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Catalogue

Basic Applied Mathematics Form 5


About the book

The Book is based on the 2009 syllabus by the Ministry of Education and Vocational T raining. The content, presentation and layout were prepared in cognizance of the competency based approach. The book is meant to be able to guide a keen student to pass the examinations even where there is scarcity of teachers. The flow adapted is from simple to complex. The student is carried along through a number of worked out examples to confirm their understanding at each stage of the course. Different levels of exercises are provided to carter for both slow and fast learners. This volume covers: calculating devices, functions, algebra, differentiation, integration and statistics.

 Author : Septine I Sillemu

Table of contents

TABLE OF CONTENTS

 

Acknowledgments.....................................................................................vii

 

Calculating Devices .................................................................................. 1

The Scientific Calculator........................................................................1

The Keyboard of Casio fx991MS Scientific Calculator........... 2

Common Functions with Casio fx991MS Scientific Calculator ..3

Operations using the Scientific Calculator...............................3

The Computer.......................................................................................... 5

Structure of the Computer System.............................................. 5

Microsoft Calculator........................................................................ 7

Operations using the Microsoft Calculator.......................... 8

Microsoft Office Excel................................................................... 10

How to make simple calculations.......................................... 12

Graphing the Polynomials on Spreadsheets..................... 19

Statistical computation by using Excel.................................. 22

Functions.................................................................................................... 30

Basic Concepts..................................................................................... 30

Pictorial Representation of a Relation...................................... 31

Pictorial Representation of a Function...................................... 32

Types of Functions.......................................................................... 33

Basic Properties of Functions....................................................... 34

Graph of a Function............................................................................ 39

Graph of a Linear Function........................................................... 40

Graphs of Step Functions.............................................................. 44

Graph of a Quadratic Function.................................................... 48

Drawing the graphs of quadratic functions........................ 48

Graph of a Cubic Function.............................................................. 53

Graph of a Cubic Function........................................................ 53

Drawing a graph of a cubic function using the turning

point and intercepts................................................................... 57

Graph of a Rational Function....................................................... 58

Plotting Graphs using Computers.............................................. 63

Importance of Functions................................................................... 68

Supply and Demand Curves......................................................... 68

Velocity-Time Curve........................................................................ 71

 

Algebra....................................................................................................... 75

Simultaneous Equations.................................................................. 75

Formulation of Simultaneous Equations................................... 75

Solving Simultaneous Equations................................................. 78

Series....................................................................................................... 81

Finite Series....................................................................................... 82

Infinite Series..................................................................................... 82

Sums in Sigma Notation................................................................ 82

Sums of Finite Series for Arithmetic Progressions................ 84

Sums of Finite Series for Geometric Progressions............... 86

Infinite Geometric Progressions................................................. 88

Ratios...................................................................................................... 90

Application of Ratios in Currency Conversion........................ 92

Scale Drawing using Ratios.......................................................... 95

Mixtures and Ratios........................................................................ 97

Variations............................................................................................. 99

Direct Variation.............................................................................. 100

Inverse Variation........................................................................... 102

Joint Variation................................................................................ 104

 

Differentiation ...................................................................................... 108

Differentiation by the First Principle........................................... 108

Techniques of Differentiation....................................................... 112

Derivative Using the Chain Rule............................................... 112

Derivative Using the Product Rule........................................... 114

Derivative Using the Quotient Rule......................................... 115

First and Second Derivatives......................................................... 118

Implicit Differentiation..................................................................... 120

Application of Differentiation........................................................ 122

The Slope of a Curve................................................................... 122

The Rate of Change..................................................................... 124

Maxima, Minima, and Points of Inflexion............................... 125

Derivatives of Displacement and Velocity............................. 132

Marginal Revenue......................................................................... 135

Marginal Cost................................................................................ 137

 

Integration............................................................................................... 143

The Anti-derivative............................................................................ 143

Indefinite Integral.............................................................................. 144

Standard integral of the form f(x) = xn.................................. 145

Indefinite Integrals of Polynomials........................................... 146

Application of Substitution Technique in

Integrating Polynomials............................................................... 148

Definite Integral................................................................................. 149

Application of Integration.............................................................. 154

Curve Sketching............................................................................. 154

Area under a Curve...................................................................... 154

Area between a Curve and a line............................................. 157

Area between two Curves........................................................... 159

Volume of Solids of Revolution................................................. 162

Application of Integration in Real Life Problems.................. 164

Displacement and Velocity...................................................... 165

Total Cost and Total Revenue................................................ 167

 

Statistics..................................................................................................... 172

Data Collection, Organization, and Presentation...................... 172

Data Collection and Organisation............................................. 173

Data Presentation.......................................................................... 175

Frequency Distribution Tables................................................. 175

Class Intervals, Class Boundaries, Class Marks and Class Width.............................................................................................. 178

Graphical Presentation of Data.............................................. 179

Pictograms.................................................................................... 182

Measures of Central Tendency...................................................... 188

The Mode......................................................................................... 188

The Median...................................................................................... 191

The Mean.......................................................................................... 193

Arithmetic mean.......................................................................... 194

Evaluating the Mean for Grouped Data................................ 195

The Mean using the assumed mean method................... 195

The Mean using the coding mean method........................ 197

Quartiles and Percentiles................................................................. 199

The Quartiles................................................................................ 199

The Percentiles........................................................................... 204

Real life problems involving mean, median and percentile...................................................................................... 208

Measures of Dispersion................................................................... 209

The Range......................................................................................... 209

Variance and Standard Deviation.............................................. 210

Application of Statistics.................................................................... 214

The Mean or Average.................................................................. 215

The Median..................................................................................... 218

The Mode........................................................................................ 219

Variance............................................................................................ 220

Standard Deviation....................................................................... 221

Class Project.................................................................................... 222

 

Answers to the Exercises...................................................................... 226

Index........................................................................................................... 255

Additional References .......................................................................... 262