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GRADE 12
PRELIMINARY EXAMINATIONS 2016
MATHEMATICAL LITERACY
PAPER 2
Time: 3 hours
Total: 150
Read the following instructions carefully:
1. This question paper consists of 14 pages. Please check that your question paper is
complete.
2. Read the questions carefully.
3. Number your answers exactly as the questions are numbered.
4. All the necessary working details must be clearly shown.
5. Approved non-programmable calculators may be used unless otherwise stated.
6. Answers should be rounded off to two decimal digits where necessary, unless otherwise
stated.
7. It is in your own interest to write legibly and to present your work neatly.
Bridge House College
Grade 12 Mathematical Literacy Paper 2
September 2016
Page 2 of 14
Question 1: Finances
1. Linda runs a business selling beaded necklaces. The graph below shows that the monthly
income and expenditure for her business is dependent on the number of necklaces that
she makes and sells.
1.1)
Linda’s monthly expenditure is made up of a fixed monthly rental for her stall
and the cost of materials for the necklaces. How much rent does she pay per
year?
1.2)
1.3)
(3)
Use the graph and calculations to show that:
a) Linda sells each necklace for R 30,00
(2)
b) It costs Linda R 10,00 to make each necklace
(3)
Linda decides to sell her necklaces for 40% more than her normal selling price.
a) Write down an equation to describe the relationship between Linda’s
new monthly income and the number of necklaces that she sells during
the month.
(3)
b) Write down an equation to describe the relationship between Linda’s
monthly expenditure and the number of necklaces that she sells during
the month.
Bridge House College
Grade 12 Mathematical Literacy Paper 2
(3)
September 2016
Page 3 of 14
c) Use the equations from 1.3a) and 1.3b) to determine whether Linda is
making a profit or loss if she sells 5 necklaces with her new selling price.
You must show all working.
(4)
1.4)
The graph below shows the annual inflation rate for the beads that Linda uses
for her necklaces for the period 2013-2016
Inflation
InflationRate
Rate for
for Beads
Beads 2013-2016
2013-2016
16%
14%
12,3%
Inflation Rate (%)
12%
10%
8,2%
7,3%
8%
6%
6%
4%
2%
0%
2013
2014
2015
2016
Year
a) Explain what has happened to the price of the beads since 2013.
(2)
b) At the start of 2014, a collection of 100 beads cost R 24,80. Using the inflation
graph, calculate what the price of the same collection is at the end of 2016.
(4)
Bridge House College
Grade 12 Mathematical Literacy Paper 2
September 2016
Page 4 of 14
1.5)
Linda travelled to Botswana in 2008 to go buy beads for her necklaces and to sell
some of her necklaces there. Before the trip, Linda visited a money exchange to
buy Botswana Pula (P) currency. The following exchange rate board was
displayed.
a) Use the exchange rate board and the example shown above to show that
Linda received P 2 012,30 when she exchanged R 2 500,00 into Botswana
Pula (P) and a commission fee is charged on the exchange.
Bridge House College
Grade 12 Mathematical Literacy Paper 2
(6)
September 2016
Page 5 of 14
1.6)
Linda had to get cellphones for three of her employees for use during their office
hours, which fall into ‘Peak Time’ according to the cellphone companies. She
visits the ‘MT Cell Promises’ and is presented with the following two packages:
a) Explain why the cost of ‘Off-Peak’ calls would possibly not be considered by
Linda?
(2)
Consider the graph below which shows the monthly costs involved for Package 1 and
Package 2 during Peak Time:
b) Which package is represented by Line A? Explain your answer.
(2)
c) Explain why both graphs are represented as straight lines.
(2)
Bridge House College
Grade 12 Mathematical Literacy Paper 2
September 2016
Page 6 of 14
1.7)
Linda earns a fixed monthly salary of R 16 800. SARS charges tax on income and
published the following tables to the public to show how income tax is
calculated.
Taxable income = Gross Salary – UIF (1% of Gross Salary) – Pension
2017 tax year (1 March 2016 - 28 February 2017)
Taxable income (R)
Rates of tax (R)
0 – 188 000
18% of taxable income
188 001 – 293 600
33 840 + 26% of taxable income above 188 000
293 601 – 406 400
61 296 + 31% of taxable income above 293 600
406 401 – 550 100
96 264 + 36% of taxable income above 406 400
550 101 – 701 300
147 996 + 39% of taxable income above 550 100
701 301 and above
206 964 + 41% of taxable income above 701 300
Tax Rebates
Tax Rebate
Tax Year
2017
2016
Primary
R13 500
R13 257
Secondary (65 and older)
R7 407
R7 407
Tertiary (75 and older)
R2 466
R2 466
a) Explain why people over 65-years old receive an additional rebate.
