NCV 2 Mathematical Literacy Hands-On Training Activities Module 5

Mathematical Literacy 2
Module 5

Answers to Activities

Answers to activities Future Managers 1

Activity 1
Refer back to the quote that Benni Mokoena
got from EasyBuy when he approached them
for a TV quote. Compare the interest rate that
EasyBuy was charging Benni with the interest
rate that the banks were charging at the same
date.

3. How big a difference was there between the
two percentages?

Store rate = 30.50% Bank rate = 13.00%
Difference between interest rates = 17.5%

1. How much would Benni have paid for the
same TV if EasyBuy charged him the bank’s
interest rate?

3. What type of relationship exists between the
interest rate of the bank and the amount you
are paying?

Constant ratio
5. What advice would you give Benni given the
above example?

Save up for the TV, rather than buy it on credit

1. Forecasting interest rates is a gamble at the
best of times, but looking at the interest rates
table, do you spot a pattern or patterns?
Interest rates are rising

4. If indeed, what would you expect to happen in
2008 with interest rates?
They will continue to rise
6. Having the benefit of hindsight, what actually
happened in 2008?

They did continue to rise

Activity 2
1. Write down five numbers that you think should
logically follow on the numbers in the
following sets.
2 4 8 16 32 64 128 256 512 Rat
3 6 9 12 15 18 21 24 27 Dif
4 7 10 13 16 19 22 25 28 Dif
33 30 27 24 21 18 15 12 9 Dif
128 64 32 16 8 4 2 1 0.5 Rat


Activity 2
• Order the numbers from smallest to biggest
40; 90; 60; 10; 30; 80; 70; 20; 50; 100
55; 5; 15; 25; 65; 35; 75; 85; 45
16; 28; 36; 20; 12; 8; 32; 40; 4; 44

10; 20; 30; 40; 50; 60; 70; 80; 90; 100
5; 15; 25; 35; 45; 55; 65; 75; 85
4; 8; 12; 16; 20; 28; 32; 36; 40; 44


Activity 2
4.A friend tells you that he will loan you money at a
simple interest rate of 15% per annum i.e. 0,05 of
the amount per year. What will one year’s loan of
the following amounts cost you?

Loan Amt 1 Yr Cst 2 Yr Cst 3 Yr Cst Const Dif
R700 105 210 315 105
R1000 150 300 450 150
R5000 750 1500 2250 750
R10000 1500 3000 4500 1500

Activity 2
5. Fill in the missing numbers according to the pattern:
7 11 15 19 23 27 31 35
25 30 35 40 45 50 55 60
4 8 16 32 64 128 256 512
3 600 360 36 3,6 0.36 0.036 0.0036 0.00036
1,6 16 160 1 600 16 000 160 000 1,6 mil 16 mil

6. Describe the above patterns in words
(a) An increase of 4 each time
(b) An increase of 5 each time
(c) Doubling each time
(d) Dividing by 10 each time
(e) Multiplying by 10 each time

Activity 3
1. Evaluate the table on cash loans and answer the questions:
Cash loan amounts R3000 R4 000 R5 000
Monthly 12 months R361 R467 R573
repayment
24 months R226 R291 R357

a. Is there a constant difference or a constant ratio
between the loan repayment amounts for 12
months?
Constant Difference

c. Is there a direct of indirect relationship between the
loan payment amounts for the two different
payment options?
Indirect

Activity 3
1. Look at the following table for a cash loan of R3000. Monthly
repayment options depend on the repayment period

Repay period 12 months 24 months 36 months
R3000 loan R361 R226 R184
Repay amt R 4 332 R5 242 R6 624
Cost of loan R 1 332 R2 424 R3 624

a. Is there a direct or indirect relationship between the
repayment period and the monthly repayment amounts?
Indirect relationship
c. Is it better to repay the loan within 12 months or within 36
months? Give a reason for your answer.
Within 12 months, you pay less overall for the loan

Activity 4
• Work in pairs
• A student wanting to waiter at a local restaurant receives
the following remuneration package from the restaurant
owner. On his behalf, calculate the amount he will take
home every month if the sales that waiters on is R5000
per month. Tips are not part of this calculation, that is an
extra.
• 1st Month Fixed Salary + 1% Commission on Sales
• 2nd Month Fixed Salary + 2% Commission on Sales
• 3rd Month Fixed Salary + 3% Commission on Sales
• The amount of R1 500 is the input or x-value and the
amount that he receives is the output or y-value


