NCV 2 Mathematical Literacy Hands-On Training Activities Module 4

Mathematical Literacy 2Module 4

Answers to Activities

Answers to activities 1Future Managers

Activity 1Formulate 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


Activity 1Name two firms that do marketing surveys

Plus 94Synovate

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.


Activity 2Work in pairs, read the article regarding

newspaper sales in South Africa and follow the instructions below.

1. 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.

2. Compare your table with the tables of other groups. Are they similar?

3. Do they meet all the objectives of tables and graphs?


Activity 2Newspaper 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 702Answers to activities 5Future Managers

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

Sleep 8h

Eat 1.5h

Class time 7h

Travelling 2h

Homework 2h

Shopping 1h

Relaxation 2h

Walking Cindy 0.5h

Total 24

% of Total

33.33%

6.25%

29.17%

8.33%

8.33%

4.17%

8.33%

2.08%

100%

x 360

118.8

22.5

105.01

30

30

15

30

7.5

360Answers to activities 6Future Managers

Cindy's Daily Activities

34%

6%

30%

8%

8%

4%8% 2%

SleepEatClass timeTravellingHomeworkShoppingRelaxationWalking Cindy


Activity 41.From the sketch given above of the Cartesian co-

ordinate system, give the coordinate value of the points A to F.

A B

C

D

E

F

(-4; 4) (0; 3)

(3; 2)

(5; 0)

(5; -1)

(-2; 2)


Activity 4• Sketch the Cartesian co-ordinate system on square

ruled paper and plot the points

-3

-2

-1

0

1

2

3

4

5

6

7

8

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

(5; 7)

(3; 4)

(-6; 4)

(2; -2) (-1; -1)

(2; 4) (-4;5) (-3; 5)

(0; 3)

(4; 2)


• Question 3 (a)Celcius to Fareheit Conversion

0

50

100

150

200

250

-40 -20 0 20 40 60 80 100 120

Tempature in Celcius

Tem

p in

Far

enh

eit


• Question 3(b)

ºC 5 55 75

ºF 50 90 120 19041 131 167

10 32 49 88


Activity 51. 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


Circulation of Newspapers

0

100000

200000

300000

400000

500000

600000

Newspaper

Cir

cula

tio

n


Circulation of Newspapers

0

100000

200000

300000

400000

500000

600000

Newspaper

Cir

cula

tio

n

Circulation this year Circulation last year

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?

YesCirculation this year

Daily Sun

Isolezwe

Soccer Laduma

Mail and Guardian

UmAfrika

Ilanga

Son (weekly)

City Press

Sunday Sun

Ilanga Langesonto

Sunday World

Sunday Times


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

Mode: 4; 5; 6; 8; 9; 10; 10; 11; 12

The median = 9

The mode = 10 Answers to activities 16Future Managers

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

Mode: 2; 3; 4; 4; 8; 10; 12; 15; 17

The median = 8

The mode = 4 Answers to activities 17Future Managers

Activity 71. 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


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?

e. How many people work for this company?

=2+3+3+3+4+1+4+5+7+6+5+5+1+2+1 = 52

R 3000; it is the mode


Activity 72 500 (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


Activity 72 500 (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

Salary Category

Less than R3000

R 3000- R3 999

R4 000 – R4 999

R5 000 – R0 999

i. Complete the frequency table for the data

Frequency % of workers

8 15,38

22 42,31

17 32,69

5 9,68

52 100Answers to activities 21Future Managers

Activity 7

Frequency of salary categories

0

5

10

15

20

25

30

35

40

45

Less than R3000 R 3000- R3 999 R4 000 – R4 999 R5 000 – R0 999

Salary Category

Fre

qu

en

cy


Activity 71. 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


Activity 7b. 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


Activity 81. 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.


Activity 8b.

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.


Activity 82.Study the graph for the bus and the bicycle and

answer the questions

0

20

40

60

80

0 5 10 15 20 25 30

Time (Minutes)

Sp

eed

(k

m/h

)

BicycleBus


Activity 8• What was the fastest speed of the bus?

• What was the speed of the bicycle?

• Explain the horizontal line of the bus graph between 5 and 20 minutes

• What happened to the bicycle at minute 25?

80 km /h

20 km /h

The bus was going at a constant 40km/h

It stopped


Activity 83.Sort out these speed time graphs for: zero

acceleration, positive acceleration, uniform negative acceleration or none of these

Speed

TimeS

peed

Time

Speed

Time

Speed

Time

zero acceleration Constant positive acceleration

Constant negative acceleration

None of these


Activity 91. For the graph on passenger traffic at the OR

Tambo International Airport in Johannesburg, answer the following questions:


a. Is the scale on the horizontal axis uniform? Explain

b. Why is the horizontal scale not started at zero?

Yes, the number rise by the same amount each time

To start at zero, would imply starting at 0AD which is clearly impractical


c. Are there more international or local visitors to the airport?

d. What is the variable used on the vertical axis?

Domestic traffic was a greater proportion of the total traffic

Number of passengers


e. What is the range of increase in total number of passengers from 2006 to a projected valued in 2020

f. What could be the cause of the slight drop in the total domestic and international graphs around 2011

15 000 – 37 000

2010 would show artificially high growth, so 2011 would be relatively less busy than 2010, hence the slight drop


g. How do you think a forecast of passengers could be made?

h. What is one factor that could change forecast figures?

Look at past figures, compare the airport growth to similar airports around the world. Look at other factors like economic growth

War; economic downturn; announcement of a major event to be hosted in South Africa


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


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


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 38Future Managers

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


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


Activity 11• Answer the following questions with regard to

the smoking survey:

a. What percentage of all smokers is represented by women?

b.What percentage of all smokers is represented by the under-20 age group?

c. What is the average age at which the smoking habit starts?

d.What is the mode of the starting age for smoking?


Activity 11e. To represent the central tendency for cigarette

brand, would you use mode, mean or median?

f. Draw a compound bar graph as well as a broken line graph of the information

g. Do you think a pie chart would be a good method of representing the data?


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.


Week Km

3 April – 9 April 70




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 90Answers to activities 44Future Managers

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


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

3. What is the range of the distance that he ran?

Average = (70 + 82 + 91 + 67 + 86 + 89 + 78 + 94 + 83 + 85 + 82 + 90 ) / 12 = 83.08km

Range = Maximum value – Minimum Value

= 94 – 67

= 27km


4. 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.


NCV 2 Mathematical Literacy Hands-On Training Activities Module 4

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Transcript of NCV 2 Mathematical Literacy Hands-On Training Activities Module 4