NCV 2 Mathematical Literacy Hands-On Training Activities Module 5

Mathematical Literacy 2Module 5

Answers to Activities

Answers to activities 1Future Managers

Activity 1Refer 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%Answers to activities 2Future Managers

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?

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

Constant ratio

Save up for the TV, rather than buy it on creditAnswers to activities 3Future Managers

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?

4. If indeed, what would you expect to happen in 2008 with interest rates?

6. Having the benefit of hindsight, what actually happened in 2008?

Interest rates are rising

They will continue to rise

They did continue to riseAnswers to activities 4Future Managers

Activity 21. Write down five numbers that you think should

logically follow on the numbers in the following sets.

2 4 8

3 6 9

4 7 10 13

33 30 27

128 64 32

16 32 64 128 256 512

12 15 18 21 24 27

16 19 22 25 28

24 21 18 15 12 916 8 4 2 1 0.5

Rat

Dif

Dif

Dif

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; 1005; 15; 25; 35; 45; 55; 65; 75; 85

4; 8; 12; 16; 20; 28; 32; 36; 40; 44


Activity 24.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

R1000

R5000

R10000

105 210 315 105

150 300 450 150

750 1500 2250 750

1500 3000 4500 1500


Activity 25. Fill in the missing numbers according to the pattern:

7 11 15 31 35

25 30 35 60

4 8 16 32

3 600 360 36 3,6

1,6 16 160 1 600

19 23 27

40 45 50 55

64 128 256 512

0.36 0.036 0.0036 0.00036

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 timeAnswers to activities 8Future Managers

Activity 31. Evaluate the table on cash loans and answer the questions:

Cash loan amounts R3000 R4 000 R5 000

Monthly repayment

12 months R361 R467 R573

24 months R226 R291 R357

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

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

Constant Difference

IndirectAnswers to activities 9Future Managers

Activity 31. 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

Cost of loan

a. Is there a direct or indirect relationship between the repayment period and the monthly repayment amounts?

c. Is it better to repay the loan within 12 months or within 36 months? Give a reason for your answer.

Indirect relationship

R 4 332

R 1 332

R5 242

R2 424

R6 624

R3 624

Within 12 months, you pay less overall for the loanAnswers to activities 10Future Managers

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

• 2nd Month Fixed Salary + 2% Commission on Sales

• 3rd Month Fixed Salary + 3% Commission on Sales

=R1 500 + 0.01 x R5 000

=R1550

=R1 500 + 0.02 x R5 000

=R1600

=R1 500 + 0.03 x R5 000

=R1650Answers to activities 12Future Managers

Activity 5• Work in pairs to determine the independent and

dependent variables in the tables below1.Complete the flow diagrams:

Independent Variable

x 7 + 8 = Dependent Variable

2 x 7 + 8 =

5 x 7 + 8 =

7 x 7 + 8 =

12 x 7 + 8 =

22

43

5792


Activity 5

1 x 8 + 12 =

3 x 8 + 12 =

5 x 8 + 12 =

27 x 8 + 12 =

30 x 8 + 12 =

20

36

52228

256


Activity 51. 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

x 5 10 15 20 25 30 35 40 45

y 19 34 49 64 79 94 109 124 139

y = 3x + 4


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.

x 2 4 6 8 10 12 14 16 18

y 10 11 12 13 14 15 16 17 18

y = x/2 + 9


Activity 51. Complete the operating instructions, give the

correct formula and then complete the tables:

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

x 3 6 9 12 15 18 21 24 27

y 7 16 25 34 43 52 61 70 79

y = 3x - 2

3 2


Activity 51. 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 51. 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:______________

x 3 6 9 12

y

y = 0.4x + 0.8

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:______________

x 185 200 750 1 500

y

y = 1.5x + 50

R327.50 R350 R1 175 R2 300


Activity 7• From the pie chart, answer the following questions

Chocolate Brand Popularity

Flake3%

Dairy Milk20%

Lunch Bar16%

Bar One15%

PS13%

Kit Kat11%

Nestle8%

Crunchie5%

Beacon5%

TV Bar4%


Activity 7a. What is the subject of the pie chart?

c. Which brand has the largest recognition?

e. Which brand has the smallest recognition?

g. How many brands are represented in this pie chart?

