GRADE 12 - Maths Excellence · Directorate Curriculum: FET SCHOOLS MARKS: 70 Time: 2 hours Page 1...

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Directorate Curriculum: FET SCHOOLS MARKS: 70 Time: 2 hours Page 1 of 13 GRADE 12 TEST 1, 2014 MATHEMATICAL LITERACY

Transcript of GRADE 12 - Maths Excellence · Directorate Curriculum: FET SCHOOLS MARKS: 70 Time: 2 hours Page 1...

Directorate Curriculum: FET SCHOOLS

MARKS: 70

Time: 2 hours

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GRADE 12

TEST 1, 2014

MATHEMATICAL LITERACY

Instructions

1. This test consists of 5 questions and 2 annexures2. Answer ALL the questions3. Use annexures to answer questions that refer to them4. Show ALL calculations, where necessary5. 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 R229.28 (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 UKSize Price21oz £52,2lb £7.855.9lb £8.509.9lb £10.2519.8lb £19.30

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1g = 0,035oz 1kg = 2, 2 lb £1 = R14, 83

1.3.1 Which fire extinguisher size is equivalent to a 4,5 kg fire extinguisher? Justify your choice showing ALL relevant calculations.

(3)

1.3.2 How much is the 4.5kg fire extinguisher at Fire Extinguishers UK? Give the price in South African rands(ZAR).

(3)

1.3.3 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

(2)

1.3.4 Miller’s Fire Extinguishers sells the 4.5kg fire extinguisher at apercentage profit of 40%. They need to decide on whether to stay with thecurrent local supplier or change to Fire Extinguishers UK.

(a) Calculate the difference in profit they will make on a 4.5 kg fireextinguisher 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 includeremuneration (income from employment) such as salaries, wages, overtime pay, etc. Incometax amount varies from one individual to another depending on the amount earned. The taxtable below shows different income tax rates for individuals with different taxable income for2012/2013.

Use the table to answer the questions that follow.

2012/2013 Annual Income Tax Tables

Taxable Income (R) Rate of Tax

0 – 165 600 18% of each R1

165001 – 258 750 29 808 + 25% of amount over 165 600

258 751 – 358 110 53 096 + 30% 0f amount over 258 750

358 111 – 500 940 82 904 + 35% of the amount over 358 110

500 941 – 638 600 132 894 + 38% of the amount over 500 940

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638 601 and above 185 205 + 40% of the amount over 638 600

Tax Rebates*

Primary R12 080

Secondary (Persons 65 and older) R 18 830

Tertiary (Persons 75 and older) R 21 080

*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 R27 350.2.1.1 How much monthly tax rebate does Mr Thomas qualify for? (3)2.1.2 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 (Service fee of R225 after every 6 months)

Option 3: R450 per month plus R1,50 per copy (Service fee of R250 after every 6 months)

3.1 Calculate the annual hiring cost for Option 1. (2)

3.2 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 permonth 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)

3.3 The graphs on ANNEXURE 1 show the cost of each of the THREE options against

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0 10 20 30 40 50 60 7080 90 100Examination Marks as Percentage

GIRLS

BOYS

the number of copies made. Use the graphs on the annexure to answer the following questions.

3.3.1 Which of the three options is represented by :

(a) Graph A(b) Graph B(c) Graph C (3)

3.3.2 Which option will be the cheapest if more than 600 copies are made each month? (2)

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. (2)

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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.

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.

(2)

4.3 From which group is the top learner? (1)

4.4 Estimate the interquartile range of the boys. (3)

4.5 16 boys wrote the exam. How many of the boys scored below 70 marks. (3)[10]

QUESTION 5

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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 25th percentile and her weight-for-age ratio is on the 50th 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 (2)

5.3 Explain what it means if a 21 month old girl has a weight-for-age ratio that lies on the50th percentile.

(2)

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 2006 – 09 -24. The results of the measurements were recorded on the growth chart (ANNEXURE 2).5.4.1 Write down the date of birth of the girl twins (1)

5.4.2 Calculate the difference in height between Lona and Lulu (3)

5.4.3 One of the girls was ill for a month before the day of the visit to the clinic. Which one of thetwo girls? Justify your choice.

