2016 2014 CAPS Stats

Western Cape Education Department Examination Preparation Learning Resource 2016 STATISTIC MATHEMATICS Grade 12 Razzia Ebrahim Senior Curriculum Planner for Mathematics E-mail: Razzia.Ebrahim@wced.info / Razzia.Ebrahim@westerncape.gov.za Website: http://www.wcedcurriculum.westerncape.gov.za/index.php/component/jdownloads/category/1835- grade-12?Itemid=-1 Website: http://wcedeportal.co.za

Index Page 1. 2016 June Paper 2 3–5 2. 2016 Feb-March Paper 2 5–6 3. 2015 November Paper 2 7–8 4. 2015 June Paper 2 9 5. 2015 Feb-March Paper 2 10 – 11 6. 2014 November Paper 2 12 – 13 7. 2014 Exemplar Paper 2 14 – 15 2

Mathematics/P2 DBE/2016 SCE QUESTION 1 On a certain day a tour operator sent 11 tour buses to 11 different destinations. The table below shows the number of passengers on each bus. 8 8 10 12 16 19 20 21 24 25 26 1.1 Calculate the mean number of passengers travelling in a tour bus. (2) 1.2 Write down the five-number summary of the data. (3) 1.3 Draw a box and whisker diagram for the data. Use the number line provided in the ANSWER BOOK. (2) 1.4 Refer to the box and whisker diagram and comment on the skewness of the data set. (1) 1.5 Calculate the standard deviation for this data set. (2) 1.6 A tour is regarded as popular if the number of passengers on a tour bus is one standard deviation above the mean. How many destinations were popular on this particular day? (2) [12] Copyright reserved Please turn over 3

Mathematics/P2 DBE/2016 SCE QUESTION 2 On the first school day of each month information is recorded about the temperature at midday (in °C) and the number of 500 mℓ bottles of water that were sold at the tuck shop of a certain school during the lunch break. The data is shown in the table below and represented on the scatter plot. The least squares regression line for this data is drawn on the scatter plot. Temperature at 18 21 19 26 32 35 36 40 38 30 25 midday (in °C) Number of bottles of 12 15 13 31 46 51 57 70 63 53 23 water (500 mℓ) Scatter plot 75 70 65 60 Number of bottles of water (500 mℓ) 55 50 45 40 35 30 25 20 15 10 5 15 20 25 30 35 40 Temperature at midday (in °C) Copyright reserved Please turn over 4

Mathematics/P2 DBE/2016 SCE 2.1 Identify an outlier in the data. (1) 2.2 Determine the equation of the least squares regression line. (3) 2.3 Estimate the number of 500 mℓ bottles of water that will be sold if the temperature is 28 °C at midday. (2) 2.4 Refer to the scatter plot. Would you say that the relation between the temperature at midday and the number of 500 mℓ bottles of water sold is weak or strong? Motivate your answer. (2) 2.5 Give a reason why the observed trend for this data cannot continue indefinitely. (1) [9] Copyright reserved Please turn over 5

Mathematics/P2 QUESTION 2 NSC DBE/Feb.—Mar. 2016 A company recorded the number of messages sent by e-mail over a period of 60 working days. The data is shown in the table below. NUMBER OF MESSAGES NUMBER OF DAYS 10 <x <20 2 20 <x <30 8 30<x<40 5 40 <x<50 10 50<x<60 12 60<x<70 18 70 <x <80 3 80 <x<90 2. 2.1 Estimate the mean number of messages sent per day, rounded off to TWO decimal places. 2.2 Draw a cumulative frequency graph (ogive) of the data on the grid provided in the ANSWER BOOK. 23 Hence, estimate the number of days on which 65 or more messages were sent. Copyright reserved Please turn over (3) (4) (2) [9]

Mathematics/P2 DBE/November 2015 NSC QUESTION 1 The table below shows the total fat (in grams, rounded off to the nearest whole number) and energy (in kilojoules, rounded off to the nearest 100) of 10 items that are sold at a fast-food restaurant. Fat (in grams) 9 14 25 8 12 31 28 14 29 20 Energy 1 100 1 300 2 100 300 1 200 2 400 2 200 1 400 2 600 1 600 (in kilojoules) 1.1 Represent the information above in a scatter plot on the grid provided in the ANSWER BOOK. (3) 1.2 The equation of the least squares regression line is ŷ = 154,60 + 77,13x. 1.2.1 An item at the restaurant contains 18 grams of fat. Calculate the number of kilojoules of energy that this item will provide. Give your answer rounded off to the nearest 100 kJ. (2) 1.2.2 Draw the least squares regression line on the scatter plot drawn for QUESTION 1.1. (2) 1.3 Identify an outlier in the data set. (1) 1.4 Calculate the value of the correlation coefficient. (2) 1.5 Comment on the strength of the relationship between the fat content and the number of kilojoules of energy. (1) [11] Copyright reserved Please turn over 7

