common paper cape winelands education … sept cape wine… · grade 12 mathematical literacy paper...

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This question paper consists of 12 pages and 3 Annexures.

GRADE 12

ADE 12

2015 SEPTEMBER EXAMINATION

MATHEMATICAL LITERACY

PAPER 2

PAPER 1

COMMON PAPER

CAPE WINELANDS EDUCATION

DISTRICT

Grade 12 Mathematical Literacy Paper 2 September 2015

2

INSTRUCTIONS AND INFORMATION :

1. This question paper consists of FIVE questions. Answer ALL the questions.

2.

Number the answers correctly according to the numbering system used in this question

paper.

3. Start EACH question on a NEW page.

4. You may use an approved calculator (non-programmable and non-graphical), unless

stated otherwise.

5. Show ALL the calculations clearly.

6. Round off ALL final answers appropriately according to the given context, unless stated

otherwise.

7. Indicate units of measurement, where applicable.

8. Write neatly and legibly.


3

QUESTION 1

1.1 The Western Cape is the fourth largest of the nine provinces of South Africa. It has

an land area of 49 983,56 square miles and a population of 5,8 million people.

About two-thirds of the people in the Western Cape live in Cape Town and the

surrounding areas. The rest live in rural parts of the province.

The map of the province is shown below. Use the map and the given information to

answer the following questions.

1.1.1 Write down the name of the MOST eastern town shown on the map. (2)

1.1.2 Use a ruler to measure the direct map distance (as the crow flies) from

Hermanus to Oudtshoorn. Give your answer in millimeter.

(2)

1.1.3 Use the scale on the map to calculate the actual distance in kilometres

between Hermanus and Oudtshoorn.

(4)

1.1.4

Determine the ratio, in simplest form, of people living in Cape Town and

the surrounding areas to those living in rural areas.

(3)

1.1.5 Convert the land area of the Western Cape to the nearest km2 if

1 km = 0, 62139 miles.

(3)

1.1.6 Calculate the population density of the Western Cape in people/km2.

The formula may be used: Population density = area

population

(3)

SOUTH AFRICA N


4

1.2 To transport people to the top of the table mountain TWO cable cars are used.

The following information can be used:

Each of the cable cars can carry 65 people.

Each cable car travels at a maximum speed

of 10 m/second.

It takes the cable car 5 minutes to reach the

top of the mountain.

A cable car goes to the top of the mountain

every 9 minutes.

The maximum weight of passengers a cable car

can carry is 5 200 kg.

1.2.1 You are 338th

in the line that awaits to go to the top of the mountain. At

what time will you reach the top if the first group in the line boards the

cable car at 08:27?

(6)

1.2.2 Calculate the distance in meters travelled by a cable car to transport

people to the top of the mountain.

The formula may be used : Average speed = time

distance

(4)

1.2.3 Calculate the maximum average (mean) weight in kg of the passengers if

the maximum number of passengers is transported in the cable car.

(3)

1.3 Use the following rates for the cable car to answer the question that follows:

Rates for Cable Car: Rates (in South African Rand) are valid from 1 October 2014 to 30 September 2015:

Ticket Type Return One way

Adult 225 115

Child 4 -17 years 110 58

SA senior citizen (Fridays only at ticket office) 95 50

Students (Fridays only at ticket office) 130 68

A family( father, mother, student son and two children, 16 years and 10 years) decide

to visit table mountain on a Friday. They decide to walk up to the top and come down

by cable car so that they can save money.

How much money do they save?

(5)

[35]


5

QUESTION 2

2.1 Monthly petrol prices (in cents per litre) in South Africa for the period 2013 – 2014

are given on the table in ANNEXURE A. On the same annexure a graph shows the

monthly prices in US Dollars per barrel of Brent crude oil in 2014.

(1$ = R12,80)

Use the information on ANNEXURE A to answer the following questions.

2.1.1 Give the price of 93 LRP petrol of the inland region on 6 March 2013 in

South African Rand (ZAR).

(2)

2.1.2 Determine the maximum price of a barrel of Brent crude oil, in Rand, in

February 2014.

(3)

2.1.3 If the maximum price of 95 LRP increased by 14.51% between January

and August 2013, calculate the value of X on the ANNEXURE A.

(3)

2.1.4 Describe any TWO trends between the price of Brent crude oil and that of

95 LRP at the coast, for the period January to August 2014.

(4)

2.2 This is an extract from a newspaper article on 28 August 2014:

‘The price of Brent crude oil in August was down with 8 percent compared to

June.’

