St John s College UPPER V Mathematical Literacy Paper II - Applications July 2008 Time: 3 hours Examiner: BT Marks: 150 Moderator: DG Read the following instructions and information carefully: 1. This question paper consists of 11 pages and a Candidate Answer Booklet. There are 6 questions in the paper. Please check that your paper is complete. 2. Answer all questions. Questions 1c) ii), Question 2, Question 5b) & c) and Question 6 must be answered in the Candidate Answer Booklet. All other questions must be answered on the sheets provided. 3. The Candidate Answer Booklet must be handed in together with your answer scripts. 4. Start each question on a new page. 5. Number your answers clearly and exactly as the questions are numbered in the question paper. 6. You may use an approved non-programmable, and non-graphics calculator. 7. Where necessary, answers must be rounded off to two decimal digits, unless otherwise stated. 8. It is in your interests to show all your working details, to write legibly and to present your work neatly. 9. Diagrams are not drawn to scale unless this is stated in the diagram.
QUESTION 1 (25 MARKS) The South African textile industry has been facing extremely difficult conditions. Because clothing produced in some overseas countries can be sold for a cheaper price than clothing produced in South Africa, some local textile mills and clothing manufacturers have had to close down and their staff members have been retrenched. The number of jobs in the industry declined from 70 500 in 2003 to just below 50 500 in 2006. In order to revitalise the textile industry in South Africa, the government has introduced a limit on the number of clothing items that are allowed into South Africa (see the table below). Knitted clothing (jerseys, sweaters) Woven clothing (shirts, trousers, blouses, skirts) 2006 2007 2008 113 496 000 74 907 000 81 666 000 140 395 000 101 084 000 109 931 000 a) One of the responsibilities of government is to promote responsible trade. i) Calculate the percentage decline in the number of workers employed in the textile industry in South Africa from 2003 to 2006. (3) ii) iii) Calculate the percentage decrease in the number of woven clothing items allowed into South Africa from 2006 to 2007. (3) Is the decision to decrease the number of woven clothing items allowed into South Africa justified? Give a reason for your answer. (2) b) In 2008 the government intends allowing more clothing imports into South Africa than in 2007. i) What is the difference between the number of knitted items allowed in 2007 and in 2008? (1) ii) If the government decides to increase the number of knitted items by that amount each year, what will be the first year when the number of imported knitted items will be more that the number of knitted items imported in 2006? (4) Phumzile Ngcobo was employed in the textile industry and in May 2007 she was one of the unfortunate workers to be retrenched. Phumzile noticed that the government is encouraging small business entrepreneurs to venture into the clothing industry, so she put her retrenchment package into setting up a business sewing T-shirts. She bought 12 industrial sewing machines and now rents a small workshop. Page 2 of 11
QUESTION 1 (cont.) c) The table below shows the number of workers needed and the time taken to sew 300 T-shirts. Number of workers 1 2 3 4 6 10 12 Time taken in hours 300 150 100 75 50 30 25 i) From the table explain which is the independent and which is the dependent variable. (2) ii) iii) Use the axes provided in the answer booklet to draw a graph to illustrate the data shown in this table. Label your axes and graph appropriately. (6) Write down a formula that shows the relationship between the number of workers needed and the time taken to sew 300 T-shirts. (2) iv) If it takes one worker one hour to sew a T-shirt, how long will it take 6 workers to sew 1 800 T-shirts? (2) QUESTION 2 (33 MARKS) In February 2008 Phumzile s T-shirt business was doing very well and she decided to employ a manager to oversee the workers and to take on general management and administration. On 1 March 2008 Patsy Smith started work. Patsy asked Phumzile to explain to her how her tax would be calculated and how she could plan for taxes over the year. The South African Revenue Services (SARS) is responsible for collecting taxes from taxpayers on behalf of the government. As the government needs money on an ongoing basis to fund services such as education, health, security and welfare, every employer must deduct PAYE (pay as you earn) from their employee s salaries and pay it over to SARS every month. Once a year every employee who earns more than R60 000 per annum has to complete a tax form listing their income received and their allowable deductions for the tax year starting on 1 March of one year and ending on the last day of February the following year. The 2009 assessment year began on 1 March 2008 and will end on 28 February 2009. At the end of a tax year an employer has to give each employee an IRP5 certificate, which lists the total employment income earned as well as the total PAYE taxes that were deducted and paid to SARS. Patsy Smith earns R10 560 per month. From her salary she pays a monthly contribution to a pension fund and to a medical aid scheme and Phumzile deducts employee tax in the form of PAYE. Page 3 of 11
