20

2013 Matric Q&a guide

©Copyright Times Media Pty (Ltd)

MARKS: 150 TIME: 3 hours

Question 1 Solethu is an African sculptor who gets orders from all over the world. One of his biggest challenges is getting his sculptures safely to their destination. Solethu has to send a sculpture to Port Elizabeth.

His sculpture fits quite neatly into the standard rectangular box with length 0,45 m, width 400 mm and height 35 cm. He could be charged for either the weight or volumetric mass depending on which is more.

Volumetric mass is calculated by multiplying the length, breadth and height (in centimetres) of a rectangular

prism and dividing this by 6 000. This is shown in the formula: Volumetric mass (in kg) = l×b×h

__ 6000

1.1 Calculate the volumetric mass of Solethu’s parcel. (5)1.2 If Solethu’s parcel weighed 8,9kg, would he be charged on weight or volumetric mass?

Explain your answer. (2)

Solethu realises that with some careful planning he can reduce the volumetric mass of his parcel if he makes his own box with different dimensions. Solethu needs to work the smallest dimensions of the box for his sculpture. The sculpture, shown below has circumference of 110 cm around its widest part.

110 cm

35 cmPossible Formulae:

Circumference = 2πr Area = πr2

1.3 Determine the volumetric mass, correct to 1 decimal place, using the minimum dimensions of the box that Solethu can use to package his sculpture. He must have a centimetre around the sides and on top of his sculpture. (12)

1.4 Do you think it is better for Solethu to make his own box? Explain your answer. (2) [21]Question 2Solethu now needs to send his parcel off to his clients. He wants to send it counter to door and can either send it via the South African Post Office or use the local RSA Courier Service. The two service costs are listed below.

SA Post Office RSA Courier Service

A flat rate of R50,30 and then R32,10 per kilogram or any part thereof.

R45,50 per kilogram or any part thereof

2.1 The total cost to send a parcel with the SA Post Office is given by the following formula: Total Cost (in rand) = 50 + 32 × (mass of the parcel, in kilograms)

2.1.1 Write down a formula which can be used to calculate the total cost, in rand, to send a parcel with RSA Courier Services. (2)

2.1.2 If Solethu’s parcel weighs 1 250 grams, determine how much it will cost to send using the SA Post Office. (4)

2.2 The table below is given to the workers at the SA Post Office and RSA Courier Services. However, some of the information has been left out. Help them to fill in the missing values (a) – (d) using the information above.

Mass 0 1 2 3 ... (d)

SA Post Office (R) (a) 82,40 114,50 (c) … 339,20

RSA Courier Services (R) 0,00 45,50 (b) 136,50 … 409,50 (8) 2.3 The following line graph shows the total cost to send a parcel counter to door, for RSA Courier Services

according to weight of the parcel. On the same set of axes draw a line graph to illustrate the total cost of sending a parcel with the SA Post Office.

MATHS LITERACY PAPER 2

QUESTIONS

2.4 2.4.1 Describe what is happening where the two lines are intersecting. (2)2.4.2 At what mass will it be irrelevant which company Solethu chooses to send his parcel with?

Mark this point with the letter A on your graph. (2)2.4.3 What factors other than cost could motivate Solethu to use a certain company above

another? (2)

According to the SA Post Office the following tree diagram shows the popularity of services chosen to send parcels via speed services. Study the tree diagram and answer the questions that follow:

Counter to counter

Counter to door

Insured

87%

(a)

(b)

(c)

(e)

(d)

0,45%

3 _ 10

Insured

Not Insured

Not Insured C-C & not 0,39

2.5 2.5.1 Determine the values of (a) to (e). (7)

2.5.2 According to the tree diagram what are the chances that a parcel will not be insured? Give your answer as a percentage. (6)

2.6 As far as insurance goes the Post Office enquires: Are you sending valuable items? If it is a valuable item, you must insure the item. In the event

of loss or damage, due to negligence on the part of Speed Services Couriers, liability is limited to a maximum of R50,00 (fifty rand) per consignment. Optional liability cover, up to a maximum of R10 000 (ten thousand rand) per parcel, is available at a premium of 3% of the declared/insured value. 2.6.1 What amount would Solethu have to pay for insurance if his sculpture has a value of R7 600? (3)2.6.2 Would you recommend that a person insure their parcels or not. Give at least TWO reasons why. (2)

[41]Question 3Solethu’s parcel arrives at the Post Office in Govan Mbeki Avenue, Port Elizabeth (indicated by A on the map). From here it is dispatched to its destination which is 25 Kelly Street, Port Elizabeth (indicated B on the map).

A B C

1

N

2

3

4

Scale: 1: 1 500

3.1 Give the grid reference for 25 Kelly Street, Port Elizabeth. (2)

3.2 In which general direction is 25 Kelly Street, Port Elizabeth from the Post Office in Govan Mbeki Avenue? (2)

3.3 3.3.1 Describe the route that is outlined from the Post Office in Govan Mbeki Avenue (A) to 25 Kelly Street (B). (4)

3.3.2 Hence, work out the approximate distance of the route using the given scale, to the nearest kilometre. (4)

3.4 If the parcel left the post office at 10:15 and was transported at an average speed of 45 km/h, determine what time Solethu’s parcel would arrive at its destination of 25 Kelly Street, Port Elizabeth. Round your time to the nearest minute. The following formula may be used: Average speed = distance __ time (5)

3.5 The driver followed the route outlined above once he had delivered Solethu’s parcel. What was his next

destination? He turned North West into Perkins Street until he reached Cawood Street where he turned right. When he reached Govan Mbeki, he turned right again. He then proceeded halfway down the block and stopped to go to the shop on his right. (2)

[19]Question 4Solethu likes to use the SA Post Office as it is close to his studio and very seldom busy. However, he is a little concerned about theft and crime within the Post Office as well as their delivery service. He does some research and finds the following: In a Quality Service survey it was established that over the last two and a half years the following percentage of mail was delivered according to delivery standards. The percentages were calculated 4 times a year.