Use the information in this extract and ANNEXURE A to answer the following

questions:

2.2.1 Write down (in US dollars):

(a) The maximum price of Brent crude oil in June 2014 (2)

(b) The minimum price of Brent crude oil in August 2014. (2)

2.2.2 Is the newspaper article statement correct?

Justify your answer showing ALL necessary calculations.

(4)


6

2.3 A cylindrical barrel (drum) contains 42 gallons of oil. The diameter of this barrel is

18 inches.

You may use the following information:

1 gallon = 3,78541 litres

1 inch = 2,54 cm

1 ml = 1 cm3

Volume = π × r2 × h, let π = 3,142

Area of a circle = π × r2

Surface area of cylinder with a closed lid and base = (2 × π × r2) + (2 × π × r × h)

2.3.1 Determine the radius of a barrel (drum) in centimetres. (3)

2.3.2 Show, by calculations, that the height of the barrel of oil is 96,82 cm. (5)

2.3.3 Calculate the surface area of this barrel in m2. (5)

[31]

PICTURE OF A BARREL/DRUM:


7

QUESTION 3

3.1 Ms Qongqo works for the Department of Education in the Western Cape. Her salary

advice for the month of June 2015 is given on ANNEXURE B. Use the information

on the salary advice to answer the following questions.

3.1.1 How old in years and months was Ms Qongqo on the pay date? (2)

3.1.2 Express as a percentage the monthly housing allowance to the monthly

repayments that Ms Qongqo makes at Nedbank for her house.

(3)

3.1.3 Show by calculation how the gross salary value of R58 316,08 was

calculated.

(2)

3.2 The amount of monthly tax Ms Qongqo must pay to SARS is represented by P on the

salary advice. Ms Qonqgo can calculate the value of P by using the SARS tax tables

below. Use Ms Qongqo’s salary advice on ANNEXURE B and the SARS income tax

table to answer the following questions.

Income Tax Tables 2014/15

1 March 2014 - 28 February 2015

Taxable Income Tax Rate

R 0 - R 165 600 18% of the taxable income

R 165 601- R 258 750 R 29 808 + (25% of amount above R 165 600)

R 258 751 - R 358 110 R 53 096 + (30% of amount above R 258 750)

R 358 111 - R 500 940 R 82 904 + (35% of amount above R 358 110)

R 500 941 - R 638 600 R 132 894 + (38% of amount above R500 940)

R 638 601 and above R 185 205 + (40% of amount above R638 600)

Primary Rebate (to all taxpayers) R 12 080

Secondary Rebate (Persons 65 and older) R 6 750

Tertiary Rebate (Persons 75 and older) R 2 250

3.2.1 Calculate Ms Qongqo’s annual taxable income and use the formula:

Taxable income = annual gross salary – employee’s pension fund contribution

NB: GEPF refer to Government Employees Pension Fund.

This person contributes 7,5 % of the basic salary towards the GEPF.

(3)


8

3.2.2 Rebate and annual medical tax credits are deducted after income tax

calculations. Use this information and the income tax tables to calculate

the value of P on ANNEXURE B on Ms Qongqo’s salary advice.

(8)

3.2.3 Hence determine:

(a) the value of Q (2)

(b) the value of R,

if Nett Salary = Gross Salary - Deductions

(2)

3.3 The diagram below shows a parking area of a local clinic in Bloekombos near Cape

Town. The clinic wants to pave the area using paving bricks. The type of paving

bricks they want to use is shown alongside the parking area diagram.

The following information can be used:

The dimensions of a paving brick is: 50 × 100 × 200 mm

All the dimensions on the diagram are in mm.

Use the given information to answer the following questions.

3.3.1 Give a reason for the width of the first parking bay to be wider than the

other three parking bays.

(2)

3.3.2 Calculate the total area that needs paving in m2. (4)

3.3.3 Calculate the number of paving bricks per pallet if a pallet covers 10 m2. (3)

3.3.4 Determine the number of pallets required to pave the parking area. (4)

[35]


9

QUESTION 4

4.1 The following bar-of-pie chart below shows the results of a survey conducted on a

sample of 200 students in the age group 18 – 20 years about their chicken

preferences.

Use the chart to answer the following questions.

4.1.1 Show how the value of 31% in the category ‘Other’ was calculated. (2)

4.1.2 Calculate the difference between the number of students who prefer KFC

over Maxi’s.

(4)

4.1.3 Write down TWO possible factors that affect student’s chicken

preferences.