Chocolate Brand Popularity

Dairy Milk (20%)

Flake (3%)

10 Brands


Activity 71. 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 7a. What does the table tell you?

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

f. What is your monthly repayment if you take out a loan of R2 000 and repay it within 12 months.

The monthly repayments for different sized loans vs different periods

No, his total repayment amount will still be higher

R293,79Answers to activities 26Future Managers

Activity 7a. How much more than R2 000 will you have repaid at

the end of 12 months?

e. If you repay this R2 000 loan within 24 months, how much will you have repaid at the end of 24 months?

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

(R293,79 x 12) – R2 000

=R1 525.48

191,70 x 24 = R4600,80

R4600,80 – R2000 = R2600,80Answers to activities 27Future Managers

Activity 7• From the bar graph, answer the following

questions:


a. Which was the most popular brand in 2007?

c. Was this the case in 2006 as well?

e. Which brand is no longer one of the top 10 coolest brands and who is the newcomer?

g. Which cell phone service provider is the most popular among 16-19 year olds?

Coca-Cola

No, Nike was most popular

LG has been replaced by Reebok

VodacomAnswers to activities 29Future Managers

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?

c. How much will it cost to make a local call during “callmore” time, if the call lasts five minutes?

Postpaid call charges

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”?

f. How many more minutes can you speak during “call more” time at the same cost?

Cost = Minimum charge + (time charge) x time

= R0,59c + 5 x 0,38

= R2,49

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

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20

Time (min)

Co

st

(R)

Standard TimeCallmore Time


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

0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90 100

Celcius

Far

enh

eit


a. Read from the graph to fill in the following table:

C 35 52 75 95

F 36 53 150 185

2 12

91.4 125.6

66

16785

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 100Food and Household R2 000Travel Costs R500Cell phone R400Cigarettes R200Lotto R160Clothes R150Other R350

Pie chart or bar chart


Budget of Rosie

Rent

Food and household

Travel Costs

Cell phone

Cigarettes

Lotto

Clothes

Other


Budget of Rosie

0

500

1000

1500

2000

2500

Rent

Food

and h

ouse

hold

Trave

l Cos

ts

Cell p

hone

Cigare

ttes

Lotto

Clothe

s

Other

Item

R


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)

0

20

40

60

80

100

120

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

Year

mm


Rainfall (mm)

0

20

40

60

80

100

120

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

Year

mm


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 amongst child bearing women

0

5

10

15

20

25

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

SA 5500 11% 18% 51,0Answers to activities 49Future Managers

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

KZN 1520

GAU 1370

FS 380

MP 440

NW 470

EC 630

Limpopo 380

NC 60

WC 250

SA 5500

% of SA

27%

25%

7%

8%

9%

11%

7%

1%

5%

100%

x 360

97.2

90

25.2

28.8

32.4

39.6

25.2

3.6

18

360Answers to activities 50Future Managers

HIV Distribution in South Africa

KZN 27%

GAU 25%FS

7%

MP 8%

NW 9%

EC 11%

Limpopo 7%

NC 1%

WC 5%


HIV Prevalence in SA

0

200

400

600

800

1000

1200

1400

1600

KZN GAU FS MP NW EC Limpopo NC WC

Province

HIV

in

fec

tio

ns

(0

00s

)


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

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

KZN

GAU FS

MP

NW

EC

Limpo

po NC W

C SA

Province

Infe

ctio

n r

ate


a. In which province is life expectancy the highest?

The Western Cape


Activity 12Portfolio of evidence projectCollect, 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


Project2. 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.


NCV 2 Mathematical Literacy Hands-On Training Activities Module 5

Education

Transcript of NCV 2 Mathematical Literacy Hands-On Training Activities Module 5