Mathematical Literacy 2
                   Module 4


                        Answers to Activities




Answers to activit...
Activity 1
Formulate the questions that you think had to be
  asked to obtain the given results.
• Who do you think will w...
Activity 1
Name two firms that do marketing surveys
Plus 94
Synovate
How do you think the percentages were calculated?
All...
Activity 2
Work in pairs, read the article regarding
   newspaper sales in South Africa and follow the
   instructions bel...
Activity 2
Newspaper                   Circulation this year    Circulation last year
Daily Sun                   494 875 ...
Activity 3
• Summarised below are the daily activities of Freida and
  her dog Cindy. Can the following activities be
  re...
Cindy's Daily Activities



                        8%    2%
           4%
                                               ...
Activity 4
1.From the sketch given above of the Cartesian co-
  ordinate system, give the coordinate value of the
  points...
Activity 4
• Sketch the Cartesian co-ordinate system on square
  ruled paper and plot the points
                         ...
• Question 3 (a)
                                                    Celcius to Fareheit Conversion

                     ...
• Question 3(b)

ºC                5                            55    75
                             10   32             ...
Activity 5
1. From your table drawn up for the various
   newspaper circulations, do the following:
  a. Draw a bar graph ...
Circulation

                                               D




                                                        ...
b. Is it possible to represent all of the tabulated data in one
                 bar graph? Yes
                          ...
c. Could a pie chart be used instead of a bar chart?
    Yes              Circulation this year




                      ...
Activity 6
•    For the following two sets of data, calculate:
    a. the mean, median and mode
    b. explain the signifi...
Activity 6
•    For the following two sets of data, calculate:
    a. the mean, median and mode
    b. explain the signifi...
Activity 7
 1.     In a group of two, study the salaries of Company A’s
        employees that us given in the table below...
Activity 7
2 500 (2)                 6 000 (3)    4 000 (4)            3 550 (6)   2 600 (1)
2 900 (3)                 3 2...
Activity 7
2 500 (2)                    6 000 (3)    4 000 (4)           3 550 (6)   2 600 (1)
2 900 (3)                  ...
Activity 7
2 500 (2)                     6 000 (3)    4 000 (4)           3 550 (6)   2 600 (1)
2 900 (3)                 ...
Activity 7
                                         Frequency of salary categories
            45

            40

       ...
Activity 7
1.     The Salaries of Company B are as follows:
2 350 (3)                    2 500 (7)     2 750 (6)          ...
Activity 7
a. Compare the statistics of the two companies in a
   table
                            Company A             ...
Activity 8
1.        Describe the following graphs. Use words such as “increase”,
          “remains constant” and “rate o...
Activity 8
b.




For the first three minutes the distance increases to 300m. For the
next four minutes the distance remai...
Activity 8
       2.Study the graph for the bus and the bicycle and
         answer the questions
               80

     ...
Activity 8
• What was the fastest speed of the bus?
  80 km /h
• What was the speed of the bicycle?
  20 km /h
• Explain t...
Activity 8
3.Sort out these speed time graphs for: zero
  acceleration, positive acceleration, uniform
  negative accelera...
Activity 9
1. For the graph on passenger traffic at the OR
   Tambo International Airport in Johannesburg,
   answer the f...
a. Is the scale on the horizontal axis uniform?
   Explain
   Yes, the number rise by the same amount
   each time
d. Why ...
a. Are there more international or local visitors to
   the airport?
   Domestic traffic was a greater proportion of
   th...
a. What is the range of increase in total number
   of passengers from 2006 to a projected valued
   in 2020
    15 000 – ...
a. How do you think a forecast of passengers
   could be made?

    Look at past figures, compare the airport
    growth t...
Activity 10
• For the horizontal bar graph on top sellers in the
  motor car industry, answer the following
  questions:

...
a. How many VW Polo / Polo Classics were sold in
   May?

   About 3 200

   Answers to activities   Future Managers   36
a. How many of these top seller cars were sold in
   May

Add all of the values: 3200 + 2800 + 2700 + 2200 +
1700 + 1600 +...
c. It is reported that 52 534 cars were actually sold
   in May, and that the projection for June is 56
   070 cars. Calcu...
d. If 60 000 cars are sold in South Africa in a given
   month. how many new cars are brought onto our
   roads each day?
...
f. Think of a way to persuade people not to desire a
   car.
   Tax cars and petrol and improve and subsidise
   the publi...
Activity 11
• Answer the following questions with regard to
   the smoking survey:
b.What percentage of all smokers is rep...
Activity 11
a. To represent the central tendency for cigarette
   brand, would you use mode, mean or median?
b. Draw a com...
Activity 12
•Work in pairs, study the drawing below, follow
the instructions and answer the questions.

