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 this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy and recording, without 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