FACULTY OF SCIENCE
DEPARTMENT OF MATHEMATICS AND STATISITICS
STUDY GUIDE
NAME OF SUBJECT(MODULE)
Business Mathematics I
NQF
LEVEL
NQF
CREDITS
QUALIFICATION & SAQA ID
COURSE CODE
5
12
Diploma in Accounting
BMD115D
5
12
Diploma in Financial Planning
BMS115D
5
12
Higher Certificate in Accounting
IBM115C
Ms M Nyakale
(2022)
1
©COPYRIGHT : Tshwane University of Technology
Private Bag X680
PRETORIA
0001
All rights reserved. Apart from any reasonable quotations for the purposes of
research criticism or review as permitted under the Copyright Act, no part of
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permission in writing from the publisher.
Printed and distributed by:
FACULTY OF SCIENCE
Tshwane University of Technology
Private Bag X680
Pretoria
0001
2
ORGANISATIONAL COMPONENT CONTENTS: ..................Ошибка! Закладка не
определена.
1. Introduction .......................................................................................................... 5
1.1
Word of welcome .......................................................................................... 5
1.2
Instructions for using the study guide: ........................................................... 5
2. Staff ..................................................................................................................... 6
2.1
Contact Details .............................................................................................. 6
2.2
Staff availability ............................................................................................. 6
3.
Requirements, resources and recommended material. .................................... 6
3.1
4.
Assessment ...................................................................................................... 7
4.1
Assessment rules and regulations ................................................................ 7
4.2
Assessment criteria and methods ................................................................. 7
4.3
Predicate ....................................................................................................... 8
4.4
Promotion requirements ................................................................................ 8
4.5
Moderation .................................................................................................... 8
5.
6.
Requirements for the course ......................................................................... 6
Code of conduct ............................................................................................... 8
5.1
Attendance .................................................................................................... 9
5.2
Classroom behaviour .................................................................................... 9
5.3
Responsibilities of students ........................................................................... 9
5.4
Academic dishonesty and plagiarism ............................................................ 9
5.4.1
Rules........................................................................................................ 10
5.4.2
Terms..................................................................................................... 100
5.4.3
So-called exceptions to copyright infringement ........................................ 11
5.4.4
Plagiarism .............................................................................................. 111
Overview of the subject .................................................................................. 13
3
6.1
Purpose of the subject ................................................................................ 13
6.2
Module credits ........................................................................................... 133
7.
Module composition: Semester plan ............................................................ 133
7.1
Module Outline .......................................................................................... 144
7.2 Learning outcomes, critical cross-field outcomes and learning outcomes,
assessment methods and criteria ....................................................................... 156
4
SECTION
A
1.
INTRODUCTION
1.1
WORD OF WELCOME
ORGANISATIONAL COMPONENT
Welcome to Business Mathematics. This is a semester subject which provides students with
the ability to understand basic concepts of quantitative methods applicable to different
business settings. It is offered as a full time subject with three hours contact time each week.
We trust you will enjoy the subject, and find it interesting and informative.
1.2
INSTRUCTIONS FOR USING THE STUDY GUIDE:
The study guide is for use by the student in various ways and serves as route map through
the subject. It should be used as first point of reference when the student is unclear about a
subject related matter, but should be supplemented with additional sources and consultation
with the lecturer when appropriate.
1.2.1
The study guide should assist the student in preparing for the next class by identifying
learning topics and the scope of work to be covered during each session.
1.2.2
The study guide also serves as memory aide when reviewing the learning material
after each contact session, preparing for class and written tests and for the
examination. In the study guide learning topics and key issues are brought to the fore.
5
2.
STAFF
2.1
CONTACT DETAILS
LECTURER NAME
CAMPUS
ROOM NO
Mrs R Maluleke
Ga-Rankuwa
10-G09
Mrs L PhadimE
Ga-Rankuwa
10 – G09
Ms M. Nyakale
Ga-Rankuwa
10-G10
Tuesdays: 12:30h-14:00h
Mr M.Netshiozwi
Polokwane
Boardroom
Mondays: 11h-13h
Mr Q.Ndlangamandl Mbombela
2.2
CONSULTATION TIMES
1-G96
STAFF AVAILABILITY
If, after attending class and making every effort from your side to master content, you still have
problems with understanding key concepts or principles or their application, lecturers are
available for consultation. It is advisable to make an appointment with the lecturer to discuss
specific learning problems. This will ensure that sufficient time is made available to attend to
your questions in full. Appointments can be made personally, telephonically or by email.
3.
3.1
REQUIREMENTS, RESOURCES AND RECOMMENDED MATERIAL.
REQUIREMENTS FOR THE COURSE
3.1.1 PRESCRIBED RESOURCES
The following tables indicate what literature and other resources are essential for successful
completion of this course. You are strongly advised to acquire all the prescribed resources.
6
PRESCRIBED LITERATURE
CATEGORY
AUTHOR
NAME
PUBLISHER
ISBN NO
BOOKS
John S. Croucher
Introductory
Mathematics &
Statistics for
Business. 6th Edition
McGraw-Hill
9780070284890
Notes
Numeracy
OTHER PRESCRIBED RESOURCES
CATEGORY
DESCRIPTION
CALCULATOR
Any DAL pocket calculator
4.
ASSESSMENT
4.1
ASSESSMENT RULES AND REGULATIONS
SHARP, CASIO etc
Assessment of this course will include online and written (semester) tests. The purpose of
each assessment is to determine whether you have achieved the learning outcomes. The
various assessment methods therefore will focus on criteria that will enable the lecturer to
determine whether you have achieved the learning outcomes.
The assessment criteria
relevant to each learning outcome are detailed 4.2.
4.2
ASSESSMENT CRITERIA AND METHODS
The general rules of TUT regarding assessment apply. You are advised to familiarise yourself
with these rules, as they are applied stringently. The rules are available on the TUT website
(www.tut.ac.za) Part 1, chapter4 of TUT Prospectus.

