Mathematical Literacy Assignment 2 16th May 2013
MARKS: 100
TIME: 2 hours
This question paper consists of 11 pages including two annexure
INSTRUCTIONS AND INFORMATION
1. This question paper consists of FOUR questions. Answer ALL the questions.
2. Answer QUESTON 2.1.3 on the attached ANNEXURE B.
3. Number the answers correctly according to the numbering system used in this question paper.
4. Start EACH question on a NEW page.
5. An approved calculator (non-programmable and non-graphical) may be used, unless stated otherwise.
6. ALL the calculations must be clearly shown.
7. ALL the final answers must be rounded off to TWO decimal places, unless stated otherwise.
8. Units of measurement must be indicated where applicable.
9. Maps and diagrams are NOT necessarily drawn to scale, unless stated otherwise.
10. Write neatly and legibly.
QUESTION 1
1.1
The Nkosi family (two adults and three children) lives in Bontheuwel. They neede to travel by train to Cape Town for a weekend.A portion of the Cape Town Metro Rail train route map is given on ANNEXURE A.
Use the train route map (on ANNEXURE A) to answer the following questions:
1.1.1 In which general direction is Bontheuwel from Cape Town? (2)
1.1.2 Thomas, Mnr. Nkosi’s cousin, from Nyanga plans to visit the family during the Easter holidays. The day, on which he is planning to visit, there will only be evening trains to Phillipi and Lavistown. On which station will you advise him to go to and why?(3)
1.1.3 List the shortest route that the train takes from Bontheuwel to Cape Town, naming ALL the stations the train passes. (3)
1.2
Nkosi’s family intended to buy the following items on their way to Cape Town, just a few minutes after boarding the train:· Airtime at R30 per child and R60 per adult
· Cold drink at R8,00 per can
· Simba at R4,00 per packet
· Mobile phone disposable charger at R5,00
Below is an extract of the departure time for Khayelitsha to Cape Town
FROM KHAYELITSHA-KAPTEINSKLIM-SAREPTA-LANGA TO KAAPSTAD
TRAIN NO / 9428 / 9216 / 9516 / 9438 / 9518 / 9442 / 9522 / 9524
NYANGA / 06:43 / 06:51 / 07:03 / 07:09 / 07:16 / 07:31 / 07:34 / 07:41
HEIDEVELD / 06:47 / 06:55 / 07:07 / 07:13 / 07:19 / 07:35 / 07:38 / 07:45
NETREG / 06:51 / 06:59 / 07:11 / 07:17 / 07:23 / 07:39 / 07:42 / 07:49
BONTHEUWEL / 06:54 / 07:02 / 07:14 / 07:20 / 07:27 / 07:42 / 07:45 / 07:52
LANGA / 06:58 / 07:06 / 07:18 / 07:24 / 07:31 / 07:46 / 07:49 / 07:56
MUTUAL / 07:02 / 07:10 / ... / 07:28 / ... / 07:50 / ... / ...
YSTERPLAAT / 07:08 / 07:16 / ... / 07:34 / ... / 07:56 / ... / ...
PAARDENEILAND / ... / ... / ... / ... / ... / ... / ... / ...
ESPLANADE / 07:13 / 07:21 / ... / 07:39 / ... / 08:02 / ... / ...
PINELANDS / ... / ... / 07:23 / ... / 07:36 / ... / 07:54 / 08:01
NDABENI / ... / ... / 07:25 / ... / 07:38 / ... / 07:56 / 08:03
MAITLAND / ... / ... / 07:28 / ... / 07:41 / ... / 07:59 / 08:06
KOEBERG ROAD / ... / ... / 07:30 / ... / 07:43 / ... / 08:01 / 08:08
SALTRIVER / ... / ... / 07:33 / ... / 07:46 / ... / 08:04 / 08:11
WOODSTOCK / ... / ... / 07:36 / ... / 07:49 / ... / 08:07 / 08:14
KAAPSTAD / 07:18 / 07:26 / 07:40 / 07:44 / 07:53 / 08:06 / 08:11 / 08:18
* Children aged 0 – 5 years travel free if accompanied by an adult with a valid ticket
* Scholars aged 6 – 11 years pay 50% of the full adult fare
* Scholars aged 12 years and older pay full adult fare
# Mr Nkosi’s three children are Rahab (12 years old), Odi (8 years old) and Kgosi (5 years
old).
Study the departure time table given above to answer the following questions:
1.2.1 Explain why there are no times listed for Paardeneiland? (2)
1.2.2 Calculate the distance (rounded off to the nearest km) from Bontheuwel to Cape
Town, 9428 travels at an average speed of 50 km/h. (4)
1.2.3 Rahab and her mother ensured that their mobile phones were fully charged but Mr
Nkosi did not charge his before they left for Cape Town. Odi and Kgosi do not have mobile phones. Rahab requested that her father should not buy her anything, instead she said she will appreciate to have the money that could have been used for her before they get to Cape Town with 12,5% interest.
Mr. Nkosi stated that the total cost for the family on a single trip, including his R6,20 train fare will be more than R300,00. Verify whether or not Mr Nkosi’s statement is correct. All calculations must be shown. (10)
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QUESTION 2
2.1
A car manufacturer uses 5 colours to paint their cars. Each sector of the pie-chart given below represents the percentage of cars with different colours sold per month.If the car manufacturer makes a certain number of cars per month, calculate the following:
2.1.1 The total number of cars made per day. [Assume that the month has 4 weeks and the manufacturer operates from Monday to Friday] (5)
2.1.2 The manufacturer budgets R95160,00 on batteries for the black cars. Do you think that each car will end up with a battery if each battery cost between R180,00 and R200,00?
