Table of Contents

Table of Contents
Preface……………………………………………………………………………………………. v
CHAPTER

1 Arithmetics……………………………………………………………………………………….. 1
Arithmetic Terms………………………………………………………………………………………………. 1
Multliplication Table………………………………………………………………………………………….. 2
Directed Numbers…………………………………………………………………………………………….. 2
Sample Airframe and Powerplant Technician General Problems……………………….. 3
Factors ……………………………………………………………………………………………………………… 3
Prime Numbers…………………………………………………………………………………………………. 4
Greatest Common Factor (GCF)…………………………………………………………………. 4
Least Common Multiple (LCM)…………………………………………………………………. 4
Least Common Denominator (LCD)………………………………………………………….. 5
Finding the Least Common Denominator………………………………………………….. 5
Arithmetical Precedence……………………………………………………………………………………. 6
Fractions……………………………………………………………………………………………………………. 6
Addition of Fractions………………………………………………………………………………….. 7
Subtraction of Fractions……………………………………………………………………………… 8
Multiplication of Fractions………………………………………………………………………….. 8
Division of Fractions…………………………………………………………………………………… 9
Decimal Fractions……………………………………………………………………………………………… 9
Addition and Subtraction……………………………………………………………………………. 10
Multiplication and Division………………………………………………………………………… 10
Weight and Measures………………………………………………………………………………………… 10
Ratio and Proportion…………………………………………………………………………………………. 11
Averages and Percentages……………………………………………………………………………. 12
Percentage…………………………………………………………………………………………………… 13
Powers and Roots………………………………………………………………………………………………. 13
Powers………………………………………………………………………………………………………… 13
Roots………………………………………………………………………………………………………….. 14
Miscellaneous Exercises…………………………………………………………………………………… 15

2 Algebra………………………………………………………………………………………………………. 41
Operation………………………………………………………………………………………………………….. 41
Basic Laws…………………………………………………………………………………………………………. 42
Equations………………………………………………………………………………………………………….. 43
Solving Linear Equations…………………………………………………………………………….. 43
Equations Requiring Multiplication or Division………………………………………….. 44
Equations Requiring Addition or Subtraction…………………………………………….. 44
Equations Containing Unknowns on Both Sides…………………………………………. 45
Equations Containing Brackets…………………………………………………………………… 45
Equations Containing Fractions………………………………………………………………….. 45
Transposition in Equations………………………………………………………………………………… 46
Construction of Equations………………………………………………………………………….. 48
Simultaneous Equations…………………………………………………………………………………….. 49
Quadratic Equations………………………………………………………………………………………….. 51
Miscellaneous Exercises (Algebra)…………………………………………………………………… 53

3 Numbers………………………………………………………………………………………………………. 81
Indices and Powers……………………………………………………………………………………………. 81
Standard Form…………………………………………………………………………………………………… 83
Numbering Systems…………………………………………………………………………………………… 83
Decimal System of Numeration………………………………………………………………….. 83
Binary System of Numeration…………………………………………………………………….. 84
Octal System of Numeration……………………………………………………………………….. 85
Conversion to Other Bases…………………………………………………………………………. 85
Logarithms………………………………………………………………………………………………………… 87

4 Geometry…………………………………………………………………………………………………….. 89
Angular Measurement……………………………………………………………………………………….. 89
Angles Associated with Parallel Lines…………………………………………………………. 90
Geometric Constructions………………………………………………………………………………….. 90
Triangle………………………………………………………………………………………………………. 90
Triangle Types…………………………………………………………………………………………….. 91
Similar and Congruent Triangles………………………………………………………….. 92
Quadrilaterals……………………………………………………………………………………….. 92
Parallelogram……………………………………………………………………………………….. 93
Rectangle………………………………………………………………………………………………. 93
Rhombus………………………………………………………………………………………………. 93
Square…………………………………………………………………………………………………… 93
Trapezium…………………………………………………………………………………………….. 93
Circles…………………………………………………………………………………………………… 93
Radian Measurement……………………………………………………………………………. 95
Area and Volume………………………………………………………………………………………………. 95
Area……………………………………………………………………………………………………………. 95
Calculation of Areas of Shapes…………………………………………………………………………… 98
Volumes……………………………………………………………………………………………………… 99

5 Graphs…………………………………………………………………………………………………………… 101
Construction……………………………………………………………………………………………………… 102
Graphs and Mathematical Formulas…………………………………………………………… 104
Function and Shape…………………………………………………………………………………….. 105
Nomographs……………………………………………………………………………………………………… 108

6 Trigonometry…………………………………………………………………………………………….. 109
Trigonometric Calculations and Formulas…………………………………………………………. 111
Construction of Trigonometric Curves……………………………………………………….. 113
Valued in Four (4) Quadrants……………………………………………………………………………. 115

7 Co-Ordinate Geometry…………………………………………………………………………. 117
Polar/Rectangular Co-Ordinates……………………………………………………………………….. 119
Miscellaneous Exercises (Geometry and Progress Tests)………………………………… 121
Answers Key – Miscellaneous Questions (Arithmetics)…………………………………….. 133
Answers Key – Miscellaneous Questions (Algebra) …………………………………………… 141
Answers Key – Miscellaneous Questions (Geometry and Revision)…………………… 148
Math Revision…………………………………………………………………………………………………… 149
Short Progress Test……………………………………………………………………………………………. 149
Miscellaneous Aviation Application Mathematics
(General) Related Problems………………………………………………………………………… 151
Conversion of Units Table…………………………………………………………………………………. 153
Place Value Table……………………………………………………………………………………………….. 154
Reading a Ruler…………………………………………………………………………………………………. 154
Glossary………………………………………………………………………………………………………………………………… 155
References……………………………………………………………………………………………………………………………… 159