Activity 4
• 1st Month Fixed Salary + 1% Commission on Sales
=R1 500 + 0.01 x R5 000
=R1550
• 2nd Month Fixed Salary + 2% Commission on Sales

=R1 500 + 0.02 x R5 000
=R1600
• 3rd Month Fixed Salary + 3% Commission on Sales

=R1 500 + 0.03 x R5 000
=R1650

Activity 5
• Work in pairs to determine the independent and
dependent variables in the tables below
1.Complete the flow diagrams:

Independent x7 +8 = Dependent
Variable Variable
2 x7 +8 = 22
5 x7 +8 = 43
7 x7 +8 = 57
12 x7 +8 = 92


Activity 5

1 x8 + 12 = 20
3 x8 + 12 = 36
5 x8 + 12 = 52
27 x8 + 12 = 228
30 x8 + 12 = 256


Activity 5
1. Complete the following tables according to the
formulas or written instructions
Formula: y = 5x+ 7
(a) Do the calculation below
(b) Write this calculation in words
x 1 2 3 4 5 6 7 8 9
y 12 17 22 27 32 37 42 47 52

Take the input value, multiply it by 5 and then
add 7


Activity 5
(a) To get the y-value, multiply the x-value
by three and then add 4
(b) Write the formula for this instruction and
use it to complete the table

y = 3x+ 4

x 5 10 15 20 25 30 35 40 45
y 19 34 49 64 79 94 109 124 139


Activity 5
• To get the y-value, divide the x-value by two and
add 9 to the answer. Write a formula for this
instruction and complete the table.

y= x + 9
/2

x 2 4 6 8 10 12 14 16 18
y 10 11 12 13 14 15 16 17 18


Activity 5
1. Complete the operating instructions, give the
correct formula and then complete the tables:

Multiply the x-value by _____ and subtract ____
3 2
from the answer.
Formula:__________________
y = 3x- 2

x 3 6 9 12 15 18 21 24 27
y 7 16 25 34 43 52 61 70 79


Activity 5
1. Choose the correct formula for the table and
then complete the table using the pattern of the
y-values
a. y = 3x+ 7
b. y = 7x– 5
c. y = 5x+ 8

x 2 4 6 8 10 12 14 16 18
y 18 28 38 48 58 68 78 88 98


Activity 5
1. Choose the correct formula for the table and
then complete the table using the pattern of the
y-values
a. y = 8x+ 4
b. y = 8x– 2
c. y = 8x+ 7

x 5 6 7 8 9 10 11 12 13
y 47 55 63 71 79 87 95 103 111


Activity 6
• Complete the following tables after studying the
problem and writing a formula for it:

a. A ticket on Metrorail costs 80c per ticket
plus 40c per kilometre.
Formula:______________
y = 0.4x+ 0.8

x 3 6 9 12
y R2 R3,20 R4,40 R5,60


Activity 6
• Complete the following tables after studying the
problem and writing a formula for it:

a. A long distance bus company charges R1,50
per kilometre plus a fixed amount of R50,00
per ticket.
Formula:______________
y = 1.5x+ 50

x 185 200 750 1 500
y R327.50 R350 R1 175 R2 300


Activity 7
• From the pie chart, answer the following questions
Chocolate Brand Popularity
TV Bar
Beacon 4%
5% Flake
Crunchie 3%
Dairy Milk
5%
20%
Nestle
8%

Kit Kat
11% Lunch Bar
16%

PS
13% Bar One
15%


Activity 7
a. What is the subject of the pie chart?
Chocolate Brand Popularity
c. Which brand has the largest recognition?
Dairy Milk (20%)
e. Which brand has the smallest recognition?
Flake (3%)
g. How many brands are represented in this pie
chart?

