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Transcription

Solutions for all
Mathematical
Literacy
Grade 12
Learner’s Book
Schools Development Unit
00i-vi E MathLit GR12.indd 1
2013/05/09 12:20 PM
Solutions for all Mathematical Literacy
© Schools Development Unit, 2013
© Illustrations and design Macmillan South Africa (Pty) Ltd, 2013
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form
or by any means, electronic, photocopying, recording, or otherwise, without the prior written permission of the
copyright holder or in accordance with the provisions of the Copyright Act, 1978 (as amended).
Any person who commits any unauthorised act in relation to this publication may be liable for criminal prosecution
and civil claims for damages.
First published 2013
11 13 15 17 16 14
0 2 4 6 8 10 9 7 5 3 1
Published by
Macmillan South Africa (Pty) Ltd
Private Bag X19
Northlands
2116
Gauteng
South Africa
Typeset by Future Pre Press
Cover image from Gallo Images
Cover design by Deevine Design
Illustrations by Alex Fleming, Andre Gericke, Andre Plant, Butch Stoltz, Chris Berens,
David Doubell, Ian Greenop, Michael Souter, Sean Strydom and Wouter de Wit
e-ISBN: 9781431024360
WIP: 4524M000
It is illegal to photocopy any page of this book
without written permission from the publishers.
The publishers have made every effort to trace the copyright holders.
If they have inadvertently overlooked any, they will be pleased to make the
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Photographs by:
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With special thanks to:
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2013/05/09 12:20 PM
CONTENTS
Introduction ....................................................................................................... 1
Chapter 1
Conversions and Time ................................................................. 2
Unit 1
Metric and imperial conversions..................................................... 4
Unit 2
Other conversions .......................................................................... 7
Unit 3
Temperature ................................................................................... 9
Unit 4
Understanding time .......................................................................11
Unit 5
Schedules and planning ............................................................... 14
Unit 6
Speed ........................................................................................... 18
Summary practice exercise ............................................................................... 19
Word bank
..................................................................................................... 22
Chapter summary .............................................................................................. 22
Chapter 2
Financial documents and tariffs ............................................... 23
Unit 1
Revising financial documents for households .............................. 25
Unit 2
Quotations, invoices and receipts ................................................ 29
Unit 3
Income- and expenditure-statements and budgets ...................... 34
Unit 4
Tariffs ............................................................................................ 41
Word bank
..................................................................................................... 49
Chapter summary .............................................................................................. 50
Chapter 3
Financial tools ............................................................................ 51
Unit 1
Income and expenditure............................................................... 53
Unit 2
Cost of production, cost price, selling price.................................. 60
Word bank
..................................................................................................... 71
Chapter summary .............................................................................................. 71
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Chapter 4
Interpretation of data ................................................................. 73
Unit 1
Developing questions to support research ................................... 76
Unit 2
Collection data ............................................................................. 80
Unit 3
Classifying data and organising ungrouped data ......................... 85
Unit 4
Organising grouped data.............................................................. 93
Unit 5
Summarising ungrouped data ...................................................... 98
Unit 6
The box-and-whisker plot ........................................................... 106
Unit 7
Working with bar graphs and pie charts ......................................114
Unit 8
Working with graphs to represent two or more sets of data .......118
Unit 9
Broken line graphs ..................................................................... 122
Unit 10
Representing bivariate data using scatter plots ......................... 125
Unit 11
Representing continuous data using a histogram ...................... 128
Unit 12
Analysing data to reveal misrepresentation ............................... 130
Unit 13
Interpreting data and analysing data ......................................... 133
Summary practice exercise ............................................................................. 135
Word bank
................................................................................................... 145
Chapter summary ............................................................................................ 145
Chapter 5
Interest, banking and inflation ................................................ 148
Unit 1
Bank accounts............................................................................ 150
Unit 2
Calculating interest..................................................................... 156
Unit 3
Instalment accounts and personal loans .................................... 158
Unit 4
Interest earned on investments .................................................. 163
Unit 5
Amortisation – Home loans and car finance .............................. 171
Unit 6
Inflation....................................................................................... 178
Word bank
................................................................................................... 186
Chapter summary ............................................................................................ 186
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Chapter 6
Scale and mapwork.................................................................. 188
Unit 1
How scale works ........................................................................ 190
Unit 2
Bar scales and ratios.................................................................. 196
Unit 3
Directions ................................................................................... 202
Unit 4
Elevations................................................................................... 206
Unit 5
Calculating cost and time taken for a journey ............................ 209
Word bank
................................................................................................... 217
Chapter summary ............................................................................................ 218
Chapter 7
Measuring length, mass, volume and temperature .............. 219
Unit 1
Measuring length and distance .................................................. 221
Unit 2
Measuring mass ......................................................................... 226
Unit 3
Measuring volume ...................................................................... 231
Unit 4
Measuring temperature .............................................................. 238
Word bank
................................................................................................... 243
Chapter summary ............................................................................................ 244
Chapter 8
Calculating perimeter, area and volume ................................ 245
Unit 1
Calculating Perimeter and area.................................................. 247
Unit 2
Surface area............................................................................... 255
Unit 3
Volume ....................................................................................... 262
Word bank
................................................................................................... 266
Chapter summary ............................................................................................ 267
Chapter 9
Revision of Chapters 1-8 ......................................................... 268
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Chapter 10 Taxation ..................................................................................... 282
Unit 1
Value-Added Tax ........................................................................ 285
Unit 2
Calculating unemployment insurance (UIF) contributions.......... 290
Unit 3
Income tax.................................................................................. 293
Unit 4
Other forms of tax ...................................................................... 295
Word bank
................................................................................................... 304
Chapter summary ............................................................................................ 305
Chapter 11 Exchange rates......................................................................... 306
Unit 1
Revising exchange rates calculations ........................................ 308
Unit 2
Travelling in another country ...................................................... 313
Word bank
................................................................................................... 324
Chapter summary ............................................................................................ 325
Chapter 12 Plans and other representations of the physical world ....... 326
Unit 1
Instructions and assembly.......................................................... 332
Unit 2
Scale and plans.......................................................................... 349
Unit 3
Quantities of materials ............................................................... 356
Unit 4
Elevations................................................................................... 360
Word bank
................................................................................................... 363
Chapter summary ............................................................................................ 367
Chapter 13 Probability................................................................................. 365
Unit 1
Working with expressions of probability ..................................... 367
Unit 2
Predicting outcomes................................................................... 371
Unit 3
Representations for determining possible outcomes ................. 377
Unit 4
Evaluating expressions involving probability .............................. 383
Word bank
................................................................................................... 388
Chapter summary ............................................................................................ 388
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Chapter 14 Maps, plans and other representations of the
physical world .......................................................................... 390
Unit 1
Packaging .................................................................................. 392
Unit 2
Packaging space ........................................................................ 400
Unit 3
Interior planning and design ....................................................... 405
Unit 4
Models of buildings .................................................................... 412
Word bank
................................................................................................... 417
Chapter summary ............................................................................................ 417
Chapter 15 Revision of Chapters 10-14 ..................................................... 419
Formal Assessment Tasks............................................................................ 431
Note to the teacher:
Please refer to the Teacher’s Guide for possible assessment tasks, exemplar control tests and
exemplar examination papers.
2013/05/09 12:20 PM
2013/05/09 12:20 PM
IntroductIon
Welcome to the Solutions for All Mathematical Literacy Grade 12
Learner’s Book
In Mathematical Literacy, you will be exposed to both mathematical content and real-life
contexts. You will have many opportunities to analyse problems and devise ways of using
Mathematics to solve problems in different contexts.
Mathematical Literacy involves:
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the use of elementary mathematical content
authentic real-life contexts
solving familiar and unfamiliar problems
decision-making and communication
the use of integrated content and/or skills in solving problems.
How to use the Solutions for All Mathematical Literacy Grade 12
Learner’s Book
This Mathematical Literacy series aims to be accessible to all learners no matter what their level
of ability or background.
In the Solutions for All Mathematical Literacy Learner’s Book, every exercise and activity
gradually progresses from easier questions to more difficult questions, in manageable steps.
Within each chapter of the Solutions for All Mathematical Literacy Learner’s Book you will find:
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chapter opener page – you are given an overview of what content will be covered within the
chapter.
check myself – you are given an opportunity to check whether you have acquired the knowledge
and skills taught in previous chapters or in Grade 11.
revision – you will be reminded of the skills you were taught in either a previous chapter or in
Grade 11.
units – each chapter is broken down into manageable units that use real-life examples to teach the
skills and knowledge necessary for you to be successful during this year.
Examples and solutions – full worked examples and solutions are given in each unit.
Summary practice exercise – you are given an opportunity to check whether you have mastered
the skills taught in the chapter.
Word bank – difficult words found within the chapter are explained.
chapter summary – you are given a summary of the work covered in the chapter.
The Summary practice exercise at the end of each chapter is useful for both learners who have
mastered the skills taught in the chapter, and those who may not have mastered all the skills.
The publisher and authors wish you all the best in your study of Mathematical Literacy in
Grade 12.
1
001-147 E MathLit GR12.indd 1
2013/05/09 11:41 AM
Ch
1
er
a pt
Conversions
and time
What you will learn about in this chapter
You will:
• convert different units of measurement using given data or tables
• express measurement values and quantities in units appropriate to the context
• read, record and perform calculations involving time values
• convert between different units of time
• calculate elapsed time involving the different time formats
• work with timetables including examination timetables, train and bus timetables
• plan time-based events
• calculate average speed.
Let’s talk about this chapter
In this chapter you will revise conversion between different metric units of
measurement and conversions between the imperial and metric systems. You will work
with time and timetables as well as do calculations involving average speed.
2
•
Conversions and time
2013/05/09 11:41 AM
Chapter 1
Check
myself
1
How is time linked to distance and speed?
2
If the speed of a car is described in kilometres per hour:
a) Why would you describe the speed of a space rocket in
kilometres per second?
b) Why would you describe the speed of a snail in centimetres
per minute?
Revision
You use different units to measure mass, length (distance) and volume. South Africa
uses the metric system of measurement, but there are many countries that still use
the imperial system of measurement.
Look at the conversion tables below and on the following page that give useful hints
for converting systems of measurement.
Converting between metric measurements
Cool fact
1 metric
tonne =
1 000 kg
Unit
Mass
Length
Capacity
Thousands
Kilogram (kg)
1 000 g = 1 kg
Kilometre (km)
1 000 m = 1 km
Kilolitre (kl)
1 000 ℓ = 1 kl
BASE UNIT
Gram (g)
Metre (m)
Litre (ℓ)
Centigram (cg)
100 cg = 1 g
Centimetre (cm)
100 cm = 1 m
Centilitre (cl)
100 cl = 1 ℓ
Milligram (mg)
1 000 mg = 1 g
Millimetre (mm)
1 000 mm = 1 m
Millilitre (ml)
1 000 ml = 1 ℓ
Hundredths
x
100
x
Thousandths 1 000
•
3
2013/05/09 11:41 AM
Converting between metric and imperial units of
measurement
Length
Imperial to Metric
Metric to Imperial
1 mile
1,609 km
1 609 m
1 km
0,6215 miles
1 yard
91,44 cm
0,9144 m
1m
3,2808 feet
1 foot
30,48 cm
304,8 mm
1 cm
0,3937 inches
1 inch
2,54 cm
25,4 mm
Mass
1 ton
0,907 metric tonnes
1 pound
0,4536 kg
1 ounce
28,4 g
453,6 g
Cool fact
1 metric tonne
1,102 ton
1 kg
2,204 pounds
1g
0,035 ounces
1 litre
0,22 gallons
1 litre
1,76 pints
1 000 kg =
1,102 ton
Capacity
1 gallon
4,5461 ℓ
1 pint
0,5682 ℓ
568,2 ml
Unit 1 Metric and imperial conversions
It is important that you use the appropriate unit of measurement for a given
situation.
Example
a)
Pumeza works in Johannesburg, but she needs to attend a workshop at the
University of Pretoria. Which unit of measurement should she use to measure
the distance from Johannesburg to Pretoria?
Jana and Kelly have lived next door to each
other for many years. They decide to
measure the distance between their houses.
Which unit of measurement should they use
to measure the distance from one house to
the other?
A horticulturist studies and cultivates plants
for human use. What unit of measurement
would she use to measure the size of the
flower on a plant?
b)
c)
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2013/05/09 11:42 AM
Chapter 1
Solution
a)
b)
c)
Kilometres
Metres
Centimetres or millimetres, depending on the size of the flower.
Example
a)
b)
Convert 15 ℓ to ml.
Convert 50 miles to kilometres.
Solution
a)
1 ℓ = 1 000 ml
15 ℓ × 1 000 ml = 15 000 ml
b)
1 mile = 1,609 kilometres
50 miles × 1,609 kilometres = 80,45 kilometres
Classwork activity 1.1
1
What unit of measurement would you use
to measure:
a) the mass of an apple
b) the capacity of a cup
c) the width between a set of soccer goal
posts?
2
Convert:
a) 12 m to mm
b) 4,3 metric tonne to kg
c) 83 km to m
d) 40,34 ℓ to ml.
3
Convert:
a) 3 kg to pounds
b) 7 inches to cm
c) 4,8 ℓ to pints.
4
Which tin of paint would you buy
to paint:
a) an entire house
b) a tree in a picture
c) one wall of a bedroom.
250 ml
1ℓ
5ℓ
20 ℓ
•
5
2013/05/09 11:42 AM
d) the roof of a shopping mall
e) a kitchen chair?
5
8′0″
Tia lives in California, United States. She
wants to build a new house from scratch.
She gets this plan of a starter home: (Hint:
’ = feet and ” = inches)
a) Calculate the length of the house in
metres.
b) Calculate the width of the house in
metres.
c) Calculate the width of the door in
millimetres.
d) (i) Calculate the perimeter of your
classroom floor using a tape
measure.
(ii) Is the perimeter of the house
bigger or smaller than your
classroom?
shower
toilet
stove
15′0″
3′0″
attic ladder
window seat
Homework activity 1.1
6
1
Convert:
a) 1,12 mm to cm
b) 14 ml to ℓ
c) 15,3 kg to g.
2
Convert:
a) 450 ml to pints
b) 16 gallons to ℓ
c) 228 km to miles.
3
Jerry needs 4 tonnes of stone to mix with cement to
lay a foundation of a house. The stone can only be
bought in bags of 25 kg. Calculate how many bags
he needs to order. (Hint: convert all weights to
kilograms.)
4
Rosalchen and David are from Kent in the United
Kingdom. They have recently had their first child
and realised that they need a bigger living space.
Unfortunately they cannot afford an expensive
house.
•
lb is the abbreviation
for pound.
1 lb = 0,4536 kg
2013/05/09 11:42 AM
Chapter 1
They consult a builder and he provides them with the following information:
To build a low cost house in the United Kingdom, the following building materials are
needed:
Cement
74 127,54 lb
Sharp sand
148 255,08 lb
Water
568,79 gallons
Gravel (stone)
a)
b)
296 510,11 lb
How many kg of cement, sand and gravel (stone) are needed?
How many litres of water are needed?
Unit 2 Other conversions
There are many other ways in which to measure quantities. You can use spoons,
cups, wheelbarrows and other containers to measure quantities.
This table shows different measures:
is the same as
5 ml
(1 teaspoon)
3 g flour
5 g butter or
margarine
4 g rice
4 g sugar
3 g mielie meal
25 ml
15 g flour
25 g butter or
margarine
20 g rice
60 g flour
80 g rice
250 ml
(1 cup)
80 g
sugar
12 g mielie
meal
100 ml
100 g butter
or margarine
20 g
sugar
150 g
flour
250 g butter
or margarine
200 g rice
200 g
sugar
125 g mielie
meal
50 g mielie
meal
Here is another conversion table for spoons and cups:
1 teaspoon
5 ml
1 tablespoon
15 ml
1 cup
250 ml
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2013/05/09 11:42 AM
Another method of measuring liquid capacity
is to use the units cm3 and m3:
1 cm3
1 ml
1 000 cm3
1ℓ
1 m3
1 000 ℓ
Cool fact
Juice from a 1 ℓ bottle will fit
into the cube shown here:
Fruity
Juice
Example
1
Convert 4 4 cups into ℓ.
