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MATHEMATICAL LITERACY

(Second Paper) NQF LEVEL 3

NOVEMBER 2010

(10401023)

24 November (Y-Paper)

13:00 – 16:00

Drawing instruments including rulers, pairs of compasses and protractors may be

used.

Calculators may be used.

This question paper consists of 8 pages and 2 answer sheets.

NATIONAL CERTIFICATE (VOCATIONAL)

(10401023) -2- NC1640(E)(N24)V

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TIME: 3 HOURS

MARKS: 100

_______________________________________________________________________

INSTRUCTIONS AND INFORMATION

1.

2.

3.

4.

5.

6.

7.

Answer ALL the questions.

Read ALL the questions carefully.

Number the answers according to the numbering system used in this question paper.

Clearly show ALL calculations, diagrams, graphs, et cetera you have used in

determining the answers.

Diagrams are NOT necessarily drawn to scale.

Write your examination number and centre number on the attached ANSWER

SHEET and hand the completed ANSWER SHEET in with the ANSWER BOOK.

Write neatly and legibly.

(10401023) -3- NC1640(E)(N24)V

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QUESTION 1

1.1 The overtime worked by a worker was recorded for a month. The data below shows

the hours the worker worked overtime:

3 2,5 4 3 1

2 2,5 3,5 4 1,5

3 2 4 3 2

1.1.1 Determine the median. (3)

1.1.2 Determine the mean/average hours that the worker worked overtime. (4)

1.1.3 If the worker is paid R65,00/hour for overtime, what did she earn for

working overtime for that month?

(3)

1.2 The prize money for a lottery stands at R3 million. If there is more than one winner,

the winners will share the prize money equally.

The table below shows the equal share (in thousands of rand) that each winner will

receive if there is more than one winner.

Number of winners 1 2 4 5 8 (c) 20

Equal share

(in R1 000s) 3 000 (a) 750 (b) 375 300 150

Formula: 0001winners of No.

money PrizeShare Equal

×

=

This formula was developed by the competition coordinator to share the prize money

equally in thousands of rands.

1.2.1 Use the formula to calculate the values of (a), (b) and (c). (8)

1.2.2 Complete: If the number of winners increase, the … (2)

1.2.3 Is the relationship an example of a DIRECT or an INVERSE proportion?

Choose the correct answer.

(2)

(10401023) -4- NC1640(E)(N24)V

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1.3 A consultant uses the table below to assist clients in calculating monthly instalments

on funeral cover that suits their needs.

INSURED MINIMUM COVER

MAXIMUM COVER

MONTHLY PREMIUM

Life insured up to the age of 59

R5 000 R15 000 R1,25 per R1 000

Life insured age 60 – 64

R5 000 R15 000 R3,95 per R1 000

Spouse up to the age of 59

R5 000 R15 000 R1,25 per R1 000

Spouse age 60 – 64

R5 000 R15 000 R3,95 per R1 000

Children up to the age of 24

R1 000 R5 000 R1,10 per R1 000

Parents/In-laws, extra spouses, extended family members - Up to the age of 64 - Age 65 – 69 - Age 70 – 74

R1 000 R1 000 R1 000

R8 000 R8 000 R8 000

Per R1 000 per person R3,40 R11,90 R16,80

Show how the consultant will calculate the monthly instalment of the following

clients:

1.3.1 A man and his spouse at the age of 38 and 33 respectively for minimum

cover

(3)

1.3.2 A woman with the information given in the table below for maximum

cover:

Persons to be

insured

Their ages in

years

Herself 34

Her spouse 41

Her son 19

Her daughter 16

Her father 60

Her mother-in-law 66

(8)

1.4

Phuti runs a small bakery from home. She bakes muffins and sells them at a college.

She keeps her sugar in a rectangular tin with the following dimensions:

Length: 250 mm

Breadth: 190 mm

Height: 60 mm

1.4.1 Calculate the volume of the sugar in the tin in cm3. (3)

1.4.2 Determine the mass of the sugar in the tin if 1,12 g = 1 cm3. (2)

1.4.3 A recipe for baking 12 muffins requires 33,6 g of sugar. Determine the

number of muffins you can bake with the sugar in the tin.

(2)

1.4.4 Determine the number of tins required to bake 600 muffins. (3)

[43]

(10401023) -5- NC1640(E)(N24)V

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QUESTION 2

2.1 The Student Representative Council (SRC) receives a portion of the student

registration fees every year. Every student will contribute to the SRC fund which is

normally used for various student activities.

The table below shows two types of students enrolled at a college in 2010.

Study this table carefully and answer the questions that follow.

Type of student

Number of students enrolled in January 2010

Contribution to SRC Fund at enrolment

Fees paid in a year

Number of enrolment periods (When?)

Year course 660 R50,00 Once off Once (In January)

Semester course

350 R25,00 Two payments

Twice (In January and in July)

2.1.1 How much will a semester student contribute to the SRC fund per year? (2)

2.1.2 Calculate the income of the SRC fund for January 2010. (4)

2.1.3 Calculate the total income for the whole year if only 328 students enrolled

for the second semester.

(4)

2.2 The table below shows how the SRC track their annual budget and how the money

was spent up to the end of the second quarter.

