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Mathematics
Table of Contents
1 Mathematics................................................................................. 3
1.1 Arithmetic........................................................................3
1.1.1 Basic Arithmetic Operations .................................................. 3
1.1.1.1 Basic Terms of Arithmetic and Algebra ........................................ 3
1.1.1.2 Basic Arithmetic Operations with Integers..................................... 5
1.1.1.3 Basic Arithmetic Operations with Fractions ................................. 10
1.1.2 Mathematical Operations with Powers ................................. 16
1.1.2.1 The Term ’Power’ .......................................................................... 16
1.1.2.2 Basic Operations with Powers........................................................ 20
1.1.2.3 Polynomials and Factoring ............................................................ 23
1.1.2.4 Scientific Notation.......................................................................... 25
1.1.2.5 Powers with Fractional Number Exponents (Roots) ..................... 25
1.1.3 Roots and Radicals................................................................ 26
1.1.3.1 Definition of the Terms ’Root’ and ’Radical’................................. 26
1.1.3.2 Finding the Root............................................................................. 28
1.1.3.3 Mathematical Operations with Roots............................................. 28
1.1.3.4 Simplification of Roots.................................................................. 30
1.1.3.5 Simplifying Radical Expressions................................................... 30
1.1.4 Calculation of Percentage..................................................... 32
1.1.4.1 Percentage....................................................................................... 32
1.1.4.2 Average Value................................................................................. 33
1.1.5 Physical Quantities, Standards and Units ............................ 34
1.1.5.1 The Role of Quantities and Standards ........................................... 34
1.1.5.2 Basic Units of the SI System ......................................................... 37
1.1.5.3 Unit Conversions............................................................................ 44
1.2 Algebra ............................................................................47
1.2.1 Algebraic Operations ............................................................ 47
1.2.1.1 Arithmetic Operations with Literal Numbers ................................ 47
1.2.1.2 Algebraic Equations ...................................................................... 50
1.2.1.3 Linear Equations with one Variable .............................................. 50
1.2.1.4 Linear Systems of Equations with Two Variables......................... 52
1.2.1.5 Formulas ....................................................................................... 54
1.2.1.6 Functions and Graphs ................................................................... 54
1.2.2 Mathematical Operations with Logarithms .......................... 56
1.2.2.1 Logarithms..................................................................................... 56
1.2.3 Number Systems ................................................................... 63
1.2.3.1 Decimal System ........................................................................... 63
1.2.3.2 Other Number Systems..................................................................64
1.2.3.3 Mathematical Conversion of Number Systems .............................68
1.3 Geometry ...................................................................... 70
1.3.1 Simple Geometry...................................................................70
1.3.1.1 Coordinate Systems.......................................................................70
1.3.1.2 Definitions, Terms and Basic Constructions.................................71
1.3.1.3 Plane Geometry ............................................................................76
1.3.1.4 Deduction of Mathematical Triangle Theorems............................85
1.3.1.5 Solid Geometry .............................................................................89
1.3.2 Plane Trigonometry ...............................................................94
1.3.2.1 Right Triangle Trigonometry..........................................................94
1.3.2.2 Trigonometric Functions................................................................96
1.3.2.3 Oblique Triangles...........................................................................103
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