Mathematical Literacy P2 Past Paper FEBRUARY/MARCH 2016 - GRADE 12 NATIONAL SENIOR CERTIFICATE
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1. This question paper consists of FIVE questions. Answer ALL the questions.
2.
2.1 Use the ANNEXURES to answer the following questions:
ANNEXURE A for QUESTION 1.1
ANNEXURE B for QUESTION 1.3
ANNEXURE C for QUESTION 3.1
ANNEXURE D for QUESTION 4.1 and QUESTION 4.2
2.2 Answer QUESTION 3.3.3 on the ANSWER SHEET attached.
2.3 Write your centre number and examination number in the spaces on the ANSWER SHEET. Hand in the ANSWER SHEET with your ANSWER BOOK.
3. Number the answers correctly according to the numbering system used in this question paper.
4. Start EACH question on a NEW page.
5. You may use an approved calculator (non-programmable and non-graphical), unless stated otherwise.
6. Show ALL calculations clearly.
7. Round off ALL final answers appropriately according to the given context, unless stated otherwise.
8. Indicate units of measurement, where applicable.
9. Maps and diagrams are NOT drawn to scale, unless stated otherwise.
10. Write neatly and legibly.
QUESTION 1
1.1
| In recent years households in South Africa have experienced a large increase in electricity costs. Mr Chan would like to replace his electric stove with a gas stove. He received quotations from The Alternative Heat Company (Option 1) and TG Gas Stove Specialist (Option 2), as shown in ANNEXURE A. Some information has been omitted |
Use ANNEXURE A to answer the questions that follow.
1.1.1 Calculate the total quotation amount for Option 1. (5)
1.1.2 Mr Chan estimates that the difference in total cost between the two options is less than R1 000,00.
Verify, showing ALL calculations, whether Mr Chan's estimation is valid. (5)
1.1.3 Give ONE reason why Mr Chan may choose the more expensive option. (2)
1.2
A certified gas dealer sells 9 kg gas bottles. These cylindrical bottles are stored outside the shop in a steel cage, as shown below. There is a gap of 10 mm on either side of each gas bottle when placed on the shelf in the steel cage. |
1.2.1 Calculate the maximum number of gas bottles that can fit into ONE steel cage. (2)
1.2.2 A company sells rectangular metal sheets with dimensions 3,4 m by 2,1 m.
Determine, showing ALL calculations, the maximum number of shelves for the steel cage that could be cut from ONE metal sheet. (8)
1.3
| A certified gas dealer who is 48 years old earned a taxable income of R0,742 million during the 2014/2015 tax year and contributed to a registered medical aid scheme for herself and four dependants. She projected that her taxable income would remain the same during the 2015/2016 tax year. |
Study the tax table and the medical aid credits in ANNEXURE B to answer the questions that follow.
1.3.1 Explain the impact of the tax rebate and the medical aid credits on the tax payable. (4)
1.3.2 The dealer calculated that her annual tax due to SARS (South African Revenue Service) would increase by only R150,00 from the 2014/2015 tax year to the 2015/2016 tax year.
Verify, showing ALL calculations, whether her calculation is valid. (8)
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QUESTION 2
2.1
2.1.1 It was calculated that a worker on Wage Rate A lost a total of R10 834,85 in wages during the strike.
(a) Show, with calculations, how this loss was calculated. (6)
(b) Hence, state ONE other negative financial implication of a prolonged strike for a worker. (2)
2.1.2 Verify, showing ALL calculations, whether a worker on Wage Rate H would be able to make up the loss of income (due to the no work, no pay principle) by the end of June 2015, using the improved wage offer, without working overtime or having an extra job. (6)
2.2
Use the graph and the table above to answer the questions that follow.
2.2.1 Interpret the employment change data for the first quarter in 2008. (2)
2.2.2 Identify the year during which the greatest number of job losses occurred AND calculate the total number of jobs lost in that year. (5)
2.2.3 During this period there was only one year during which there was an increase in employment for each quarter for that year.
Identify the year AND calculate the mean quarterly increase in employment numbers for that year.
2.2.4 Determine the number of people employed at the end of March 2013, if 15 million people were employed at the end of December 2013. (3)
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QUESTION 3
3.1
| Pablo, a Mexican student, is studying in the United Kingdom (UK). He plans to meet his family in Las Vegas, USA, to attend a boxing match. He will travel by air from London Heathrow Airport (LHR) to McCarran International Airport (LAS). ANNEXURE C is a diagram showing the seating plan of a Boeing 767-300. An aisle is the passage between rows of seats. |
Use ANNEXURE C to answer the questions that follow.