Semester test schedule
Two semester tests will be written during the semester. The tests are compulsory and they
will both contribute towards the predicate. The schedule is given below and venues and time
will be communicated to all students during lectures but will also be posted on “D2L
Brightspace”. There will not be an optional test for students to improve their predicate marks.
Sem. Test No
Weights
Date
Duration
Time
Chapters
Test 1
30%
TBA
90 minutes
TBA
1-5
Test 2
40%
TBA
90 minutes
TBA
7-13
Replacement
TBA
90 minutes
TBA
ALL
Sick Test
7

Class (Online) tests schedule
Class Test No
Weights
Date
Duration
Chapters
Test 1
15%
TBA
60 minutes
1-4
Test 2
15%
TBA
60 minutes
6-10
Test 3
15%
TBA
60 minutes
7-13
Three class tests shall be written during the year. Note that the best 2 class tests contribute
for final mark.
Venues and time will be announced in class and be posted on “D2L
Brightspace”.
4.3
PREDICATE

The two semester tests will contribute 70% towards the predicate mark

The two class tests will contribute 30% towards the predicate mark
Students are urged to attend at least one tutorial class per week and sign the attendance register that
will be circulated in every class.
All marks will be available on the TUT web (www.tut.ac.za) 2 weeks after a test is written. Any
query must be communicated to the lecturer not later than a week after the marks were
published on the web. All test memorandums will be published on D2L Brightspace.
4.4
PROMOTION REQUIREMENTS
A minimum of 50% is required to pass this subject.
The final mark is calculated as a percentage of the total of all marks obtained from all tests.
4.5
MODERATION
The subject will be moderated internally to ensure fairness of the papers, that the papers
adequately cover the curriculum, and that it is correct.
5.
CODE OF CONDUCT
Please take note of the following regulations. These regulations are in addition to the standard
rules and regulations as determined by the TUT. Please familiarise yourself with the TUT rules
8
and regulations as set out in Prospectus; Part 1 Student Rules and regulations, and in the
student diaries received on registration.
5.1
ATTENDANCE
Regular attendance of all the lectures is of primary importance. It is the learner’s responsibility
to ensure that they attend all scheduled classes. 100% attendance is mandatory for the
subject.
5.2
CLASSROOM BEHAVIOUR
Students are required to arrive before or on time for lectures. No food or eating will be allowed
in class and the use of cell phone text (sms/bbm/whatsapp) messages or calls are strictly not
permitted during the lectures. Phones will be switched off for the duration of each lecture.
5.3
RESPONSIBILITIES OF STUDENTS
It is the responsibility of a student to make a success of learning in this subject. To this end
you are encouraged to attend class, write all tests on the set dates.
Students are expected to be fully prepared when they attend classes. This includes having
reviewed and revised the work from previous classes, identify and clarify any aspect of the
work that might be unclear, done the preparatory work for the upcoming class, being prepared
for tests that may be set, and having done substantial work on given class and home
exercises.
5.4
ACADEMIC DISHONESTY AND PLAGIARISM
Refer to student rules. It remains good academic practice to reference appropriate sources
to substantiate and support the writings, theories, postulates or academic position in any work
submitted for evaluation by the student. However, there are strict rules regarding the citation
of the sources referenced or quoted from. Each student is supplied with an electronic version
of the TUT Citation Guide, and it is the responsibility of the student to ensure that they are
familiar with, and adhere to the principles set out in the Guide.
9
5.4.1 RULES