Samuel is a long-d...
Week                            Km
 3 April – 9 April               70
 10 April – 16 April             82
 17 April – 23 ...
1.Organise and represent the data of the distance
  (number of km) per week. Draw your own
  frequency table.

           ...
1. What is the average number of kilometres that
   he ran per week?

     Average = (70 + 82 + 91 + 67 + 86 + 89 + 78
   ...
1. During which month did he prepare best.
   Motivate your answer.
  He prepared best during the week of 22-28 May
  as h...
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NCV 2 Mathematical Literacy Hands-On Training Activities Module 4

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Solutions to activities from Module 4 NCV 2 Mathematical Literacy Hands-On Training published by Future Managers (www.futuremanagers.net)

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NCV 2 Mathematical Literacy Hands-On Training Activities Module 4

  1. 1. Mathematical Literacy 2 Module 4 Answers to Activities Answers to activities Future Managers 1
  2. 2. Activity 1 Formulate the questions that you think had to be asked to obtain the given results. • Who do you think will win the soccer world cup in 2010? • Who do you think is the strongest team in Africa? • Do you intend to watch the games live? • Would you bunk work to watch the games Answers to activities Future Managers 2
  3. 3. Activity 1 Name two firms that do marketing surveys Plus 94 Synovate How do you think the percentages were calculated? All percentages are calculated by dividing the number of the item/people that you are interested in by the total number of items/people and multiplying by 100. Answers to activities Future Managers 3
  4. 4. Activity 2 Work in pairs, read the article regarding newspaper sales in South Africa and follow the instructions below. 2. Organise the data into a table. Your table should show the name of the newspaper as well as the paper’s circulation for both years. 3. Compare your table with the tables of other groups. Are they similar? 4. Do they meet all the objectives of tables and graphs? Answers to activities Future Managers 4
  5. 5. Activity 2 Newspaper Circulation this year Circulation last year Daily Sun 494 875 443 280 Isolezwe 96 485 88 664 Soccer Laduma 303 461 280 933 Mail and Guardian 48 292 41 723 UmAfrika 32 978 21 878 Ilanga 100 906 108 858 Son (weekly) 76 830 172 612 City Press 183 101 175 125 Sunday Sun 200 315 188 369 Ilanga Langesonto 70 291 41 474 Sunday World 184 772 155 997 Sunday Times 504 475 513 702 Answers to activities Future Managers 5
  6. 6. Activity 3 • Summarised below are the daily activities of Freida and her dog Cindy. Can the following activities be represented in a pie chart? If so, do so. Activity Time % of Total x 360 Sleep 8h 33.33% 118.8 Eat 1.5h 6.25% 22.5 Class time 7h 29.17% 105.01 Travelling 2h 8.33% 30 Homework 2h 8.33% 30 Shopping 1h 4.17% 15 Relaxation 2h 8.33% 30 Walking Cindy 0.5h 2.08% 7.5 Total 24 100% 360 Answers to activities Future Managers 6
  7. 7. Cindy's Daily Activities 8% 2% 4% Sleep 34% Eat 8% Class time Travelling 8% Homework Shopping Relaxation 6% Walking Cindy 30% Answers to activities Future Managers 7
  8. 8. Activity 4 1.From the sketch given above of the Cartesian co- ordinate system, give the coordinate value of the points A to F. A (-4; 4) B (0; 3) C (3; 2) D (5; 0) E (5; -1) F (-2; 2) Answers to activities Future Managers 8
  9. 9. Activity 4 • Sketch the Cartesian co-ordinate system on square ruled paper and plot the points 8 7 (5; 7) 6 (-4;5) (-3; 5) 5 4 (2; 4) (3; 4) (-6; 4) 3 2 (4; 2) 1 0 -7 -6 -5 -4 -3 -2 -1 -1 0 1 2 3 4 5 6 (-1; -1) -2 (2; -2) (0; 3) -3 Answers to activities Future Managers 9
  10. 10. • Question 3 (a) Celcius to Fareheit Conversion 250 200 Temp in Farenheit 150 100 50 0 -40 -20 0 20 40 60 80 100 120 Tempature in Celcius Answers to activities Future Managers 10
  11. 11. • Question 3(b) ºC 5 55 75 10 32 49 88 ºF 41 50 90 131 167 120 190 Answers to activities Future Managers 11