(2)

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TOTAL: 70 Marks

ANNEXURE 1

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0 200 400 600 800 10000

500

1000

1500

2000

Monthly Hiring cost of a Photocopy Machine

C

B

A

Number of copies

Cost in Rand

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X

*

*

X

KEYLona = X

Lulu = *

Lona (X) and Lulu(*)

ANNEXURE 2:

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Directorate Curriculum: FET SCHOOLS

MARKS: 70

QUESTION 1[22]

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GRADE 12

TEST 1, 2014

MEMORANDUM

MATHEMATICAL LITERACY

Question Solution Description Marks1.1 = 379 ÷ 1,14 OR 379 ÷ 114 × 100

= R332,461 M divide1 A 1,141 A solution

(3)

1.2

= 28,229

28,22946,332

× 100%

= 28,229

18,103

×100%= 45%

1 M1 S difference1 CA

(3)

1.31.3.1 4.5kg x (2.2lb/1kg) = 9.9lb

Therefore, the 9.9lb fire extinguisher is equivalent to the 4,5kg extinguisher.

2 conversion1 choice (3)

1.3.2 £1 = R14, 83Therefore £10.25 = 14,83 × 10.25

= R152,01≈R152,00

1 M multiply1 CA cost in Rand

(2)

1.3.3 = £10.25 × 1,375 OR 152,00 × 1,375 = £14,09375= £14,09375 × 14.83= R209

1 M percentage increase1 A

(2)

1.3.4 Cost of 4.5kg fire extinguisher in SA =

11.4

×selling price

= R192,14Profit = R269 – R192.14 = R76,86If they buy from UK, new profit will be:R269,00 – R209,00 = R60Difference in profit = R76,86 – R60 = R16,86

1 dividing 1 for 1.41 cost price1 profit

1 new profit1 answer (6)

1.3.5 They should keep the current supplier because if they movethey 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 advise2 valid justification

(3)[22]

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QUESTION 2[9]

Question

Solution Description Marks

2.12.1.1 Annual tax rebate = R18 830

Monthly tax rebate = R18830/12 = R1569,17

1 correct rebate1 dividing by 121 answer (3)

2.1.2 Mr Thomas’s annual salary = R27350 x 12 = R328200His annual tax = R53096 + 30% of (R328200 – R258750) - Rebate = R53096 +R20835 – R18830 = R55101His monthly tax = R55101/12 = R4591,75

1 annual salary1 tax bracket1 substitution1 annual tax1 dividing by 121 answer

(6)

[9]

QUESTION 3[17]

Question

Solution Description Marks

3.1 = 1250 × 12 = R15 000

M multiplyA annual cost

(2)

3.2 Option 1: R15 000 Option 2 = (500×12) + 1,20 × 400 + (225×2) = 6000 + 480 + 450 = 6930 Option 3= (450×12) + 1,50 × 400 + (250×2) = 5400 + 600 + 500 = 6500

Conclusion: her statement is NOT valid since option 3 is the cheapest of the three

1 S substitute

1 A

1 S substitute1 S simplify1 A

2 conclusion(8)

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3.3.1 a)Graph A = Option 3b)Graph B = Option 2c)Graph C = Option 1

1 for each correct answer

(3)

3.3.2 Option 1 2 Answer (2)3.4 One can easily read off the graph at which

stage which option is more economical. 2 for any valid statement (2)

[17]

QUESTION 4[10]

Question

Solution Description Marks

4.1 55 1 answer, accept 54,56 & 57 (1)

4.2 Girls. Higher median or valid reason? 1 answer1 any valid reason (2)

4.3 Boys 1 Answer (1)

4.4 IQR = Q3 - Q1 = 70 – 41 =29

1 A values1 subtraction1 answer (3)

4.5 Q3 = 70= 75% of 16M= 12 scored below 70 marks

1 identifying Q3

1 calculating 75% of 161 answer (3)

[10]

QUESTION 5[12]

Question

Solution Description Marks

5.1 Length = 79 cmWeight = 11 kg

1 Answer1 Answer (2)

5.2 26 inches = 66 cmAge = 5,5 months

1 length in cm1 age

(2)

5.3 It means 50% of girls that are 21 month old 2 answer (2)

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have the same weight as the girl5.45.4.1 2004 – 09 - 24 1 answer (1)5.4.2 Lulu = 88cm

Lona = 86cmDifference = 88cm – 86cm = 2cm

1 reading both heights frm graph1 subtraction1 answer (3)

5.4.3 Lulu was ill. This can be deduced from the low weight of the girl compared to her twin sister.

1 choice1 valid justification (2)

[12]TOTAL: 70

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