NCV 2 Mathematical Literacy Hands-On Training Activities Module 5
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Transcript of 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
Answers to activities 5Future Managers
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
Answers to activities 6Future Managers
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
Answers to activities 7Future Managers
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
Answers to activities 11Future Managers
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
Answers to activities 13Future Managers
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
Answers to activities 14Future Managers
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
Answers to activities 15Future Managers
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
Answers to activities 16Future Managers
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
Answers to activities 17Future Managers
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
Answers to activities 18Future Managers
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
Answers to activities 19Future Managers
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
Answers to activities 20Future Managers
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
Answers to activities 21Future Managers
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
Answers to activities 22Future Managers
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%
Answers to activities 23Future Managers
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
Answers to activities 24Future Managers
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
Answers to activities 25Future Managers
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:
Answers to activities 28Future Managers
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
Answers to activities 30Future Managers
Activity 8• Study the table below, follow the instructions
and answer the questions.
Answers to activities 31Future Managers
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
Answers to activities 32Future Managers
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
Answers to activities 33Future Managers
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
Answers to activities 34Future Managers
a. Write a formula for the graphs:
For standard time:
y = 0.38x + 0.59
For Callmore time
y = 0.17x + 0.59
Answers to activities 35Future Managers
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
Answers to activities 36Future Managers
Celcius vs Farenheit
0
50
100
150
200
250
0 10 20 30 40 50 60 70 80 90 100
Celcius
Far
enh
eit
Answers to activities 37Future Managers
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
Answers to activities 38Future Managers
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
Answers to activities 39Future Managers
Budget of Rosie
Rent
Food and household
Travel Costs
Cell phone
Cigarettes
Lotto
Clothes
Other
Answers to activities 40Future Managers
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
Answers to activities 41Future Managers
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
Answers to activities 42Future Managers
Rainfall (mm)
0
20
40
60
80
100
120
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Year
mm
Answers to activities 43Future Managers
Rainfall (mm)
0
20
40
60
80
100
120
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
Year
mm
Answers to activities 44Future Managers
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
Answers to activities 45Future Managers
Prevalence of HIV amongst child bearing women
0
5
10
15
20
25
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
Year
%
Answers to activities 46Future Managers
Prevalence of HIV amongst child bearing women
0
5
10
15
20
25
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
Year
%
Answers to activities 47Future Managers
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%
Answers to activities 48Future Managers
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%
Answers to activities 51Future Managers
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
)
Answers to activities 52Future Managers
b.What would be a good way to represent the data in the second column. See if you can do it.
A bar chart
Answers to activities 53Future Managers
% 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
Answers to activities 54Future Managers
a. In which province is life expectancy the highest?
The Western Cape
Answers to activities 55Future Managers
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
Answers to activities 56Future Managers
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.
Answers to activities 57Future Managers