Expenses: First Quarter Expenses: Second Quarter

ACTIVITY BUDGET Jan Feb Mar Apr May Jun TOTAL

Educational Tours

R50 000 R12 000 R12 000

R12 000

(a)

Petty cash R3 000 R300 R300 R300 R300 R300 R1 500

Cultural Activities

R10 000 R5 000 R5 000

Sports Trips R50 000 R10 000 (b) R11 000 R30 000

Cultural Day R17 000 R0

Valentine's Day

R10 000 R11 000 R11 000

Administration R10 000 R500 R500 R500 R500 R500 (c)

Other R2 000 R0

TOTAL (d) TOTAL EXPENSES (e)

SURPLUS/DEFICIT (f)

2.2.1 Calculate the value of the following:

(a) Expenditure on educational tours (2)

(b) Sports trips for March (2)

(10401023) -6- NC1640(E)(N24)V

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(c) Expenditure on administration (2)

(d) Total budget (2)

(e) Total expenditure (2)

(f) Surplus or deficit (Surplus = Budgeted – Expenses) (2)

2.2.2 In which TWO months were the expenses the lowest and what could be

the reasons for it?

(3)

2.2.3 Evaluate if the SRC will (under-spend/break even/over-spend) at the end

of the year. Justify your choice.

(2)

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QUESTION 3

Siphiwe sells products for an insurance company and she earns commission for every new

client. The table below shows what her total commission would be for the number of clients to

whom she sells the products.

Number of clients (x) 5 10 15 (a) 26 (b) 40

Commission earned (R) (y) 525 1 050 1 575 2 100 (c) 3 150 (d)

3.1 What is the independent variable in this table? (2)

3.2 How much commission (R) does Siphiwe earn per client? (2)

3.3 Write down a formula that can be used to calculate the commission. (2)

3.4 Calculate the values of (a), (b), (c) and (d). (8)

3.5 Use the completed table to plot a graph on ANSWER SHEET 1 (attached). (5)

3.6 After Siphiwe reached her target of 50 clients, the company doubled her commission

for every new client.

Calculate the total commission that she will earn if she manages to sell products

to 58 clients in one month.

(5)

[24]

(10401023) -7- NC1640(E)(N24)V

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QUESTION 4

The stacked bar graph below shows the causes of death of both males and females in homicide

cases in one particular year. At least 18 000 people were killed in that year. A police officer

needs to further analyse the data.

Study the graph and answer the questions that follow.

4.1 What percentage of females were killed by fire arms? (2)

4.2 What percentage of males were killed by sharp objects? (2)

4.3 Determine the number of females killed if 10 600 males were killed. (2)

4.4 Determine the number of females killed by fire arms. (2)

4.5 Determine the number of males killed by strangulation. (2)

4.6 More males than females were killed with sharp objects. Is the statement TRUE or

FALSE? Motivate your answer.

(3)

4.7 Fewer males than females were killed by poisoning. Is the statement TRUE or

FALSE? Motivate your answer.

(3)

4.8 Give ONE example that could be represented by 'other' on the graph. (2)

4.9 Give a title for the graph. (2)

4.10 Consider only the information for females to draw a bar graph. Use the attached graph

paper on ANSWER SHEET 2 and submit it with your ANSWER BOOK.

(6)

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(10401023) -8- NC1640(E)(N24)V

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QUESTION 5

The sketch below shows property that need to be renovated and rented to tenants. Section A is

a rectangular lawn with a circular swimming pool. The swimming pool is 1 metre deep and it

has a radius of 1,8 m. Section B is the floor plan of a bachelor flat. Study the sketch and answer

the questions that follow.

5.1 Calculate the area of the swimming pool.

Use the formula: 2πrA = where r = radius and π = 3,14.

(3)

5.2 Determine the cost of replanting the entire lawn at R53,75/m2. (6)

5.3 Calculate the volume of the swimming pool.

Use the formula: hπrV2

= where r = radius, h = height and π = 3,14.

(3)

5.4 Determine the cost to fill the swimming pool with water up to 10 cm from the top at

R6,90 per kilolitre.

HINT: 1 000 cm3

= 1 ℓ.

(7)

5.5 Calculate the area of the veranda. (3)

5.6 Determine the cost to tile the kitchen, lounge and the bathroom at R102,95/m2.

Consider the following: The bath, toilet and basin's total area are 3,2 m2.

(8)

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TOTAL: 100

Bath room 3,6 m

3,6m

2,5 m 2,5 m

Ver

anda

SECTION A SECTION B

4 m 4 m 2,5 m

2 m

5 m

2 m

1

m

3 m

Lawn

Swimming pool

Kitchen Lounge

Bedroom

Bathroom

(10401023) -9- NC1640(E)(N24)V

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ANSWER SHEET 1

Complete and submit with your ANSWER BOOK.

Examination

No

Centre No 9 9 9 9

QUESTION 3.5

0

750

1500

2250

3000

3750

4500

5250

6000

6750

7500

0 5 10 15 20 25 30 35 40 45

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(10401023) -10- NC1640(E)(N24)V

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ANSWER SHEET 2

Complete and submit with your ANSWER BOOK.

Examination

No

Centre No 9 9 9 9

QUESTION 4.10

0

10

20

30

40

50

60

70

80

90

100

Fire arm Sharp Object Strangulation Poisoning Other

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