Justify your answer by means of calculations (4)
2.1.3 Use ANNEXURE B and the information in the pie chart to draw a bar graph representing the percentage of cars with different colours.
NOTE: The number of cars should be used instead of percentages. (6)
2.1.4 What is the probability that a red car and a blue car would NOT be manufactured? Write your answer in the form of a decimal fraction. (2)
2.1.5 Which two car colours form part of the rainbow colours? (2)
2.2
Ms Annah a social worker wants to buy a red car which costs approximately R80000,00. She has R12500,00 of which she intends to use R5000,00 as a deposit and send the remaining balance to her mother. She then approaches Mamamia Finances for a loan. The table below shows the vehicle finance calculations used by Mamamia Finances specifically for Ms Annah.Vehicle Finance Calculations
Price including VAT / R80000,00 / R80000,00 / R80000,00
Deposit / R5000,00 / R5000,00 / R5000,00
Trade In / 0 / 0 / 0
Loan amount / R75000,00 / R75000,00 / R75000,00
Interest / 16,36% / 24,75% / C
Terms / 24 / B / 48
Payment terms / Monthly instalments / Monthly instalments / Monthly instalments
Payment / A / R2599,00 / R2086,88
Didi, Ms Annah’s son, suggest she takes the loan over 36 months, but his mother insists on the 24 months payment plan. They then approach you for advice.
2.2.1 Write down a formula that can be used to calculate the monthly payments to be made by Ms Annah in the form:
Monthly payment = ......
(NOTE: where i is the interest rate and n is the number of monthly instalments) (2)
2.2.2 Calculate the missing values of A, B, and C to give your advice on the better option between the two options that mother and son are disagreeing on. Justify your answer by showing all calculations. (9)
2.2.3 Ms Annah sends the balance to her mom, in China. How much will this amount be in Chinese Yen (CNY)?
Use the exchange rate: R1,00 (ZAR) = ¥ 0,89 (CNY) (3)
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QUESTION 3
3.1
Mr Piet wants to open a clothing shop to sell the new Bafana kit 2012, which is the new South African soccer jersey for the 2012/2013 season. Puma unveiled the new Bafana kit 2012 on November 7, 2011 at the Design Museum in London at the Interpretations of Africa: Football, Art and Design exhibition. The new South Africa jersey 2012/2013 uses Bafana’s traditional colours and also has the Puma logo in green along with a special rainbow graphic.Below is a photo of the new Bafana 2012/2013
strip, made by the South African artits
Hasan en Husain Essop.
Number of jerseys vs the amount (in R)
Mr Piet will be spending a minimum of R2500,00 every month as a fixed cost to run the shop. He hopes to get the jerseys for R75,00 each and can buy a maximum of 120 jerseys in the first month. He can sell the jerseys at a maximum price of R100,00 each.
3.1.1 Give two examples of fixed costs in a business. (2)
3.1.2 An Income graph represents the number of jerseys sold and the selling price thereof. If S is the selling price and N the number of jerseys sold, write down a formula linking S and N. (2)
3.1.3 Name which graph is represented by A, B and C. (3)
3.1.4 Determine the minimum number of jerseys Mr Piet has to sell in order not to make any loss. (Assume that all jerseys were sold.) (2)
3.1.5 Determine the profit when he sells 120 jerseys. (2)
3.2
Mr Piet has 15 grandchildren who love attending the Bafana Bafana matches.The following are the ages of Mr Piet’s grandchildren:
Age (years) / 20 / 7 / 19 / 25 / 16 / 8 / P / 23 / 11 / 14 / 9
Frequency / 2 / 1 / 3 / 1 / 2 / 1 / 1 / 1 / 1 / 1 / 1
3.2.1 If the range of the grand children years is 22
a) Calculate the value of P, Mr Piet’s eldest grand child’s age. (2)
b) Hence calculate the median age. (2)
c) The average years of Mr Piet’s grandchildren (3)
3.2.2 The lower quartile and the upper quartile of Mr Piet’s grandchildren are 11 and 20 years respectively.
a) How many grandchildren are below the lower quartile age? (2)
b) Give two practical reasons why the grandchildren in 3.2.2 a) are not supposed to
go to the stadium. (4)
c) Calculate the inter quartile range. (2)
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QUESTION 4
Jane has decided to build her own hut on a piece of tribal land near Upington.The diameter of the hut is 3,5 m and the height of the walls is 2,4 m. She used one door and two windows of the same size as indicated in her plans. The door is 900 mm wide and
2,1 m high. Each window is 1,2 m wide and 0,8 m high.
M6 BRICK
190 mm
140 mm
390 mm
4.1 Jane marks the circumference of her hut off so that she and her friends can dig the foundation. They use two wooden sticks, one which they hammer into the ground and one tied onto a rope. Help Jane and her friends to calculate the circumference of her hut. (3)
4.2 Calculate the total area of the wall of her hut in metres. (9)
4.3 How many bricks will Jane need to build the wall of her hut? (5)
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NAME: ______
ANNEXURE A
QUESTION 1
NAME: ______
ANNEXURE B
QUESTION 2.1.3
______
(6)
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