NCV 2 Mathematical Literacy Hands-On Training Activities Module 4

Mathematical Literacy 2
Module 4

Answers to Activities

Answers to activities Future Managers 1

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


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.


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?


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

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

Cindy's Daily Activities

8% 2%
4%
Sleep
34% Eat
8%
Class time
Travelling
8% Homework
Shopping
Relaxation
6% Walking Cindy

30%


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)

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


• 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

• Question 3(b)

ºC 5 55 75
10 32 49 88
ºF 41 50 90 131 167 120 190


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

Circulation

D

100000
200000
300000
400000
500000
600000

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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

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Newspaper

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


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

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

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


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


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


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

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

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


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

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.


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.

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)


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


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

Activity 9
1. 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
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


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


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


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


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%

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:
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?


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?


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
Answers to activities 90
Future Managers 44

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


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


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.


NCV 2 Mathematical Literacy Hands-On Training Activities Module 4

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