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University Mathematics I
Book · October 2019
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V OLUME 1
U NIVERSITY M ATHEMATICS
O LANIYI E VANS
Pan-Atlantic University
www.unimath.hevanz.com
Copyright © 2020 by Olaniyi Evans.
All rights reserved. No part of this book may be reproduced
or transmitted in any form or by any means, electronic or
mechanical, including photocopying, recording or by any
information storage and retrieval system, without prior
written permission of the author, except for the inclusion of
brief quotations in a review.
Limits of Liability/Disclaimer of Warranty: Every effort has
been made to make this book as complete and as accurate as
it possibly can. However, there may be mistakes, both
typographical and content. Therefore, this book should be
harnessed as helpful information and not as the ultimate
bringer of mathematical genius. The author and publisher
shall have neither liability nor responsibility to any person
or entity regarding any loss or damage caused, or alleged to
have been caused, directly or indirectly, from the
information contained in this book.
ISBN: 978-978-977-880-5
Published by
Hevanz International
Km. 42 Lekki-Epe Expressway
Lekki, Lagos, Nigeria
+2348127455000
evans@hevanz.com
DEDICATION
Dedicated to all students who study punctiliously and
voraciously
for
undergraduate,
postgraduate
or
professional exams.
PREFACE
Dear Student:
Bravo! It is with a resolute yet helping hand that I take you
through this most remarkable journey in a manner that you
will appreciate every time you have to refresh & amplify
your mathematics. One of my objectives is to keep you
motivated as you proceed through the book. To that end,
every chapter starts off with a “CAN YOU?”. With the
motivation, start by reading the solved examples, then test
yourself by attempting the examples & then the workouts,
as well as the fill-in-the-blanks & the multiple-choice
questions. Thanks for choosing University Mathematics –
and good luck!
Kindest regards,
Olaniyi Evans01/01/2020
ACKNOWLEDGEMENTS
My immense gratitude goes to the reviewers. My thanks also
goes to my colleagues & students. My appreciation extends
to my wife, Chichi, whose support goes far & beyond
mathematics, and Ayomi Greatly, Olami Xcel & Ifemi Mightia,
whom I love to the moon & back.
C ONTENTS
1. Algebra, Factorization & Surds
Algebra
Factorization
Surds
1
1
5
7
2. Linear Equations
Solving Linear Equations
Graphing
Applications
14
14
19
21
3. Quadratic Equations
Standard Form
Factoring
Completing the Square
The Quadratic Formula
Graphing
Further Applications
26
26
28
28
30
34
39
4. Simultaneous Equations
2 Variables
Elimination Method
Substitution Method
Graphical Method
One Linear and One Quadratic
3 Variables
Elimination Method
Substitution Method
Applications
47
47
48
49
50
54
56
56
57
59
5. Indices, Logarithms & Growth
Indices
Logarithms
Exponential Equations
68
68
71
74
Logarithmic Equations
Growth Rates
76
79
6. Sequences and Series
Sequences
Arithmetic Progression
Geometric Progression
Convergence
85
85
86
92
96
7. Remainder & Factor Theorem
Remainder Theorem
Factor Theorem
102
102
103
8. Trade & Cash Discount
Trade Discount
Discount Series
Cash Discount
Partial Payments
107
107
109
111
115
9. Markup & Markdown
Markup
Rate of Markup
Markdown
Rate of Markdown
121
121
124
125
125
10. Simple & Compound Interest
Simple Interest
Compound Interest
134
134
138
11. Discounted Cash Flow Techniques
Payback Period
Discounted Payback Period
Net Present Value
Internal Rate of Return
147
149
150
153
157
Modified Internal Rate of Return
Profitability Index
162
168
12. Annuities & Perpetuities
Annuities
Deferred Annuity
Perpetuity
174
174
179
204
13. Trigonometry
Triangle
Pythagorean Theorem
Trigonometric Identities
Scalene Triangles
Law of Sines/Cosines
Elevation & Depression
187
187
189
193
197
198
203
14. Coordinate Geometry
Distance between two Points
Mid-Point of a Line Segment
Gradient of a Straight Line
Equation of a Straight Line
Parallel Lines
Perpendicular Lines
209
209
211
213
214
217
218
15. Descriptive Statistics
Measures of Location
Mean
Median
Mode
Percentiles
Quartiles
Measures of Dispersion
Range
Interquartile Range
Variance and Standard Deviation
224
224
225
226
227
227
228
232
232
232
234
Coefficient of Variation
Measures of Association
Covariance
Correlation Coefficient
Grouped Data
235
238
238
239
244
16. Probability
Assigning Probabilities
Basic Relationships of Probability
Addition Law
Conditional Probability
The Multiplication Law
Bayes’ Theorem
250
250
256
257
262
262
267
17. Regression
Simple Regression
Coefficient of Determination
Correlation Coefficient
Multiple Regression
275
275
284
285
290
Suggestions for Further Reading
302
Math practice makes math perfection.
Olaniyi Evans
Purchase the full book at:
www.unimath.hevanz.com
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forever. When you buy University Mathematics (I & II)
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