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time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F Question 1 complete tally chart; fraction of days; simplify fraction; interpret percentage; use probability words Question 2 * complete pictogram; interpret key; read bar chart; compare results Question 3 given small data set, find mode, median & mean; criticise a claim; discuss sampling method Question 4 * calculate percentage of an amount; compare ways of working it out Question 5 read a scatter diagram; comment on a hypothesis; draw a scatter diagram to support a hypothesis Question 6 given a bag of counters, find probability; find number of counters Question 7 * design observation sheet; find evidence to decide hypothesis Question 8 share amount in given ratio Question 9 find winnings for probability game Grade boundaries * The quality of written communication is specifically assessed in questions 2, 4 and 7 1 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 1 The table shows the weather in London each day for 40 days 10 18 4 8 1(a) Complete the table 2 marks 1(b) What fraction of the 40 days are sunny? 10 Give your answer in its simplest form. 40 answer ¼ 2 marks 2 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 1(c) In Manchester for the 40 days • 16 days are sunny • 50% of the days have rain • there is no snow 1(c) (i) Complete the table for Manchester 16 50% of 40 days is 20 20 0 20 + 16 + 0 = 36 4 40 – 36 = 4 3 marks 3 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 16 20 0 4 1 (c) (ii) One of the 40 days in Manchester is chosen at random. Use a suitable probability word to complete the sentences. impossible The chance of choosing a day with snow is …………………………………………… evens The chance of choosing a day with rain is ……………………………………………… 2 marks 4 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 2* Nick takes four tests. The pictogram shows his scores. 2(a) Nick scores 60% in English. Complete the key. 20 1 mark 2(b) In which subject is his highest score? answer Mathematics 1 mark 5 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 2 (c) Jen takes the same four tests. The bar chart shows her scores. 6 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 2(c) (i) Nick wants to compare his scores with Jen’s scores. Draw a suitable diagram that he can use. Jen Nick 4 marks 7 time allowed: 1 hour marks: 54 2 (c) (ii) Write down three facts comparing 2010 November UNIT 1F 43601F their scores Jen Nick Fact: Jen scored higher than Nick in English, Geography and Science Fact: Nick scored higher than Jen in Mathematics Fact: both scored 40% or more in every test; they both had a highest score of 90% 8 3 marks time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 3 A company makes bags of toffees The company checks that the bags contain 50 toffees. 3(a) The number of toffees in a sample of 11 bags is 51 50 51 51 52 43 50 50 51 51 50 3(a) (i) Write down the mode answer 51 1 mark the mode is the data that occurs the most 3(a)(ii) Work out the median. You must show your working the median is halfway along the ordered list of data 43 50 50 50 50 51 51 51 51 51 52 answer 51 2 marks 9 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 3(a) The number of toffees in a sample of 11 bags is 51 50 51 51 52 43 50 50 51 51 50 3(a) (iii) Work out the mean the mean is calculated by adding all the data together, then dividing the total by the number of items 51 + 50 + 51 + 51 + 52 + 43 + 50 + 50 + 51 + 51 + 50 = 550 550 ÷ 11 = 50 answer 50 3 marks 10 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 3(b) The company claims there are 50 toffees in a bag 3(b) (i) Give a reason why this claim seems fair. All the averages are 50 or bigger than 50 1 mark 3(b) (ii) Give a reason why this claim seems unfair one of the sample bags only had 43 sweets in it 1 mark 11 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 3(c) The company uses the first 11 bags produced each Monday to check the contents. State two ways this method of sampling can be improved Take several samples during the week Take bigger samples Take samples at different times and on different days Take every hundredth bag during production to be part of the sample 3 marks 12 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 4(a) * Work out 70% of £986 70% is the same as 0.7 70% of 986 = 0.7 × 986 = answer £690.20 2 marks 690.2 13 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 4(b) Circle the calculations that have the same answer as 57% of 372 0.57 × 372 = 212.04 A 58% of 371 No ! B 5.7% of 37.20 No ! 