(4)

Nandos

17%

KFC

33%

Chicken Licken

8%

Maxi's

11%

Hungry Lion

14%

Zebros

15%

Joe's chicken

2%

Other

31%

Student's chicken prefences


10

4.2 The tree diagram below shows the outcomes of a special HIV Test (RHT) done on the

same person twice.

Study the tree diagram above and answer the following questions.

4.2.1 Give the probability of obtaining both accurate outcomes after a person

has been tested twice.

(2)

4.2.2 Give the probability that the outcome will be ONE inaccurate and ONE

accurate after a person has been tested twice.

(2)

4.2.3 Presently a certain clinic uses a different kind of HIV test that has an

accuracy rate of 95,1%.

The clinic is considering using the RHT. The senior counsellor remarked

that the difference between the inaccuracate results of the two tests is

insignificant.

(a) After applying the clinics HIV test only once, how many people per

1000 will have an inaccurate result?

(2)

(b) Calculate how many people will have an inaccurate result if the RHT

is applied only once per 1000 people.

(2)

(c) Do you agree with the senior cousellor’s remark? Motivate your

answer.

(2)

[20]

First test result Second test Outcomes

of a person of the same

person

Accurate Accurate; Accurate

99,94% 99,97%

Accurate

99.97%

Inaccurate Accurate; Inaccurate

HIV test 0.03% 0.029991%

Accurate Inaccurate; Accurate

Inaccurate 99.97% 0.029991%

0,03%

Inaccurate Inaccurate; Inaccurate

0.03% 0.000009%


11

QUESTION 5

5.1 Measuring household infrastructure involves the measurement of the four indicators:

Access to running water,

Proper sanitation,

Refuse removal, and

Electricity.

The diamond graph below show the percentage of households with access to proper

sanitation, access to running water, refuse removal and electricity of Cape Winelands

District Municipality and South Africa in 2010/2011.

The number of households in South Africa at that stage was 14 450 161 and in Cape

Winelands is 133 786.

100

56

70

Sanitation

Water

Electricity

Refuse

Infrastructure of Cape Winelands and South Africa

Cape Winelands District South Africa

0


12

5.1.1 Determine the percentage difference of refuse removal between Cape

Winelands and South Africa.

(2)

5.1.2 Calculate the number of households in South Africa in 2011 with access

to running water.

(3)

5.1.3 John argue that the availability of proper sanitation are not more than 1,5

times higher in Cape Winelands than in South Africa. Verify, showing all

calculations, whether John’s statement is correct.

(4)

5.1.4 Calculate the difference in the number of households in South Africa and

Cape Winelands without electricity.

(6)

5.2 Use the annual financial statements of 2011 and 2012 of the Cape Winelands District

Municipality on ANNEXURE C, to answer the following questions:

5.2.1 Calculate the value of A, and motivate why the budgeted amount of 2012

is less than 2011.

(3)

5.2.2 Determine the actual government grants and subsidies amount as a

percentage to the total income in 2012.

(4)

5.2.3 Show how the amount of R -2 383 386 was determined. (2)

5.2.4 Thandi makes the following statement:’

The actual surplus of 2011 was more than the actual surplus of 2012.’

Verify, showing all calculations in determining the missing values B and

C, whether Thandi’s statement is valid.

(5)

[29]

TOTAL: 150


13

ANNEXURE A: QUESTION 2

101

102

103

104

105

106

107

108

109

110

111

112

Jan Feb Mar Apr May Jun Jul Aug

Pry

s p

er

dro

m /

Pri

ce p

er

bar

rel (

in U

S d

olla

rs)

$

Months/Maande

Prys per Brent ru-olie/Price of Brent crude oil: January - August, 2014

Petrol price in cents: 2014 - 2013

Inland Coast

Inland Coast

LRP LRP LRP LRP

2014 93 95 2013 93 95

6 August 2014 1408 1392 7 August 2013 1332 X

2 July 2014 1408 1392 3 July 2013 1300 1286

4 June 2014 1379 1361 5 June 2013 1216 1202

7 May 2014 1401 1383 1 May 2013 1224 1210

2 April 2014 1416 1398 3 April 2013 1297 1283

5 March 2014 1411 1395 6 March 2013 1287 1273

5 February 2014 1375 1359 6 February 2013 1206 1192

1 January 2014 1336 1357 2 January 2013 1165 1151


14

ANNEXURE B: QUESTION 3

Betaalpunt Persalnommer Van & Voorletters Instansie

0001/180455 11001226 Qongqo N West Cape Province Education

Pay Point Persal No. Surname & Initials Organisation

Identiteitsnommer Werksbenaming Aanstellingsdatum

6502116237083 Chief Education Specialist 1990/01/01

Identity number Job Appointment Date

WES-KAAP ONDERWWYS

SALARISADVIES

WESTERN CAPE EDUACTION

SALARY ADVICE

Belastingnommer

Tax number

Belastingstatus

Tax Status

Medical

Tax credits

Medical

Fringe

benefit

Number of

medical

dependants

Pensioen NR

Pension No

Kerf

Notch

22/88000/144 R710.00 R1 014.00 Main

Adult

1 child

97844867 R688 993.00

Verlofkrediete:

