MATHEMATICAL LITERACY

Transcription

1 Directorate Curriculum: FET SCHOOLS GRADE 12 TEST 1, 2014 MATHEMATICAL LITERACY MARKS: 70 Time: 2 hours Page 1 of 12

2 Instructions 1. This test consists of 5 questions and 2 annexures 2. Answer ALL the questions 3. Use annexures to answer questions that refer to them 4. Show ALL calculations, where necessary 5. Write neatly and legibly QUESTION 1 Miller s Fire Extinguishers sells a range of fire extinguishers as indicated below. All prices include 14% VAT (Value Added Tax). 1.1 Calculate the price of a 9 kg refillable fire extinguisher without VAT. (3) 1.2 Calculate the percentage profit on a 9 kg refillable fire extinguisher if the cost price (excluding VAT) is R (3) 1.3 The management of Miller s Fire Extinguishers is not satisfied with the quality of the 4,5 kg fire extinguishers. They are looking for new suppliers. Only Fire Extinguishers UK, an international company, manufactures 4,5 kg fire extinguishers. The table below shows the price list for different fire extinguishers at Fire Extinguishers UK. Price List of Fire Extinguishers UK Size Price 21oz 5 2,2lb lb lb lb Page 2 of 12

3 1g = 0,035oz 1kg = 2, 2 lb 1 = R14, Which fire extinguisher size is equivalent to a 4,5 kg fire extinguisher? Justify your choice showing ALL relevant calculations How much is the 4.5kg fire extinguisher at Fire Extinguishers UK? Give the price in South African rands(zar). (3) (3) Fire Extinguishers UK adds 37.5% to the selling price when goods have to be exported to South Africa. This additional amount covers import tax, transport costs and other levies. Determine the amount, in rands, that Miller s Fire extinguisher will pay for a 4.5kg fire extinguisher if they buy it from the UK Miller s Fire Extinguishers sells the 4.5kg fire extinguisher at a percentage profit of 40%. They need to decide on whether to stay with the current local supplier or change to Fire Extinguishers UK. (a) Calculate the difference in profit they will make on a 4.5 kg fire extinguisher if they choose to buy it from Fire Extinguishers UK (5) (b) Should Miller s fire Extinguisher change the current supplier for the 4.5kg fire extinguisher? Justify. (3) [22] QUESTION 2 Income tax is the amount of money one must pay to the South African Revenue Services (SARS) for earning an income. Examples of earnings an individual may receive include remuneration (income from employment) such as salaries, wages, overtime pay, etc. Income tax amount varies from one individual to another depending on the amount earned. The tax table below shows different income tax rates for individuals with different taxable income for 2012/2013. Use the table to answer the questions that follow. 2012/2013 Annual Income Tax Tables Taxable Income (R) Rate of Tax % of each R % of amount over % 0f amount over % of the amount over Page 3 of 12

4 % of the amount over and above % of the amount over Tax Rebates* Primary R Secondary (Persons 65 and older) R Tertiary (Persons 75 and older) R *Rebate is a discount on tax based on some qualifying criteria. E.g. age 2.1 Mr Thomas is a 66-year old pensioner earning a monthly salary of R How much monthly tax rebate does Mr Thomas qualify for? (3) Calculate Mr Thomas s monthly tax (6) [9] QUESTION 3 Esta s Communications Solutions (EC solutions) wants to hire an extra photocopy machine. The company hiring out photocopying machines gave EC solutions the following three options: Option 1: R1 250 per month (unlimited number of copies and service fee is included) Option 2: R500 per month plus R1,20 per copy Option 3: R450 per month plus R1,50 per copy (Service fee of R225 after every 6 months) (Service fee of R250 after every 6 months) 3.1 Calculate the annual hiring cost for Option The manageress at EC Solutions makes a statement that Option 1 will be the cheapest option if they hire the machine for a year. The predicted average number of copies per month is 400. Verify whether her statement is valid. You may use the following structure: Annual cost of Option 1: Annual costs of Option 2: Annual costs of Option 3: Conclusion: (8) Page 4 of 12

5 3.3 The graphs on ANNEXURE 1 show the cost of each of the THREE options against the number of copies made. Use the graphs on the annexure to answer the following questions Which of the three options is represented by : (a) Graph A (b) Graph B (c) Graph C (3) Which option will be the cheapest if more than 600 copies are made each month? 3.4 Name one advantage of the graph, compared to a table of values, as a tool to investigate the cost of hiring for the 3 option. [17] QUESTION 4 The box-and-whisker plots below represent the September 2013 learner performance of boys and girls in a grade 12 Mathematical Literacy class. GIRLS BOYS Examination Marks as Percentage 4.1 Estimate the median percentage mark for the girls. (1) 4.2 Which of the two groups (boys or girls) had the better exam performance? Explain your choice. 4.3 From which group is the top learner? (1) 4.4 Estimate the interquartile range of the boys. (3) boys wrote the exam. How many of the boys scored below 70 marks. (3) [10] Page 5 of 12

