Math Handbook of Formulas, Processes and Tricks
Math Handbook of Formulas, Processes and Tricks
(mathguy.us)
Algebra and PreCalculus
Prepared by: Earl L. Whitney, FSA, MAAA Version 3.5
October 17, 2022
Copyright 2008-22, Earl Whitney, Reno NV. All Rights Reserved
Algebra Handbook Table of Contents
Page Description
Chapter 1: Basics
9
Order of Operations (PEMDAS, Parenthetical Device)
10
Graphing with Coordinates (Coordinates, Plotting Points)
11
Linear Patterns (Recognition, Converting to an Equation)
12
Identifying Number Patterns
13
Completing Number Patterns
14
Real Number Sets (Sets of Numbers, Real Number Set Tree)
Chapter 2: Operations
15
Operating with Real Numbers (Absolute Value, Add, Subtract, Multiply, Divide)
16
Properties of Algebra (Addition & Multiplication, Zero, Equality)
Chapter 3: Solving Equations
18
Solving Multi-Step Equations
19
Tips and Tricks in Solving Multi-Step Equations
Chapter 4: Probability & Statistics
20
Probability and Odds
21
Probability with Dice
22
Combinations
23
Statistical Measures
Chapter 5: Functions
24
Introduction to Functions (Definitions, Line Tests)
25
Special Integer Functions
26
Operations with Functions
27
Composition of Functions
28
Inverses of Functions
29
Transformation ? Translation
30
Transformation ? Vertical Stretch and Compression
31
Transformation ? Horizontal Stretch and Compression
32
Transformation ? Reflection
33
Transformation ? Summary
34
Building a Graph with Transformations
Cover art by Rebecca Williams, Twitter handle: @jolteonkitty
Version 3.5
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Algebra Handbook Table of Contents
Page Description
Chapter 6: Linear Functions
35
Slope of a Line (Mathematical Definition)
36
Slope of a Line (Rise over Run)
37
Slopes of Various Lines (8 Variations)
38
Various Forms of a Line (Standard, Slope-Intercept, Point-Slope)
39
Slopes of Parallel and Perpendicular Lines
40
Parallel, Perpendicular or Neither
41
Parallel, Coincident or Intersecting
Chapter 7: Inequalities
42
Properties of Inequalities
43
Graphs of Inequalities in One Dimension
44
Compound Inequalities in One Dimension
45
Inequalities in Two Dimensions
46
Graphs of Inequalities in Two Dimensions
47
Absolute Value Functions (Equations)
48
Absolute Value Functions (Inequalities)
Chapter 8: Systems of Equations
49
Graphing a Solution
50
Substitution Method
51
Elimination Method
52
Classification of Systems of Equations
53
Linear Dependence
54
Systems of Inequalities in Two Dimensions
55
Parametric Equations
Chapter 9: Exponents (Basic) and Scientific Notation
56
Exponent Formulas
57
Scientific Notation (Format, Conversion)
58
Adding and Subtracting with Scientific Notation
59
Multiplying and Dividing with Scientific Notation
Version 3.5
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Algebra Handbook Table of Contents
Page Description
Chapter 10: Polynomials ? Basic
60
Introduction to Polynomials
61
Adding and Subtracting Polynomials
62
Multiplying Binomials (FOIL, Box, Numerical Methods)
63
Multiplying Polynomials
64
Dividing Polynomials
65
Factoring Polynomials
66
Special Forms of Quadratic Functions (Perfect Squares)
67
Special Forms of Quadratic Functions (Differences of Squares)
68
Factoring Trinomials ? Simple Case Method
69
Factoring Trinomials ? AC Method
70
Factoring Trinomials ? Brute Force Method
71
Factoring Trinomials ? Quadratic Formula Method
72
Solving Equations by Factoring
Chapter 11: Quadratic Functions
73
Introduction to Quadratic Functions
74
Completing the Square
75
Table of Powers and Roots
76
The Quadratic Formula
77
Quadratic Inequalities in One Variable
79
Fitting a Quadratic through Three Points
Chapter 12: Complex Numbers
80
Complex Numbers - Introduction
81
Operations with Complex Numbers
82
The Square Root of i
83
Complex Numbers ? Graphical Representation
84
Complex Number Operations in Polar Coordinates
85
Complex Solutions to Quadratic Equations
Chapter 13: Radicals
86
Radical Rules
87
Simplifying Square Roots (Extracting Squares, Extracting Primes)
88
Solving Radical Equations
89
Solving Radical Equations (Positive Roots, The Missing Step)
Version 3.5
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Algebra Handbook Table of Contents
Page Description
Chapter 14: Matrices
90
Matrix Addition and Scalar Multiplication
91
Matrix Multiplication
92
Identity Matrices and Inverse Matrices
93
Inverse of a 2x2 Matrix
94
Determinants ? The General Case
95
Matrix Division and Inverses
96
Calculating Inverses ? The General Case (Gauss-Jordan Elimination)
97
Calculating Inverses Using Adjoint Matrices
99
Cramer's Rule ? 2 Equations
100
Cramer's Rule ? 3 Equations
101
Augmented Matrices
102
2x2 Augmented Matrix Examples
103
3x3 Augmented Matrix Example
104
Characteristic Equation and Eigenvalues
105
Eigenvectors
106
2x2 Eigenvalues and Eigenvectors ? General Case
107
Calculating Inverses Using Characteristic Equations
Chapter 15: Exponents and Logarithms
109
Exponent Formulas
110
Logarithm Formulas
111
e
112
Table of Exponents and Logs
113
Converting Between Exponential and Logarithmic Forms
114
Expanding Logarithmic Expressions
115
Condensing Logarithmic Expressions
116
Condensing Logarithmic Expressions ? More Examples
117
Graphing an Exponential Function
118
Four Exponential Function Graphs
119
Graphing a Logarithmic Function
122
Four Logarithmic Function Graphs
123
Graphs of Various Functions
124
Applications of Exponential Functions (Growth, Decay, Interest)
125
Solving Exponential and Logarithmic Equations
Version 3.5
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October 17, 2022
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