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MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
Mr Jacob does his banking with First National Bank. The statement below (TABLE 3) was sent
to Mr Jacob at the end of November. An extract of banking fees for his Smart Account is given
as TABLE 1 and TABLE 2 is the bank charges for Bates Bank.
1.1 How many days does this statement cover? (2)
1.2 How many statements did Mr Jacob receive for this account? (2)
1.3 What is the monthly account fee payable on this account? (2)
1.4 What is the monthly deposit fee for October? (2)
1.5 Calculate the bank charges for the month of October. (2)
1.6 If Mr Jacob had to make a deposit of R3 545. Calculate the deposit fee for this
amount.
(3)
1.7 How much money was deposited by Mr Jacob into this account for the time
period of this statement?
(2)
1.8 Show by calculations how R11,25 VAT was calculated. (2)
1.9 In December Mr Jacob made the following transactions.
2 cash withdrawal of R600 at a FNB ATM
1 deposit of R900 at the FNB ATM
1 deposit of R2500 in the bank
Calculate the total service fee for these transactions.
(7)
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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1.10 Mr Jacob wants to make a withdrawal of R1200. He has the option to withdraw this amount from a FNB ATM or use another bank’s ATM. Show with calculations which will be a cheaper option with regards to service fees.
(5)
1.11 Given a reason why it may not be suitable to use this account as a savings account
(2)
1.12 Give a reason why it costs more to make a deposit in the bank as compared to
using the FNB ATM.
(2)
1.13 The client used his cash withdrawal amounts to pay for his weekly expenses
for airtime, petrol, meals and purchasing groceries.
Suggest TWO cost effective ways that he could use to save on cash withdrawal fees.
(4)
1.14 Jacob states that if he had a Bates Bank PLUS savings account, then his bank fees will be less than his present bank. Use TABLE 2, the bank charges for Bates Bank and verify with calculations whether Jacobs statement is correct.
(8)
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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(TABLE 1) Extract of Banking Fees for SMART ACCOUNT
Pay-As-You-Use Pricing Option
Monthly Account Fee R12,50
Cash Withdrawals
Cash@Till FREE
FNB Slimline R5,00
FNB ATM R3,95 + R1,30 per R100
Other Banks’ ATM R6,50 + FNB ATM fee
FNB Branch/Cheque R50,00 + R1,65 per R100
Deposits
Cash Deposit at FNB ATM R0,70 per R100 (minimum R5,50)
Cash Deposit at FNB Branch R1,65 per R100 (minimum R5,50)
Cheque deposit at FNB branch and ATM R22,50
Card purchases/payments FREE
TABLE 2 Extract of banking fees for Bates PLUS account
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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TABLE 3 Mr Andy Jacob SMART ACCOUNT : 397465859939 56 Stable Road Uppertown Copy Tax Invoice/Statement Number : 13 1856 29 August 2015 to 28 November 2015
Statement Date : 28 November 2015
Bank Charges Statement Balances Interest Rates Bank charges R91,60 Subscription Fees R0,00
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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1.1
What amount was the previous bill?
(2) 1.2 Is solid waste-Residential charged, a fixed or variable cost? (2) 1.3 Calculate the missing value of A. (3) 1.4 And hence the value of B. (2) 1.5 If the total amount payable is $106, 65. How much will John Doe pay in S.A currency if
1$=R15, 75? (2)
1.6 Calculate the total amount payable in two years’ time if it is invested and it
Is compounded annually at the rate of 9, 25% p.a? (4)
1.7 A sewer water usage is calculates at 80% of the water consumption, If Thembi used
16Kl of water. Calculate how much in rands she will pay for her sewer charge, if rate is charged at 0, 19 per kilolitre ($)?
(6)
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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SESSION 3
TOPIC : FINANCE
SECTION: TARIFF SYSTEMS
CONTEXT: PLANNING A TRIP
Terminology:
VAT, Break-even point, Rental, Budget, costs, quotation,
Teachers notes;
Basic skills required;
- Conversions (cents to rands, minutes to hours,
- Calculation of time
QUESTION 1
Mr Mthembu from Pretoria plans to take his family of five members, for the Easter holiday
trip to Cape Town of their youngest daughter who was born on the 26th of March 2015. to
celebrate the birthday. He wants to hire Toyota Avanza for the trip and requested two
quotations from two car rental companies;company X and Y. He intends to collect the car on
Thursday, 24 March 2016 and return it on the Monday, 28 March 2016. Mr Mthembu plans to
travel via Bloemfontein for the trip, the distance between Pretoria to Cape Town via
Bloemfontein is 1460km.