Solution
1 cup = 250 ml
ℓ
10 cm
1
250 ml × 4 4 = 1 062,5 ml = 1,063 ℓ
Round off to three
decimal places.
Show all calculations:
1
Convert:
a) 35 ml to teaspoons
c) 16 m3 to ℓ
2
Which has the greater capacity:
8
•
5,4 ℓ to cm3
1,5 ℓ to cups.
1
a)
c)
3
b)
d)
2 4 cups or 600 ml
b) 4 cm3 or 10 ml
8 tablespoons of oil or 130 ml of oil?
The following table shows the capacity of some dams in South Africa.
Complete the table.
Dam
Size (m3)
Farm dam
2 400 000
Sterkfontein
Dam
2 616 950
Size (ℓ)
Photo
2013/05/09 11:42 AM
Chapter 1
5 340 600 000
000
Gariep Dam
Convert:
1
2,75 ℓ to cups
2
5 tablespoons to ml
3
24 ℓ to cm3.
Unit 3 Temperature
In some countries the unit of measurement for temperature is
Fahrenheit, in other countries it is Celsius.
Example
Convert:
a)
16 °C to °F
b)
–23 °F to °C.
To convert from °Celsius to
°Fahrenheit: °F = (1,8 × °C) + 32
To convert from °Fahrenheit to
°Celsius: °C = (°F – 32) ÷ 1,8
Solution
a)
°F = (1,8 × °C) + 32 = (1,8 × 16) + 32 = 60,8 °F
b)
°C = (°F – 32) ÷ 1,8 = (–23 – 32) ÷ 1,8 = –30,56 °C
1
Convert:
a) 10 °F to °C
b) 250 °C to °F
2
Bongi lives in Pretoria and has decided to
visit New York in December.
•
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2013/05/09 11:42 AM
The weather statistics for December 2011 for the cities of Pretoria (°C) and New York (°F) are
shown in the following table:
Temperatures for New York, USA
Temperatures for Pretoria, South Africa
December, 2011
December, 2011
Maximum
Maximum
Average
Average
Max.
Temperature
62 °F
50 °F
Max.
Temperature
28 °C
21 °C
Mean
Temperature
59 °F
44 °F
Mean
Temperature
23 °C
20 °C
Min.
Temperature
56 °F
37 °F
Min.
Temperature
22 °C
17 °C
a)
b)
c)
d)
What is the highest temperature reached in New York? Write your answer in °F.
What is the highest temperature reached in Pretoria? Write your answer in °C.
Convert New York’s highest temperature to °C.
Calculate the difference in temperature between the highest temperature in Pretoria and
the highest temperature in New York. Do your calculations in °C.
1
Which is the higher temperature:
a) 0 °C or 0 °F?
b) 200 °C or 395 °F?
2
This table shows the time it
takes for concrete to set at a
given temperature:
70 °F
6 hours
60 °F
8 hours
50 °F
11 hours
40 °F
14 hours
30 °F
19 hours
20 °F
Concrete will freeze
a)
b)
10
•
At what temperature
(°F) will it take 14 hours
for the concrete to set?
Sifiso is laying the foundations for his home. The outside temperature is 17 °C.
Approximately how long will it take for the concrete in his foundations to set?
2013/05/09 11:42 AM
Chapter 1
Unit 4 Understanding time
This unit focuses on time and the conversions between various units of time.
Time values can be expressed in the following formats:
pm
11
12
1
pm
2
10
9
3
4
8
7
6
5
8 o’clock
08:00
8:00 p.m./20:00
When recording time you use the format: 1 h 12 min 20 sec.
You use different units of time depending on the amount of time that needs to be
measured or the situation in which you find yourself.
Example
1
Convert 7 2 minutes to seconds.
Solution
1 minute = 60 seconds
1
7 2 minutes × 60 seconds = 450 seconds
Example
Write 1 782 minutes in days, hours and minutes.
Solution
1 782 minutes ÷ 60
29 hours × 60 minutes
There are (1 782 – 1 740)
∴ 1 782 minutes
24 hours
∴ 29 hours
∴ 1 782 minutes
= 29,7 hours
= 1 740 minutes
= 42 minutes remaining.
= 29 hours 42 minutes
= 1 day
= 1 day and 5 hours
= 1 day 5 hours 42 minutes
•
11
2013/05/09 11:42 AM
1
2
Tania’s birthday is on 23 September.
She looks at the calendar for the
S
M
month of September 2013 as shown
1
2
alongside:
8
9
a) How many days are there in the
15
16
month?
22
23
b) On which day is 23 September
29
30
2013?
c) How many Mondays in
September 2013 before the 23rd? List the dates.
SEPTEMBER 2013
T
W
T
F
S
3
4
5
6
7
10
11
12
13
14
17
18
19
20
21
24
25
26
27
28
Lerato is the opening batswoman for her team.
a)
b)
3
a)
b)
12
•
She started batting at 09:44
and was bowled out at
12:32.
For how long did she bat?
In the following innings she
started batting at 1:22 p.m.
and batted for 73 minutes.
At what time was she
caught out?
Study the stopwatch:
(i) How many hours, minutes and seconds has the stopwatch
timed?
(ii) If the stopwatch continued timing for another 58 minutes
what timing would be shown on the stopwatch?
Nikiwe took part in a triathlon. Her times were recorded as
follows:
Swim: 37 minutes
Cycle: 1 hour 20 minutes
Run: 58 minutes
(i) How long did she take to complete the triathlon?
(ii) What time did she finish if she started at 08:00?
2013/05/09 11:42 AM
Chapter 1
1
Convert:
a) 190 seconds to minutes and seconds
b) 7 weeks into days
c) 524 days into years, months and days (assume that the first day is 1 January, and that
these are not leap years).
2
The calendar for 2014 is shown here:
JANUARY
W
T
FEBRUARY
S
M
T
F
1
2
3
4
5
6
7
8
9
10
12
13
14
15
16
M
T
W
T
F
S
11
2
3
4
5
6
7
17
18
9
10
11
12
13
25
19
20
21
22
23
24
27
28
29
30
31
M
T
W
T
F
S
8
2
3
4
5
6
7
8
14
15
9
10
11
12
13
14
15
22
16
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25
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30
31
16
17
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25
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27
28
1
MAY
S
W
T
F
S
1
2
3
4
5
7
8
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11
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15
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11
12
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20
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25
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18
19
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22
27
28
29
30
25
26
27
28
29
S
M
T
W
T
F
S
S
M
T
1
2
3
4
5
4
M
5
T
JUNE
T
6
M
S
1
APRIL
S
MARCH
S
26
S
W
6
JULY
7
T
F
S
S
M
T
W
T
F
S
1
2
3
1
2
3
4
5
6
7
8
9
10
8
9
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23
24
22
23
24
25
26
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28
30
31
29
30
F
S
S
M
T
W
T
F
S
1
2
1
2
3
4
5
6
AUGUST
W
SEPTEMBER
T
6
7
8
9
10
11
12
3
4
5
6
7
8
9
7
8
9
10
11
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19
10
11
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25
26
24
25
26
27
F
S
20
21
22
23
24
27
28
29
30
31
17
18
19
20
21
22
23
21
22
23
24
25
26
27
28
29
30
28
29
30
S
M
1
2
3
4
5
6
7
8
9
10
11
12
13
31
OCTOBER
T
NOVEMBER
S
M
T
W
F
S
1
2
3
4
5
6
7
8
9
10
11
DECEMBER
S
M
T
W
T
F
S
2
3
4
5
6
7
8
1
T
W
T
12
13
14
15
16
17
18
9
10
11
12
13
14
15
14
15
16
17
18
19
20
19
20
21
22
23
24
25
16
17
18
19
20
21
22
21
22
23
24
25
26
27
26
27
28
29
30
31
23
24
25
26
27
28
29
28
29
30
31
30
a)
b)
c)
How many public holidays are there in 2014?
How many months have five Fridays in the month?
How many days are there between 22 October and 30 December?
•
13
2013/05/09 11:42 AM
Unit 5 Schedules and planning
It is important to be able to plan your life using schedules and
timetables so that you know when events are going to happen and
you are able to plan for them in advance.
Example
Jannie has to travel from Johannesburg to Port Elizabeth by plane.
He has to land in Port Elizabeth by 20:00 on Friday
27 April. Look at the information he finds on the internet for flights
to Port Elizabeth.
Flight and fare options
The amounts displayed are the total fare including taxes for all passengers for the selected flight.
Depart: JNB Johannesburg (OR Tambo) to PLZ Port Elizabeth, on 27 April 2012
Economy
Business
Instant
upgrade
Sector
Flight
Departs
Arrives
SAVER
CLASSIC
SELECT
Johannesburg (OR Tambo)
(JNB) – Port Elizabeth
(PLZ)
AA901
05:10
07:50
ZAR 898
ZAR 1 560
ZAR 1 947
(PLZ)
AA1553
07:55
09:30
ZAR 890
ZAR 1 552
ZAR 1 939
(PLZ)
AA505
10:15
11:55
ZAR 898
ZAR 1 560
ZAR 1 947
(PLZ)
AA518
13:10
14:50
ZAR 1 172
ZAR 1 560
ZAR 1 947
(PLZ)
AA519
16:40
18:20
ZAR 1 366
ZAR 1 560
ZAR 1 947
(PLZ)
AA1557
17:35
19:10
ZAR 1 164
ZAR 1 552
ZAR 1 939
(PLZ)
AA325
19:40
21:20
SOLD OUT
ZAR 1 560
ZAR 1 947
a)
b)
14
Select your fare
If he needs to reach Port Elizabeth by 20:00, what is the latest flight he can take?
Jannie has to be at the airport one hour before his flight. For him to catch the flight you have chosen,
what time should he be at the airport?
•
2013/05/09 11:42 AM
Chapter 1
Solution
a)
b)
Jannie should take flight AA1557.
Jannie needs to be at the airport at 16:35.
Refiloe catches the Gautrain
from OR Tambo International
Airport to Pretoria. Her plane
lands at 18:10. She allocates
30 minutes to fetch her
luggage and walk to the
Gautrain platform. Refiloe has
to take one train from the
airport to Marlboro station,
and then take a different train
from Marlboro station to
Pretoria.
Peak Period – 16:00 to 19:00
Departure OR Tambo
Arrival Rhodesfield
Arrival Marlboro
Arrival Sandton
16:20
16:22
16:29
16:33
16:08
16:32
16:44
16:56
17:08
17:20
17:32
17:44
17:56
18:08
18:20
18:32
18:44
18:56
19:08
19:20
19:32
19:50
20:10
20:30
16:10
16:34
16:46
16:58
17:10
17:22
17:34
17:46
17:58
18:10
18:22
18:34
18:46
18:58
19:10
19:22
19:34
19:52
20:12
20:32
16:17
16:41
16:53
17:05
17:17
17:29
17:41
17:53
18:05
18:17
18:29
18:41
18:53
19:05
19:17
19:29
19:41
19:59
20:19
20:39
16:21
16:45
16:57
17:09
17:21
17:33
17:45
17:57
18:09
18:21
18:33
18:45
18:57
19:09
19:21
19:33
19:45
20:03
20:23
20:43
•
15
2013/05/09 11:42 AM
Peak Period – 16:00 to 19:00
Depart
Rosebank
Depart
Sandton
Depart
Marlboro
Depart
Midrand
Depart
Centurion
Depart
Pretoria
Arrival
Hatfield
16:06
16:18
16:10
16:20
16:29
16:37
16:44
16:30
16:22
16:14
16:34
16:38
16:44
16:53
17:01
17:08
16:42
16:54
17:06
17:18
17:30
17:42
17:54
18:06
18:18
18:30
18:42
18:54
19:06
19:18
19:30
19:42
19:56
20:14
20:34
16:46
16:58
17:10
17:22
17:34
17:46
17:58
18:10
18:22
18:34
18:46
18:58
19:10
19:22
19:34
49:46
19:58
20:18
20:38
16:26
16:50
17:02
17:14
17:26
17:38
17:50
18:02
18:14
18:26
18:38
18:50
19:02
19:14
19:26
19:38
19:50
20:02
20:22
20:42
16:32
16:56
17:08
17:20
17:32
17:44
17:56
18:08
18:20
18:32
18:44
18:56
19:08
19:20
19:32
19:44
19:56
20:08
20:28
20:48
16:41
16:49
17:05
17:13
17:17
17:25
17:29
17:37
17:41
17:49
17:53
18:01
18:05
18:13
18:17
18:25
18:29
18:37
18:41
18:49
18:53
19:01
19:05
19:13
19:17
19:25
19:29
19:37
19:41
19:49
19:53
20:01
20:05
20:13
20:17
20:25
20:37
20:45
20:57
21:05
16:56
17:20
17:32
17:44
17:56
18:08
18:20
18:32
18:44
18:56
19:08
19:20
19:32
19:44
19:56
20:08
20:20
20:32
20:53
21:12
(Source: Tables from www.gautrain.co.za)
16
1
Which train will Refiloe catch from the airport?
2
When will the train arrive at Marlboro station?
3
Which train will she catch from Marlboro station to Pretoria station?
4
When will the train arrive at Pretoria station?
5
Refiloe’s flight is delayed by 40 minutes. Determine when she will arrive at Pretoria station.
Show all your workings.
•
2013/05/09 11:42 AM
Chapter 1
Jerusha’s final school examination timetable for the National Senior Certificate is shown here:
Week 1
Monday 24/10
09:00
English HL P1 (2 hrs)
Friday 28/10
Mathematical Literacy P1 (3 hrs)
Week 2
09:00
Monday 31/10
Mathematical Literacy P2 (3 hrs)
Week 3
09:00
Wednesday 02/11
Tuesday 08/11
Thursday 10/11
Week 4
Tuesday 15/11
Friday 18/11
Week 5
14:00
14:00
Afrikaans FAL P1 (2 hrs)
Afrikaans FAL P2 (2 hrs)
14:00
1
English HL P2 (2 2 hrs)
09:00
14:00
1
English HL P3 (2 2 hrs)
1
Afrikaans FAL P3 (2 2 hrs)
Tuesday 22/11
09:00
Business Studies (3 hrs)
14:00
Wednesday 23/11
Geography (Theory) P1 (3 hrs)
Geography (Map Work) P2 (1 2 hrs)
Week 6
09:00
14:00
Wednesday 30/11
Consumer Studies (3 hrs)
1
When does Jerusha write Maths Literacy P1 and P2?
2
How many days are between English Paper 1 and
English Paper 3?
3
How many days does the whole examination period
last?
4
Jerusha needs about four days to study Consumer
Studies. If she started studying for the examination on
Friday 25 November, would she have set aside enough
time to complete her studies in that subject? Explain.
1
•
17
2013/05/09 11:42 AM
Unit 6 Speed
Speed is the distance covered per unit of time. To calculate speed you need to
know the distance covered and the time taken to cover the distance.
distance
s
Formula: Speed =
= v=
time
t
distance
s
We write
= v=
time
t
In Science v
signifies velocity
(speed), s signifies
displacement
(distance) and t
signifies time.
Example
Determine Carly’s average speed if she drove
800 km in 10 hours.
Solution
Speed =
distance
s
= v=
time
t
800
s
=
= 80 km/h
t
10
v=
1
Mpho, a triathlete, completes a race with the following times:
Event
Swim
Cycle
Run
a)
b)
2
a)
b)
18
•
Distance
(km)
Time
1,5
0:36:00
10
0:50:00
40
Average
speed
1:10:00
Complete the table by calculating the
average speed for each event.
Show all your calculations.
What was Mpho’s overall average speed
for the entire event?