10 Brands


Activity 7
1. From the table, answer the questions on the next page
Loan Amount 12 Months 18 Months 24 Months
2 000 293,79 224,24 191,70
2 500 338,99 258,74 221,19
3 000 395,49 301,86 258,05
3 500 451,99 344,89 294,92
4 000 508,49 388,11 331,78
4 500 553,69 422,61 361,28
5 000 610,18 465,73 398,14
5 500 668,68 508,86 435,01
6 000 723,18 551,98 471,87
6 500 768,38 586,48 501,36
7 000 824,88 629,60 538,23
7 500 881,38 672,73 575,09
8 000 937,88 715,85 611,96

Activity 7
a. What does the table tell you?
The monthly repayments for different sized loans
vs different periods
d. Sammy takes a loan of R6 000 from this bank and
decides to repay it within 24 months. His reason is
that the monthly repayment for a 24-month period is
much less than for a 12-month period. Do you think
that Sammy is wise to do this? Explain your answer

No, his total repayment amount will still be higher
f. What is your monthly repayment if you take out a
loan of R2 000 and repay it within 12 months.

R293,79

Activity 7
a. How much more than R2 000 will you have repaid at
the end of 12 months?
(R293,79 x 12) – R2 000
=R1 525.48
e. If you repay this R2 000 loan within 24 months, how
much will you have repaid at the end of 24 months?
191,70 x 24 = R4600,80

h. How much more is this than the original R2 000 loan
that you made?

R4600,80 – R2000 = R2600,80

Activity 7
• From the bar graph, answer the following
questions:


a. Which was the most popular brand in 2007?
Coca-Cola
c. Was this the case in 2006 as well?
No, Nike was most popular
e. Which brand is no longer one of the top 10
coolest brands and who is the newcomer?
LG has been replaced by Reebok
g. Which cell phone service provider is the most
popular among 16-19 year olds?

Vodacom

e. What do you think is represented on the
horizontal axis and why does the newspaper not
find it necessary to show this on the graphs?
The brand relationship score, it is already
mentioned in the heading, so it is
unnecessary to mention it twice


Activity 8
• Study the table below, follow the instructions
and answer the questions.


a. What is the subject of the table?
Postpaid call charges
c. How much will it cost to make a local call
during “callmore” time, if the call lasts five
minutes?
Cost = Minimum charge + (time charge) x time
= R0,59c + 5 x 0,17
= R1,44


a. How much more will the same call cost during
“standard time”?
Cost = Minimum charge + (time charge) x time
= R0,59c + 5 x 0,38
= R2,49
f. How many more minutes can you speak during
“call more” time at the same cost?

R2,49 – R1,44 = R1,05


e. Draw a line graph showing the cost of the call for both
packages if the call lasts for the following times: 5 min,
10 min, 15 min, 20 min

Standard Rates vs Callmore rates

9

8
Standard Time
7
Callmore Time
6
Cost (R)

5

4

3

2

1

0
0 5 10 15 20
Time (min)


a. Write a formula for the graphs:

For standard time:
y = 0.38x + 0.59

For Callmore time
y = 0.17x+ 0.59


Activity 9
• Refer to the module on drawing graphs for
detailed information on how to draw a graph.
Below is the temperature conversion table
between degrees Celsius and degrees Fahrenheit.
a. Complete the table of values by using the
formula:
ºF = 1,8 ºC + 32

C 0 10 20 30 40 50 60 70 80 90 100
F 32 50 68 86 104 122 140 158 176 194 212


Celcius vs Farenheit
250

200

150
Farenheit

100

50

0
0 10 20 30 40 50 60 70 80 90 100
Celcius

a. Read from the graph to fill in the following
table:
C 2 12 35 52 66 75 85 95
F 36 53 91.4 125.6 150 167 185 203


Activity 10
• Investigate the following situations and decide on one or two
good ways to represent the information.
1. Budget of Rosie – her average monthly expenses
Rent R1 100
Food and Household R2 000
Travel Costs R500
Cell phone R400
Cigarettes R200
Lotto R160
Clothes R150
Other R350

Pie chart or bar chart

Budget of Rosie

Rent
Food and household
Travel Costs
Cell phone
Cigarettes
Lotto
Clothes
Other


Budget of Rosie

2500
2000
1500
R

1000
500
0
t

s
ts

tto

er
s
ne
ld
en

he
tt e
os

th
o

Lo
ho
R

eh

t
re

O
C

lo
lp
us

a

C
el

ig
el
ho

av

C
C
Tr
d
an
od
Fo

Item

1. Rainfall figures for the month of July in a
certain region
1996: 68mm; 1997: 35mm; 1998: 55mm; 1999:
48mm;2000: 75mm; 2001: 100mm; 2002: 95mm;
2003: 82mm; 2004: 53mm; 2005: 38mm; 2006:
59mm; 2007: 70mm