  12. 12. Activity 5 1. From your table drawn up for the various newspaper circulations, do the following: a. Draw a bar graph with the newspapers on the horizontal axis and their circulation numbers on the vertical axis b. Is it possible to represent all of the tabulated data in one bar graph? c. Could a pie chart be used instead of a bar graph? 2. Find an article in a newspaper or magazine in which a graph has been used to summarise result / conclusions. Explain in your own words what the graph is representing and whether you consider that graph to be successful Answers to activities Future Managers 12
  13. 13. Circulation D 100000 200000 300000 400000 500000 600000 0 ai ly Su n Is ol Answers to activities So ez cc w er e M La ai du la m nd a G ua rd ia U n m A fr ik a Ila So ng n a Future Managers (w ee kl y) C ity Pr Newspaper es Su s Circulation of Newspapers Ila nd ng ay a Su La n ng es Su on nd to ay W 13 Su or nd ld ay Ti m es
  14. 14. b. Is it possible to represent all of the tabulated data in one bar graph? Yes Circulation of Newspapers Circulation this year Circulation last year 600000 500000 Circulation 400000 300000 200000 100000 0 y) e a s to a n es n a ld n es w rik ia Su ng m Su kl or on m ez rd du ee Pr Af Ila W Ti es ly ay ua ol La m (w ai ity ay ng ay Is nd G U D C n er nd nd La Su nd So cc Su Su a la So ng ai Ila M Newspaper Answers to activities Future Managers 14
  15. 15. c. Could a pie chart be used instead of a bar chart? Yes Circulation this year Daily Sun Isolezwe Soccer Laduma Mail and Guardian UmAfrika Ilanga Son (weekly) City Press Sunday Sun Ilanga Langesonto Sunday World Sunday Times Answers to activities Future Managers 15
  16. 16. Activity 6 • For the following two sets of data, calculate: a. the mean, median and mode b. explain the significance of these calculations A: 12; 9; 5; 6; 8; 10; 11; 4; 10 Mean = (12 + 9 + 5 + 6 + 8 + 10 + 11 + 4 + 10) / 9 Mean = 8.33 Median: 4; 5; 6; 8; 9; 10; 10; 11; 12 The median = 9 Mode: 4; 5; 6; 8; 9; 10; 10; 11; 12 The mode = 10 Answers to activities Future Managers 16
  17. 17. Activity 6 • For the following two sets of data, calculate: a. the mean, median and mode b. explain the significance of these calculations B: 3; 17; 4; 10; 8; 12; 15; 2; 4 Mean = (3 + 17 + 4 + 10 + 8 + 12 + 15 + 2 + 4) / 9 Mean = 8.33 Median: 2; 3; 4; 4; 8; 10; 12; 15; 17 The median = 8 Mode: 2; 3; 4; 4; 8; 10; 12; 15; 17 The mode = 4 Answers to activities Future Managers 17
  18. 18. Activity 7 1. In a group of two, study the salaries of Company A’s employees that us given in the table below. The monthly salaries, in rands are followed by the number of employees receiving that specific salary. 2 500 (2) 6 000 (3) 4 000 (4) 3 550 (6) 2 600 (1) 2 900 (3) 3 250 (4) 4 500 (5) 3 450 (5) 2 350 (2) 4 890 (3) 5 250 (1) 3 000 (7) 4 325 (5) 5 900 (1) a. What is the highest salary earned in company A? R6000 b. What is the lowest salary earned? R2 350 Answers to activities Future Managers 18
  19. 19. Activity 7 2 500 (2) 6 000 (3) 4 000 (4) 3 550 (6) 2 600 (1) 2 900 (3) 3 250 (4) 4 500 (5) 3 450 (5) 2 350 (2) 4 890 (3) 5 250 (1) 3 000 (7) 4 325 (5) 5 900 (1) c. What is the range of the figures? R6000 – R 2350 = R3 650 d. Which salary occurs the most often? Which measure of centre spread is this? R 3000; it is the mode e. How many people work for this company? =2+3+3+3+4+1+4+5+7+6+5+5+1+2+1 = 52 Answers to activities Future Managers 19
  20. 20. Activity 7 2 500 (2) 6 000 (3) 4 000 (4) 3 550 (6) 2 600 (1) 2 900 (3) 3 250 (4) 4 500 (5) 3 450 (5) 2 350 (2) 4 890 (3) 5 250 (1) 3 000 (7) 4 325 (5) 5 900 (1) f. Calculate the mean salary? =(2500x2 + 2900x3 + 4890x3 + 6000x3 + 3250x4 + 5250 + 4000x4 + 4500x5 + 3000x7 + 3550x6 + 3450x5 + 4325x5 + 2600 + 2350x2 + 5900)/52 = R197 495/52 = R3798 g. Is it practical to calculate the median salary? No, it takes too long Answers to activities Future Managers 20
