BASIC MATHEMATICS

By T. KUZIU

CONTENTS INTRODUCTION TO THE BOOK THE LANGUAGE OF MATHEMATICS EXPONENTS INTRODUCTION LAWS OF EXPONENTS EXPONENTIALS IN THE REAL WORLD SURDS SURD CALCULATIONS ERROR MARGINS ROUNDING OFF QUADRATIC SEQUENCES WHAT IS A QUADRATIC SEQUENCE? FINANCE DEPRECIATION SIMPLE DECAY OR STRAIGHT-LINE DEPRECIATION COMPOUND DECAY OR REDUCING-BALANCE DEPRECIATION PRESENT AND FUTURE VALUES OF AN INVESTMENT OR LOAN FINDING I FINDING N — TRIAL AND ERROR NOMINAL AND EFFECTIVE INTEREST RATES FORMULA SHEET SOLVING QUADRATIC EQUATIONS SOLUTION BY FACTORISATION SOLUTION BY COMPLETING THE SQUARE SOLUTION BY THE QUADRATIC FORMULA FINDING AN EQUATION WHEN YOU KNOW ITS ROOTS SOLVING QUADRATIC INEQUALITIES QUADRATIC INEQUALITIES SOLVING SIMULTANEOUS EQUATIONS GRAPHICAL SOLUTION ALGEBRAIC SOLUTION 10 MATHEMATICAL MODELS 10 1 INTRODUCTION 10 2 MATHEMATICAL MODELS 10 3 REAL-WORLD APPLICATIONS 11 QUADRATIC FUNCTIONS AND GRAPHS 11 1 INTRODUCTION 11 2 FUNCTIONS OF THE FORM Y = A(X + P)2 + Q 12 HYPERBOLIC FUNCTIONS AND GRAPHS 12 1 INTRODUCTION 12 2 FUNCTIONS OF THE FORM Y = A X+P + Q 13 EXPONENTIAL FUNCTIONS AND GRAPHS 13 1 INTRODUCTION 13 2 FUNCTIONS OF THE FORM Y = AB(X+P) + Q FOR B > 0 14 GRADIENT AT A POINT 14 1 INTRODUCTION 14 2 AVERAGE GRADIENT 15 LINEAR PROGRAMMING 15 1 INTRODUCTION 15 2 TERMINOLOGY 15 3 EXAMPLE OF A PROBLEM 15 4 METHOD OF LINEAR PROGRAMMING 15 5 SKILLS YOU WILL NEED 16 GEOMETRY 16 1 INTRODUCTION 16 2 RIGHT PYRAMIDS, RIGHT CONES AND SPHERES 16 3 SIMILARITY OF POLYGONS 16 4 TRIANGLE GEOMETRY 16 5 CO-ORDINATE GEOMETRY 16 6 TRANSFORMATIONS 17 TRIGONOMETRY 17 1 INTRODUCTION 17 2 GRAPHS OF TRIGONOMETRIC FUNCTIONS 17 3 TRIGONOMETRIC IDENTITIES 17 4 SOLVING TRIGONOMETRIC EQUATIONS 17 5 SINE AND COSINE IDENTITIES 18 STATISTICS 18 1 INTRODUCTION 18 2 STANDARD DEVIATION AND VARIANCE 18 3 GRAPHICAL REPRESENTATION OF MEASURES OF CENTRAL TENDENCY AND DISPERSION 18 4 DISTRIBUTION OF DATA 18 5 SCATTER PLOTS 18 6 MISUSE OF STATISTICS 19 INDEPENDENT AND DEPENDENT EVENTS 19 1 INTRODUCTION 19 2 DE?NITIONS