3.1.1 Determine the total number of Economy Plus seats. (2)
3.1.2 Determine the simplified ratio of the number of Business Class seats to Economy Class seats. (3)
3.1.3 Give a detailed description of the route a passenger in seat 2K will take to walk to a friend in seat 38B if he does not want to disturb other passengers by passing through the rows in the full aircraft. (3)
3.1.4 One of the Business Class passengers ordered coffee.
Determine the probability (as a percentage) that this passenger did NOT have an aisle seat. (3)
3.1.5 Give ONE reason why the price of a First Class aeroplane ticket is much higher than the price of an Economy Class aeroplane ticket. (2)
3.2
Calculate the average speed, in knots, at which the aircraft travelled,
The conversion table and the following formula may be used:
Distance travelled (in km) = average speed (in km/h) x time in hours) (6)
3.3.1 Calculate the missing values A, B and C. (5)
3.3.2 Determine the total income if the WBC sells 800 belts and 1 000 T-shirts.
3.3.3 The straight-line graphs for the total production cost of and total income from selling belts, as well as the income from selling the T-shirts, are drawn on the ANSWER SHEET.
- On the same system of axes provided on the ANSWER SHEET,
draw another line graph that represents the total production cost for manufacturing the T-shirts. (6) - indicate the profit reading made from the manufacture and sale of 600 T-shirts on your graph. (2)
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QUESTION 4
In South Africa there are ordinary schools and special schools. Special schools are for learners with special needs. Ordinary schools are divided into public schools and independent schools.
The government generally funds ordinary schools, and some schools levy school fees. In February 2015 a newspaper published data relating to the number of learners, teachers and schools per province in South Africa. Refer to TABLE 4 and TABLE 5 in ANNEXURED TABLE 4 shows data from 2014 relating to the number of learners, teachers and schools in the ordinary school sector per province. TABLE 5 shows data from 2012 to 2014 relating to the number of learners and teachers in the ordinary school sector per province. |
Use ANNEXURE D to answer the questions that follow.
4.1.1 Showing ALL calculations, identify the province in which approximately 46% of the total number of learners attended independent schools. (3)
4.1.2 A teacher from an ordinary public school is randomly selected to attend a national conference in 2014.
Determine the probability that this teacher will be a teacher from the Eastern Cape
(2)
4.1.3 Calculate the missing value A if the mean number of learners per province in public schools is 1 346 335. (5)
4.1.4 After reading the data in TABLE 4, a teacher stated:
'In South Africa, the teacher-to-learner ratio of independent schools is better than that of public schools.'
Verify, showing ALL calculations, whether this teacher's statement is valid. (6)
4.1.5 The number of learners in ordinary schools increased from 2012 to 2014 Give ONE possible reason for this annual increase. (2)
4.2
| When allocating the amount that will be used for the funding of schools in each province, the Minister of Education allocates R530 per child per month based on the previous year's enrolment data. |
Use ANNEXURE D to answer the questions that follow.
4.2.1 Calculate the funding amount for the 2015/2016 budget that is allocated to the Free State based on the learner enrolment data. (3)
4.2.2 Determine the annual percentage change in the learner enrolment of the province with the highest learner enrolment figure between 2013 and 2014. (3)
4.3
A company would like to build a three-dimensional (3D) model of a 21" century classroom. This must be a scaled model of an actual classroom that they have built at a school. The actual dimensions of the classroom are: length = 7,5 m; width-6,5 m and height = 3 m The 3D scale model of the classroom must fit on a rectangular table top with the following dimensions: length = 1,75 m and width - 1 m Only half of the table top area may be used for the scaled model. |
Verify, showing ALL calculations, whether a scale of 1:8 will be suitable for the scaled model. (5)
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QUESTION 5
5.1
Mrs Dundee, an Australian farmer, has four silos on her farm in which she stores fertiliser, as shown in the photograph and diagram below. The silos are cylindrical with a roof section. Fertiliser is only stored in the cylindrical part of the silos.
|
5.1.1 Calculate the diameter of a silo if the volume of the cylindrical part is 60 m3. (5)
5.1.2 Calculate the total maximum capacity (in gallons) of the four silos. (4)
5.1.3 After fertilising all her main fields, Mrs Dundee wants to use the remaining fertiliser for a wheat field, which is 1.055 acres in size.
The capacity readings of the four silos are as follows:
- Silo 1: 15% full
- Silo 2: 1/4 full
- Silos 3 and 4: empty
Verify, showing ALL calculations, whether she will have enough fertiliser left in her silos for the wheat field if the spread rate is 22,65 kg of fertiliser per acre. (6)
5.2 Table 6 below shows the total monthly rainfall in millimetre for Sydney(Australia) for 2021 to 2015.
Analyse the mean rainfall during the winter months for Sydney AND predict the chance that the mean rainfall for the winter months in 2016 will be higher than 100mm. Show ALL calculations. (7)
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Total: 150