Bar chart or line chart


Rainfall (mm)

120

100

80
mm

60

40

20

0
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Year


Rainfall (mm)

120
100
80
mm

60
40
20
0
97
98
99

00
01

02
03

04
05
06

07
96

19

19

20
20

20
20

20
20

20
19

19

20
Year


1. AIDS Statistics: HIV prevalence among child-
bearing women in South Africa 1990-1999
Yr 1 2 3 4 5 6 7 8 9 10
HIV 0,7 1,7 2,2 4,0 7,6 10,4 14,2 17,0 22,8 22,4

Bar chart or line chart


Prevalence of HIV am ongst child bearing w om en

25

20

15
%

10

5

0
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
Year


Prevalence of HIV amongst child bearing women

25

20

15
%

10

5

0
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
Year


1. Release of crime statistics from 1 April 2006 to 31 March 2007. When the
crime figures for 2006/2007 were compared recorded in the previous year,
the following findings were made:
– Eight serious crimes are grouped together as contact crime or violent
crime against the person. These crimes are murder, attempted murder,
rape, assault grievous bodily harm (GBH), common assault, indecent
assault, aggravated robbery and other robbery. These crimes account for
33.3% of South Africa’s recorded crime.
– Six of the eight contact crimes, namely rape, attempted murder, assault
GBH, common assault, indecent assault and common robbery decreased
by between 8.7% and 3.0%. These crimes are:

Common assault –8.7% Common robbery: -5.8%
Indecent assault: -5.5% Rape: -5.2%
Assault GBH: -4.9% Attempted murder: -3.0%


Activity 11
• Work in pairs
• Study the table below and answer the questions

Province Total HIV Total HIV 15-49 HIV Life Expct
KZN 1520 16% 26% 43,3
GAU 1370 14% 22% 52,4
FS 380 14% 22% 47,2
MP 440 13% 22% 46,5
NW 470 12% 20% 50,7
EC 630 9% 17% 49,4
Limpopo 380 7% 12% 56,4
NC 60 7% 11% 57,8
WC 250 5% 8% 61,8
SAAnswers to activities 5500 11% Managers
Future
18% 51,0 49

a. What would be a good way to represent that data in the first
column. See if you can do it.
Pie chart or bar chart

Province Total HIV % of SA x 360
KZN 1520 27% 97.2
GAU 1370 25% 90
FS 380 7% 25.2
MP 440 8% 28.8
NW 470 9% 32.4
EC 630 11% 39.6
Limpopo 380 7% 25.2
NC 60 1% 3.6
WC 250 5% 18
SA 5500 100% 360

HIV Distribution in South Africa

NC WC
Limpopo 1% 5%
7%
KZN
27%
EC
11%

NW
9%

MP
8% GAU
FS 25%
7%


HIV Prevalence in SA

1600

1400

1200
HIV infections (000s)

1000

800

600

400

200

0
KZN GAU FS MP NW EC Limpopo NC WC

Province


b.What would be a good way to represent the data
in the second column. See if you can do it.
A bar chart


% of HIV infections per province

18%

16%

14%

12%
Infection rate

10%

8%

6%

4%

2%

0%
NW

SA
U

C

C
ZN

EC
FS

P

o
A

N

W
M

p
K

G

po
m
Li

Province

a. In which province is life expectancy the
highest?
The Western Cape


Activity 12
Portfolio of evidence project
Collect, interpret, organise and present information

Instructions
• Form groups of three and four and conduct research amongst a
minimum of 30 people for this project
• The project must be typed
• The name of the topic and the team members must be on a cover
page
• The project must include your own completed questionnaires,
frequency tables, graphs and a report
• The graphs must be drawn neatly. Colour may be used
• The research must be completed as a group, but the representation
and report individually


Project
2. Ask the following questions to find out more how people think:
– Do you like to listen to music?
– What kind of music do you listen to?
– Do you think it is a good thing to copy cds or to buy a copied cd?
• Draw up relevant frequency tables and a compound bar graph
to represent your data
• Where it applies, use the mode, median, mean and range to
describe your data
• Consider age and/or gender
• Write your own report on your data and illustrate it with
graphs, tables and calculations where necessary.


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