(2)
b) Explain why people earning a bigger salary per year pay a bigger
percentage tax.
(2)
c) Calculate the monthly tax (including rebate) for Linda (34 years old) for
the 2017 tax year if she has a monthly taxable income of R 16 632.
(6)
d) Would a 70 year old person earning an annual taxable income of
R 219 780 have a higher or lower monthly income tax than Linda for
the 2017 tax year?
(5)
[51]
Bridge House College
Grade 12 Mathematical Literacy Paper 2
September 2016
Page 7 of 14
Question 2: Measurement
2.1)
Linda extended her business by making circular place mats and circular
tablecloths out of material with beads. The place mats have a diameter of
30cm.
The radius of the tablecloth is four times the radius of a place mat.
Use the following:
𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑎 𝑐𝑖𝑟𝑐𝑙𝑒 = 2𝜋 × 𝑟𝑎𝑑𝑖𝑢𝑠
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑐𝑖𝑟𝑐𝑙𝑒 = 𝜋𝑟²
𝜋 = 3,14
a) She sells the place mats in sets of 6. Calculate the area of material that she needs
for making one set.
(4)
b) Calculate the circumference of the tablecloth.
(2)
c) She uses a beaded edging consisting of triangular segments to decorate the edge
of each tablecloth, as shown in the diagrams below. Each segment of the beaded
edging is 47,1mm long.
47,1mm
Calculate the number of beaded segments that she will need for each
tablecloth.
(3)
d) She uses 14 feet 8 inches of thread to attach the beaded edging to the table cloth.
Would 4,5 metres of thread be enough for one table cloth?
(4)
1 foot = 12 inches
1 inch = 2,54 centimetres
Bridge House College
Grade 12 Mathematical Literacy Paper 2
September 2016
Page 8 of 14
2.2)
The 3 dimensional section below (not drawn to scale) shows how the garden is sloped
at George’s new house. George decides that he will have to level the garden by laying
more soil at the bottom end and building his garden up.
The new soil will have to be 35cm deep at its deepest point, and will have to be laid
2,5m wide horizontally from the edge of his house to the edge of the garden. The
garden extends the whole length of his 8m long house.
2,5m
35cm
8m
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡𝑟𝑖𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑖𝑠𝑚 =
1
× 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡 × 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠𝑙𝑜𝑝𝑒
2
a) Calculate how many cubic meters of soil George needs to buy in order to
level up his garden.
(4)
b) Give a reason why he would want to level up his garden.
(2)
George is told that he will need to lay a top dressing on the top surface to help the growth of
his grass. The dressing is sold in bags of 7500cm³.
1cm³ = 0,000001m³
c) Calculate the volume of top dressing in m³ contained in each bag.
(3)
d) Suppose the garden is level. If the top dressing needs to be 2cm thick and cover
the whole top area of the garden, calculate the number of bags that George will
need to buy in order to top dress his garden sufficiently.
(6)
[28]
Bridge House College
Grade 12 Mathematical Literacy Paper 2
September 2016
Page 9 of 14
Question 3: Maps and Plans
3.1)
The diagram below shows a side elevation view of George’s new house.
8m
a) Calculate the number scale of the diagram.
(4)
b) Use your scale from a) to calculate the height (in metres) of the wall of George’s
house.
3.2)
(3)
Below is the 2-dimension floor plan of George’s old house with a bar scale provided.
a) The average width of a car is approximately 1,7m. Will one or two cars be able to
park in the garage with a 0,5m gap between the cars and from the walls? Show all
working.
(5)
b) Give two reasons why this house is not well-designed.
Bridge House College
Grade 12 Mathematical Literacy Paper 2
(4)
September 2016
Page 10 of 14
3.3)
The tables given below shows the Running Costs and the Fixed Costs for diesel
vehicles.
Running Costs Table - Diesel Vehicles
Averaged Running Cost (c/km) - All costs inclusive of VAT
Engine Capacity (cc)
Fuel
Maintenance
Diesel Factor
Service And Repair Costs (in cents)
Tyre Costs (in cents)
A
B
C
< 2 000
7.40
32.14
24.00
2 001 - 2 500
8.70
35.80
27.20
2 501 - 3 000
9.88
41.18
33.70
Purchase Price
(Incl. VAT)
Fixed Costs Table
Averaged Fixed Cost (c/km) - All costs inclusive of VAT
Annual Distance Travelled
10 001
to 15 000
15 001
to 20 000
20 001
to 25 000
25 001
to 30 000
30 001
to 35 000
35 001
to 40 000
>40 001
R200 001 - R250 000 704
470
354
286
240
211
187
169
R250 001 - R300 000 788
526
396
320
269
237
210
191
R300 001 - R350 000 927
619
466
377
317
279
247
224
<10 000
Operating Cost = Fixed Cost + Running Cost
a) What is the diesel factor of a car with an engine capacity of 2 500cc?