83 84 83 86 9083 B 90 92 A

Cost for sending a parcel

Mass (in kg)

700.00650.00600.00550.00500.00450.00400.00350.00300.00250.00200.00150.00100.0050.000.00

0 2 4 6 8 10 12 14 16 18 20

Tota

l cos

t (in

ran

d)

21

2013 Matric Q&a guide

©Copyright Times Media Pty (Ltd)

4.1 The range of delivery service percentage is 10% and the mean (average) percentage was 87,4%. 4.1.1 Calculate the missing value A, the best service delivery percentage. (2)4.1.2 Hence, calculate the value of B. (5)4.1.3 Hence, determine the median delivery percentage. (4)

4.2 The lower and upper quartiles of service delivery are 83% and 90% respectively. How often is the delivery

percentage above 90%? Is this good or bad. Explain your answer. (2) 4.3 The next two and a half years showed the average percentage for delivery services to have a range of 15%,

a median of 88% and an average (mean) of 84%. Compare these statistical measures and comment on if the service delivery has improved or not and give ONE possible reason for this. (4)

As far as crime and fraud inside the Post Office goes, Solethu found the following information: • BecauseofincreasedsurveillancesecurityandtheestablishmentofarmedresponsevehiclesatCourier Services there had been a decrease in armed robberies. The Post Office also shared the following statistical graphs with Solethu. • Thefollowingpiechartshowsthenumberofdismissalsfortypeofstaffforcrimeandfraudwithinthe Post Office.

Non-Managerial Managerial319

14

4.4 What percentage of dismissed staff filled non-managerial positions? (4) Percentage decrease = new value – old value x 100% old value

4.5 If one of these dismissed persons was randomly selected. What is the probability that the person would be in a managerial position. Give your answer as a decimal correct to two decimal places. (3)

The Post Office also assured Solethu that the robbery statistics had also decreased and produced the following graph for him to study. The Post Office claimed that “The incident of robberies decrease by 11,4% from year 1 to year 2 and 3.”

160

140

120

100

80

60

20

0Year 1

12

140RobberyCIT

124 124

14 6

Year 2 Year 3

4.6 Using the statistics provided show how they calculated the 11,4% in the statement above. (4) 4.7 After studying the graph Solethu identifies that robberies are on the decrease every year. What error(s)

did Solethu make when interpreting the graph? Explain your answer. (4) 4.8 Name two other types of graphs that would have made it easier to interpret the information shown in

this graph. (2) [34]

MATHS LITERACY PAPER 2

QUESTIONScontinued

Question 5Sanjo, a 45-year-old, works for RSA Courier Company and earns a gross salary of R25 698, 80 per month. The following amounts are deducted from his gross monthly salary:

Medical Aid: ¼ of his total medical subscriptions which amount to R4 678.

Pension Fund 7,3% of gross salary.

UIF 1% of gross salary 5.1 Complete the following table to determine all of Sanjo’s deductions on his salary

Medical Aid:

Pension Fund

UIF

TOTAL DEDUCTIONS (7)

Sanjo will also have to pay income tax on his remaining annual salary. The table below describes how the amount of income tax to be paid is calculated.

Taxable income (R) Tax Rates

0 – 165 600 18% of each R1

165 601 – 258 750 R29 808 + 25% of the amount above R165 600

258 751 – 358 110 R53 096 + 30% of the amount above R258 750

358 111 – 500 940 R82 904 + 35% of the amount above R358 110

500 941 – 638 600 R132 894 + 38% of the amount above R500 940

638 601 and above R185 205 + 40% of the amount above R638 600

Tax Class Tax Rebates

Primary R12 080

Additional R6 750 (Persons 65 and older)

5.2 Complete the following table to calculate how much tax Sanjo needs to pay each month.

Gross Salary – Deductions 25 698, 80 –__________________

Monthly taxable income =

Monthly taxable monthly income ×12

= × 12

= Annual taxable income =

Tax bracket R ________+ _____ % ( Annual taxable income – _______)

ANSWER =

Less rebate –

Annual tax payable =

Monthly tax payable =

(11)5.3 Sanjo now knows what all his deductions are and would like to calculate his net salary (his ‘take-home’

salary after all deductions have been made). Help Sanjo determine his net salary. (3) 5.4 Explain what is meant by tax rebate and why it is in the tax tables. (2) 5.5 Discuss taxation mentioning at least TWO reasons why it is or isn’t important. (2) [25]

Question 6Ways of communicating have developed much further than the postal system because of technological advances over the last few years. For example, email, social networks etc. The Post Office has had to offer new products and services in order to remain useful. The graph and table below shows some of the new products and services that they have been offering. Analyse the information and answer the questions that follow:

Products & Volumes18000

16000

Ordinary mail

Receipts/payments on behalf of third parties (R million)

14000

12000

10000

8000

6000

40002000

00 1 2 3 4

Mil

lio

ns

Years

Products & Volumes (million) Year 1 Year 2 Year 3

Fast mail 59,6 57,9 86,9

Pension payments 2,7 4,8 5,6

6.1 Describe the trends over the three years for ordinary mail, receipts/payments, fast mail and pension

payments respectively from the information above. (4) 6.2 Write a critical paragraph on where you think the Post office should focus their resources and give some

possible reasons why these trends are happening. (6) [10]