QUESTION 2 (cont.) Below is a copy of Patsy s payslip. Phumzile T-shirts cc Identity number 7911120041085 Marital status single Pay date 31 March 2008 Birth date 12 November 1979 Bank BCTB Employee Patsy Smith Tax reference number 192837465 Bank account number 9638421357 Staff number 099-0015 EARNINGS AMOUNT DEDUCTIONS AMOUNT Basic salary 10560,00 Pension (7,5% of monthly salary) 792,00 Medical Aid Contribution 495,00 Pay-as-you-earn (PAYE) 1918,77 Unemployment fund 21,20 TOTAL EARNINGS 10560,00 TOTAL DEDUCTIONS NETT PAY DUE Phumzile used a table (attached at the back of this exam) to show Patsy how she can calculate her tax for the 2009 tax year. a) Patsy has R50 000 invested in a special savings account that gives her an annual interest rate of 8,2% compounded monthly. She deposited this money on 1 March 2008. Use the formula: A= P(1 + i) n where A = the amount payable at the end of the period P = the amount invested i = the interest rate per interest period n = the number of investment periods i) Calculate i, the monthly interest rate that Patsy earns on her investment. (2) ii) Use the formula given above to calculate how much Patsy s investment will be worth at the end of February 2009. (4) iii) How much interest will Patsy have earned over the year? (2) iv) Fill in the interest next to the heading Dividends from South African Banks on the table in the Candidate Answer Booklet. (1) b) Patsy earns R10 560,00 per month before deductions, and in December she receives a bonus of a 13 th cheque. This 13 th cheque consists of one month s salary, but without pension fund and medical aid having been deducted. Page 4 of 11
QUESTION 2 (cont.) i) On the table fill in: 1. her annual salary before deductions (2) 2. her bonus (1) ii) Calculate SUB-TOTAL A and fill in the amount on the table. (2) c) Before the final tax payable is calculated, all medical aid contributions that are less than R500 per month and all pension fund contributions are deducted from the income received. Fill in the following on the table, showing all calculations: i) Patsy s annual allowable medical aid contributions (3) ii) Patsy s annual pension fund contributions (2) iii) SUB-TOTAL B (2) iv) Patsy s taxable income (2) d) South Africa has a progressive income tax system, meaning that the more you earn the more you pay. The table below shows the tax rates for 2008/2009 year. TAX TABLES 2008/2009 TAXABLE INCOME (in Rands) RATES OF TAX 0-122 000 18% of each R 122 001-195 000 R21 960 + 25% of the amount over 122 000 195 001-270 000 R40 210 + 30% of the amount over 195 000 270 001-380 000 R62 710 + 35% of the amount over 270 000 380 001-490 000 R101 210 + 38% of the amount over 380 000 490 001 and above R143 010 + 40% of the amount over 490 000 Fill the following in on the table and show all working where possible: i) SUB-TOTAL C, the total tax payable on Patsy s taxable income. (Use the table above to calculate this amount and show all working.) (4) ii) SUB-TOTAL D, the total PAYE contributions that would have been paid by Patsy s employers over the year, assuming that all the information on Patsy s payslip for March remains the same throughout the 2008/9 tax year. (4) iii) The total amount either payable by Patsy, or owed to her by SARS. (2) Page 5 of 11
QUESTION 3 (15 MARKS) Having seen how much of her salary goes towards government spending, Patsy wanted to know more about how the money is spent. She found an article entitled, Education and Health Still Being Neglected. The article included the graph given below. 180 GOVERNMENT SPENDING IN BILLIONS OF RAND 171 160 146 Amount (Billions of rand) 140 120 100 80 60 40 123 111 44 48 26 29 32 54 36 62 Health Education Total 20 0 1 2 3 4 Financial Year (Index year: 2003/2004 ~ 1) Use the graph to answer the following questions: a) Which financial year does the digit 3 on the horizontal axis represent? (2) b) Calculate the percentage of the total expenditure that was spent on education i) in the 2003/2004 financial year (3) ii) in the 2006/2007 financial year (4) c) What can you deduce from your answers to b) above? (2) d) Do you agree with the headline, Education and health still being neglected? Explain fully how you reached your answer. (4) Page 6 of 11