RATE CODE COMPANY X COMPANY Y
Included Total Kilometres For Rental
800 km 800km
Cost per Additional kilometre R3.59(Incl. VAT) per km R3.29(Incl. VAT) per km
1.3 Determine the VAT exclusive of the total amount (including the additional
charges) for Budget.
3
1.4 Why is it important for Mr Mthembu to pay for the baby seat? Give two reasons. 2
1.5 How much will it cost Mr Mthembu and family for EACH company, if they were to
travel a distance of 467 Km from Pretoria to Bloemfontein?
2
1.6 Calculate the total cost for the trip, if they were to travel from Pretoria to Beaufort
West via Bloemfontein using company Y.
5
1.7 Mr Mthembu and family plan to depart from Pretoria at 09:23, at what time will
they arrive at Beaufort West?
3
1.8 If it takes 335 minutes to travel from Beaufort West to Cape Town. Use the
formula below to determine the average speed (km/h) Mr Mthembu has to travel
with in order to arrive on time.
Average speed = distance
time
4
1.9 If P is the total amount and K is the total kilometres travelled, write down a
formula that can be used to calculate the total amount that should be paid using
company Y. in the form:
Total amount payable for company Y (in rand) = ...
2
1.10 Calculate the total amount payable for the entire trip using company Y, if Mr
Mthembu intends to cover 630 km for touring around Cape Town.
5
1.11 The price of petrol for February 2016 is 1215.00 cents per litre. If the price
remains unchanged, how much should Mr Mthembu budget for the fuel of the
entire trip. Give the answer in rands.
7
1.12 State TWO other factors, that could influence the driving time on the road. 2
1.13 Use Annexure A to draw the line graphs showing the relationship between the
total amount payable and the distance covered by Mr Mthembu, using company
Y.
5
1.14 Explain the meaning of break-even point. 2
1.15 Use the graph to determine the break-even point of the two companies. 2
1.16 Based on the graph, which company would you advice Mr Mthembu to take and
why?
3
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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Annexure A
1.13
0
2000
4000
6000
8000
10000
12000
14000
16000
0 800 1600 2400 3200 4000
Tota
l Co
st (
R )
Distance (km)
Distance Travelled vs Total Cost
Company X
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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QUESTION 2
Mrs Mthembu a consultant at Vodacom got the accommodation at Ulwazi resort,
situated at the west side of the sea.35km from the city
(3)
Standard suit:R550 per room/day Executive suit: R630 per room/ day
Free break fast Free break fast
No room service Room service
Gym Gym
Wi Fi : 500MB per day and R29 for
every 100 additional megabites
Wi Fi : 1GB per day.
3 Single beds 2 double bed
Check in: 24 March 2016 at 22h00
Check out: 28 March 2016 at 11h00
2.1 How many rooms should Mthembu’s family book? 2
2.2 How many nights would they spend at the hotel? 2
2.3 Which rooms should they book for the entire family? 2
2.4 Express the Wi Fi of the standard room to the Wi Fi of the executive room as a
ratio in its simplest form.
3
2.5 Ditebogo their eldest son normally uses 623MB per day. Determine the total
amount to be budgeted for the Wi-Fi if he has to stay in the standard room and
he is the only one that will use the data.
4
2.6 Mr Mthembu has budgeted R3000 for leisure, and divided the money : Father,
Mother, Ditebogo and Sani in the ratio of 4:3:2:2. Determine the actual amount
budgeted for the mother.
3
2.7 If the family budgeted R1 500 for food, calculate the total amount they should
budget for the trip excluding car rental.
3
2.8 If he had saved R2 000 every month for the period of 10 months, will this be
enough to cater for the trip?
4
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SESSION 4 DATA HANDLING TOPIC: DATA HANDLING SECTION: CLASSIFYING, ORGANIZING, SUMMARIZING ,REPRESENTING AND ANALYZING DATA CONTEXT :HEALTH , HEIGHT AND POPULATION TERMINOLOGY: BIASED, SAMPLE, DEPENDENT, INDEPENDENT, MOTIVATE, REPRESENT AND QUESTIONNAIRE BASIC SKILLS: INTERPRETING AND COMMUNICATING ANSWERS
QUESTION 1
Read the different data collection situations. Decide whether the sampling is biased
or representative. Explain your answer by referring to sample size, groups not
included in the sample or other factors which may have an influence on the data.
