EDEXCEL FUNCTIONAL SKILLS PILOT. Maths Level 1. Test your skills. Chapters 6 and 7. Investigating election statistics

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1 EDEXCEL FUNCTIONAL SKILLS PILOT Maths Level 1 Test your skills Chapters 6 and 7 Investigating election statistics Applying skills in: handling data probability Answer all questions in this task. Write your answers in the spaces provided. Where you see this sign you must show how you get your answers as marks may be awarded for your working out. You may use a calculator. Pearson Education 2009 Functional Maths Level 1 Chapters 6 7 Test page 1 Draft for Pilot FS-Ma-L1test-Cha6-7.indd 1 4/30/09 12:03:52 PM

2 Elections for a president of a social club A social club holds elections for a new president every three years. 1 The table shows the election results for the past three elections. Name of candidate Number of votes 2002 Election 2005 Election 2008 Election Alice Adams 20 Mary Butterworth Michael Butterworth Nigel Cooper Sajid Hamid Robina Hassan 29 Henry Jackson Lorna Moore 45 David Roberts Tim Shacklock 52 a) Who gained the least number of votes for any year? When did this happen? Candidate Year b) Which candidates entered all three elections? c) What was the range in the number of votes in the 2005 election? Range d) Which election year had the biggest range in votes? Year Pearson Education 2009 Functional Maths Level 1 Chapters 6 7 Test page 2 Draft for Pilot FS-Ma-L1test-Cha6-7.indd 2 4/30/09 12:03:53 PM

3 Investigating election statistics 6 7 e) What was the mean number of votes per candidate in the 2002 election? Mean number of votes f) Investigate whether the mean number of votes per candidate has increased or decreased in the 2005 and 2008 elections, compared with the 2002 election. A total of 520 people voted in the 2008 election. g) Use the number of votes Tim Shacklock gained to work out the probability of Tim Shacklock winning a similar election. Probability h) If the same candidates enter the 2011 election as the 2008 election, and no other circumstances change, which two candidates do you judge to be likely to win? Why? Candidate 1 Candidate 2 Pearson Education 2009 Functional Maths Level 1 Chapters 6 7 Test page 3 Draft for Pilot FS-Ma-L1test-Cha6-7.indd 3 4/30/09 12:03:54 PM

4 2 Michael and Mary Butterworth are a married couple who have both entered all three elections. They want to compare how their individual numbers of votes have changed over the three elections. They decide to plot a line graph showing the number of votes received a) Provide the missing information from the graph in the box below. Title... Vertical axis label... Horizontal axis label... Key... b) What is the change in voting figures for each candidate from 2002 to 2005, and from 2005 to 2008? Michael Butterworth Mary Butterworth Pearson Education 2009 Functional Maths Level 1 Chapters 6 7 Test page 4 Draft for Pilot FS-Ma-L1test-Cha6-7.indd 4 4/30/09 12:03:56 PM

5 Investigating election statistics 6 7 One of the Butterworths must drop out of the election in 2011 as it is taking up too much time. c) Who should drop out and why? 3 Many members in the social club do not bother to vote. The club president is concerned about this and asked the club secretary to look at who voted in each election. The secretary collects information about the voters in the 2008 election and organises this information in a table. There were 520 voters in total. Group Number of voters female unemployed 260 male unemployed 110 female employed 40 male employed 110 a) Work out the probability of a voter chosen at random being an unemployed woman. Probability Pearson Education 2009 Functional Maths Level 1 Chapters 6 7 Test page 5 Draft for Pilot FS-Ma-L1test-Cha6-7.indd 5 4/30/09 12:03:57 PM

6 b) Use the graph paper below to represent this information in a bar chart female unemployed male unemployed female employed male employed c) How many more unemployed members voted than employed voters in 2008? Number of members Pearson Education 2009 Functional Maths Level 1 Chapters 6 7 Test page 6 Draft for Pilot FS-Ma-L1test-Cha6-7.indd 6 4/30/09 12:03:58 PM

7 Investigating election statistics 6 7 The secretary collects information about the voters in the 2005 election and represents this in a pie chart. Groups of votes in 2005 elections male employment female employment male unemployment female unemployment d) What fraction of the voters in 2005 were female and unemployed? Fraction e) Who were less likely to vote in 2005, men or women? Why? f) Use the pie chart above and the bar chart you have drawn to say whether the proportion of employed female voters has increased or decreased from 2005 to Pearson Education 2009 Functional Maths Level 1 Chapters 6 7 Test page 7 Draft for Pilot FS-Ma-L1test-Cha6-7.indd 7 4/30/09 12:03:59 PM

8 A Solutions Answer 1a) 20 is the smallest number of votes in the table. Alice Adams b) There are three candidates with votes entered in all three columns. Mary Butterworth Michael Butterworth Sajid Hamid 1c) d) In 2002 the range is = 75 In 2005 the range is 145 In 2008 the range is = is the biggest number e) 2002: = 425 There are five candidates so divide 425 by = 85 Check: Show working for inverse operation, e.g = 425 Or estimation of mean, e.g = = 86 which is close to 85 1f) 2005: = 462 There are six candidates so divide 462 by = : = 520 There are eight candidates so divide 520 by = 65 1g) 52 people voted for Tim Shacklock out of 520 This gives an indication of how popular Tim Shacklock is with the voters = h) Michael Butterworth and David Roberts received substantially more votes than anyone else. 2a) Title Number of votes received by Mr and Mrs Butterworth Vertical axis label Number of votes Horizontal axis label Election year Key Red line votes for Michael, blue line votes for Mary 2b) Michael Butterworth: votes dropped by 22 from 2002 to 2005 Mary Butterworth: votes increased by 23 from 2002 to 2005 but have slightly decreased by 3 in c) Suggest Mary drops out as Michael s votes have significantly increased whereas Mary s votes have slightly decreased. Mean number of votes per candidate in 2002 is 85 Mean number of votes per candidate is decreasing with each election 1 10 Michael Butterworth or David Roberts Any similar answers conveying the same meaning are acceptable Answers must be clear and include the difference between the votes for the three years for the two candidates Any similar description is acceptable Pearson Education 2009 Functional Maths Level 1 Chapters 6 7 Test page 8 Draft for Pilot FS-Ma-L1test-Cha6-7.indd 8 4/30/09 12:04:00 PM

9 Investigating election statistics 6 7 3a) There are 260 unemployed female voters out of a total of 520 Probability (voter being unemployed woman) = = 1 2 Answer 1 2 or 0.5 or 50% 3b) 280 Bar chart drawn with suitable 260 labels on both axes. For example, 240 vertical axis label Numbers of voters 220 (or something similar), horizontal 200 axis Group (or something similar). 180 Bars of equal width and gaps between 160 the bars female unemployed male unemployed female employed male employed 3c) There are = 370 unemployed voters There are = 150 employed voters = 220 3d) A quarter of the circle represents unemployed females. 3e) Men are represented by 1 4 of the pie chart and women are men represented by 3 4 of the pie chart. 3f) From the pie chart, the proportion of employed female voters in 2005 is 1 2 From the bar chart, there are 40 out of 520 employed female voters in This is less than half of the voters. 220 voters 1 4 decreased Pearson Education 2009 Functional Maths Level 1 Chapters 6 7 Test page 9 Draft for Pilot FS-Ma-L1test-Cha6-7.indd 9 4/30/09 12:04:03 PM