57 C 372 0.57 × 372 = 212.04 100 D 0.57 × 0.372 No ! E 5.7% of 3720 0.057 × 3720 = 2 marks 212.04 14 time allowed: 1 hour marks: 54 5 Freddie and Priya both like music 2010 November UNIT 1F 43601F Freddie gives some songs a score out of 10 The scatter diagram shows his results 5(a) What fraction of the two scored 10 out of 10 songs is given full marks? thirteen songs answer 2 were scored 13 1 mark 5(b) How long is the song that is given a score of 4? Give your answer in minutes and seconds. time is 5 minutes and two sections each section is 60 seconds ÷ 5 = 12 seconds answer = 5 minutes and 24 seconds 2 marks 15 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 5(c) Freddie has this hypothesis He says, “The shorter the song, the more I like it.” Comment on his hypothesis the line of best fit shows weak negative correlation which supports his hypothesis shorter songs scored high marks and long songs scored low marks 16 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 5(d) Priya also gives some songs a score out of 10. She has a different hypothesis. She says, “The longer the song, the more I like it.” Her hypothesis is strongly supported by the data she collects. Plot points on the grid to show how her scatter diagram may look • a line of best fit would show positive correlation • shorter songs score low marks and long songs score high marks • the data points would be close to the line of best fit 1 mark 17 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 6(a) A bag contains 3 red, 5 white and 8 blue counters. One counter is chosen at random. What is the probability of choosing a blue counter. 3 + 5 + 8 = 16 counters in the bag probability = 8 8 of them are blue 16 answer = ½ 2 marks 18 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 6(b) A different bag contains only black counters, pink counters and white counters. When one counter is chosen at random, each colour is equally likely. Write down two possible values for the total number of counters in this bag three colours in the bag probability of each colour is ⅓ number of counters in the bag must be a multiple of 3 answer 6 and 24 2 marks 19 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 6(c) Another bag contains only green counters and yellow counters. There are more than 10 counters in the bag. When one counter is chosen at random, the probability of choosing a green counter is ¾ Write down two possible values for the total number of counters in this bag probability of green = ¾ probability of yellow = ¼ number of counters in the bag must be a multiple of 4, bigger than 10 answer 16 and 24 2 marks 20 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 7* This poster is put up in a school dinner hall Coming soon NEW healthy eating menu The headteacher thinks the number of students who eat school dinners will increase by 25% 7(a) Design an observation sheet the headteacher can use to see if she is right tallies total old menu new menu 2 marks 21 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 7(b) The number of students who eat school dinners increases from 78 to 91. Is the headteacher correct? [She thinks the number of students who eat school dinners will increase by 25%] Show clearly how you decide. 25% of 78 = 0.25 × 78 = 19.5 a 25% increase on 78 would have to be 20 students 91 – 78 = 13 only 13 extra students ate the new lunch menu answer: this is not enough to be 25% increase 3 marks 22 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 8 Peter and Alice buy a set of golf clubs for their mother. They pay in the ratio 4 : 3 Peter pays £224 How much does Alice pay? Peter Alice 4 3 224 168 224 ÷ 4 = 56 56 × 3 = 168 answer: Alice pays £168 3 marks 23 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F 9 At the school fayre, I play a game 20 times. Each go costs 50p. Each time I win, I receive £1.50 The probability of winning is ⅕. How much money do I expect to lose? You pay 50p for each of 20 games 50p × 20 = £10 You expect to win ⅕ of the time ⅕ of 20 games = 4 Four prizes of £1.50 = £6 £10 − £6 = £4 You should expect to lose £4 3 marks 24 time allowed: 1 hour marks: 54 2010 November UNIT 1F 43601F Total: out of 54 actual ones used grade G F E D C score 10 16 22 29 36 25

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posted: | 10/3/2012 |

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