Calculate the average speed of a motor
car that travels 602 km from
Johannesburg to Durban in 5 hours and
50 minutes.
Calculate the average speed of an
aeroplane travelling from Johannesburg
to Durban in 1 hour and 5 minutes, with
a flying distance of 497 km.
2013/05/09 11:42 AM
Chapter 1
1
Calculate the average speed of a vehicle travelling 70 km in 45 minutes.
2
Calculate the average speed of a cyclist who takes 5 hours and 10 minutes to complete
a 94,7 km race.
3
A taxi left Cape Town for Port
Elizabeth. The taxi drove 769 km
1
in 10 2 hours (excluding stops).
a)
b)
c)
What was the average speed
of the taxi?
The taxi stopped for 10
minutes every two hours to
allow the driver to rest.
(i) How many times did the
taxi stop?
(ii) Calculate the total time
that the driver spent
resting.
The taxi left Cape Town at 05:15. What time did it arrive in Port Elizabeth?
Summary practice exercise
1
Convert:
a) 34,7 cm to km
c) 47 °F to °C
2
John is building a new house for his son. He needs to plaster a wall so finds these guidelines
on a website: http://www.damsforafrica.com/
b)
d)
72,5 miles to km
10 000 minutes into days, hours and minutes.
Concrete: Simple Mixes
Next Concrete Mix Design page
Back to main Concrete Mix Design page
Back to Home page
‘Simple Mixes’ for Plaster, Mortar and Concrete
Bedding Mortar Mix
1 bag cement + 3 barrows
builders sand
Plaster Mix
1 bag cement + 2 barrows
plaster sand
Concrete Mix
1 bag cement + 1,25
barrows concrete sand +
1,25 barrows stone
50 kg
sand
sand
sand
sand
sand
50 kg
50 kg
15 ℓ
15 ℓ
sand
stone
Notes
(1) Typically the concrete may be used for a farm reservoir floor slab, the mortar to construct its wall of bricks/blocks, and the plaster for
rendering the walls to improve the water retention of the reservoir.
(2) The concrete mix given here should have a strength of 25MPa providing no inferior quality sand, stone or cement has been used,
using just enough water consistent with full compaction. (Too much water results in drying shrinkage cracks, while too little water results
in voids – both these conditions are to be avoided.)
•
19
2013/05/09 11:42 AM
a)
b)
3
John follows the directions for the plaster mix.
(i) How many wheelbarrows of plaster sand does he need for every bag of cement?
(ii) Write a ratio for the quantities of cement and plaster sand used in the plaster mix.
John needs 14 × 50 kg bags of cement to finish the job. Calculate the total number of
wheelbarrows of plaster sand needed.
Dube and his friends plan a trip to Inhambane, Mozambique.
The following table indicates how they will travel from Paarl to Inhambane.
Leg Number
1
2
3
4
Paarl
Cape Town
Johannesburg
Maputo
Cape Town
Airport
Johannesburg
Airport
Maputo
Inhambane
Mode of Transport
Taxi
Aeroplane
Train
Bus
Departure Time
07:00
Arrival Time
08:05
Distance
61 km
Departure Point
Arrival Point
Following day:
07:00
1 264 km
Following day
15:30
618 km
480 km
Time Taken
Speed
a)
b)
20
•
How long does the trip from Paarl to Cape Town International Airport take?
Calculate the average speed of the taxi.
2013/05/09 11:42 AM
Chapter 1
c)
These are the flight times from Cape Town to Johannesburg:
Cape Town
O R Tambo (Johannesburg)
Departure
Arrival
Flight Number
06:30
08:30
TR 258
09:10
11:10
TR 645
09:40
11:40
TR 154
11:55
13:55
TR 587
12:20
14:20
TR 989
12:45
14:45
TR 555
14:00
16:00
TR 741
(i)
They need to be at the airport one hour before their flight. Which flight would suit them
best?
(ii) What time would they land in Johannesburg?
d) The following timetable shows the times for the train from Johannesburg to Maputo:
Johannesburg and Pretoria > Maputo
1.
Take a South African train from Jo’burg to Komatipoort
This train is the ‘Komati‘, run by Shosholoza Meyl, www.shosholozameyl.co.za. It is currently
running three times a week and has economy seats only, there are no sleepers.
Johannesburg
depart
18:10 Mon, Wed, Fri
Pretoria
depart
19:40 Mon, Wed, Fri
Nelspruit (for Kruger Park)
arr/dep
04:15 next morning
Kaapmuiden
arr/dep
05:15 next morning
Komatipoort
arrive
06:38 next morning
2.
Walk across the border from Komatipoort to Ressano Garcia
It’s only a few kilometres, see below for advice. The CFM train used to cross the border, but
this proved too difficult for the customs authorities, so now you must walk across.
3.
Take a CFM train from Ressano Garcia to Maputo
This train is run by CFM, the Carminhos de Ferro do Moçambique.
It runs daily, and has 3rd class seats. www.cfmnet.co.mz
Ressano Garcia (Mozambique)
depart
12:10 on Mon–Fri, 12:30 on Sat and Sun
Maputo (Mozambique)
arrive
16:40 on Mon–Fri, 17:20 on Sat and Sun
(Source: http://www.seat61.com/Mozambique.htm)
(i) What time would their train depart from Johannesburg?
(ii) The friends have to change to a different train at the border. How much time do they
have between trains? Explain.
•
21
2013/05/09 11:42 AM
Word bank
foundation (housing)
plaster mix
triathlete
volume
the base on which a house stands; normally trenches are
dug in the ground, filled with concrete, on top of which
walls are built
a mix of cement and plaster sand used to plaster walls
a person who competes in races that involve three
components: swimming, cycling and running
the capacity of a container; how much space is inside
the container
Chapter summary
•
•
•
•
•
•
When converting between different units of measurement, ensure that you use the correct unit
for conversion.
You can make use of spoons and cups to measure quantities.
Another method of measuring liquid capacity is to use the units cm3 and m3: 1 ml = 1 cm3.
To convert from degrees Celsius to degrees Fahrenheit use: °F = (1,8 × °C) + 32
To convert from degrees Fahrenheit to degrees Celsius use: °C = (°F – 32) ÷ 1,8
You can use various time units to measure time:
1 second
1 minute
× 60
•
•
•
× 60
1 day
× 24
1 week
×7
1 month
× approx. 4
1 year
× 12
Schedules and timetables help us to plan our lives.
Speed is calculated by dividing the distance of a journey by the time taken to complete it.
To calculate speed use the formula:
Speed =
22
1 hour
distance
s
= v=
time
t
2013/05/09 11:42 AM
Ch
2
er
a pt
Financial documents
and tariffs
You will:
• interpret financial documents in a variety of contexts including personal,
household, business and national finance
• work with a range of financial documents such as household bills, credit card
statements or till slips, household and business budgets, quotations, invoices,
receipts and financial statements
• calculate given tariffs and/or formulae with respect to municipal tariffs,
telephone tariffs and transport tariffs
• draw graphs and compare a range of different tariff systems to determine the
most appropriate option.
In Grades 10 and 11 you worked with and interpreted a range of financial documents:
bank statements, loan agreements, budgets, accounts, quotations, invoices and receipts.
You also worked with and compared different tariff systems.
In this chapter you will revise some of these skills in the context of households and
small businesses. You will also examine the documents relating to more complex
financial situations from national and global contexts.
Financial documents and tariffs
•
23
2013/05/09 11:42 AM
Check
myself
1
What information is on each of the following:
a) a till slip
b) a municipal account
c) a store account
d) a telephone account
e) a quotation
f)
an invoice
g) a receipt
h) a bank statement?
2
How would you use these documents in your budget?
Revision
This is the telephone bill for Mr D Tshabalala:
this is a tax invoice
Enquiries
For all enquiries please contact
our call centre
0800 444 885
Invoice for Mr D Tshabalala
Mr D Tshabala
53 Zambesi Street
Vereeniging
1939
2563 8547 22 Account number
30 September 2012 – 30 October 2012
Account Summary
Previous invoice
Payment
R758,00
R352,00 CR
Opening balance
R (i)
Overdue: Please pay immediately
R (ii)
This invoice (October 2012)
Line Rental
R414,77
Calls
R30,48
Discounts
Adjustments
R102,22 CR
R11,47 CR
Subtotal
r (iii)
VAT @ 14%
R (iv)
total
r377,98
Balance brought forward
October invoice:
total due:
a)
b)
c)
d)
e)
24
R (v)
R377,98
r (vi)
For which service is this account?
For which month is this account?
What is Mr Tshabalala’s account number?
Calculate all the missing values labelled (i) – (vi) on the account.
Explain why the overdue amount is the same as the opening balance.
•
2013/05/09 11:42 AM
Chapter 2
Unit 1 Revising financial documents for
households
One of the most important skills every adult should have is how to manage their
finances. In this unit you will revise the various financial documents that relate to
good financial management for personal and household management.
Have you ever bought something on impulse? Discuss
how buying something on impulse could lead to
financial problems.
Impulse buying refers to
purchases that you make
without planning for them.
Tina is a single mother. Life is tough and she has to budget very carefully. Based on her monthly
income, Tina drew up this budget at the beginning of March:
March Budget
Rent
R2 640,00
Train ticket
R165,00
Taxi fare
R180,00
School fees
R380,00
Groceries
R3 400,00
Shoes for Tumi
and Mpho
R1 200,00
Phone
R400,00
Water & Rates
R230,00
Credit card
R340,00
Electricity
R750,00
Snazz Matazz
R500,00
Emergencies
R500,00
Spending and
entertainment
R500,00
Total
R11 185,00
Savings
R1 115,00
•
25
2013/05/09 11:42 AM
1 T
ina checks her spending against her budget.
Snazzy Shoes
Pineview
Retain as proof of
Purchase
Computing Afrika
Pineview Branch
Vat Reg No:
2874569874
VAT Reg. No 556644338812
2 Flat Sandals
4 Socks
@ R130,00
R260,00
@ R35,90
R143,60
1 Running Shoes
2 Flip Flops
R450,00
@ R55,00
R110,00
1 Platform Shoes
3 Anti-Shoe smell
R375,90
@ R28,50
R85,50
1 Beach Casual Shoe
R255,00
RETAIN AS PROOF OF PURCHASE
1 8 Gb Flash Drive
199,00
1 Anti-virus
349,00
100 CD Spindle
155,00
Total includes 14% VAT
801,42
Cash Card 400078854772222
801,42
Change
Total
R1 680,00
09/03/2013 17:52 3344 5544 777 71
Cash
R2 000,00
R
Cashier: M Human
Change
17/03/2013
09:53
3689
4521
4785 22
0
Customer Helpline: 08605748322
RETURN ALL GOODS IN ORIGINAL PACKAGING
Cashier: Melanie van Wyk
VISIT OUR WEBSITE WWW.SNAZZYSHOES.CO.ZA
CUSTOMER HELPLINE: 0860 222 887
RETURN ALL GOODS IN ORIGINAL PACKAGING
a)Where and when did Tina buy her children’s shoes?
b)Calculate the change she received from the cashier.
c)Did Tina stick to her budget when she bought the shoes? Explain.
d)Tina bought some equipment at a computer shop.
(i)How much did she spend?
(ii)How would this affect her budget? Discuss.
e)Mpho was sick during the month and Tina spent R235 at the pharmacy.
Is this expense covered in her budget? Explain.
f)Discuss whether Tina was able to save as planned for in her budget.
26
•
2013/05/13 12:37 PM
Chapter 2
2
Refer to the following statement from Snazz Matazz, then answer the questions that follow:
Ms T Matlare
PO Box 43111
Pineview
3330
STATEMENT
Date
Snazz Matazz
Credit Available: R8 952,00
Date: 30-March-13
Account Number: 226687TM002
Details
Opening Balance
Amount
Balance
R1 588,20
15/03/13
21/03/13
Activewear
Jeans
R600,50
R425,25
23/03/13
Accessories
R178,25
27/03/13
Cosmetics
R354,50
02/03/13
EFT Payment
R500,00 –
R2 188,70
Closing Balance
Instalment: R450,00
Overdue: R0,00
Total due: R450,00
Due date: 7 April 2013
Credit Limit R11 598,70
Late charges of 22,5% p.a. will be
added to overdue accounts
Help Line: 0800 555 687 2
Tel: 0442 589 6325
Email: [email protected]
a)
b)
c)
d)
e)
How much did Tina spend at the store in March?
Show calculations to prove that her closing balance is R2 646,70.
Does Tina’s budget cover the minimum amount payable? Explain.
Did Tina make the payment by the due date? Explain.
Calculate how much would be added to the account at
the end of the month if the account were not paid by the
An opening balance or a
due date.
balance brought forward is
f) According to the statement, Tina has a credit limit of
the balance from the previous
R11 598,70. What does this mean?
month which needs to be
g) How much can Tina still spend on her account? Find the
added to (debited) or
subtracted from (credited)
amount on the statement.
the new balance in order to
h) What financial implications would there be if Tina spent
calculate the total balance.
more money on her account? Discuss.
3
Do you think it’s important to budget? Write 3–4 sentences in
response to this question.
Use Tina’s financial situation to substantiate your argument.
•
27
2013/05/09 11:42 AM
1
This is a portion of Donald’s bank statement:
z Securebank z
Newtown Central Branch
PO Box 23441 Newtown 2101
Customer Care Centre: 0861 282 3141
Mr D. Triumph
22 Jacaranda Ridge
Sunnyside
2305
23 April 2013
Statement No 55
Vat Reg No. 147-233
Page 1 of 3
Date
22-02-2013
Description
Carried fwd
22-02-2013
Salary Metermaid Inc.
22-02-2013
ATM 2309188888
24-02-2013
Debit
Credit
R9 082,64
Balance
–R2 731,45
R6 351,19
R1 500,00
R4 851,19
Pretty & Prim
R300,00
R4 551,19
25-02-2013
Cell & All
R365,00
R4 186,19
25-02-2013
Ready Card
R400,00
R3 786,19
25-02-2013
ATM 647372888-22
R1 000,00
R2 786,19
26-02-2013
Paytoday Supermarket
R874,39
R1 911,80
28-02-2013
Bank Charges
R253,70
R1 658,10
28-02-2013
ATM 22999911771
R800,00
R858,10
01-03-2013
SatV
R579,50
R278,60
02-03-2013
Computaconnect
R326,50
–R47,90
02-03-2013
ATM 9171727374888
R500,00
–R547,90
03-03-2013
Fairfoods
R253,95
–R801,85
04-03-2013
Electricity Coupon Services
R500,00
–R1 301,85
04-03-2013
Municipality Services
R300,00
–R1 601,85
An overdraft facility
allows one to continue
to withdraw money
when there is a zero
balance on the account.
This means that the
person is actually
borrowing from the
bank. Banks charge
interest on any funds
drawn in this way.
a)
b)
How much did Donald earn as a salary?
Explain why Donald’s balance was only R6 351,19 after his salary was added to
his account.
c) How much cash did Donald withdraw between 22 February and 2 March?
Include any transactions on 2 March.
d) Comment on Donald’s financial situation by 4 March. Explain whether he is in a good or
bad financial position, and why.
28
•
2013/05/09 11:42 AM
Chapter 2
2
This is Donald’s municipal account:
Sunnyside
Municipal
Services
Mr D Triumph
22 Jacaranda Ridge
Sunnyside
2305
Tax invoice number 5872341000
Customer VAT registration number
Account number 284-115-225
Distribution code
Business partner number 522XC3
Tel: 086 010 3089 Fax: 086 010 3090
Tel: Clients abroad +27 21 401 4701
Account summary as at 26/03/2013
At 22 Jacaranda Ridge, Sunnyside, Erf 88440
Due date: 21/04/2013
Previous account balance
762,60
Less payments (04/03/2012) Thank you
300,00–
462,60
462,60
612,58
612,58
1 075,18
1 075,18
Latest account
Current amount due
Total
1 075,18
Total liability
1 075,18
a)
b)
How much did Donald pay on his municipal account?