  21. 21. Activity 7 2 500 (2) 6 000 (3) 4 000 (4) 3 550 (6) 2 600 (1) 2 900 (3) 3 250 (4) 4 500 (5) 3 450 (5) 2 350 (2) 4 890 (3) 5 250 (1) 3 000 (7) 4 325 (5) 5 900 (1) h. The company would like to have four categories that all salaries would fit into. Suggest a range for these four categories i. Complete the frequency table for the data Salary Category Frequency % of workers Less than R3000 8 15,38 R 3000- R3 999 22 42,31 R4 000 – R4 999 17 32,69 R5 000 – R0 999 5 9,68 52 100 Answers to activities Future Managers 21
  22. 22. Activity 7 Frequency of salary categories 45 40 35 30 Frequency 25 20 15 10 5 0 Less than R3000 R 3000- R3 999 R4 000 – R4 999 R5 000 – R0 999 Salary Category Answers to activities Future Managers 22
  23. 23. Activity 7 1. The Salaries of Company B are as follows: 2 350 (3) 2 500 (7) 2 750 (6) 3 000 (8) 4 500 (2) 12 740 (1) 15 800 (1) 2 600 (5) 3 250 (5) 2 000 (3) 5 000 (3) 3 500 (2) 1 800 (2) 2 800 (2) 3 700 (2) a. Calculate the mean and the mode of company B. Mean = (2350x2 + 12740 + 5000x3 + 2500x7 +15800 + 3500x2 + 2750x6 + 2600x5 + 1800x2 + 3000x8 +3250 x 5 +2800x2 + 4500x2 + 2000x3 + 3700x2) ÷ 52 = R3 152,69 Mode = R 775 Answers to activities Future Managers 23
  24. 24. Activity 7 a. Compare the statistics of the two companies in a table Company A Company B Mode R3 550 R3 000 Mean R3534,52 R3 152,69 Range R3 650 R14 000 c. Which of these two companies do you think will soon be challenged by the employees for higher salaries? Motivate your answer Company B, as the range between the highest and lowest wages is much bigger than for Company A Answers to activities Future Managers 24
  25. 25. Activity 8 1. Describe the following graphs. Use words such as “increase”, “remains constant” and “rate of change” a. For the first three minutes the distance increases to 300m. For the next four minutes the distance remains constant (person stationary). For the last two minutes the distance increase by 100m. Therefore after nine minutes, this person is 400m from where he/she started. Answers to activities Future Managers 25
  26. 26. Activity 8 b. For the first three minutes the distance increases to 300m. For the next four minutes the distance remains constant (person stationary). For the last two minutes the distance increase by 100m. Therefore after nine minutes, this person is 400m from where he/she started. Answers to activities Future Managers 26
  27. 27. Activity 8 2.Study the graph for the bus and the bicycle and answer the questions 80 Bicycle 60 Bus Speed (km/h) 40 20 0 0 5 10 15 20 25 30 Time (Minutes) Answers to activities Future Managers 27
  28. 28. Activity 8 • What was the fastest speed of the bus? 80 km /h • What was the speed of the bicycle? 20 km /h • Explain the horizontal line of the bus graph between 5 and 20 minutes The bus was going at a constant 40km/h • What happened to the bicycle at minute 25? It stopped Answers to activities Future Managers 28
  29. 29. Activity 8 3.Sort out these speed time graphs for: zero acceleration, positive acceleration, uniform negative acceleration or none of these zero acceleration Constant positive Speed acceleration Speed Time Time Constant negative None of these Speed acceleration Speed Time Time Answers to activities Future Managers 29
  30. 30. Activity 9 1. For the graph on passenger traffic at the OR Tambo International Airport in Johannesburg, answer the following questions: Answers to activities Future Managers 30
  31. 31. a. Is the scale on the horizontal axis uniform? Explain Yes, the number rise by the same amount each time d. Why is the horizontal scale not started at zero? To start at zero, would imply starting at 0AD which is clearly impractical Answers to activities Future Managers 31
  32. 32. a. Are there more international or local visitors to the airport? Domestic traffic was a greater proportion of the total traffic d. What is the variable used on the vertical axis? Number of passengers Answers to activities Future Managers 32