Leave Credits:

Gekontroleerde

verlof

Capped leave

Huidige Siklus

Current Cycle

Siekverlof

Sick leave

212 25 30

Betaaldatum

Pay Date

Deposito-

instelling

Deposit

institution

Rekeningnommer

Account Number

Bruto Salaries

Gross Salary

Aftrekkings

Deductions

Netto

Salaris

Nett Salary

2015/06/30 FNB 62076650891 R58 316.08 B C

Vedienste/Earnings Aftrekkings/Deductions

Beskrywing

Description

Bedrag

Amount

Item Beskrywing

Description

Verwysig

Reference

Bedrag

Amount

Basic Salary

Housing

allowance

R57 416.08

R900.00

001 TAX RSA

GEPF: employer

R7 464.09

MEDSHIELD:

Employer 1014

NEDBANK LTD:

housing

Sanlam

PSCBC

22/88000/144

97844867

55010521897

803984572021

433809774

11001226

A

R4 306.21

R2 540.00

R5 550.00

R598.95

R1.11

007

0010

0010

0202

BOODSKAP/MESSAGE

No Work, No Pain. No Pain, No Gain. No Gain, No Pay. Therefore, No work, No Pay

Other information:

FNB : First National Bank

GEPF : Government Employees Pension Fund

PSCBC : Public Services Central Bargaining Committee


15

ANNEXURE C: QUESTION 5.2

CAPE WINELANDS DISTRICT MUNICIPALITY ANNUAL FINANCIAL STATEMENTS FOR THE YEAR 30 JUNE 2012

2011 2012 2012 2011

Budget Budget Revenue Actual Actual

435 000 ‐ Property rates

‐ 442 637

161 000 160 000 Service charges 570 302 1 446 109

‐ ‐ Property rates ‐ penalties imposed and collection ‐ 50 171

148 100 166 500 Rental of facilities and equipment 55 914 117 458

9 000 ‐ Interest received (trading) 24 2 313

5 500 000 8 161 007 Income from agency services 6 910 073 7 500 000

309 496 323 311 434 223 Government grants & subsidies 284 366 851 281 118 083

34 478 789 27 965 792 Contribution from Surplus ‐ ‐

9 988 200 3 654 348 Other income 13 583 002 2 887 351

‐

25 200 000

‐

25 000 000

Gain on disposal of assets and liabilities

Interest received ‐ Investments

‐

24 401 118

‐

25 334 704

385 416 412 A 329 887 284 318 898 826

Expenses

‐103 722 886

‐136 210 672

Employee related Cost

‐139 938 116

‐137 427 173

‐7 071 800 ‐9 596 819 Remuneration to councillors ‐9 335 836 ‐7 310 196

‐10 977 800 ‐13 119 745 Depreciation and amortisation ‐8 318 323 ‐8 113 171

‐7 890 730

‐443 100

‐

‐94 696 768

‐158 910 367

‐11 962 700

‐454 600

‐

‐33 030 655

‐153 065 006

Finance Cost

Debt impairment

Collection cost

Repairs and Maintenance

General expenses

‐10 946 945

‐

‐

‐27 065 656

‐124 776 257

‐10 193 884

‐1 005 180

‐

‐29 937 611

‐132 377 568

‐3 200

‐

‐2 200

‐

Loss on sale of assets

Actuarial gain ‐858 815

‐690 181

‐451 372

‐4 575 322

‐383 716 651 ‐357 442 397 ‐321 930 129 B

9 740

‐

Shortfall on pension fund

Gain or loss on disposal of assets and liabilities

‐

51 422

‐2 643 030

259 644

385 416 412

‐383 716 651

9 740

376 541 870

‐357 442 397

‐

Revenue

Expenses

Other

329 887 284

‐321 930 129

51 422

318 898 826 -331 391 477

‐2 383 386

1 709 501 19 099 473 (Deficit)/ Surplus for the year 8 008 577 C

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