1.1. Ten grade 11 learners were asked which cold drink is their favourite. The
results were used to predict which types and how many of the different cold
drinks must be bought by the tuck shop manager.
(2)
1.2 A school has 560 learners. The school wants to develop the cafeteria
area. To find out the opinion of all the students, 25 learners from each
grade (8 to 12) were asked for their opinions by answering a
questionnaire. Males and females from all racial groups were included
in the sample.
(2)
1.3 A market researcher stands outside a supermarket from 08:00 to 10:00
on a Monday, and asks questions about grocery purchases, to predict
the grocery purchasing habits in that suburb.
(2)
1.4 A bookseller wants to know how many people in Gauteng read novels,
hence she asked a sample of people whether they have read a novel in
the past month.
1.4.1 Would a representative sample be obtained if the bookseller
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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stood outside a bookstore? Motivate. (3)
1.4.2 Explain why the sample would not be representative if the
bookseller went to a cattle farm and asked the workers on the
farm this question.
(2)
1.4.3 Suggest how a representative sample could be obtained.
(2)
1.2 The life orientation teacher, Mr Bruinders, Involved his grade 8 learner in a project to
investigate the time spend doing homework per week and the results on the report
cards at the end of the second term. The time row indicates the total time that they
effectively spend on doing homework (it includes studying). The results row gives
the average percentages that the learners had on their reports at the end of the
second term.
Time 10 12 8 20 17 10 9 5 17
Results 57% 69% 44% 90% 70% 86% 49% 41% 83%
Time 16 13 8 23 13 15 11 18 19
Results 74% 63% 47% 65% 59% 65% 54% 84% 85%
Time 14 16 12 17 16 24 19 16 5
Results 66% 79% 57% 73% 69% 92% 86% 81% 38%
1.2.1 Draw a scatter plot on a graph paper. Name the graph and label the axes.
Record the Time on the horizontal axis. Make provision for percentage
ranging from 30% to 100% on the vertical axis.
2
(5)
1.2.2 Use your scatter plot to answer the following questions:
(a) Is there a correlation between the hours spent on homework and the
performance of learners?
1 (1)
(b) What type of correlation is this? Positive or negative? 1 (1)
(c) Are there any sets of co-ordinates that does not fit into the pattern
that evolved from this scatter graph?
1 (1)
(d) Write down the two sets of ordered pairs that seems to be completely
out of line. Give possible explanations for each of these exceptions.
4 (3)
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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QUESTION 2
2.1 The Ebola-virus outbreak in West Africa during August 2014 is recorded as the
biggest outbreak of the virus. PIE CHART 1 below shows the number of Ebola
cases recorded in the three countries that were effected severely. PIE CHART 2
shows the number of Ebola deaths in the 3 countries. Use the pie charts to answer
the questions that follow:
PIE CHART 1 PIE CHART 2
[Adapted from WHO, Aug 2014]
2.1.1 The total number of Ebola deaths for the three counties totaled 961 in
August 2014. Determine how many more people died in Sierra Leone
compared to Guinea.
2
(4)
2.1.2 Determine what percentage of all the people who got infected with the
Ebola-virus, died of Ebola.
1
(2)
2.1.3 Express the number of people from Liberia who died from Ebola compared
to the number in Liberia who got infected as a unit ratio. Show all
calculations.
2
(4)
2.2 Health Workers from inside the countries as well as volunteers from all over the
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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world got involved in the treatment of the Ebola patients. The Ebola statistics for
health workers below, should be used to answer the questions that follow.
TABLE 1: Ebola Virus Disease infections in health workers in Guinea, Liberia and Sierra Leone
2.2.1 Explain why the data can be classified as discreet data. 1 (2)
2.2.2 Determine the values of A and B. 1 (4)
2.2.3 Is the statement below correct? If not, motivate your answer.
“ More than 50% of the health workers in the three countries died of Ebola.”
4
(2)
2.2.4 Which set of data value is not suitable to be compared with the others.
State whether you expect the total should be lower or higher. Substantiate
your answers.