  33. 33. a. What is the range of increase in total number of passengers from 2006 to a projected valued in 2020 15 000 – 37 000 c. What could be the cause of the slight drop in the total domestic and international graphs around 2011 2010 would show artificially high growth, so 2011 would be relatively less busy than 2010, hence the slight drop Answers to activities Future Managers 33
  34. 34. a. How do you think a forecast of passengers could be made? Look at past figures, compare the airport growth to similar airports around the world. Look at other factors like economic growth e. What is one factor that could change forecast figures? War; economic downturn; announcement of a major event to be hosted in South Africa Answers to activities Future Managers 34
  35. 35. Activity 10 • For the horizontal bar graph on top sellers in the motor car industry, answer the following questions: Answers to activities Future Managers 35
  36. 36. a. How many VW Polo / Polo Classics were sold in May? About 3 200 Answers to activities Future Managers 36
  37. 37. a. How many of these top seller cars were sold in May Add all of the values: 3200 + 2800 + 2700 + 2200 + 1700 + 1600 + 1550 + 1200 + 900 + 900 = 1875 Answers to activities Future Managers 37
  38. 38. c. It is reported that 52 534 cars were actually sold in May, and that the projection for June is 56 070 cars. Calculate the percentage increase. = (56070 – 52534)/52534 x 100 = 6,73% Answers to activities Future Managers 38
  39. 39. d. If 60 000 cars are sold in South Africa in a given month. how many new cars are brought onto our roads each day? = 60 000 cars ÷ 30 days = 2 000 new cars per day e. Do you think that our road can carry this kind of increase indefinitely? No, definitely not Answers to activities Future Managers 39
  40. 40. f. Think of a way to persuade people not to desire a car. Tax cars and petrol and improve and subsidise the public transport system. g. Why would the industry not approve of your solution? They make their living by selling cars Answers to activities Future Managers 40
  41. 41. Activity 11 • Answer the following questions with regard to the smoking survey: b.What percentage of all smokers is represented by women? c. What percentage of all smokers is represented by the under-20 age group? d.What is the average age at which the smoking habit starts? e. What is the mode of the starting age for smoking? Answers to activities Future Managers 41
  42. 42. Activity 11 a. To represent the central tendency for cigarette brand, would you use mode, mean or median? b. Draw a compound bar graph as well as a broken line graph of the information c. Do you think a pie chart would be a good method of representing the data? Answers to activities Future Managers 42
  43. 43. Activity 12 •Work in pairs, study the drawing below, follow the instructions and answer the questions. Samuel is a long-distance runner. He keeps a logbook of the number of kilometres he runs every week. This is his logbook for the 12 weeks before an important race. Answers to activities Future Managers 43
  44. 44. Week Km 3 April – 9 April 70 10 April – 16 April 82 17 April – 23 April 91 24 April – 30 April 67 1 May – 7 May 86 8 May – 14 May 89 15 May – 21 May 78 22 May – 28 May 94 29 May – 4 June 83 12 June – 18 June 85 19 June – 26 June 82 27 June – 3 August Answers to activities 90 Future Managers 44
  45. 45. 1.Organise and represent the data of the distance (number of km) per week. Draw your own frequency table. Distance Frequency 60 – 69 km 1 70 – 79km 2 80 – 89 km 6 90 – 100 km 3 Answers to activities Future Managers 45
  46. 46. 1. What is the average number of kilometres that he ran per week? Average = (70 + 82 + 91 + 67 + 86 + 89 + 78 + 94 + 83 + 85 + 82 + 90 ) / 12 = 83.08km 5. What is the range of the distance that he ran? Range = Maximum value – Minimum Value = 94 – 67 = 27km Answers to activities Future Managers 46
  47. 47. 1. During which month did he prepare best. Motivate your answer. He prepared best during the week of 22-28 May as he ran the most kilometers during that time. Answers to activities Future Managers 47

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