Why do you think he paid less than he should have?
Refer to his bank statement to answer this question.
c) Do you think he made a wise decision? Discuss.
d) Explain how the total liability of R1 075,18 was calculated.
Unit 2 Quotations, invoices and receipts
Do you remember the difference between a quotation, an invoice and a receipt?
An invoice is a formal
list of goods or services
delivered, and the
amount owing.
A quotation is a formal
statement of goods or
services to be supplied, and
the cost thereof.
A receipt is a
formal statement
of goods or
services paid for.
•
29
2013/05/09 11:42 AM
•
•
•
•
•
•
The reference number and date are used to identify the document.
A quotation is valid for a specified time, after which prices could change.
You do not have to accept a quotation. You might choose to accept only part of the
quotation, or accept a cheaper quotation from someone else.
It is your responsibility to check the invoice to make sure that you have not been
overcharged.
It is your responsibility to pay the invoiced amount by the due date. If you pay after
the due date, you could be charged interest.
It is your responsibility to check that the receipt records the correct details.
1
Answer the questions relating to the following quotation:
Nyaminyami Designs
QUOTATION NUMBER: vad00212
PO Box 322178
Polokwane 0700
Date: 12 July 2014
Quantity
15
70
50
10
100
For Mr Albert van Deventer
82 Chroom Street
Polokwane
0699
Description
Leather Necklace
Nyaminyami Pendant – Silver
Nyaminyami Pendant – Bone
Nyaminyami Pendant – Wood
Windchimes
Total excluding VAT
Unit Price
R40,00
R120,00
R50,00
R45,00
R90,00
R
R
R
R
R
Line Total
VAT @ 14%
TOTAL
TermsandConditions•Quotevalidfor30days
A50%depositisrequiredonacceptance•50%requiredondelivery
a)
b)
c)
d)
e)
f)
g)
Write down the quotation number.
Why is it important to have a quotation number?
On what date will the quotation expire?
What is the unit price of the wind chimes?
Calculate the line totals of each item.
Calculate the total, excluding VAT.
Show that the VAT amount on the items
is R2 933,00.
h) How much must the customer pay in total if
he accepts the quote?
30
•
Cool fact
A quick way to calculate the VATinclusive amount at 14% is to multiply
the VAT-exclusive price by 1,14.
2013/05/09 11:42 AM
Chapter 2
2
The customer’s order was different from the quotation. The following invoice relates to the
order he placed.
Nyaminyami Designs
TAX INVOICE
For Mr Albert van Deventer
Invoice Number 00588
82 Chroom Street
Ref Number: vad00212
Polokwane
PO Box 322178
0699
Polokwane 0700
VAT Reg No: 5588 332211
Date: 8 August 2014
VAT Reg no. 4578 9658 22
Quantity Description
Unit Price
Line Total
15
Leather Necklace
R40,00
R600,00
50
Nyaminyami Pendant – Silver
R120,00
R6 000,00
10
Nyaminyami Pendant – Bone
R50,00
R500,00
8
Nyaminyami Pendant – Wood
R45,00
R360,00
50
Windchimes
R90,00
R4 500,00
Total VAT exclusive
R11 960,00
VAT @ 14%
R1 674,40
Grand Total
R13 634,40
Deposit – 22 July 2014
R6 817,20
Now due – 8 August 2014
120 Days
90 Days
60 Days
30 Days
Current
R6 817,20
a)
b)
How does Nyaminyami Designs match the invoice with the quotation?
By how much does the invoice amount differ from the original quotation?
Show your calculations.
c) Show how the deposit of R6 817,20 was calculated.
d) If the customer was 2 months late with his payment, into which box would the
outstanding amount be typed?
e) The interest for late payment is 11% per year. How much interest would he pay if he was
2 months late with his payment?
3
The following receipt was issued to the customer:
No 522
22/07/2014
Received from
Ontvang van
A Van Deventer
The sum of
Die som van
For
Vir
R
_______________________________________ Rand
______________ cents/sent
deposit – ref number vad00212
T. Gumede
c
6 817 20
With Thanks/Met dank (cash)
•
31
2013/05/09 11:42 AM
a)
b)
c)
d)
What is the receipt number?
When was the deposit paid?
How can the quotation, invoice and receipt be linked to one another?
Write down the deposit amount in words.
Answer the questions relating to the quotation, invoice and receipt that follow.
Frangipani Landscapers
104 Frangipani Crescent, Randburg Ridge, Johannesburg, 2169
Tel: 0117930000, Fax: 0117930001
e-mail: [email protected]
17 December 2014
QUOTE NUMBER:
0014569
Invoice Address: Ms D Nkosi, 504 Hume Road, Dunkeld, 2196
Description
Labour
Quantity Unit
Price ex VAT
VAT Amount Price incl VAT
16
120,00
1 920,00
268,80
2 188,80
Planting
Wisteria
Lawn
Gazania
Clivia
Aloe
2
50
30
65
15
150,00
80,00
20,00
23,00
60,00
300,00
4 000,00
600,00
1 495,00
900,00
42,00
560,00
84,00
209,30
126,00
Total Planting
342,00
4 560,00
684,00
1 704,30
1 026,00
8 316,30
Grand Total
1 290,10
10 505,10
This quote is valid for 14 working days only.
A deposit of 25% is payable on acceptance of this quote.
50% of the total amount is payable 2 days after commencement.
32
•
2013/05/09 11:42 AM
Chapter 2
Tel: 0117930000, Fax: 0117930001
17 December 2014
From: Frangipani Landscapers
VAT Number: 25556778001
To: Ms D Nkosi, 504 Hume Road, Dunkeld, 2196
Description
Labour
Quantity
Unit
TAX INVOICE
Invoice Number: 112587
Ref Number: 0014569
Price ex VAT
VAT Amount
Price incl
VAT
10
128,40
1 284,00
179,76
(i)
2
50
12
150,00
80,00
60,00
(ii)
4 000,00
720,00
42,00
560,00
100,80
(iii)
4 560,00
820,80
(v)
(vi)
882,56
7 186,56
Planting
Wisteria
Lawn
Aloe
Total Planting
Grand Total
(iv)
Now due (25%):
Work commencing on 5 February 2015
Due on 7 February 2015 (50%):
Due on completion (25%):
Late payments will attract interest @ 22,4% per annum
9% discount if paid in full
Tel: 0117930000, Fax: 0117930001
17 December 2014
RECEIPT
Received from:
Ms D Nkosi, 504 Hume Road, Dunkeld, 2196
Date
Description
25 January 2015
Deposit
7 February 2015
Payment
31 March 2015
Payment
Receipt Number: 10224
Ref Number: 0014569
Amount
2 000,00
3 600,00
Total
Account paid in full, thank you
1
Answer the following questions relating to the quotation.
a) Did the customer accept the quotation as is? Explain.
b) What is the deposit amount required if the quote is accepted?
c) What amount is due 2 days after commencement?
•
33
2013/05/09 11:42 AM
2
Answer the following questions relating to the invoice.
a) Which services have been left off the original quotation?
b) Calculate the missing amounts labelled (i) to (vi).
c) What is the price difference between the quotation and the invoice?
d) How do you know that Frangipani Landscapers is registered for VAT?
e) How much must the customer pay to Frangipani Landscapers on presentation of
the invoice?
f) (i) What percentage interest will the customer have to pay if she is late with her
payment?
(ii) If she is one month late with her final payment of R1 796,64 calculate the interest
she will be charged.
3
Answer the following questions relating to the receipt.
a) How much deposit was paid?
b) Was the deposit more or less than the due amount? Explain.
c) (i) What percentage of the total due was payable by 7 February? Find the answer on the
invoice.
(ii) Calculate how much of the total due was payable by 7 February.
d) Did the customer meet the conditions as stated on the invoice? Explain.
Unit 3 Income– and expenditure–
statements and budgets
Any organisation has to budget carefully. Companies and government departments
draw up budgets based on their spending in the previous year. They normally
compare spending and earning patterns for more than one year to ensure that their
budgets are realistic.
34
•
2013/05/09 11:42 AM
Chapter 2
Example
Study the income- and expenditure-statement that follows, then answer the questions
relating to it.
A company
budget
forms part
of their
financial
report.
SIMunYE HIGH ScHooL FInAncIAL rEPort
2013
2012
2012
2011
Budget
Actual
Budget
Actual
31-Dec
31-Dec
IncoME
School fees
Registration fees
R60 490,00
R49 765,00
R54 990,00
R45 825,00
R7 000,00
R5 900,00
R6 300,00
R5 300,00
R2 983,55
R3 200,00
R2 800,00
R13 500,00
R12 270,00
R10 670,00
Interest
Subsidy
R14 850,00
Book fines
R467,50
Uniform sales
R6 764,85
Donations
R7 600,00
R198,00
R5 000,00
Fundraising
totAL IncoME
r82 340,00
r86 980,90
r76 760,00
r69 793,00
Staff costs
R55 280,00
R50 254,00
R51 600,00
R44 870,00
Other costs
R38 200,00
R33 425,67
R31 800,00
R27 643,75
totAL EXPEnSES
r93 480,00
r83 679, 67
r83 400,00
r72 513,75
–R11 140,00
–R3 301,23
–R6 640,00
–R2 720,75
EXPEnSES
Surplus/Shortfall to fundraise
Retained income at start of year
R11 958,50
R9 237,75
Retained income at year end
R15 259,73
R6 517,00
a)
b)
c)
d)
e)
What was the total budgeted income for 2013?
Calculate the percentage increase on budgetted school fees from 2012 to 2013.
Hint: use the ‘Budget’ figures, not the ‘Actual’ figures. Write your answer
correct to one decimal place.
Write down the three categories that contributed the most income in 2012.
Write down one possible expense that would be included in the ‘other costs’
figure.
(i) What is meant by ‘shortfall’?
(ii) Explain why the school had a shortfall in their budget for 2013.
(iii) How could they overcome the shortfall?
•
35
2013/05/09 11:42 AM
Solution
a)
R82 340,00
b)
× 1 ≈ 10%
School fees, the subsidy and donations.
Maintenance, printing paper, etc.
(i) This refers to the difference between the income and the expenses.
When the expenses are greater than the income, the money needed
is referred to as the shortfall.
(ii) The difference between their income and expenditure would be
(R82 340 – R93 480), that is, –R11 140. Their expenses were greater
than their income.
(iii) They could raise funds and look for donations or cut down on
their expenses
60 490 − 54 990
54 990
c)
d)
e)
100
Example
At the end of the financial year, companies have to publish a financial statement
that indicates their revenue (income) and expenditure. Look at the financial
statement that follows, and try to answer the questions on your own before you
check the solutions.
Willander Holdings
CONDENSED CONSOLIDATED STATEMENT OF COMPREHENSIVE INCOME
R’000
Revenue
Retail Sales
For the financial
For the financial
year ending March year ending March
2012
2011
8 143
7 117
7 104
6 114
Other revenue
1 039
1 003
Costs and expenses
Cost of sales
6 178
4 588
5 212
3 817
946
810
644
585
1 965
375
1 905
314
Profit before taxation
Taxation
2 340
2 219
197
178
Total comprehensive income
2 143
2 041
Selling expenses
Administrative and other operating
expenses
Profit from operating activities
Net finance income
a)
b)
14,4
18,5
3,1
5,0
In which year was this financial statement published?
(i) What does R’000 mean?
(ii) What was the total revenue for 2012? Write the amount out in full.
(iii) Show that the revenue was 14,4% more than in 2011.
Show how the 2011 total costs and expenses figures were calculated.
Write down the total costs and expenses for 2011 in words.
c)
d)
36
% Change
•
2013/05/09 11:42 AM
Chapter 2
e)
f)
Write an equation for the calculation to show where ‘profit from operating
activities’ comes from.
Although revenue for the company increased by 14,4%, the total income only
increased by 5%. What is the reason for this?
Solution
a)
b)
2012
(i) It means that all figures represent thousands of rands.
(ii) R8 143 000,00
(iii)
c)
d)
e)
f)
8 143 − 7 117
7 117
×
100
1
=
1 026
7 117
×
100
1
≈ 14, 4%
3 817 + 810 + 585 = 5 212
Five million two hundred and twelve thousand rand
Profit from operating activities = Revenue – Costs and expenses
The percentage increase in costs and expenses of the company was greater than
the percentage increase in revenue.
1
Here is the financial statement of a school. Answer the questions that follow.
2011 Budget
INCOME
Fees
Enrolment Fees
Interest
Subsidy
Consumables
Outings
Transferred from special funds
Bad debt recovered
Book fines
Uniforms Sales
Parent contribution to
development
Donations
Donations and contributions
transferred to special funds
Fundraising
R
6 526 355
22 500
40 000
1 341 120
565 125
210 210
72 000
8 777 310
2010 Actual
2009 Actual
2010 Budget
31-Dec
31-Dec
R
R
R
5 340 711
5 351 655
4 490 493
33 820
18 000
29 700
70 659
20 000
165 314
1 008 181
763 986
804 313
508 155
505 125
396 055
189 405
192 090
150 339
72 000
342 000
72 000
1 512
345
205
27 680
16 502
101 270
4 582 459
–3 595 709
3 059 133
–1 502 269
154 393
8 494 881
93 212
7 774 997
7 192 856
•
37
2013/05/09 11:42 AM
EXPENSES
Staff costs
Other costs
Surplus/Shorfall to fundraise
Retained income at start of year
Retained income at end of year
8 128 014
2 025 200
10 153 214
6 624 976
1 866 126
8 491 102
6 888 724
1 850 000
8 738 724
6 072 639
1 696 583
7 769 222
1 375 904
3 779
54 853
58 632
–1 545 868
5 775
49 078
54 853
(Source: http://www.vulekaschool.co.za/about-us/annual-report/vuleka-school-financial-statements-and-budgets/)
a)
b)
In which year was this budget drawn up? Give a reason for your answer.
What is the difference in the fees received in 2009, and the budgeted fees for 2011?
c) What were the actual fees received in 2010? Write your answer in words.
d) How much money was recovered from bad debts in 2010? Write your answer to the
nearest hundred rand.
e) Did the school budget enough for staff costs in 2010? Give a reason for your answer.
f) What was the difference between the budgeted income and the actual income in 2010?
g) (i) Explain why there is a shortfall in the budget for 2011.
(ii) Suggest two ways for the school to make up the shortfall.
2
Look at the budget that was drawn up for the Knysna Municipality for the financial
year 2013/14.
2013/2014 Revenue and Expenditure Framework
Description
Revenue by Source
Property rates
Property rates – penalties and collection charges
Service charges – electricity revenue
Service charges – water revenue
Service charges – sanitation revenue
Service charges – refuse revenue
Service charges – other
Rental of facilities and equipment
Interest earned – external investments
Interest earned – outstanding debtors
Dividends received
Fines
License and permits
Agency services
Transfers recognised – operational
Other revenue
Gains of disposal of PPE
Total revenue including capital transfers and
contributions
38
•
R’000
147 478
1 993
246 289
43 306
10 441
14 975
2 278
5 503
7 553
3 909
–
2 422
2 062
1 715
65 318
4 518
166
559 926
2013/05/09 11:42 AM
Chapter 2
Expenditure by Type
Employee related costs
Remuneration of councillors
Debt impairment
Depreciation and asset impairment
Finance charges
Bulk purchases
Other materials
Contracted services
Transfers and grants
Other expenditure
Loss on disposal of PPE
Total expenditure
162 616
6 411
16 639
36 831
18 036
173 772
15 182
13 548
6 457
101 565
–
551 055
(Source: Adapted from Knysna Municipality Medium Term Revenue and Expenditure Framework (MTREF). Available from:
http://mfma.treasury.gov.za/Documents/02.%20Budget%20Documentation/2011-12/03.%20Revised%20Budgets/02.%20Local%20
municipalities/WC048%20Knysna/WC048%20Knysna%20Revised%20budget%202011-12.pdf (Accessed: October 2012.))
a)
b)
c)
Explain the difference between ‘revenue’ and ‘expenditure’.