Mathematics/P2 DBE/November 2015 NSC QUESTION 2 A group of 30 learners each randomly rolled two dice once and the sum of the values on the uppermost faces of the dice was recorded. The data is shown in the frequency table below. Sum of the values Frequency on uppermost faces 2 0 3 3 4 2 5 4 6 4 7 8 8 3 9 2 10 2 11 1 12 1 2.1 Calculate the mean of the data. (2) 2.2 Determine the median of the data. (2) 2.3 Determine the standard deviation of the data. (2) 2.4 Determine the number of times that the sum of the recorded values of the dice is within ONE standard deviation from the mean. Show your calculations. (3) [9] Copyright reserved Please turn over 8

Mathematics/P2 QUESTION 1 SCE DBE/2015 The data below shows the ages (in years) of people who visited the library between 08:00 and 09:00 on a certain morning. 3 | 4] 4} 5 | 23 | 29 | 32 | 36 | 40 | 47 | 56 | 66 | 68 | 76 | 82 1.1 Determine: 111 The mean age of the visitors 1.1.2 The median of the data 1.1.3 The interquartile range of the data 1.1.4 The standard deviation of the data 1.2 Draw a box and whisker diagram for the data. 1.3 By making reference to the box and whisker diagram, comment on the skewness of the data set. Mathematics/P2 DBE/2015 SCE QUESTION 2 Fourteen learners attended a Geometry training course spread over 12 Saturdays. Learners wrote a Geometry test at the end of the course. One learner was absent for this test. The number of Saturdays attended and the mark (as a %) each learner obtained for the test are shown in the table below. Number of Saturdays attended | 12] 11} 10|10}9|9/]7/}6/]5/]4 1/12/11] 6 Mark (as a %) 96 | 91 | 78 | 83 | 75 | 62 | 70 | 68 | 56 | 34 | 88 | 90 | 59 2.1 Calculate the equation of the least squares regression line. 2.2 Calculate the correlation coefficient. a0 Comment on the strength of the relationship between the variables, 24 The learner who was absent for the test attended the course on 8 Saturdays. Predict the mark that this learner would have scored for the test. 9 Q) () (3) (2) (3) (1) [12] (2) [3]

Mathematics/P2 NSC QUESTION 1 DBE/Feb.-Mar. 2015 The table below shows the distances (in kilometres) travelled daily by a sales representative for 21 working days in a certain month. 131 132 140 140 141 144 146 147 149 150 151 159 167 169 169 172 174 175 178 187 189 1.1 Calculate the mean distance travelled by the sales representative. 1.2 Write down the five-number summary for this set of data. 1.3 Use the scaled line on DIAGRAM SHEET 1 to draw a box-and-whisker diagram for this set of data. 1.4 Comment on the skewness of the data. 1.5 Calculate the standard deviation of the distance travelled. 1.6 The sales representative discovered that his odometer was faulty. The actual reading on each of the 21 days was p km more than that which was indicated. Write down, in terms of p (if applicable), the: 1.6.1 Actual mean 1.6.2 Actual standard deviation Copyright reserved 10 Please turn over (2) (4) 2) 0) (2) (1) (1) [13]

Mathematics/P2 DBE/Feb.—Mar. 2015 NSC QUESTION 2 An ice-cream shop recorded the sales of ice cream, in rand, and the maximum temperature, in °C, for 12 days in a certain month. The data that they collected is represented in the table and scatter plot below. Temperature in °C 24,2 | 26,4 | 21,9 | 25,2 | 28,5 | 32,1 | 29,4 | 35,1 | 33,4 | 28,1 | 32,6 | 27,2 Sales of ice cream in rand | 215 | 325 | 185 | 332 | 406 | 522 | 412 | 614 | 544 | 421 | 445 | 408 Scatter plot 650 ; 1 600 ° | 550 ° e 500 3 I 5 450 - t t e = 400 + : : eo (e @ : 350 - i; T 3 i 2 | : bad = 300 ml . | & 250 - S I n | e 200 + 150 + - = 24 26 28 30 32 34 36 38 Temperature in °C 2.1 Describe the influence of temperature on the sales of ice cream in the scatter plot. qd) 22 Give a reason why this trend cannot continue indefinitely. qd) 2.3 Calculate an equation for the least squares regression line (line of best fit). (4) 2.4 Calculate the correlation coefficient. () 2.5 Comment on the strength of the relationship between the variables. qd) [8] Copyright reserved Please turn over ll

