = 3 | 8 . There are 75 more double rooms than single rooms. Work out the number of single rooms. … [2]

15 marks

Mark scheme: 3(a)(i) 12 07 2 B1 for 1 [hour] 20 [min] or 80[min] or 28 [min] seen 3(a)(ii) 10 27 drawn correctly on clock 1 face. 3(b) 21 3 B2 for 20 as final answer 22:10  07:10 or M2 for  60 oe 45 or M1 for  22:10  07:10   60 oe 3(c) 57.75 3  10  5  M2 for 50   1   1   oe  100  100  or B2 for 1.155  10  or M1for 50   1   oe  100   5  or 50   1   oe  100   5  or their 55   1   oe  100   10  5  or  1   1   oe  100  100  3(d)(i) 232 1 3(d)(ii) 125 1 3(d)(iii) The number of workers who travel 1 to work by train but who do not travel on a bus oe. 3(d)(iv) 9 1 FT their 3(d)(i) in denominator. oe 232 3(e) 45 2 75 M1 for  k oe k  1, 3, 8 8  3

This question in 0580/31 May/June 2024