MTH 001: Access Mathematics COURSE DEVELOPMENT Course Developer Dr C. Bolaji Ahmadu Bello University, Zaria Unit Writer Dr C. Bolaji Ahmadu Bello University, Zaria Course Coordinators Dr F. Peters Ahmadu Bello University, Zaria A. M. Balogun National Open University of Nigeria Lagos Programme Leader Dr (Mrs) M. E. Aina National Open University of Nigeria Lagos National Open University of Nigeria National Open University of Nigeria Headquarters National Open University of Nigeria 14/16 Ahmadu Bello Way Victoria Island Lagos Abuja Annexe Office 245 Samuel Adesujo Ademulegun Street Central Business District Opposite Arewa Suites Abuja E.mail: [email protected] URL: www.nou.edu.ng 0 National Open University of Nigeria 2004 First published 2004 ISBN 978-058-096-4 Published by Longman Nigeria Plc for National Open University of Nigeria Access mathematics: course guide Contents 1 Introduction 2 What you will learn in this course a) Aims of the course b) Course objectives 3 Working through this course a) Course materials b) Study units c) Set textbooks and other resources d) Computer software 4 Assessment a) Tutor-marked assignments b) Final examination and grading c) Course marking scheme d) Course overview 5 How to get the most from this course 6 Summary 7 Tutors and tutorials Introduction This course is on remedial mathematics, which is a non-credit course for students having the need to update their secondary school leaving certificate examinations' results or remedy their defi- ciency in mathematics before their admission directly into the diploma or the degree programme of the NOUN. The course is therefore very essential for all students who need a very good founda- tion in mathematics to undergo any degree programme in the sciences. The course treats a very broad combination of all the major mathematics topics contained in the syllabuses of the West African Examination Council (WAEC), National Examinations Council (NECO) and Joint Admissions and Matriculation Board (JAMB). By the time you have successfully gone through this course, you would have mastered so many methods of solving various fundamental problems in mathematics that are essential to your subsequent studies in higher mathematics or any science programme that employs much of math- ematics. You are expected to diligently go through the course materials, do the exercises contained in the course and do the tutor-marked assignments (TMAs) at the end of each unit. Before you end this course, you would have become more grounded in your understanding of general basic math- ematics essential for your intended undergraduate programme. However, to profitably go through this course and communicate with your course tutor over the internet, you will need to have access to a computer system that has the minimum configuration listed under the course materi- als. What you will learn in this course This course is aimed at taking you through all the various topics in mathematics at a pre-degree level in order to lay a good foundation for a sound mathematics baaground which is a pre- requisite for all science and science-related courses of NOUN's undergraduate programmes. Mathematics MTH 001 C Aims of the course The above overall aim are to: i) Solve problems involving bases, indices and logarithms. ii) Identify and solve various types of equations such as linear, simultaneous and quadratic equations and those involving surds. iii) Solve various problems of mathematics covering areas in sets, trigonometry, differentia- tion, integration, measuration, plane and coordinate geometry and simple statistics. iv) Lay a good foundation in the basic concepts and applications of mathematics principles. Course objectives On successful completion of the course, you should be able to: i) Solve problems in different number bases. ii) Explain the relationship between indices and logarithms. iii) Identify surds and solve equations involving surds. iv) Distinguish between arithmetic progression and geometric progression. v) State the properties of sets and represent them using Venn diagrams. vi) Solve linear and simultaneous equations, and to also solve the latter by graphical method. vii) Identify quadratic equations, solve them using various methods and plot their graphs. viii) Solve inequalities and represent them graphically. ix) Explain various types of variation and how to convert them into equations. x) Solve problems involving matrices and calculate determinants of matrices. xi) Employ various properties of plane geometry involving polygons, angles and circles to solve related problems. xii) Calculate volumes of solid shapes. xiii) Define trigonometric ratios and apply them in solving problems of triangles and bearings. xiv) Coordinate geometry. xv) Discuss various ways of representations of statistical data and solve simple probability problems. xvi) Define differentiation and integration of a function and apply the definitions in so!