No copyrighted work may be duplicated or reproduced by any staff member or student of TUT
on any of its premises or any premises under its control, by any means, unless such
reproduction complies with the Copyright Act or permission has been obtained from either the
author or the creator or the owner of such copyright, or else unless TUT is the owner of such
work and the aim of the duplication is exclusively for the normal day-to-day activities of TUT,
or else, unless provision is made for such duplication in this document.
If there is a need for duplication of any copyrighted work, as identified in this document, the
copyright office shall, at the written request of the person or institution, obtain the necessary
permission from the author, creator or owner of such work.
No duplication in any way of any copyrighted work, in accordance with this document, is
permissible on any TUT equipment or equipment under the control of TUT, except where
written permission has been obtained from the copyright office.
5.4.2 TERMS
“copyright” means the exclusive right granted to the owner of an original work for a period of
50 years in South Africa, in terms of which right the copyright owner may be the author, creator,
publisher or producer of the work;
"Copyright Act" means the Copyright Act, 1978 (Act No. 98 of 1978);
“copyright infringement” means the infringement of a copyrighted work when it is reproduced,
beyond “fair dealing” or performed or distributed by being sold, publicly displayed, translated,
rearranged, adapted, abridged, etc, without permission of the copyright owner;
Copyright and plagiarism are important issues in any academic work, Copyright needs to be
strictly adhered to under all circumstances.
Section 23 of the Copyright Act provides for copyright infringement. Section 23(1) provides
that “copying shall be infringed by any person, not being the owner of the copyright, who,
without the licence of such owner, does or causes any other person to do, in the Republic,
any act which the owner has the exclusive right to do or to authorise”.
10
5.4.3 SO-CALLED EXCEPTIONS TO COPYRIGHT INFRINGEMENT
The acts of infringement are limited by what is called the “fair dealing” provisions. Section
12(1) provides that “copyright shall not be infringed by any fair dealing with a literary work –
13
(a) for the purposes of research or private study by, or the personal or private use of, the
person using the work;
(b) for the purposes of criticism or review of that work or of another work;
(c) for the purpose of reporting current events;
(d) in a newspaper, magazine or similar periodical;
(e) by means of broadcasting or in a cinematograph film:
Provided that, in the case of paragraphs (b) and (c)(i), the source be mentioned, as well as
the name of the author if it appears on the work”.
With regard to published editions, section 19A of the Copyright Act provides that section
12(1),(2),(4),(5),(8)(12) and (13) shall mutatis mutandis apply.
5.4.4 PLAGIARISM
Plagiarism is viewed as a serious misconduct and will be viewed as a gross misconduct on
the part of the student.
“Plagiarism” means “the offering of one’s own work the words, ideas or arguments of another
person, without appropriate attribution by quotation, reference or footnote. Plagiarism occurs
both when the words of another are reproduced without acknowledgement, and when the
ideas or arguments of another are paraphrased in such a way as to lead the reader to believe
that they originated with the writer.” (R. D. Mawdsley, in an article Academic Misconduct:
Cheating and Plagiarism, 1994 (Topeka: NOLPE) (Source: Wood)
Types of plagiarism:
11

Collusion: for example, when one student produces work and allows another student
to copy it. If both students submit the work, both students will be deemed to have
colluded.