Name three forms of revenue for the Knysna Municipality.
On the document, all figures are given as thousand rands. Write down the actual revenue
received from licences and permits. Write your answer in numbers and in words.
d) What is the biggest expense in the municipality’s budget?
e) According to the budget, will the municipality have a shortfall or a surplus in the
financial year? Explain.
•
39
2013/05/09 11:42 AM
This financial statement was published in newspapers in 2012 for a retail store:
FairFoods
CONSOLIDATED STATEMENT OF COMPREHENSIVE INCOME
R’000
2012
March
52 Weeks
2011
March
53 Weeks
%
Change
Revenue
12 062 447
10 913 094
11
Retail sales
11 766 765
10 673 364
10
295 682
239 730
23
10 320 624
9 483 552
9
Cost of sales
6 843 063
6 201 640
10
Selling expenses
2 645 495
2 505 393
6
832 066
776 519
7
1 741 823
1 429 542
22
44 392
54 662
(19)
1 786 215
1 484 204
20
569 114
473 950
20
1 217 101
1 010 254
20
Other revenue
Costs and expenses
Administrative and other operating expenses
Profit from operating activities
Net finance income
Profit before taxation
Taxation
Total comprehensive income
40
1
Write down the total revenue for 2012.
2
Write down the total costs and expenses for the same period.
3
Show how the profit from operating activities was calculated.
4
Where did the company make most of its revenue?
5
Which line item on the financial statement includes the cost of salaries and rent? Explain.
6
How much tax did the company pay for the year?
7
Show that the costs and expenses for 2012 were ≈ 9% higher than they were for 2011.
8
Explain why the percentage change (% change) for the line item ‘Net finance income’ is
written in brackets.
9
What was the total comprehensive income for 2012? Write your answer in words.
10
Do you think the company has performed well in 2012 compared to 2011? Explain.
•
2013/05/09 11:42 AM
Chapter 2
Unit 4 Tariffs
Tariffs provide a framework for costs when services or rates are charged per unit, for
example, per second, per minute, per litre, per kilowatt, per kilometre. Tariffs often
favour consumers who use less. Those who use more, pay more.
Example
CallMe offers three contract options – RedSpeak, YellowSpeak and GreenSpeak.
The following table compares the three tariffs:
YellowSpeak 100
GreenSpeak100
R1,70
R2,35
R1,70
R0,80
R1,80
R2,70
R2,30
R0,80
R1,60
R1,75
R1,60
R0,80
R0,95
R1,15
R0,90
R1,00
R0,95
R1,10
CallMe to landline
R0,95
R0,95
R0,95
SMS per msg
R0,36
R0,36
R0,34
Monthly fee
Inclusive monthly minutes
redSpeak 100
R250
100 anytime
R115
100 off-peak
R0,00
0
Inclusive monthly SMSs
PEAK cALLS p/m
CallMe to CallMe
CallMe to other mobiles
CallMe to landline
SMS per msg
oFF-PEAK cALLS p/m
CallMe to CallMe
CallMe to other mobiles
a)
b)
c)
d)
Which contract option does not have a monthly subscription?
What do ‘peak’ and ‘off-peak’ refer to?
Why do you think off-peak rates are cheaper?
(i) Complete this table, which compares the cost of phone calls during peak
hours.
callMe to callMe peak rates
Minutes
50
redSpeak
250,00
YellowSpeak
205,00
75
80,00
120,00
100
250,00
125
292,50
150
295,00
160,00
335,00
385,00
240,00
175
377,50
430,00
280,00
475,00
320,00
200
225
462,50
250
505,00
275
300
GreenSpeak
590,00
360,00
565,00
400,00
610,00
440,00
655,00
480,00
•
41
2013/05/09 11:42 AM
(ii) From your table, what can you conclude about the rates for RedSpeak and
YellowSpeak at 75 minutes?
The following graph represents the information in the table. Answer the
questions that follow.
e)
700,00
Remember
to include
the monthly
fee in your
calculations.
600,00
Cost
500,00
400,00
300,00
200,00
100,00
0,00
0
25
50
75 100 125 150 175 200 225 250 275 300
Minutes
(i) Which colour graph represents the RedSpeak CallMe to CallMe peak rates?
Explain.
(ii) Which colour graph represents the GreenSpeak CallMe to CallMe peak
rates? Explain.
(iii) Write down the coordinates of the point of intersection of the dark purple
and black graphs.
(iv) What does the point in question (iii) represent?
Solution
a)
b)
GreenSpeak 100
They refer to the time of day that the phone is used. ‘Peak’ refers to business
hours and ‘off-peak’ refers to early morning, night time and weekends.
Demand is less in off-peak hours. Cheaper rates in these hours may be
intended to encourage customers to use their phones more in those hours.
(i)
CallMe to CallMe Peak Rates
c)
d)
Minutes
50
75
100
125
150
175
200
225
250
275
300
42
•
RedSpeak
YellowSpeak GreenSpeak
250,00
205,00
80,00
250,00
250,00
120,00
250,00
295,00
160,00
292,50
340,00
200,00
335,00
385,00
240,00
377,50
430,00
280,00
420,00
475,00
320,00
462,50
520,00
360,00
505,00
565,00
400,00
547,50
610,00
440,00
590,00
655,00
480,00
2013/05/09 11:42 AM
Chapter 2
e)
(ii) The rate is the same.
(i) The dark-purple graph. RedSpeak offers 100 free anytime minutes.
This is represented as the horizontal portion of the graph.
(ii) The light-purple graph. There is no monthly subscription, which is why
the graph starts at zero on the vertical axis.
(iii) (75; 250)
(iv) At this point the rate is the same for both contracts. In other words,
whether you have YellowSpeak or RedSpeak, it will cost R250 if you
speak for 75 minutes in peak time.
Municipalities and Eskom charge different tariffs for electricity. The following table compares the
Eskom tariff structure with the tariff structure in Pretoria municipality.
Pretoria
Fixed demand charge (R)
Eskom
700,09
Service charge (R)
11,25 per day
Network access charge (R)
13,08 per day
Energy charge (R/kWh )
0,865
Environmental levy charge (R)
0,7234
0,0228
1
What charges does Eskom levy in place of a fixed demand charge?
2
Sharon receives her electricity from Eskom. How much will she pay for her service charge and
her network access charge if she uses the facility for 21 days?
3
Adam receives his electricity from Pretoria municipality. What is his fixed demand charge if he
uses the facility for 21 days?
4
Calculate Sharon’s monthly account if:
• the month has 30 days
• she uses 950 kWh of electricity.
5
Calculate Adam’s monthly account if:
• the month has 30 days
• he uses 950 kWh of electricity.
6
Which user pays less?
•
43
2013/05/09 11:42 AM
The following graph compares the cost of electricity from Eskom and Pretoria, for a
30-day month. All levies have been included.
a) Explain why both
R1 800,00
graphs intersect the
R1 600,00
vertical axis above
R700.
R1 400,00
b) Which is the cheaper
R1 200,00
supplier when
R1 000,00
consuming 100 kWh?
Pretoria
Read your answer
Eskom
R800,00
from the graph.
R600,00
c) Which supplier would
R400,00
you choose if you
used 350 kWh per
R200,00
month? Explain.
0
d) If you were to use
2 000 kWh per month,
Number of kWh
which would be the
most economical
supplier? Explain.
e) Estimate the amount of electricity you could get from each supplier if you spent R1 000
per month.
8
The following bar graph represents the cumulative charges per day for Adam (Pretoria) and
Sharon (Eskom) if they have the same electricity consumption per day.
a) What label
R1 800,00
would you
give to
R1 600,00
Series 1?
R1 400,00
b) What label
R1 200,00
would you
give to
R1 000,00
Series 2?
R800,00
c) Explain why
R600,00
the purple
R400,00
bars
increase at a
R200,00
faster rate
0
than the
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
Day number
grey bars
Series 1
Series 2
do.
d) What
happens by day 29?
1 100
1 000
900
800
700
600
500
400
300
200
100
Total cost
0
Total cost
7
44
•
2013/05/09 11:42 AM
Chapter 2
Water is charged per kilolitre. There are different water tariffs for domestic use and commercial and
school use.
Domestic use – water is charged on a sliding scale where the more water you use the more
expensive it becomes.
Other tariffs
From
To
Rand per kl
(incl VAT)
R per kl
> 0,0
6,0
R0,00
Commercial
> 6,0
10,5
R4,55
Schools
> 10,5
20,0
R9,70
> 20,0
35,0
R14,38
> 35,0
50,0
R17,76
> 50,0
R10,47
R9,25
R23,43
Why do you think the Domestic tariffs change depending on the volume of water used?
2
Show that it costs R93,23 for 18 kilolitres of water on the Domestic tariff.
3
How much does a school pay for 18 kl? Show your calculations.
4
Would a business pay more or less for 18 kl of water than a domestic user? Without doing
any calculations, give a reason for your answer.
5
The following graph shows the total cost of water used by the three different types of users.
a) What colour is the
R1 200,00
Domestic graph?
b) What is the reason for
R1 000,00
the domestic water
charge having a flat
R800,00
line at the beginning?
c) Which graph
R600,00
represents the Schools
tariff – the purple or
R400,00
the black graph?
Explain how you know
R200,00
this.
d) Describe the shape of
R0,00
the Commercial and
20
40
60
80
0
Number of kl
School graphs.
e) Why are they this
shape?
f) What does it mean when the domestic graph is below the school graph?
g) Will the school graph ever intersect with the commercial graph? Explain.
h) Use the graph to estimate how much water each type of consumer can use for R400.
Total cost
1
•
45
2013/05/09 11:42 AM
1
Look at the electricity account that follows:
Account Summary as at 30/11/2012
Due Date:
24/01/2013
Previous Balance
R523,22
Less Payments
R500,00
Latest Balance
Current Amount Due
R253,76
Electricity (Period 26/10/2012 to 26/11/2012 –....... days)
At 2 056 Miller Road Claremont/Erf 22448
Meter number: 11490003/Consumption 378 kWh/Daily average.......
Consumer charge:
Domestic Lifeline
From 26/10/2012: (1) 50 kWh free (2) 100 kWh @R0,6160
(3) 200 kWh @R0,8104 (4) 28 kWh @ R1,0743
R253,76
a)
b)
c)
d)
e)
f)
g)
What is the date of the account?
When must the account be settled?
What was the previous balance?
How much did the account holder pay the previous month?
Calculate the shortfall.
For what period will electricity be charged?
The table shows how the cost for 378 kWh of electricity is broken down. Do the
calculations to prove that the total charge for the 378 kWh is R253,76.
kWh used
Cost per kWh (R)
0–50
0
> 50–150
0,616
> 150–350
0,8104
> 350–600
1,0743
> 600
1,1806
h) Calculate the total cost for a usage of 700 kWh.
46
•
2013/05/09 11:42 AM
Chapter 2
2
The Sol Plaatje Municipality has put forward the following budget for 2010/2011–2012/2013:
nc091 Sol Plaatje – table A4 Budgeted Financial Performance
(revenue and expenditure)
description
r thousand
ref
1
2010/11 Medium term revenue and Expenditure
Framework
Budget Year
2010/11
Budget Year
+2
Budget Year
+1
2011/12
2012/13
Revenue by Source
Property rates
2
208 320
224 570
238 443
Service charges – electricity revenue
2
372 787
424 203
506 370
Service charges – water revenue
2
135 923
154 050
165 016
Service charges – sanitation revenue
2
42 408
47 482
48 840
Service charges – refuse revenue
2
31 074
32 771
34 471
408
424
447
Rental of facilities and equipment
13 289
13 947
14 581
Interest earned – external internal
investment
6 000
8 000
8 000
38 000
43 000
44 000
5 778
6 125
6 462
Property rates – penalties and
collection charges
Service charges – other
Interest earned – outstanding debtors
Dividends received
Fines
Licences and permits
2 891
3 065
3 233
Agency services
2 600
2 756
2 908
129 037
145 963
160 517
29 915
31 682
33 355
1 018 430
1 138 036
1 266 643
329 043
348 557
369 499
14 612
16 635
17 633
Transfers recognised – operational
Other revenue
2
Gains of disposal of PPE
total revenue (excluding capital
transfers and contributions)
Expenditure by Type
Employee related cost
2
Remuneration of councillors
Debt impairment
3
95 000
113 000
126 000
Depreciation and asset impairment
2
49 732
50 995
52 071
20 686
38 178
40 208
241 000
287 570
355 996
–
–
–
Finance charges
Bulk purchases
2
Other materials
8
Contracted services
Transfers and grants
Other expenditure
4, 5
1 450
1 400
1 450
266 907
281 7801
305 786
1 018 430
1 138 036
1 266 643
Loss on disposal of PPE
total expenditure
•
47
2013/05/09 11:42 AM
a)
b)
c)
List the five service charges that bring in revenue for the Sol Plaatje Municipality.
The actual figures are given as R thousand. What does this mean?
Convert the projected income for the rental of facilities and equipment for 2011/2012
into rands.
d) How much revenue is the Sol Plaatje municipality planning to generate from fines in
2012/2013? Write the value in words.
e) What brings in the most revenue for the municipality?
f) List the top three expenditure items for 2012/2013.
g) How much is budgeted for councillors’ salaries in 2012/2013? Write your answer in Rand.
h) Show that the percentage increase in total expenditure between 2011/12 and 2012/13 was
budgeted at 11,3%.
3
Bulelani plans to hire a car and does an internet search. This is the information from one car
hire company:
Your rental so far
Pick-up Branch
Durban: King Shaka
International Airport
drop off Branch:
Durban: King Shaka International
Airport
Pick-up date/time
31 May 2012 05h00
drop off date/
time
8 June 2012 05h00
deliver my vehicle
No
collect my vehicle
No
If you wish to change your travel date and times, click on the update button
Update
Choose your vehicle type and rental preferences
Please select your vehicle from the range of vehicles we have available over the dates you have chosen. We
have defaulted the choice to a Group B category but please feel free to change to any of the available vehicles.
Select your vehicle: Group B:
Quick 4 door Hatch A/C or similar
We have displayed all pricing over the period you want to travel for your vehicle choice. Please select what best
suits your needs by clicking the ‘select’ button on the pricing grid. Please also check any extras you require
below and click the Submit button at the bottom of the page to retrieve your rental cost estimate.
description
rate/day
Excess kms
reduced liability
100 kms free per day
R299,00
R2,25/km
R13 000,00
200 kms free per day
R383,00
R2,25/km
R 3 000,00
Unlimited mileage
R412,00
R0,00/km
R 3 000,00
Select
Extras
Additional drivers @ R175/driver/rental contract
GPS Unit (R59/day, billed separately and not included in this quote)
All Glass and Tyre Waiver (R15/day)
Personal Accident Insurance (R25/day)
Baby seat, now complimentary (We can only assist with one baby seat per rental.
Subject to availability and available on request – email us on [email protected].)
Click to note any special requirements.
continue to retrieve your cost estimate next step >
48
•
2013/05/09 11:42 AM
Chapter 2
a)
b)
For how many days does Bulelani need a car?
Besides the Personal Accident Insurance, Bulelani does not pay any extra costs.
Calculate the total cost if he were to select the option with 200 free km per day.
c) Bulelani will travel an average of 280 km per day. Would it be cheaper to choose the
unlimited mileage option or the option with 200 free km? Support your answer by
showing all calculations.
d) Mpho also considers hiring a car. This table shows his driving schedule.
Day
1
2
3
4
5
Kilometres to travel
240
0
80
160
220
(i) Calculate the average number of kilometres Mpho will drive per day.
(ii) Would it be cheaper for Mpho to choose the 100 free km or the 200 free km per day?