(2)
b) Calculate the fixed cost (in Rands) of a vehicle that cost R 270 000 and travels
an annual distance of 32 000km if the vehicle did a trip of 200km.
(3)
c) Calculate the Operating Cost of the trip of the vehicle in b) if the running cost for
this vehicle is R 1,45 per km.
d) Why do you think the Running Cost increase with engine size?
(3)
(2)
[26]
Bridge House College
Grade 12 Mathematical Literacy Paper 2
September 2016
Page 11 of 14
Question 4: Probability
4.1)
When a cricket team tours South Africa, the captain who wins a toss of the coin before
the match has to choose whether to bat first or bowl first. Here is a summary of the
number of times a team has won when batting first or second at the major cricket
grounds in South Africa:
Batting
Batting
first
second
Wanderers, Johannesburg
17
21
38
Supersport Park, Centurion
18
23
41
St. George’s Park, Port Elizabeth
17
15
32
Newlands, Cape Town
24
11
35
Chevrolet Park, Bloemfontein
10
13
23
Kingsmead, Durban
17
14
31
Buffalo Park, East London
9
10
19
112
107
219
TOTAL
TOTAL
(Source: www.espncricinfo.com (ODI match statistics sourced 19 December 2011)
a) Calculate the probability of a team winning if they bat first at Kingsmead. Express
your answer as a percentage.
(3)
b) Overall in South Africa, does it matter whether a team bats first or second? Show
calculations to prove your answer.
(3)
c) There is one ground in South Africa where it is important to make the right choice.
Which ground is that? Give a reason for your answer.
(2)
[8]
Bridge House College
Grade 12 Mathematical Literacy Paper 2
September 2016
Page 12 of 14
Question 5: Data Handling [37]
Mr Smith of Sunny High School is the educator in charge of the English Olympiad.
He finds that the number of girls who enter the first round of the Olympiad is three times the
number of boys who enter.
TABLE 1: Number of boys and girls entering the first round of the English Olympiad
Number of boys
3
50
B
Number of girls
A
150
180
5.1)
Use the given information to determine the missing values A and B in TABLE 1.
5.2)
Suppose 2 550 boys entered the first round of the Olympiad. Calculate the total
number of learners who entered for the first round of the Olympiad.
5.3)
(4)
(3)
Sally and Sam wrote some Olympiad practice tests at school. Their marks, in
percentages, are given in the table below.
TABLE 2: Percentage scored in practice tests
Sally
48
48
48
53
58
62
70
72
80
Sam
36
42
48
58
60
61
62
76
86
86
a) Sam’s median mark is 60%. Determine Sally’s median mark.
(2)
b) Sally’s mean mark is 62,5%. Calculate Sam’s mean mark.
(3)
c) Calculate the interquartile range of Sally’s marks.
(4)
d) Sally stated that she did better in her practice tests than Sam. Give two
reasons to support Sally’s claim.
Bridge House College
Grade 12 Mathematical Literacy Paper 2
(4)
September 2016
Page 13 of 14
5.4)
A National Youth Risk Behaviour Survey was conducted amongst students from
various high schools in South Africa.
The bar-of-pie chart below shows information on the number of students surveyed
who were classified as being underweight, normal weight, overweight, or obese.
918
1468
8
6376
390
a) How many students make up this survey?
(2)
b) What percentage of students have a weight status that is less than normal
weight?
(2)
c) Give an example of how schools can assist with students to maintain a normal
weight.
(2)
d) What method of measurement could the South African Medical Research Council have
used to determine the students’ weight status?
Bridge House College
Grade 12 Mathematical Literacy Paper 2
(2)
September 2016
Page 14 of 14
5.5)
The graph below illustrates the monthly bookings of Malong Caravan Park during
2014.
a) Why do you think the caravan park’s bookings for December is greater than those
for the month of February?
(2)
b) Calculate the total number of bookings made by pensioners for the first three
months of the year.
(2)
c) The cost per night at Malong Caravan Park for a site is R150. Pensioners get a 40%
discount. Use calculations to determine whether the Park received more money
from pensioner bookings or non-pensioner bookings in June.
(5)
[37]
TOTAL FOR THIS PAPER : 150
Bridge House College
Grade 12 Mathematical Literacy Paper 2
September 2016