Mathematics/P2 DBE/November 2014 NSC QUESTION 1 At a certain school, only 12 candidates take Mathematics and Accounting. The marks, as a percentage, scored by these candidates in the preparatory examinations for Mathematics and Accounting, are shown in the table and scatter plot below. Mathematics 52 82 93 95 71 65 77 42 89 48 45 57 Accounting 60 62 88 90 72 67 75 48 83 57 52 62 Scatter plot 100 Percentage achieved in Accounting 90 80 70 60 50 40 40 50 60 70 80 90 100 Percentage achieved in Mathematics 1.1 Calculate the mean percentage of the Mathematics data. (2) 1.2 Calculate the standard deviation of the Mathematics data. (1) 1.3 Determine the number of candidates whose percentages in Mathematics lie within ONE standard deviation of the mean. (3) 1.4 Calculate an equation for the least squares regression line (line of best fit) for the data. (3) 1.5 If a candidate from this group scored 60% in the Mathematics examination but was absent for the Accounting examination, predict the percentage that this candidate would have scored in the Accounting examination, using your equation in QUESTION 1.4. (Round off your answer to the NEAREST INTEGER.) (2) 1.6 Use the scatter plot and identify any outlier(s) in the data. (1) [12] Copyright reserved Please turn over 12

Mathematics/P2 DBE/November 2014 NSC QUESTION 2 The speeds of 55 cars passing through a certain section of a road are monitored for one hour. The speed limit on this section of road is 60 km per hour. A histogram is drawn to represent this data. Histogram 18 17 16 14 13 12 Frequency 10 9 8 7 6 5 4 2 2 1 1 0 40 50 60 70 0-20 2020-30 3030-40 40-50 50-60 60-70 70-80 8080-90 9090-100100 100-110 Speed (in km per hour) 2.1 Identify the modal class of the data. (1) 2.2 Use the histogram to: 2.2.1 Complete the cumulative frequency column in the table on DIAGRAM SHEET 1 (2) 2.2.2 Draw an ogive (cumulative frequency graph) of the above data on the grid on DIAGRAM SHEET 1 (3) 2.3 The traffic department sends speeding fines to all motorists whose speed exceeds 66 km per hour. Estimate the number of motorists who will receive a speeding fine. (2) [8] Copyright reserved Please turn over 13

Mathematics/P2 DBE/2014 NSC – Grade 12 Exemplar QUESTION 1 Twelve athletes trained to run the 100 m sprint event at the local athletics club trials. Some of them took their training more seriously than others. The following table and scatter plot shows the number of days that an athlete trained and the time taken to run the event. The time taken, in seconds, is rounded to one decimal place. Number of days 50 70 10 60 60 20 50 90 100 60 30 30 of training Time taken 12,9 13,1 17,0 11,3 18,1 16,5 14,3 11,7 10,2 12,7 17,2 14,3 (in seconds) Scatter plot 20 18 Time taken (in seconds) 16 14 12 10 8 0 20 40 60 80 100 120 Number of days of training 1.1 Discuss the trend of the data collected. (1) 1.2 Identify any outlier(s) in the data. (1) 1.3 Calculate the equation of the least squares regression line. (4) 1.4 Predict the time taken to run the 100 m sprint for an athlete training for 45 days. (2) 1.5 Calculate the correlation coefficient. (2) 1.6 Comment on the strength of the relationship between the variables. (1) [11] Copyright reserved Please turn over 14

Mathematics/P2 DBE/2014 NSC – Grade 12 Exemplar QUESTION 2 The table below shows the amount of time (in hours) that learners aged between 14 and 18 spent watching television during 3 weeks of the holiday. Time (hours) Cumulative frequency 0 ≤ t < 20 25 20 ≤ t < 40 69 40 ≤ t < 60 129 60 ≤ t < 80 157 80 ≤ t < 100 166 100 ≤ t < 120 172 2.1 Draw an ogive (cumulative frequency curve) on DIAGRAM SHEET 1 to represent the above data. (3) 2.2 Write down the modal class of the data. (1) 2.3 Use the ogive (cumulative frequency curve) to estimate the number of learners who watched television more than 80% of the time. (2) 2.4 Estimate the mean time (in hours) that learners spent watching television during 3 weeks of the holiday. (4) [10] Copyright reserved Please turn over 15