Group work – for example, some coursework assessments will involve students
working together on a particular project. Such assessments may require students
sharing ideas, research and having a joint responsibility for the development of a
project. Assignments for group work, however, should be written independently identical assessments will be considered to be collusion.

Complete plagiarism: when a piece of work is copied entirely from one or more
sources. Even if the source(s) is acknowledged, and even properly referenced, it is still
considered to be plagiarism as it contains no original work, or interpretation of the
information, from the student.

Partial plagiarism: when inserting sections of directly copied and unacknowledged
source(s) for example, within an assignment.

Copy and paste: it is for example, when information is copied from electronic resources
without proper referencing.

Word switch: when for example, you copy a sentence or paragraph into your work and
change a few words, without proper referencing, it will still be considered as plagiarism.

Concealing sources: all text used in a work must be properly referenced.

Self-plagiarism: occurs when you re-use your own previously written work or data in a
new work and do not reference it appropriately. (Source : University of Sussex)
The consequences of plagiarism will be that the student will get a zero mark for the work
submitted, and that departmental disciplinary (and further) steps will be taken against such a
student. This may results in the student being expelled from the university.
Dishonesty in the form of copying/working together is also viewed as a serious matter. Unless
specifically specified otherwise, all assignments are to be completed on an independent and
individual basis.
Sharing and duplicating of information in tests, examinations and
assignments is not permitted. Where two or more students are found to have worked together
and/or to have shared information, departmental (and further) disciplinary steps will be taken
against such students. This may results in the students being expelled from the university
after a disciplinary hearing.
12
SECTION
6.
B
LEARNING COMPONENT
OVERVIEW OF THE SUBJECT
This subject covers Introductory Mathematics
6.1
PURPOSE OF THE SUBJECT
The course is designed to provide students with the ability to understand basic concepts of
quantitative methods applicable to different business settings. Students will also be taught on
how to use simple mathematical models to solve business problems. The course will help the
students to achieve the following objectives: Describe mathematical relations and functions;
explain and use of different quantitative models and functions in solving business problems.
6.2
MODULE CREDITS
Credits: 5
7.
MODULE COMPOSITION: SEMESTER PLAN
This course comprises a theory component. This is assessed through the tests during the
year.
The following outline provides an overview of the content to be covered in this subject.
13
7.1
MODULE OUTLINE
Learning
Topic
Chapter
Weeks
1
1
2-5
2
Logarithms and exponents
6
1
Factors
7
1
Sigma Notation
8
1
5
Formulae
9
1
6
Graphical representation of data +
10
1
Problem solving
11
1
Simple interest calculations
12
1
Compound interest calculations
13
Units
1
Numbers
2
Using the calculator, Common fractions,
Decimal fractions, and percentages
CLASS TEST 1
??
SEMESTER TEST 1:
CLASS TEST 2: ??
7
CLASS TEST 3: ???
SEMESTER TEST 2:
8
SICK TEST: 20-27/06
Please note that this schedule may vary because of unforeseen circumstances.
14
Duration
7.2
LEARNING OUTCOMES, CRITICAL CROSS-FIELD OUTCOMES AND LEARNING OUTCOMES, ASSESSMENT
METHODS AND CRITERIA
The following table clearly indicates what you have to achieve (the learning outcomes) and how you will be assessed (assessment criteria) to
determine whether you have achieved the required knowledge and competences:
Unit 1: Numerals are symbols for amounts
Purpose of the Unit: To demonstrate that symbols represent numbers in the number system
CCFO
o Symbols are
used to
represent the
simplest
numbers in the
number system
o Numerals
represent
natural numbers
Unit Learning Outcome
o Indicate how numerals
represent numbers
o To provide insight into how
natural numbers are used to
count whole objects
o Carry out calculations
involving whole numbers
o Use and understand
scientific notation
Teaching & Learning
activities
o Lecture
o Independent learning
o Class room
exercise(s), peer-topeer discussion
15
Assessment method
o
o
o
o
Tutorial
Class test
Written test