Word bank
bad debts
commercial
financial year
liability
revenue
sliding scale
a debt that the business is not able to collect
private business
the 12-month period that a company’s accounts cover
the financial year usually runs from 1 April to 31 March
legal responsibility to settle a debt
the amount of money a company receives in a given
period
a system in which the rate at which something is paid,
varies according to a set of factors. Electricity and
water is charged on a sliding scale because people who
use more, are charged at a different rate
•
49
2013/05/09 11:42 AM
3
Chapter summary
•
•
•
Bank documents include statements, balance enquiries, loan agreements,
investment agreements, and rate and fee charges.
Tariffs are a schedule of prices and fees. Not all services are used in the same
way by all people. For example, in a parking lot, there is the option to park
per hour, per day or per month. Users of cell phones have the option of
making lots of calls, using more data, using the phone for business purposes,
and so on. Users of electricity have the option of using more or less
electricity. In each of these examples there is a schedule offering different
ways to use the service. Each option has a different pricing structure.
To calculate interest for part of a year, when the interest rate is quoted per
annum (per year) use the following formula:
Interest = Principal sum × rate × time
For example, you owe R150 and the payment is 2 months overdue. You are
charged interest at a rate of 7% p.a. Calculation of interest owing:
Interest = Principal sum × rate × time
7
= 150 × 100 ×
= R1,75
50
•
2
12
Interest for
1 year:
150 × 7%
= R10,50
Interest for
1 month:
R10,50 ÷ 12
= R0,875
2013/05/09 11:42 AM
Ch
3
er
3
a pt
Financial tools
You will:
• identify and perform calculations involving income, expenditure, profit and loss values,
including:
❍
fixed, variable, occasional, high-priority and low priority values
❍
values expressed in thousands, hundreds of thousands, millions and billions
• analyse and prepare income and expenditure statements and budgets
• understand the importance of saving for occasional or future expenses
• identify the costs associated with producing/manufacturing an item or rendering a
service
• determine the cost of production and/or cost price of an item or service
• understand the difference between the production cost and cost price
• decide on an appropriate selling price for an item and/or service based on an expected
percentage profit
• determine break-even values by:
❍
drawing graphs and reading off the points of intersection of the graphs
• understand that the break-even point is always made up of two values and the relevance
of the break-even values is determined by the context in which the break-even values
occur.
Financial tools put us in control of our finances. They allow us to analyse a financial
situation and make careful business decisions.
Financial tools
•
51
2013/05/09 11:42 AM
Check
myself
Hold a class discussion. Talk about how business owners ensure that
they are not running at a loss.
Revision
Looking Up Landscaping Designs have drawn up a schedule of their income for
July 2012.
Income Schedule July 2012
description
Sales
Plants
Maintenance
Houses
Sales
Landscaping
Sales
Pond
•
New garden
Compost
New pond
Pond
52
Soil
Pond repair
Amount
R5 685,00
R1 874,00
R9 340,00
R21 591,00
R2 256,00
R4 859,00
R700,00
Financial tools
2013/05/09 11:42 AM
Chapter 3
a)
b)
c)
d)
What was the income from selling plants, soil and compost?
(i) If the average cost of maintenance is R1 870 per month, how many houses
did the company service for the month?
(ii) What was the total income from maintenance?
Calculate the business’s total income for July 2012.
The total income for June 2012 is shown in this table:
June 2012
Total
Landscaping
R40 554,00
Pond building
R12 150,00
Maintenance
Sales
Grand total
(i)
(ii)
(iii)
(iv)
(v)
R9 340,00
R8 453,00
Which item produced the highest income in June?
Which item increased significantly from June to July?
List the variable income values for the business.
List the occasional income values for the business.
Why are there no fixed income values for the business?
Unit 1 Income and expenditure
Cool fact
Expenditure is the payment of cash for goods or for a service provided. Personal expenditure can
take the form of living expenses (food, clothing and entertainment), accounts (electricity, water and
telephone), fees (school and bank), insurance, tax, repayment of loans and putting money aside in
order to save.
Income
Expenditure
• Income is an amount of money which is received
• E xpenditure is the payment of cash for
• F ixed income value is an income received over a
• F ixed expenditure refers to fixed amounts
• V ariable income value is an income which is
• V ariable expenditure refers to regular
when you sell goods or when you offer a service.
You can earn income from a business deal or from
a salary. You can also get income as a gift or
inheritance.
certain period (weekly, monthly) on a regular
basis.
received on a regular basis but is not a fixed
amount.
goods or services provided.
paid regularly, such as rent or school fees.
payments where the amount is not fixed,
such as a telephone or electricity account.
Financial tools
•
53
2013/05/09 11:42 AM
Income
Expenditure
•O
ccasional income value is an income
•O
ccasional expenditure refers to payments that
which occurs occasionally, such as a gift or
an inheritance. It can also be used to
describe the income of a person who earns
money from part-time, irregular
employment.
are not regular, such as paying a doctor’s bill,
buying a gift for someone or paying to fix your
computer.
•H
igh priority expenditure refers to payments
that have to be made, such as paying bills.
• L ow priority expenditure refers to payments
you do not have to make if you cannot afford
them, such as buying new clothes or paying for
entertainment.
Example
Work through the example as a class, making sure you understand all the concepts.
Penguin Cellular is a small business that sells airtime and cell phones.
The following statement shows the income for the business over a period of
three months:
description
november
december
January
cellular phone sales
Blokia 2761
Simsing Smartphone A23
Orange 2311
IncoME
StAtEMEnt
•
R3 150,00
R5 250,00
R36 250,00
R43 500,00
R21 750,00
R4 089,00
R2 726,00
R6 815,00
r41 389,00
r49 376,00
r33 815,00
Vadi-Air R29
R3 277,00
R5 887,00
R3 016,00
Vadi-Air R129
R10 191,00
R29 799,00
R9 288,00
Vadi-Air R250
R9 750,00
R14 750,00
R3 250,00
Indigo R29
R5 133,00
R3 944,00
R1 218,00
Indigo R59
R5 192,00
R14 219,00
R5 369,00
Indigo R150
R15 750,00
R25 350,00
R8 250,00
Madrigal R15
R3 285,00
R3 795,00
R2 160,00
Madrigal R45
R3 195,00
R4 140,00
R4 365,00
Madrigal R99
R11 682,00
R15 246,00
R6 237,00
r67 455,00
r117 130,00
r43 153,00
r108 844,00
r166 506,00
r76 968,00
Airtime
total
54
R1 050,00
Financial tools
2013/05/09 11:42 AM
Chapter 3
This is the expenditure statement for the same period:
description
november
Rental
EXPEndIturE
december
January
R3 350,00
R3 350,00
R3 350,00
Salaries
R12 478,00
R12 478,00
R12 478,00
Bonuses
R6 862,90
Transport
R745,00
R892,00
R633,00
Electricity
R477,77
R543,45
R484,32
Coffee, tea etc
R252,00
R274,00
R211,00
Blokia
R703,50
R2 110,50
R3 517,50
Simsing
R24 287,50
R29 145,00
R14 572,50
Orange
R3 598,32
R2 398,88
R5 997,20
Vadi-Air
R12 413,50
R27 827,00
R7 665,50
Indigo
R18 381,50
R29 680,66
R9 166,34
Madrigal
R10 805,30
R12 067,65
R6 295,30
r94 355,29
r120 767,14
r64 370,66
a)
b)
c)
d)
e)
f)
Which months do the income and expenditure statements refer to?
Reorganise the expenses into three lists – fixed, variable and occasional
expenses.
How would you classify the company’s income – fixed, variable or occasional?
Explain your answer.
How much profit did the company make for each of the three months?
Organise your answers in a table.
(i) Calculate the total money the company spent on airtime in December.
(ii) How much profit did the company make on airtime over the same period?
(iii) What percentage of the income from airtime was profit? Write your answer
correct to one decimal place.
Why do you think the sales in January were lower than the sales in December?
Solution
a)
b)
c)
d)
November, December and January
Fixed expenses: rental and salaries
Variable expenses: transport, electricity, coffee, etc., Blokia, Simsing, Orange,
Vadi-Air, Indigo and Madrigal
Occasional expenses: bonuses
Variable. The income depends on how much of each item is sold. This varies
from month to month.
Income
Expenditure
Profit = Income – Expenditure
november
108 844,00
94 355,29
14 488,71
december
166 506,00
120 767,14
45 738,86
76 968,00
64 370,66
12 597,34
January
Financial tools
•
55
2013/05/09 11:42 AM
(i) R27 827,00 + R29 680,66 + R12 067,65 = R69 575,31
(ii) Income from airtime in December = R117 130,00
Profit = 117 130 – 69 575,31 = R47 554,69
e)
(iii)
f)
47 554,69
117 130,00
×
100
1
≈ 40,6%
December is the holiday period and people spend more money. In January
people have less money to spend.
1
Martin Mabuza has a bursary to study full time at University of Johannesburg. He is a father
and works weekends and evenings to earn money to support his child. Over weekends, he
sells computer equipment. He only earns commission, not a salary. In the evenings he works
as a waiter, where he earns a small salary as well as tips.
The following bank statement shows Martin’s transactions for a certain period:
Hammanskraal
154A Hamman Ave
Hammanskraal
Tel: 012 447 5599
Statement Number:
Statement Date:
Account Number:
Mr M V Mabuza
3 778 Curie
Street
Hammanskaal
0407
Cheque ACCount
tax Invoice
00058
31 August 2012
1245 336 22
Bank VAT Reg No: 1145884
VAT Inclusive @ 14%
Debits
03/08/2012
05/08/2012
05/08/2012
05/08/2012
06/08/2012
08/08/2012
09/08/2012
10/08/2012
12/08/2012
15/08/2012
15/08/2012
15/08/2012
17/08/2012
19/08/2012
19/08/2012
20/08/2012
23/08/2012
24/08/2012
25/08/2012
26/08/2012
26/08/2012
56
•
Brought Fwd
Service Fee
ComputaAfrica
CallMe CasualChat Contract
ATM withdrawal 2019384T
Cash Deposit
BDHoldings Bursary
Fee payment UJ
ComputaAfrica
Maintenance Payment P Arnold
Cash Deposit
Truly Man clothing
Computaticket
ComputaAfrica
Fairfoods
BluRay connect
Fairfoods
Snazzy Shoes
Varsity Books
ComputaAfrica
Carried Fwd
Credits
124,00
875,00
205,00
300,00
700,00
4 500,00
3 500,00
320,00
3 000,00
600,00
375,95
220,00
1 160,00
172,88
625,00
134,70
425,00
759,00
1 240,00
Balance
2 003,51
1 879,51
2 754,51
2 549,51
2 249,51
2 949,51
7 449,51
3 949,51
4 269,51
1 269,51
1 869,51
1 493,56
1 273,56
2 433,56
2 260,68
1 635,68
1 500,98
1 075,98
316,98
1 556,98
1 556,98
Financial tools
2013/05/09 11:42 AM
Chapter 3
a)
b)
What was Martin’s opening balance on the statement?
Martin earns commission from ComputaAfrica and also banks some of the money he
earns in tips. Calculate the total earnings that were banked for the month.
c) Martin received money from his bursary. He used some of it to pay his university fees and
some to buy textbooks. Calculate whether the income from his bursary payment covered
his expenses.
d) List the two fixed expenses reflected on the bank statement.
e) Did Martin’s income cover his expenses for the month? Explain.
2
The following table shows the audited income statement for the Eastern Cape Provincial
Government for a period of three years.
Summary of Provincial Receipts
R’000
Transfer receipts from national
Equitable share
Conditional grants
Total receipts from National
Provincial own receipts
Tax receipts
Casino taxes
Horse racing taxes
Liquor licences
Motor vehicle licences
Sales of goods and services other than capital assets
Transfers received
Fines, penalties and forfeits
Interest, dividends and rent on land
Sales and capital assets
Financial transactions in assets and liabilities
Total provincial own receipts
Total provincial receipts
In which year was this statement issued?
Give a reason for your answer.
b) (i) List five ways in which the province gets
income from the public.
(ii) Could the income be classified as fixed,
variable or occasional? Explain.
c) Calculate the percentage increase or decrease
in income from 2007/2008 to 2008/2009 and
from 2008/2009 to 2009/2010, for:
(i) liquor licences
(ii) fines, penalties and forfeits.
d) (i) The income is represented as R’000.
Explain this statement.
2007/08
2008/09
Audited
2009/10
27 344 125
3 047 971
30 392 096
32 131 702
3 971 290
36 102 992
37 314 768
4 958 221
42 272 989
333 644
82 433
4 190
5 931
241 090
130 979
16
6 255
494 003
4 768
38 582
1 008 247
31 400 343
384 390
87 718
4 799
1 977
289 896
138 058
−
8 223
372 219
12 100
50 492
965 482
37 068 474
422 138
81 793
7 541
4 462
328 342
136 543
−
6 727
142 142
4 703
49 696
761 949
43 034 938
a)
Cool fact
There is a difference between a
province and a municipality. In South
Africa there are 46 municipalities in 9
provinces. Each municipality forms
part of the province. Each municipality
runs its own budget but these budgets
form part of the provincial budget.
Each province runs its own budget, but
these budgets form part of the national
budget.
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2013/05/09 11:42 AM
e)
3
(ii) The income from Casino taxes is recorded as 87 718, in 2008/2009. Write down the
actual amount received from casino taxes, in rands.
How much did the province receive in total from the national government in the
2009/2010 year?
The following document shows the Eastern Cape provincial expenditure for the same period:
Summary of provincial payments and estimates by vote
R’000
2007/08
Basic Education
Health
Social Development and Special Programmes
Office of the Premier
Provincial Legislature
Roads and Public Works
Local Government and Traditional Affairs
Rural Development & Agrarian Reform
Economic Development & Environmental Affairs
Transport
Human Settlements
Provincial Treasury
Sport, Recreation, Arts & Culture
Safety and Liaison
Total
14 485 498
8 013 849
886 100
291 779
161 517
2 403 064
610 754
1 083 639
736 168
551 253
396 886
156 377
398 053
33 281
30 208 218
2008/09
Audited
17 523 692
10 499 083
1 324 145
343 976
216 079
3 087 251
612 415
1 265 889
856 200
1 056 676
1 230 905
255 773
753 629
41 992
39 067 705
2009/10
20 750 351
12 090 018
1 443 896
359 724
255 960
3 202 686
745 113
1 432 933
1 080 585
1 276 198
1 532 801
234 113
780 691
47 720
45 232 789
a)
58
•
(i) What is the biggest expenditure item in the budget?
(ii) Write down the total amount spent on this item in the 2009/2010 year, in words.
b) How much more money was spent on the Office of the Premier than on Safety and
Liaison in the 2009/2010 year? Write your answer as a percentage.
c) Comment on your answer to b). Do you think the expenditure is fair? Discuss.
d) RefertotheincomestatementinQuestion2.Didtheprovince’sincomecoverits
expenditure over the three years? Answer this question by referring to each financial
year individually.
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2013/05/09 11:42 AM
Chapter 3
Burning Beauty Candles supplies
decorative candles to flea-market
stallholders and to curio shops.
The following statement shows income
and expenditure for the six months
from July to December 2014.
