Algebra Study Guide

Boost Your grades with this illustrated Study Guide. You will use it from high school all the way to graduate school and beyond.

Features

Includes both Algebra I and II
Clear and concise explanations
Difficult concepts are explained in simple terms
Illustrated with graphs and diagrams
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Use your down time to prepare for an exam.
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Table of Contents

Introduction: Simple Operations | Exponents and Powers | Order of Operations | Variables and Expressions | Working With Negative Numbers | Solving Equations Using Properties of Mathematics

Real Numbers: Integers and the Number Line | Absolute Value | Rational Numbers | Adding Rational Numbers | Postulates for The Natural Numbers | Combining Like Terms | Real Numbers | Irrational Number

Functions: Function as Box | Function as Relation | Domain and Range | Terminology | Piecewise-defined function | Even and odd functions | Composite function | Inverse function

Solving Equations: Quadratic equations | Factorization | Completing the square | Quadratic Formula | Weda's Theorem | Systems of Linear Equations | Solving Equations Properties | Solving simultaneous linear and nonlinear equations

Linear Inequalities: Solving linear inequalities | Properties | Solving Inequalities | Compound Inequalities | Solving Inequalities with Absolute Value

Systems of Linear Equations: Linear Equation | Systems of Simultaneous Equations | Linear Simultaneous Equations with Two Variables | Solving Linear Simultaneous Equations | Elimination by Addition Method | Elimination by Substitution Method | Slopes of Parallel and Perpendicular Lines | Solving Systems of Simultaneous Equations Involving Equations Of Degree 2 | Solving Systems of Simultaneous Equations Using a Graphing Calculator

Polynomials: Polynomial Equations | Solving Polynomial Equations | Rational roots of polynomial equations | Factoring Polynomials | Binomial Theorem | Quadratic Functions | Cubic Equation

Conic Sections: Circle | Analytic results | Properties | An alternative definition of a circle | Calculating the parameters of a circle | Fundamental Number Pi | Ellipse | Eccentricity, Equations | Semi-latus rectum and polar coordinates | Area | Parabola | Definitions | Derivation of the focus | Analyzing the Parabola | Hyperbola | Definitions | Equations | Conic Sections

Logarithms and Exponentials Functions: Logarithms definition | Properties of Logarithms | Change of Base Formula | Operations With Exponential Function | Multiplication | The Laws of Exponents | Logarithmic Functions | Laws of Logarithmic Functions | Iteration

Complex Numbers: Introduction | Definition | Properties | The Argand Plane | Euler's formula | Forming trigonometric identities

Sequences and Series: Sequence | Sequences in analysis | Series | Infinite sequences | Series | Infinite series | Types of infinite series | Power series | Arithmetic progression | Geometric progression

Discrete Functions: Combinatorics | Permutation | Combination | Binomial Coefficient | Pascal's triangle | Combinatorics and statistics | Formulae involving binomial coefficients | Generating functions | Newton's binomial series