4
(4)
2.3 On 9 May 2015 updated statistics were released by the Word Health Organisation.
Use the to answer the following questions.
2.3.1 Name the country and the relevant age group in which the highest
percentage of that group was confirmed to be infected. Justify your answer
by showing the relevant percentage calculations.
2
(4)
2.3.2 Which country was least affected by the Ebola outbreak. Motivate your
choice.
(3)
A
B
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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SESSION 5
DATA HANDLING: INTERPRETATION
QUESTION 1
Every December, many South Africans lose their loved ones in road fatalities.
Transport Minister Dipuo Peters told reporters in Pretoria at the release of the
preliminary festive season road death statistics for the period 1 December 2013
to 7January 2014.
Provincial accident statistics
Gauteng recorded 268 fatalities, while KwaZulu-Natal had the highest number of
fatalities, 284. Limpopo 134 fatalities, the Eastern Cape with 190 fatalities, and
the Free State 121 fatalities. The Western Cape had 114 fatalities, the North
West had 88 fatalities, and Mpumalanga had 134 fatalities. The Northern Cape
had 43 fatalities.
A fatality is a death resulting from an accident such as road accidents.
1.1 Calculate the mean number of fatalities recorded for the period 1
December 2013 to 7January 2014.
(3)
1.2 What percentage do the fatalities recorded in Kwa-Zulu Natal represent?
(3)
1.3 Identify two possible causes of fatalities during the time of festive season
(2)
1.4 The number of fatalities per province has been provided below:
268 284 190 121 114 88 134 43 134 .
1.4.1 Calculate the inter-quartile range from the data (3) 1.4.2 What is the upper quartile? (2)
1.5 A box-and-whisker plot to represent the fatalities has been drawn below: 43 101 134 229 284
Use the box-and whisker plot to answer the following questions:
1.5.1 Determine the median (2) 1.5.2 How many provinces had fatalities above the median? (2) 1.5.3 What percentage of the fatalities is below the lower quartile? (3) 1.5.4 What percentage of fatalities recorded is located between the
lower quartile and the median? (3)
1.5.5 Provide two sets of advice that you would give to motorists to minimise road accidents during festive seasons
(2)
[25]
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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QUESTION 2 – SOCCER PREMIER LEAGUE
Below is 2015/165+ South African Soccer Premier League table. Use it to
answer the questions that follow :
Absa Premiership
Pos Team Pld W D L GF GA GD Pts
1 Mamelodi Sundowns 19 14 3 2 37 14 23 45
2 Bidvest Wits 19 11 3 5 32 17 15 36
3 Black Aces 19 10 6 3 25 14 11 36
4 Kaizer Chiefs 19 9 8 2 28 15 13 35
5 Platinum Stars 18 8 7 3 27 19 8 31
6 Chippa United 19 9 1 9 27 29 -2 28
7 Golden Arrows 18 7 3 8 18 21 -3 24
8 SuperSport United 19 6 6 7 19 24 -5 24
9 Orlando Pirates 18 6 5 7 21 20 1 23
10 Ajax Cape Town 18 6 5 7 25 25 0 23
11 Bloem Celtic 19 5 7 7 16 17 -1 22
12 Free State Stars 18 6 4 8 20 26 -6 22
13 Polokwane City 19 6 3 10 20 30 -10 21
14 Jomo Cosmos 19 4 5 10 13 22 -9 17
15 University of Pretoria 19 3 4 12 10 26 -16 13
16 Maritzburg Utd 18 1 6 11 20 39 -19 9
2.4.1 Calculate the median of the goal difference (GD). (3)
2.4.2 Determine the mean of the points for (GF) to the nearest
integer.
(3)
2.4.3 What were the modal goals against (GA)? (2)
2.4.4 Calculate the range of the points against (Pts). (3)
2.4.5 Which measure of central tendency provides the most accurate
representation of the points against (GF) data? Give ONE
reason for your answer.
(3)
.
[14]
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QUESTION 3
3.1 The 2015 Cricket World Cup was hosted in Australia and New Zealand during February and March. In an innings (INN) each team had to bat for 50 overs and they had to aim to get as many runs as possible. TABLE 1 shows the 25 players who obtained the highest total number of runs for the tournament.