Burning Beauty Candles
Income–Expenditure Statement
July–December 2014
description
Week 1
Week 2
Week 3
Week 4
total sales to
flea markets
Cape curio
market
Stella’s Curios
Candle Affair
Wick-ed
total sales
from stores
total Sales
Aluminium Tape
Paraffin Candle
Wax
Candle Dye
Thermometer
Fragrance
Container Wicks
Moulds
Steric Acid
Cellophane
Labels
Transport
Rent
Phone contract
total
Expenditure
July
R1 406,00
R1 644,00
R828,00
R974,00
r4 852,00
Income
August
September
R1 466,00
R1 457,00
R915,00
R1 144,00
R914,00
R835,00
R855,00
R988,00
r4 150,00
r4 424,00
october
R1 533,00
R1 207,00
R864,00
R997,00
r4 601,00
november
R1 628,00
R1 411,00
R984,00
R1 032,00
r4 023,00
december
R2 505,00
R2 432,00
R3 949,00
R3 194,00
r12 080,00
R1 327,50
R0,00
R2 600,00
R3 500,00
R0,00
R500,00
R0,00
R250,00
R450,00
r2 027,50
R850,00
R250,00
R450,00
r1 550,00
R2 350,00
R250,00
R450,00
r5 650,00
R2 500,00
R250,00
R450,00
r6 700,00
R2 170,00
R1 650,00
R1 500,00
r5 320,00
R0,00
R400,00
R650,00
r1 550,00
r6 879,50
r5 700,00 r10 074,00
Expenditure
r11 301,00
r9 343,00
r13 630,00
R840,00
R2 460,00
R959,00
r4 259,00
R920,00
R2 460,00
R959,00
r4 339,00
R300,00
R3 345,00
R420,00
R78,00
R185,00
R450,00
R520,00
R2 460,00
R959,00
r8 717,00
R270,00
R570,00
R1 570,00
R340,00
R475,00
R945,00
R300,00
R430,00
R2 460,00
R959,00
r7 479,00
R292,40
R845,00
R2 460,00
R959,00
r5 126,40
R765,00
R2 460,00
R959,00
r6 454,00
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2013/05/09 11:42 AM
1
List the expenditure items that are:
a) occasional
b) variable
2
Which month saw the least total sales from the flea markets?
3
Identify the months where the expenditure was greater than the income.
4
Was the expenditure greater than the income for the total period of six months? Justify your
answer with calculations.
5
Why do you think stores bought more candles in October than in November or December?
6
Why do you think flea-market stallholders bought the most candles in December?
c)
fixed.
Unit 2 Cost of production, cost price,
selling price
In this unit you will revise some of the ideas from Grades 10 and 11.
How are these concepts related? Discuss this as a class and then check your answers.
Cost of
production
Cost of
production:
The costs to
produce an
item. These
include fixed
and variable
expenses.
Cost price
Selling price
•
Profit
Percentage
profit
➧
Cost price =
cost of
production
number of
items
➧
Selling price: The price the
customer pays. Selling price
has to cover the cost of
production, but must take
into account whether there
is a market for your goods.
Selling price must be
competitive.
Break-even point:
The point at which income = expenditure.
At the break-even point the business
makes zero loss and zero profit.
60
Break-even
point
➧
Profit =
Income –
Expenditure
You start to
make a
profit after
you have
reached your
break-even
point.
➧
To calculate what percentage profit the business
makes:
Percentage profit =
selling price – cost price
cost price
×
100
1
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2013/05/09 11:42 AM
Chapter 3
Example
A small-scale dairy farmer has calculated his profit for producing milk:
Dairy farmer’s profit
Income
Milk sales
R280 000,00
Total
R308 000,00
Trading income
Variable costs
R28 000,00
Purchased feed
R81 000,00
Veterinary costs
R30 000,00
Labour
R25 000,00
Home-produced feed
Transport
Cartage
Miscellaneous
Udder wash, ear tags etc.
Total variable costs
Profit before fixed costs
a)
b)
c)
d)
R62 000,00
R8 000,00
R12 000,00
R8 000,00
R6 000,00
R232 000,00
R76 000,00
What was his total income?
List two examples of variable costs for the farmer. In each case, explain why
this would not be a fixed or occasional cost.
Show how the farmer calculated his profit before fixed costs.
If the farmer’s total fixed costs are R23 211,84, what is his real profit?
Solution
a)
b)
c)
R308 000,00
Feed – the market prices could vary.
Veterinary costs – this depends on what the animals need the vet for.
Transport – this depends on how much driving the farmer does.
Labour – this is listed as a variable expense because at different times of the
year the farmer needs more or less help on the farm. The farmer would also
have labour as a fixed expense because he would have some permanent farm
labour.
Cartage – this would vary depending on how many animals or how much
milk must be transported to market.
Udder wash, ear tags, and so on – this would vary depending on how many
animals need the service.
Profit = Income – expenditure
= R308 000,00 – R232 000,00
= R76 000,00
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2013/05/09 11:42 AM
Real profit = R76 000,00 – R23 211,84
= R52 788,16
d)
Example
On another dairy farm, the farmer has
Cool fact
fixed expenses of R16 450 per month.
Her variable expenses work out to
One cow can produce an average of
R190 per cow per month.
17 ℓ of milk per day. A farm with
a)
If her cows produce an average of
80 cows would produce (17 × 80 × 30)
17 ℓ of milk per day, calculate her
= 40 800 ℓ of milk per month.
income from each cow per 30-day
month, if:
(i) she is paid R1,00/ℓ for milk
(ii) she is paid R1,20/ℓ for milk.
b)
How many cows does she need to make her business profitable? Organise your
answer in a table. Show both price points in your table, to determine the breakeven point for each price point.
c)
Draw a neatly labelled graph to show the break-even point for the farmer at
each price point.
d)
Using the table and graph, estimate how many cows the farmer should keep in
order to break even, if she receives:
(i) R1,00 per litre. Write your answer as a multiple of five.
(ii) R1,20 per litre. Write your answer as a multiple of five.
Solution
(i) 17 × 30 × R1,00 = R510,00
(ii) 17 × 30 × R1,20 = R612,00
a)
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•
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2013/05/09 11:42 AM
Chapter 3
b)
Number
of cows
Fixed costs
Variable
costs at R190
per cow
Total
expenditure
0
R16 450,00
R0,00
R16 450,00
R0,00
R0,00
5
R16 450,00
R950,00
R17 400,00
R2 550,00
R3 060,00
10
R16 450,00
R1 900,00
R18 350,00
R5 100,00
R6 120,00
15
R16 450,00
R2 850,00
R19 300,00
R7 650,00
R9 180,00
20
R16 450,00
R3 800,00
R20 250,00
R10 200,00
R12 240,00
25
R16 450,00
R4 750,00
R21 200,00
R12 750,00
R15 300,00
30
R16 450,00
R5 700,00
R22 150,00
R15 300,00
R18 360,00
40
R16 450,00
R7 600,00
R24 050,00
R20 400,00
R24 480,00
35
R16 450,00
45
R16 450,00
50
R16 450,00
55
60
70
80
c)
R9 500,00
R10 450,00
R16 453,00
R12 350,00
R16 455,00
R14 250,00
R16 454,00
75
R8 550,00
R16 451,00
R16 452,00
65
R6 650,00
R16 456,00
R11 400,00
R13 300,00
R15 200,00
R23 100,00
R25 000,00
R25 950,00
R26 901,00
R27 852,00
R28 803,00
R29 754,00
R30 705,00
R31 656,00
Income at
R510 per
cow
R17 850,00
R22 950,00
R25 500,00
R28 050,00
R30 600,00
R33 150,00
R35 700,00
R38 250,00
R40 800,00
Income at
R612 per
cow
R21 420,00
R27 540,00
R30 600,00
R33 660,00
R36 720,00
R39 780,00
R42 840,00
R45 900,00
R48 960,00
Small-scale dairy farmer’s break-even position
Income @ R612 per cow
50 000
45 000
Income @ R510 per cow
40 000
Rand value
35 000
Expenditure
30 000
25 000
20 000
15 000
10 000
5 000
0
d)
0
10
20
30
40 50 60 70
Number of cows
80
90 100
(i) She should keep 55 cows.
(ii) She should keep 40 cows.
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1
Penguin Cellular wants to determine
a reasonable selling price for their
Blokia cell phone. The business has
the following budgeted fixed
expenses:
Rent – R950,00; Electricity – R800,00;
Telephone – R500,00;
Insurance – R1 400,00;
Salary R9 700,00.
The Blokia phone costs R250 from the
supplier, and the salesperson receives
R25 commission on each phone sold.
a) Calculate the fixed expenses for
the business.
b) Explain why the cost of the
phone and the commission paid
are variable expenses.
c) Complete this table:
Number of
cell phones
1
Fixed
expenses
5
15
Variable
expenses
Total cost of
production
R4 125,00
20
60
80
Cost price
R14 725,00
R2 945,00
R29 850,00
R497,50
100
R408,50
d) The business owner wants to make 35% profit on sales of the phone. Assuming that he will
sell 60 phones per month, how much should he charge for each phone?
e) The business owner researches cheap cell phones and finds that his nearest cell phone
vendor is selling a similar cell phone for R695,00. He decides on a selling price of R675,00.
Selling price = cost price + (cost price × percentage profit)
(i)
Complete the following table, which shows the profit that would be made at a selling
price of R675,00.
Number of cell phones
Income
Expenditure
Profit @ R675 per phone
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•
1
R675,00
15
25
30
35
40
45
R13 625,00
–R12 950,00
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2013/05/09 11:42 AM
Chapter 3
f)
g)
2
(ii) Use the table to determine how many cell phones need to be sold to break even.
You might have to do additional calculations if the break even position does not
appear in the table.
(iii) Draw a neatly labelled graph to show the break even point.
Prepare a new table to show how the situation would change if the phones were sold at
R690 each.
How many phones need to be sold to break even, at a selling price of R690?
A small pasta making business charges R29,95 for a 500 g bag of pasta.
These are the monthly expenses of the business:
Factory rent: R10 500,00
Electricity: R1 552,00
Water: R926,32
Gas: R782,45
Taxes: R826,05
Salaries: R41 418,77
IT Maintenance contract: R130,00 Internet and telephone: R1 300,00
Office expenses: R720,00
A 500 g bag of pasta has the following ingredients: 500 g of flour and 4 eggs.
FLOUR
This is the cost of the ingredients:
Flour: R55,21 per 10 kg
Eggs: R55,68 per 60 eggs (5 dozen)
a) (i) Calculate the fixed costs.
(ii) Calculate the variable cost for 1 × 500 g bag of pasta.
(iii) Calculate the cost of production for 2 500 bags of pasta.
(iv) Calculate the cost price for 2 500 bags of pasta.
b) The company charges R29,95 per bag. Calculate the income if they sell 2 500 bags
of pasta.
c) How would income and profit be affected if the selling price changed?
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2013/05/09 11:42 AM
Complete the table below to determine the break-even point for different selling prices.
Number –
Bags Pasta
Fixed Cost
Variable Cost
1
250
500
1 000
2 000
5 000
R58 155, 59
R58 155, 59
R58 155, 59
R58 155, 59
R58 155,59
R58 155,59
R6,47
Cost of
Production
R58 162, 06
Cost Price
R58 162,06
Income @
R29,95 per bag
R239,09
R29,95
Income @
R24,95 per bag
Income @
R32,95 per bag
d) Draw a neatly labelled sketch of the cost of production graph, and graphs for the three
different selling prices, to show the three break-even points.
e) A different brand of pasta is selling for R22,95 per 500 g bag. Could the business sell their
pasta for R22,95 if they sold 2 500 bags? Explain.
1
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•
Lesley is a tour operator. She calculates a suitable price for a 1-day tour to the winelands.
Her monthly expenses are:
Office rental – R2 000,00
Tour operator monthly levy
– R58,00
Stationery – R150,00
Insurance – R1 604,00
Cell phone – R825,00
Internet and landline
– R700,00
Vehicle rental – R6 550,00
per month
Average petrol cost per trip
– R350,00
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2013/05/09 11:42 AM
Chapter 3
a)
b)
c)
List Lesley’s fixed costs.
List Lesley’s variable costs.
These are the prices charged by other tour
operators for similar tours:
Sikunjalo Tours
Winelands tour: R2 800,00 per person
Trendy
Tourist
Wonderful
Winelands
R2 600,00 per tour
TourAfrika
0,00
R2 44
per
n
perso
Tour the
Winelands
Lesley considers charging R2 350 per tour.
Complete the following table to determine the financial position of her business if she charges
R2 350,00 per tour.
Number of
tours
1
2
3
5
6
8
10
15
20
25
Fixed costs
Variable costs
R7 000,00
Cost of
production
R13 987,00
Cost price
Income
Profit
R2 350,00
R4 463,00
(i) How many tours would Lesley have to run before she starts to make a profit?
(ii) What would Lesley’s income be if she did five tours in the month?
(iii) What would her profit be if she did 20 tours in the month?
d) The graph shows the financial situation, depending on the number of tours. Study the
graph and answer the questions that follow.
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2013/05/09 11:42 AM
50 000,00
40 000,00
Profit
Rand amount
30 000,00
Cost of
production
20 000,00
10 000,00
0,00
0
1
2
5
6
8
10
15
20
25
–10 000,00
–20 000,00
Number of tours
e)
f)
2
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•
(i) Explain why the ‘Cost of production’ graph cuts the vertical axis at R11 887,00.
(ii) Why does the ‘Profit’ graph cut the vertical axis at –R11 887,00?
(iii) What does the point of intersection of the two graphs represent?
(iv) Compare the slope of the two graphs, and explain why they are different.
Copy the graphs into your book, and then add a graph that shows the profit if Lesley
charges R2 800 per tour.
Use your graph to estimate how many tours Lesley should run to break even, if she
charges R2 800 per tour.
Free-range egg farming is
easy if you have space.
The chickens feed on insects
and plants and lay eggs, which
the farmer can sell. Farmers
can get a government grant to
cover start-up costs. On one
farm, the farmer has fixed
expenses of R4 250 per month.
His variable expenses work
out to R22,30 per hen per
month.
a) If the hens produce an
average of 0,8 eggs per
day, calculate the income
from each hen per 30-day
month, if:
(i) he is paid R1,33 per
egg
(ii) he is paid R1,21 per egg.
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2013/05/09 11:42 AM
Chapter 3
b)
How many hens does he need to make the business profitable? Organise your answer in
a table. Show both price points in your table, to determine the break-even point for each
price point.
c) Draw a neatly labelled graph to show the break-even point for the farmer at each
price point.
d) Using the table and graph, estimate how many hens the farmer should keep in order
to break even, if he receives:
(i) R1,33 per egg. Write your answer as a multiple of 20
(ii) R1,21 per egg. Write your answer as a multiple of 20.
1
Mandisa is in Grade 12. She plans to do a National Diploma in radiography at the University
of Technology. Based on the number of courses she has to do, her fees for the first year will be
R14 260.
a) Mandisa saves up to pay the deposit of 12,5% of the total fees at the start of the year.
(i) Calculate how much she needs to save.
(ii) If her weekend job pays R850 per month and she saves 35% of her earnings, how
many months would it take her to save the money needed?
b) Her grandfather offers to give her R200 for every R500 she saves. Calculate the amount her
grandfather would pay towards the deposit.
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2
Marco, a pasta maker, is saving up to buy new equipment.
He tabulates his income based on sales, to see if he is able to save the R82 000,00 needed:
Number of
bags sold
1
1 000
2 000
5 000
7 500
10 000
Cost of
production
R58 158,97
R61 534,76
R64 913,92
R75 051,42
R83 499,34
R91 947,26
R29,95
R29 950,00
R59 900,00
R149 750,00
R224 625,00
R299 500,00
Income
a)
b)
How much profit will Marco make if he sells 2 000 bags of pasta in the month?
Marco sells 7 500 bags of pasta. Calculate how much he will invest if he saves 25% of his
profits in the company’s savings account.
c) Marco’s average sales per month are 5 000 bags of pasta and he saves 22% of his profits.
(i) Calculate the amount Marco puts into the savings account every month.
(ii) How many months will it take for Marco to save R82 000,00 for the equipment?
d) Marco raises the price on his pasta to R32,50 per bag.
(i) Calculate the income for 5 000 bags.
(ii) Calculate the profit he makes if he sells 5 000 bags at R32,50 per bag.
(iii) Calculate the savings if he saves 26% of his profits.
(iv) How long will it take for him to save the R82 000,00?
3
Burning Beauty Candles has monthly fixed expenditure of R3 760. The variable costs to make
one fragrant 500 g candle are R14,03.
a)
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•
Calculate the cost of production for 200 candles. Show all your calculations.