QUESTION 4 (11 MARKS) Part of Patsy s responsibilities at Phumzile T-Shirts is to pay bills such as electricity and water. In May 2008 Patsy received a notice from the local Municipality regarding water tariff increases effective from July 2008. The following table was included with the notice: Water tariffs for small business premises installed with a water meter Kilolitres (Kl) 2007/2008 2008/2009 per connection Tariff Tariff per month (R/ Kl) (R/ Kl) 0-6 FREE R2,20 7-10 R4,40 R4,40 11-15 R5,90 R5,90 16-20 R7,40 R7,86 21-30 R8,80 R9,43 31-40 R8,80 R9,52 41+ R10,40 R11,36 Patsy must do a report to show Phumzile how these tariff increases will affect water costs for the business. Except for the month of December, the business uses between 28 and 37 Kl of water in any given month. Use the table to answer the following questions: a) Calculate the percentage increase in water tariff from 2007/2008 to 2008/2009 in the 21 30 Kl bracket (2) b) Patsy noticed that in February 2008, the business used 29 Kl of water. The cost for the month was calculated as follows: 29 Kl = 6 Kl + 4 Kl + 5 Kl + 5 Kl + 9 Kl Cost (in Rand) = (6 Kl R0,00) + (4 Kl R4,40) + (5 Kl R5,90) + (5 Kl R7,40) + (9 Kl R8,80) i) Calculate the cost of water for February 2008. (2) ii) Assuming that the same amount of water is used in February 2009, what will be the amount payable then? Show full working. (3) iii) What percentage increase is there in the amount payable in February 2009 when compared with February 2008? (2) iv) How does this compare with the percentage increase in the tariff for the 21 30 Kl bracket? Use the answer you obtained in a) i) above to explain any differences fully. (2) Page 7 of 11
QUESTION 5 (18 MARKS) Phumzile sets Patsy the task of finding the number of T-shirts that the business should produce each month in order to make a maximum profit. a) The business purchases two different T-shirt materials. Material X costs R20 per running metre and material Y costs R15 per running metre. The maximum that the business can spend on material in any month is R30 000. Write a constraint to express the monthly costs for the material. (4) The business has orders for twice as many T-shirts made from material X as they do for material Y. However, the machines cannot cope with more than 2 000 T-shirts per month. The constraint for this is: X + 2Y 2 000. b) Sketch the graphs of the two constraints on the set of axes given in the answer booklet. (6) c) On your graph clearly indicate the feasible region for the profit for the business. (2) d) The profit on T-shirts made from material X is R30, and the profit on T-shirts made from material Y is R38. i) Write an equation to express the total profit P. (3) iii) Find the number of T-shirts made from each material that will give the maximum profit. (3) Page 8 of 11
QUESTION 6 (48 MARKS) Patsy suggested to Phumzile that they paint the interior of the shop. Before Phumzile gives the go-ahead she wants to know exactly what the costs will be. Below is a floor plan of the workshop. The walls are all 3m high to the ceiling. N 8m 12 m Patsy is investigating painting the bottom half of the walls in a blue gloss enamel paint because of wearand-tear. The top half of the walls and the ceiling will be painted in a white PVA. Below are plans of the four walls viewed from inside the workshop showing windows, the door and a notice board. 0,5m Eastern wall Door Window 1,5m 0,5m Northern wall 1,5m Notice Board 6m 1,5m 900mm 0,5m 0,5m Window 0,5m 1,5m Southern wall Window 2,5m Western wall 1,5m Page 9 of 11
QUESTION 6 (cont.) Use the given plans (which are not drawn to scale) and the table in the Candidate Answer Booklet to answer the questions that follow. On the sheet In the Answer Booklet containing the table there is a column in which full working should be shown. a) Calculate the area of ceiling to be painted. (1) b) Consider the plan of the eastern wall. i) Calculate the area of the wall that needs painting (that is, excluding the notice board). (3) ii) Calculate the area to be painted in blue gloss enamel. Fill this in the table. (1) iii) Calculate the area to be painted in white PVA and fill this in the table. (1) c) Consider the western wall. i) Calculate the area that is to be painted in blue gloss enamel. (3) ii) Calculate the area that is to be painted in white PVA. (3) d) Consider the southern wall. i) What area is to be painted in blue gloss enamel? (1) ii) Show that the area to be painted in white PVA is 15m 2. (2) e) Consider the northern wall. i) State the area to be painted in blue gloss enamel. (3) ii) Calculate the area to be painted in white PVA. (3) f) Use the table to total up to the nearest square metre how much area is to be painted using each of ceiling paint, white PVA and blue gloss enamel. (3) Page 10 of 11
QUESTION 6 (cont.) g) Patsy was given a price list for different paints in the table below. Brand of paint CEILING WHITE Coverage Tin size (m 2 /l) Cost (without VAT) A 10l 8 R189,99 B 20l 11 R419,99 WALL PVA WHITE Brand of Coverage Cost (without Tin size paint (m 2 /l) VAT) C 5l 12 R269,99 D 10l 12 R379,00 E 20l 12 R529,99 Brand of paint WALL PVA ASS. COLOURS Coverage Cost (without Tin size (m 2 /l) VAT) F 5l 12 R279,99 WALL GLOSS ENAMEL ASS. COLOURS Coverage Tin size (m 2 /l) Brand of paint Cost (without VAT) G 5l 6 R189,00 H 10l 6 R389,00 Use the table to answer the following questions and for this exercise ignore the quality of the different paint products. Show all calculations. i) Which enamel paint is more cost effective? (2) ii) Which PVA would be the most cost effective for the job? (3) iii) Show all calculations to find out which ceiling paint is more cost effective. (5) h) Complete the table to find out the total cost for painting the workshop. (14) Page 11 of 11