TABLE 1 2015 - World Cup Cricket Top 25 run scorers
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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3.1.1 How many teams had players in the top 25 run-scorers? (2)
3.1.2 The strike rate is determined by using the following formula:
Strike Rate = number of runs scored
number of ball faced 100
Use this formula to determine the value of A in the table.
(2)
3.1.3 The first column (POS) indicates the position of a player in the top 25 list.
(a) Determine the median number of runs scored by the 25 players. (2)
(b) Calculate the range of the runs obtained by the top 25 run scorers. (2)
3.1.4 In cricket the average number of runs scored is calculated by dividing the total number of runs by the number of innings (INN) in which the batsman was out. Steven Smith (Australia) had an average of 67. He was not out in only one of the seven innings. He was therefore out in six innings, hence his average was calculated as follows: 402 ÷ 6 = 67.
Calculate in how many of the 7 innings AB de Villiers (South Africa) was not dismissed.
(2)
3.1.5 The numbers in the columns under the 4s and 6s indicate how many times the batsman scored 4 runs / 6 runs of one ball.
(a) Calculate the total number of runs that AB de Villiers scored by hitting fours and sixes.
(3)
(b) Determine what percentage of his total score was obtained by hitting boundaries (4s and 6s)
(2)
3.2 Find the most suitable statement from column B which will fit the term in column A. Write the number and the letter of the statement (e.g. 3.2.5 F)
COLUMN A COLUMN B
3.2.1 Mode A The difference between the highest and the lowest value in the data set
3.2.2 Mean B When the values on the horizontal axis increase, the corresponding values on the vertical axis decrease
3.2.3 Negative correlation C The 75th percentile value
3.2.4 Quartile 3 D The sum of the data divided by the number of data items
E The data item/value which appears most often in the data set
(4)
[19]
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QUESTION 4
Mr Tshabalala, a Mathematics teacher, compared the November 2014 examination
results of his two grade 11 Mathematics classes to see which class performed
better.
In class A there are 28 learners and in class B there are 24 learners.
The results of the examination for the two groups are represented by the two box-
and-whisker diagrams below:
The ordered marks of class B, are given below as rounded percentages.
15 18 18 24 33 32 37 40 46 55 58 S
63 65 67 T 73 74 74 76 80 85 87 93
4.1 Use the box-and-whisker plot and/or the data values for class B, to answer
the following:
4.1.1 Use the median to determine the value of S. (3)
4.1.2 Determine the missing value of T if the mean percentage of class
B is 56,083% .
(3)
0 10 20 30 40 50 60 70 80 90 100
1
2CLASS B
CLASS A
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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4.2 Determine the interquartile range for class A. (3)
4.3 How many learners in class A scored between 56% and 77% in the test? (2)
4.4 Decide whether the following statement is correct. Motivate your decision
by referring to specific quartile values and the number of learners. “In total
at least fifteen learners from the 2 classes obtained a distinction (80%
and above) in Mathematics.”
(3)
4.5 Explain why it can be said that class B performed better in the examination.
Compare marks at specific quartile/percentile markers or quartile ranges in
the box-and-whisker plot, to substantiate this statement. Provide two
reasons.
(4)
4.6 Calculate the probability of randomly selecting the name of a learner from
class B who obtained a percentage mark of less than 34%.
(2)
4.7 Give 2 possible reasons why learners in schools are not performing well in
Mathematics. One reason should refer to an educator cause and the other
to a learner cause. Be specific and clear.
(2)
[20]
MATHEMATICAL LITERACY GRADE 12 LEARNER’S NOTES SSIP MATERIAL 2019
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QUESTION 5
5.1 The sales manager at “Water IQ”, a company that sells water tanks,
collected data on the number of tanks that his three top performing
marketing agents sold per month, over a period of one year. He
summarised the data in the box-and-whisker plots below.
5.1.1 Estimate the lower quartile value of the number of water tanks sold by agent C.
(2)
5.1.2 For how many months did agent A sell 40 or less tanks? Show/explain your reasoning steps
(3)
5.1.3 Determine the minimum and the maximum number of tanks sold
per month by marketing agent B, during the three months that he recorded his lowest sales.
(4)
5.1.4 Agent B received the award for the “Top Salesman” in 2014. Do
you think he awarded the correct salesman? Give 3 reasons for your answer.
(7)
5.1.5 If the minimum commission that an agent can earn per tank, is
R713.76, determine the lowest amount that agent C could have earned in 2014.