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Chapter 3
b)
This table gives the costing for various numbers of candles.
Candles
Fixed costs
Variable costs
Cost of production
Cost price
Income at R50
1
20
100
250
500
1 000
2 000
R3 760,00
R3 760,00
R3 760,00
R3 760,00
R3 760,00
R3 760,00
R3 760,00
R14,03
R280,60
R1 403,00
R3 507,50
R7 015,00
R14 030,00
R28 060,00
R3 774,03
R4040,60
R5 163,00
R7 267,50
R10 775,00
R17 790,00
R31 820,00
R3 774,03
R202,03
R51,63
R29,07
R21,55
R17,79
R15,91
R50,00
R1 000,00
R5 000,00
R12 500,00
R25 000,00
R50 000,00
R100 000,00
(i)
Between which two columns would the break-even point be? Write your answer in
terms of the number of candles produced.
(ii) Without doing calculations, write down an estimated number of candles that would
ensure all costs were covered.
(iii) What would the profit be if 500 candles were sold? Show your calculations.
c) How would the situation change if the company charged R65 each for the candles?
Organise your answer by first extending the table, and then discussing the new
break-even point.
d) Draw a graph showing the cost of production and the two different selling points.
Word bank
audited
cartage
curio shops
free-range egg
radiography
small-scale farming
all figures have been checked for accuracy
fee charged for carting (transporting) goods
shops that sell goods for tourists to take home as a
reminder of the country they visited
eggs that are laid by hens who are allowed to roam
freely and who eat natural food
the process where x-rays are taken and produced
farming that uses simple means and does not depend
on sophisticated equipment. Such farmers normally
produce for local markets, but might also sell to big
organisations
Chapter summary
•
Income is an amount of money received in exchange for goods, labour or for
a service. Income sources can be broken down into fixed, variable and
occasional income values:
❍ fixed income value is an income received over a certain period (weekly,
monthly) which does not change, for example, a salary, rent received.
❍ variable income value is an income which is received on a regular basis
based on the number of items sold or the amount of work done.
❍ occasional income is not regular income. Examples are a gift or an
inheritance or income from part-time, irregular employment.
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2013/05/09 11:42 AM
•
•
Expenditure is the money paid for goods or services.
Personal expenditure includes living expenses (food, clothing, transport and
entertainment), services (electricity, water and telephone), fees, insurance and
repayment of loans.
Expenditure can be broken down into fixed, variable and occasional
expenditure:
❍ fixed expenditure refers to regular expenses where the value stays the
same every month, for example, rent.
❍ variable expenditure refers to regular expenses where the amount changes
every month, for example, electricity and water. In a business, variable
expenses increase as the number of items produced increases.
❍ occasional expenditure refers to expenses that are not made every month,
for example, paying to fix the television set.
High priority expenditure refers to expenses that must be paid, for example,
rent.
Low priority expenditure refers to expenses that you would only make when
you can afford it, for example, buying the latest cell phone.
Cost of production: the total cost to produce an item. The cost of production
= total fixed expenses + total variable expenses. It includes all the costs
involved to produce the goods.
Cost price: the amount it costs to make an item.
To calculate the cost price take the cost of production and divide it by the
number of items being produced.
•
•
•
•
•
•
Cost price =
•
cost of production
number of items
Selling price: the price a customer pays for an item. Calculations for selling
prices vary and are dependent on market place demands and competition.
Expected percentage profit – the percentage profit a business expects to make
on an item.
•
Percentage profit =
•
cost price
×
100
1
The break-even point is where the income and expenditure are equal. At the
break-even point the business does not make a profit or a loss.
You can read the break-even point on a graph. This is the point of intersection
of the cost graph and the income graph.
Once the break-even point has been passed the company begins to realise
a profit. This occurs when the income is greater than the expenses.
When the expenditure is greater than the income, the business makes a loss.
Saving money helps us to protect our future. It enables you to afford the
things you need as well as the things that you want.
•
•
•
•
72
selling price – cost price
•
Financial tools
2013/05/09 11:42 AM
Ch
4
er
a pt
Interpretation
of data
You will:
• develop questions that require the collection of data to investigate problems
• recognise that the way in which questions are phrased can impact on the data collected
and, hence, on the findings of the investigation
• ask questions about the reliability of a questionnaire
• choose an appropriate method for data collection
• select an appropriate sample from a population, being aware of the impact that the
choice of sample will have on the reliability of the data collected
• classify collected data as categorical or numerical, discrete or continuous
• sort collected numerical data according to more than two categories, grouping into
intervals where appropriate
• organise collected data
• recognise that the way in which data is classified, sorted and/or grouped will affect
how data is organised, summarised and represented
• summarise and compare multiple sets of collected ungrouped data using the measures
of central tendency and spread, including quartiles, inter-quartile ranges and percentiles
• understand the role and impact of outliers on measures of central tendency and spread.
• represent multiple sets of collected data using a variety of graphs
• interpret box-and-whisker plots as a graphical representation of quartiles
• understand that each type of representation offers a different picture of the data and
that certain types of representations are more appropriate for particular types of data
• understand the effect that the scale of a set of axes and the point at which the axes cross
can have on the impression created by a graph
• read information from graphs and, if necessary, use estimation to determine values on
the graphs
• analyse data presented in graphs
• recognise trends in the data to facilitate finding answers to the questions posed on
issues relating to national and global issues
• ask questions about the way in which data has been collected, organised, summarised
and represented to reveal possible sources of error, bias or misinterpretation.
In this chapter you will revise some concepts learnt in Grade 11 and learn some new
ways to summarise and compare multiple sets of collected data, including how to
interpret box-and-whisker plots. You will consider the six inter-connected stages of the
research process.
Interpretation of data
•
73
2013/05/09 11:42 AM
Pose a question
Graph data
Collect data
Analyse data
Summarise data
Organise data
Every stage in the process is dependent on the stage before it and directly affects
the stage that follows. If the data that is collected is biased, then when it is
analysed it will not tell an accurate story. If the data is incorrectly summarised,
then the analysis of the data will be incorrect. Use the diagram as the centre of a
mind map and brainstorm what you know about each stage in the research
process.
Check
myself
This is an extract from a publication entitled Road Traffic Accident Deaths
in South Africa 2001–2006.
Road traffic accident death
rates were highest in the age
group 35–49 and were
lowest in the age groups
0–14 and 15–24.
The road traffic accident
death rate for males was
more than two and a half
times that for females.
Discuss these questions in groups, or as a class.
1
How are statistics like these obtained?
2
How reliable do you think this type of information is?
Revision
a)
74
Which research instruments would you use to collect data for:
(i) counting how many commuters use the Gautrain
(ii) researching drug abuse amongst unemployed people in the Western Cape
(iii) comparing the number of people using public transport versus the
number of people using their cars to get to work?
•
2013/05/09 11:42 AM
Chapter 4
b)
c)
Define, with examples, a population and a sample.
Thabo collected data on the different shoe sizes of some of the learners in his
class.
Here are his results:
Boys
7
7
8
12
10
8
9
9
12
11
6
12
10
10
6
8
8
12
11
10
Girls
d)
6
6
6
7
4
4
5
5
7
7
7
5
4
5
6
8
4
4
5
5
(i) For the boys’ shoe sizes, calculate:
• the mean
• the mode
• the median
• the range.
(ii) For the girls’ shoe sizes, calculate:
• the mean
• the mode
• the median
• the range.
The frequency table shows the number of unemployed people in Worcester
over a 10-year period:
Year
Jan
2002
Jan
2003
Jan
2004
Jan
2005
Jan
2006
Jan
2007
Jan
2008
Jan
2009
Jan
2010
Jan
2011
Jan
2012
Unemployed
4 600
4 843
4 240
4 000
3 990
4 120
4 200
4 190
4 400
4 360
4 526
e)
(i) Draw a broken line graph to represent the data.
(ii) What is the trend in unemployment from January 2003 to January
2006?
(iii) How is the trend from January 2007 to January 2010 different? Explain.
The frequency table shows how long Grade 12 learners spend studying for
their exams. Represent the data as a histogram.
Time
(minutes)
>30–60
>60–90
>90–120
>120–150
>150–180
>180–210
Number of
learners
156
330
172
150
104
82
•
75
2013/05/09 11:42 AM
Unit 1 Developing questions to support
research
All research starts with a question relating to a problem or issue. The research
question should clearly indicate the purpose of the research.
Research questions often need to be broken down into a set of simpler questions that
can be answered by collecting data using a questionnaire, interview or by observing
and recording.
A good set of questions should:
• be simple and clear
• be relevant to the research problem
• be easy to analyse
• be phrased carefully to answer the research question.
When designing questions for a survey, think about the type of response you need to
answer the research question.
•
•
•
When the information being collected is factual, you can design suitable
categories for answers beforehand.
The way in which questions are phrased can impact on the data collected.
If questions are phrased in a way that makes people feel uncomfortable
or pressurised to give a particular answer, the findings of the research
will be unreliable.
It is important to ask every participant exactly the same questions in the
same way. This ensures that participants are not influenced differently.
Example
This is an extract from the Arrive Alive Festive Season Road Safety Report for
1 December 2011 to 10 January 2012. During this period, around 1 500 people died
in car accidents in South Africa.
Most common trends
The following common fatal crash trends have been recorded during the past Festive
Season:
The most vulnerable road user group/s
The most vulnerable ages:
Most common occurrence per time of the day:
Most fatal crashes per day of the week:
Most common road types for crashes:
Top three road factors:
Pedestrians and public transport passengers
19–29
From 19h00–23h00
Thursday evening, Friday, Saturday and Sunday
Urban and peri-urban (unmarked tar)
Sharp bend, poor road surface and visibility
(Source: Road Traffic Management Corporation. Final Festive Season Road Safety Report for the period 1 December 2011 to
10 January 2012. Available from: http://www.arrivealive.co.za/documents/Festive%20Season%20Road%20Safety%20
76
•
Report%20-%2016%20January%202011.pdf. (Accessed: October 2012)
2013/05/09 11:42 AM
Chapter 4
The data for the Arrive Alive report is collated using police accident reports.
a)
The report states who the most vulnerable road user groups are.
What information did they collect to find out who the most vulnerable
road users were?
b)
If you wanted to know how many adults and children were victims in fatal
crashes, what question/s would you need to ask?
c)
If you wanted to know how many young children, teenagers, young adults and
adults were victims in fatal crashes, how would you phrase your question/s?
d)
On a questionnaire, respondents often choose from a list of options or
categories. The options make the form easier to understand. For example,
to record the ages of the victims at an accident, the question may be phrased
as follows:
How many victims are there within each of the following age groups?
0–9
e)
10–19
20–29
30–39
40–49
50–59
60–69
70 +
Now design questions with options to find out:
(i) the most common time of day fatal crashes occur, using four-hourly
intervals
(ii) the most fatal crashes per day of the week.
What factors do you think might influence visibility of drivers?
Solution
a)
b)
c)
d)
To say who the most vulnerable road user groups are, information listing all
the different people using the road, from pedestrians and cyclists to passengers
and drivers of cars, buses and minibuses would need to be collected.
How many victims were children?
How many victims were adults?
How many victims were young children?
How many victims were teenagers?
How many victims were young adults?
How many victims were adults?
(i) The times you choose to include in your table could vary but you should
have six intervals of four hours each:
At what time did the accident occur?
1 a.m. –
5 a.m.
5 a.m. –
9 a.m.
9 a.m. –
1 p.m.
1 p.m. –
5 p.m.
5 p.m. –
9 p.m.
9 p.m. –
1 a.m.
(ii) On what day did the accident occur?
Mon
Tue
Wed
Thurs
Fri
Sat
Sun
•
77
2013/05/09 11:42 AM
e)
Visibility would refer to any circumstance that might make it harder for a
driver to see. Time of day could be a factor if the driver is driving into the sun.
Weather conditions such as mist, fog or rain affect visibility. Bends in the road
and hills affect how visible oncoming traffic is.
The South African Department of Trade and Industry (DTI) conducted a National Consumer Survey in 2003
to find out how many consumers were aware of their consumer rights so that they could develop a
system to protect consumer rights.
The following bar chart indicates the level of education of the participants in the survey.
Other (for example secretarial)
4
Degree +
3
Technikon diploma
4
Level of education
1
Matric
25
Some high school
38
Primary school
10
No education/some primary
16
0
a)
b)
2
•
40
60
80
Percentage (%)
100
Draw up a possible question which the participants were asked.
Consider the question: 'What is your level of education'?
(i) Do you agree that there would be many different answers?
(ii) If there are too many different answers to a question, what are the disadvantages to
the researcher?
Look at this table. Draw up a possible set of questions that might have been asked to complete
this table.
Black
(n = 649)
White
(n = 105)
Coloured
(n = 106)
Indian
(n = 40)
%
%
%
%
English
85
100
83
100
Afrikaans
57
98
99
35
Any African language
100
5
8
8
Language understood
78
20
2013/05/09 11:42 AM
Chapter 4
3
Think about these questions:
Is it unlawful to buy counterfeit
goods such as brand-name
shoes that are not made by that
brand?
Do you agree that it is unlawful
to buy counterfeit goods such as
brand name shoes which are not
made by that brand?
a)
b)
Which of these questions
would influence
participants’ responses
more? Explain.
Should questions be posed
in such a way that
participants’ responses are
influenced? Explain.
Look at this bar graph which shows the reported incidence of consumer rights violations
among the participants in the National Consumer Survey.
Consumer rights violation
1
Been dissatisfied with guarantees
9
Been misled by advertising
8
Been misled on costs/hidden costs
7
Experienced abuse of information
6
Experienced unfair contract terms
4
Been given no information on safety 2
0
a)
b)
20
40
60
80
Percentage (%)
100
Design a question that could have been asked in order to draw this bar graph.
Make sure that there are categories for the participants’ responses.
Explain why the percentages in the bar graph do not add up to 100%.
•
79
2013/05/09 11:42 AM
2
Look at the bar graph of the employment status of the participants in the National Consumer
Survey. Design a question that could have been asked in order to draw the bar graph.
Unemployed – not looking 2
Employment status
Unemployed – looking
32
Retired
12
Student
14
Housewife
7
Working part-time
7
Working full-time
25
0
20
40
60
80
Percentage (%)
100
Unit 2 Collecting data
The process of collecting data is an important stage in the research process as the
outcome of research depends on reliable and representative data. You need to decide
who to collect the data from and what data collection instrument to use.
The defined group of people from whom the researchers want to collect data from is
called the target population. It is not always possible to collect information from
everybody in the population, so researchers often choose a sample of people in that
population to represent the whole population.
The sample should be fair and representative so that the researcher gets a true picture of
the target population. If the sample is not chosen in a fair and representative way, the
result will be biased and the data will be unreliable.
A simple random sample is a sample where everyone is equally likely to be chosen. In a
stratified random sample the population is first organised into separate groups
according to set criteria, for example, gender or age. Within each group a simple random
sample is selected.
80
•
2013/05/09 11:42 AM
Chapter 4
Data can be collected using different instruments:
• Observations: the researcher gets information by observing participants’
behaviour.
• Interviews: questioning for the purpose of obtaining information which is
relevant to the research.
• Questionnairesorsurveys:formswithspecificquestionsdesignedto
collect information.
Example
Three learners want to investigate the level of knowledge about HIV/AIDS amongst
learners at their school. There are more than 1 000 learners so they have to select only
a sample of the learners.
a)
What is the research question that the learners are investigating?
b)
What does the word ‘representative’ mean?
c)
Here are the different methods that they could use to select a sample:
Choose learners from one class only.
Choose 50 boys in the playground.
Choose 50 learners from Grade 11.
Ask three learners from each class in the school.
Get a list of all the learners at the school and ask every tenth learner.
Ask 10 learners as they arrive at school in the morning.
Ask learners who are interested to stay behind after assembly.
•
81
2013/05/09 11:42 AM

units - Macmillan South Africa

Transcription

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