Written exam
Assessment criteria
o Importance of numerals
o Numerals are symbols
Unit 2: The place-value numeral system; Arithmetic operations
Purpose of the Unit: To illustrate the basic principles of Arithmetic operations
CCFO
o The place-value
system positioning
of number groups
Unit Learning Outcome
Teaching & Learning
activities
o How number groups are
o Lecture
positioned within the place- o Independent learning
value system
o Class room
o Demonstrate the rounding
exercise(s), peer-tooff of numbers
peer discussion
Assessment method
Assessment criteria
o
o
o
o
o Place-value numeral system is defined
o Number groups are positioned in a
place-value system
o Apply basic principles of how numbers
are added, subtracted, multiplied and
divided
o Indicate how numbers are rounded off
Tutorial
Class test
Written test
Written exam
o Application of basic
principles of how
numbers ae added,
subtracted,
multiplied and
divided
Unit 3: Decimals and percentages
Purpose of the Unit: Carry out calculations that involve the use of decimals and percentages
CCFO
o Components of a
decimal: integer,
decimal point and
another integer
demonstration
Unit Learning Outcome
Teaching & Learning
activities
Assessment method
Assessment criteria
o Carry out calculations
involving decimals
o Carry out calculations
involving percentages
o
o Lecture
o Independent learning
o Class room
exercise(s), peer-topeer discussion
o
o
o
o
o Decimal numbers are explained
o Basic principles of how decimal
numbers are added, subtracted,
multiplied and divided are illustrated
o Rounding off decimal numbers is
explained
16
Tutorial
Class test
Written test
Written exam
o Numbers are converted to and from
a percentage
o Percentages are rounded off.
o Problems are solved using addition,
subtraction, multiplication and
division of percentages
o Three basic types of percentage
calculation is demonstrated.
o Expression of
numbers in decimal
form, zeros on the
right hand end after
last digit do not
change the number’s
value
Unit 4: Positive and negative numbers ; Introduction to Algebra and operations
Purpose of the Unit: The illustration of basic principles of Algebra.
CCFO
o Measurement for
opposites, addition,
subtraction,
multiplication and
division
Unit Learning Outcome
Teaching & Learning
activities
Assessment
method
Assessment criteria
o Algebraic operations are
introduced
o How to do simple Algebraic
calculations
o Lecture
o Independent learning
o Class room
exercise(s), peer-topeer discussion
o
o
o
o
o Opposites are identified and
measured
o Addition, subtraction, multiplication
and division of signed numbers is
applied
o Mathematical expressions are
explained
o Exponents are calculated
o Terms of equations are presented
o An overview of solving equations
o Terms are simplified
o Addition, subtraction, multiplication
and division of terms is applied
o Illustration of
mathematical concepts
and expressions, solving
equations
17
Tutorial
Class test
Written test
Written exam
Unit 5: Graphs
Purpose of the Unit: The plotting of linear graphs to solve linear equations
CCFO
o Identify and solve
problems in which
responses display that
responsible decisions
using critical and
creative thinking have
been made.
Unit Learning Outcome
Teaching & Learning
activities
Assessment
method
Assessment criteria
o Plot ordered pairs on a
graph
o Plot and interpret straightline graphs
o Solve simple simultaneous
equations using graphs
o Lecture
o Independent learning
o Class room
exercise(s), peer-topeer discussion
o
o
o
o
o Plotting linear graphs
o Solving linear equations using graphs
o Interpret the findings from the graphs
Tutorial
Class test
Written test
Written exam
o Use simultaneous
equations to solve
problems in break-even
analysis
Unit 6: Simple and Compound interest calculations
Purpose of the Unit: To know basic principles of Financial Calculations
CCFO
Unit Learning Outcome
Teaching & Learning
activities
18
Assessment
method
Assessment criteria
o Identify and solve
problems in which
responses display that
responsible decisions using
critical and creative
thinking have been made.
o
o Apply financial
calculations formula
o Manipulate financial
calculation formula
o Interpret the findings
o Lecture
o Independent learning
o Class room exercise(s),
peer-to- peer
discussion
19
o
o
o
o
Tutorial
Class test
Written test
Written exam
o Correct formula used for
simple/compound interest.
o Correct calculations of
simple/compound interest
o Make formula component subject of the
formula
o Interpretation of calculated amount
20