Cool Math Guy – College Algebra

College Algebra, also known as Algebra III or Advanced Algebra, primarily extends concepts previously studied in Algebra II.

For example, the study of functions extends to higher degree functions, transformations of graphs, and inverse functions. The study of quadratic functions in Algebra II extends to polynomial functions of higher degree and transformations of graphs. The study of matrices extends to operations with matrices and applications. Exponential and logarithmic functions as well as the study of conics are included. Use of the graphing calculator is emphasized.

Topics in College Algebra are fully contained in Precalculus.

Chapter P – PREREQUISITES

P.1 Real Numbers
P.2 Exponents and Radicals
P.3 Polynomials and Factoring
P.4 Rational Expressions
P.5 The Cartesian Plane
P.6 Representing Data Graphically

Chapter 1 – FUNCTIONS AND THEIR GRAPHS

1.1 Graphs of Equations
1.2 Lines in the Plane
1.3 Functions
1.4 Graphs of Functions
1.5 Shifting, Reflecting, and Stretching Graphs
1.6 Combinations of Functions
1.7 Inverse Functions

Chapter 2 – SOLVING EQUATIONS AND INEQUALITIES

2.1 Linear Equations and Problem Solving
2.2 Solving Equations Graphically
2.3 Complex Numbers
2.4 Solving Quadratic Equations Algebraically
2.5 Solving Other Types of Equations Algebraically
2.6 Solving Inequalities Algebraically and Graphically
2.7 Linear Models and Scatter Plots

Chapter 3 – POLYNOMIAL AND RATIONAL FUNCTIONS

3.1 Quadratic Functions
3.2 Polynomial Functions of Higher Degree
3.3 Real Zeros of Polynomial Functions
3.4 The Fundamental Theorem of Algebra
3.5 Rational Functions and Asymptotes
3.6 Graphs of Rational Functions
3.7 Quadratic Models

Chapter 4 – EXPONENTIAL AND LOGARITHMIC FUNCTIONS

4.1 Exponential Functions and Their Graphs
4.2 Logarithmic Functions and Their Graphs
4.3 Properties of Logarithms
4.4 Solving Exponential and Logarithmic Equations
4.5 Exponential and Logarithmic Models
4.6 Nonlinear Models

Chapter 5 – LINEAR SYSTEMS AND MATRICES

5.1 Solving Systems of Equations
5.2 Systems of Linear Equations in Two Variables
5.3 Multivariable Linear Systems
5.4 Matrices and Systems of Equations
5.5 Operations with Matrices
5.6 The Inverse of a Square Matrix
5.7 The Determinant of a Square Matrix
5.8 Applications of Matrices and Determinants

Chapter 6 – SEQUENCES, SERIES, AND PROBABILITY

6.1 Sequences and Series
6.2 Arithmetic Sequences and Partial Sums
6.3 Geometric Sequences and Series
6.4 Mathematical Induction
6.5 The Binomial Theorem
6.6 Counting Principles
6.7 Probability

Chapter 7 – CONICS AND PARAMETRIC EQUATIONS

7.1 Circles and Parabolas
7.2 Ellipses
7.3 Hyperbolas
7.4 Parametric Equations