6 QUESTION 5 Doctors and nurses use growth charts to monitor growth and development of babies and children. Use the growth chart of baby girls (birth to 36 months) on ANNEXURE 2 to answer the questions that follow: 5.1 An 18 month old girl length for-age ratio is on the 25 th percentile and her weight-forage ratio is on the 50 th percentile. Estimate the length in cm and the weight in kg of the baby girl. (4) 5.2 A girls length is 26 inches. Convert the girl s height to cm 5.3 Explain what it means if a 21 month old girl has a weight-for-age ratio that lies on the 50 th percentile. 5.4 The height and weight of girl twins Lona and Lulu were measured at a nearby clinic on their second birthday which falls on The results of the measurements were recorded on the growth chart (ANNEXURE 2) Write down the date of birth of the girl twins (1) Calculate the difference in height between Lona and Lulu (3) One of the girls was ill for a month before the day of the visit to the clinic. Which one of the two girls? Justify your choice. [12] TOTAL: 70 Marks Page 6 of 12

7 Cost in Rand ANNEXURE Monthly Hiring cost of a Photocopy Machine C B A Number of copies Page 7 of 12

8 ANNEXURE 2: Lona (X) and Lulu(*) Lona = X Lulu = * KEY Page 8 of 12

9 Directorate Curriculum: FET SCHOOLS GRADE 12 TEST 1, 2014 MEMORANDUM MATHEMATICAL LITERACY MARKS: 70 Page 9 of 12

10 QUESTION 1[22] Question Solution Description Marks 1.1 = 379 1,14 OR = R332,46 1 M divide 1 A 1,14 1 A solution (3) ,46 229,28 = 100% 229,28 103,18 = 100% 229,28 = 45% kg x (2.2lb/1kg) = 9.9lb Therefore, the 9.9lb fire extinguisher is equivalent to the 4,5kg extinguisher = R14, 83 Therefore = 14, = R152,01 R152, = ,375 OR 152,00 1,375 = 14,09375 = 14, = R Cost of 4.5kg fire extinguisher in SA = = R192,14 Profit = R269 R = R76,86 If they buy from UK, new profit will be: R269,00 R209,00 = R60 Difference in profit = R76,86 R60 = R16, They should keep the current supplier because if they move they will make less profit. OR They should change to the new supplier and lose R16,86 on profit but keep customers satisfied with the quality of the fire extinguisher. 1 M 1 S difference 1 CA (3) 2 conversion 1 choice (3) 1 M multiply 1 CA cost in Rand 1 M percentage increase 1 A 1 dividing 1 for cost price 1 profit 1 new profit 1 answer (6) 1 advise 2 valid justification (3) [22] Page 10 of 12

11 QUESTION 2[9] Questio n Annual tax rebate = R Monthly tax rebate = R18830/12 = R1569,17 Solution Description Mar ks Mr Thomas s annual salary = R27350 x 12 = R His annual tax = R % of (R R258750) - Rebate = R R20835 R18830 = R55101 His monthly tax = R55101/12 = R4591,75 1 correct rebate 1 dividing by 12 1 answer (3) 1 annual salary 1 tax bracket 1 substitution 1 annual tax 1 dividing by 12 1 answer (6) [9] QUESTION 3[17] Question Solution Description Marks 3.1 = = R M multiply A annual cost 3.2 Option 1: R Option 2 = (500 12) + 1, (225 2) = = 6930 Option 3= (450 12) + 1, (250 2) = = S substitute 1 A 1 S substitute 1 S simplify 1 A 2 conclusion Conclusion: her statement is NOT valid since option 3 is the cheapest of the three a)graph A = Option 3 1 for each correct answer b)graph B = Option 2 c)graph C = Option 1 (3) Option 1 2 Answer 3.4 One can easily read off the graph at which 2 for any valid statement stage which option is more economical. [17] (8) Page 11 of 12

12 QUESTION 4[10] Question Solution Description Marks answer, accept 54,56 & 57 (1) 4.2 Girls. Higher median or valid reason? 1 answer 1 any valid reason 4.3 Boys 1 Answer (1) 4.4 IQR = Q 3 - Q 1 = = Q 3 = 70 = 75% of 16 M = 12 scored below 70 marks 1 A values 1 subtraction 1 answer (3) 1 identifying Q 3 1 calculating 75% of 16 1 answer (3) [10] QUESTION 5[12] Question Solution Description Marks 5.1 Length = 79 cm 1 Answer Weight = 11 kg 1 Answer inches = 66 cm Age = 5,5 months 1 length in cm 1 age 5.3 It means 50% of girls that are 21 month old 2 answer have the same weight as the girl answer (1) Lulu = 88cm Lona = 86cm 1 reading both heights frm graph 1 subtraction Difference = 88cm 86cm = 2cm Lulu was ill. This can be deduced from the low weight of the girl compared to her twin sister. TOTAL: 70 1 answer (3) 1 choice 1 valid justification [12] Page 12 of 12