‘ ing related problems. xvii) Solve simple problems of permutations and combinations. Working through this course Course materials You will need some materials to have a successful study trip through this course. The materials are mainly the reference textbooks listed below under set textbooks. One of your essential tools for this course is a -,:omputer system with the minimum configura- tion listed below: i) Pentium Processor (preferably an Intel Processor, 233 MHz or above) ii) 10G hard disk space iii) 64 MB RAM iv) Standard keyboard v) Mouse and pad vi) 14" SVGA display colour monitor vii) Windows 98 or a better operating system viii) Multimedia components Study units This course is made up of five (5) modules of thirty (30) units. The titles of the units are as presented below: vi Mathematics MTH 001 Units Titles 1 Number bases 2 Indices 3 Logarithms 4 Surds 5 Venn diagrams 6 Sequences: arithmetic progressions 7 Sequences: geometric progressions 8 Sets and their properties 9 Operations of sets 10 Linear equations in one variable 11 Simultaneous linear equations 12 Solutions of sirnultaneous equations by graphical method 13 Quadratic equations 14 Graphs of quadratic equations 15 Inequalities and their solutions 16 Variations —7'17 Matrices and determinants 18 Plane geometry: polygons and angles 19 Circles and their properties 20 Volumes of solids 21- Trigonometric ratios 22 Applications trigonometry: bearings 23 Coordinate geometry 24 Representation of statistical data 25 Graphical representations in statistics 26 Probability 27 Differentiation of a function 28 Applications of differentiation 29 Simple integration 30 Permutations and combinations Set textbooks and other resources References and other resources for this course are as follows: Backhouse, J. K. and S. P. T. Houldsworth (1999): Pure Mathematics I, Longman. MAN (1991): Senior Secondary Mathematics, Books 1 - 3, University Press. Adamu, S. 0. and T. L. Johnson (1975): Statistics for Beginners, Onibonoje Press. Clarke, L. H. and C. G. Lambe (1976): Advanced Level Mathematics (Pure and Applied), Hodder & Stoughton. Abbott, P. (1973): Teach Yourself Geometry, ELBS. Abbott, P. (1973): Teach Yourself Calculus, ELBS. Godman, A. and J. F. Talbert (1975): Additional Mathematics (Pure and Applied), Longman. Hayslett, H. T. (1981): Statistics Made Simple, Heinemann. Assessment The assessment in this course are made up of tutor-marked assignments and your final examination at the end of the course. Tutor-marked assignments- . There are tutor-marked assignments (TMAs) at the end of each unit. You are expected to do the assignments and submit them to your tutor for assessment. Mathematics MTH 001 C vii Final examination and grading The successful completion of this course depends on passing an examination at the end of the course and the satisfaction of all the conditions given by the National Open University of Nigeria. Course marking scheme You can have access to the solutions of all your assessment questions from your tutor for the course. How to get the most from this course To get the most from this course, you need to keep diligently to the study guidelines given by the National Open University of Nigeria. Such guidelines include the study hours expected to put into your study and doing all your assessments. Summary This course is an indispensable course you need as a trainee preparing for a degree programme in any of the sciences or science-related programmes. For example, you cannot be sufficiently prepared to pursue a successful programme in computer science if you do not have a good background in mathematics because computer programming utilises a great deal of mathematical principles and expressions. It takes discipline and constant practice to master almost any mathematics topic. Hence you need to study closely all the examples and also do all the exercises in this course. A list of a number of references is included in this course to give you opportunity to explore the rich resources you need to build yourself up as a good student of basic mathematics. Tutors and tutorials You need to interact with your tutors and attempt all tutorial classes for a better understanding of this course. viii Mathematics . MTH 001 Number bases Contents 1.1 Introduction 1.2 Objectives 1.3 Number bases Some general principles The binary number system Conversion from decimal to binary Mathematical operations with binary numbers Addition of binary numbers Subtraction of binary numbers Multiplication of binary numbers Division of binary numbers The octal number systems Conversion of octal numbers to decimal Conversion of decimal to octal number system Conversion of octal number to binary and vice-versa Mathematical operations of octal numbers Addition and subtraction of octal numbers Multiplication of octal numbers Division of octal numbers 1.4 Conclusion 1.5 Summary 1.6 Tutor-marked assignment 1.7 References 1.1 Introduction Generally, number systems have bases or radixes (or scales) around which they revolve. For example, our most familiar number system, that is, the decimal system is based on number 10 and it has 10 symbols or digits. It has generally been assumed that the use of the decimal system was developed from the fact that human hands have 10 fingers which are readily available for calculations.