R A Review of Basic Concepts and Skills

R.1 The Language, Notation and Numbers of Mathematics

R.2 Algebraic Expressions and the Properties of Real Numbers

R.3 Exponents, Polynomials and Operations on Polynomials

R.4 Factoring Polynomials

R.5 Rational Expressions

R.6 Radicals and Rational Exponents

1 Equations and Inequalities

1.1 Linear Equations, Formulas and Problem Solving

1.2 Linear Inequalities in One Variable with Applications

1.3 Solving Polynomial and Other Equations

1.4 Complex Numbers

1.5 Solving Non-Factorable Quadratic Equations

2 Functions and Graphs

2.1 Rectangular Coordinates and the Graph of a Line

2.2 Relations, Functions and Graphs

2.3 Linear Functions and Rates of Change

2.4 Quadratic and Other Toolbox Functions

2.5 Functions and Inequalities A Graphical View

2.6 Regression, Technology and Data Analysis

3 Operations on Functions and Analyzing Graphs

3.1 The Algebra and Composition of Functions

3.2 One-to-One and Inverse Functions

3.3 Toolbox Functions and Transformations

3.4 Graphing General Quadratic Functions

3.5 Asymptotes and Simple Rational Functions

3.6 Toolbox Applications: Direct and Inverse Variation

3.7 Piecewise-Defined Functions

3.8 Analyzing the Graph of a Function

4 Polynomial and Rational Functions

4.1 Polynomial Long Division and Synthetic Division

4.2 The Remainder and Factor Theorems

4.3 The Zeroes of Polynomial Functions

4.4 Graphing Polynomial Functions

4.5 Graphing Rational Functions

4.6 Additional Insights into Rational Functions

4.7 Polynomial and Rational Inequalities An Analytic View

5 Exponential and Logarithmic Functions

5.1 Exponential Functions

5.2 Logarithms and Logarithmic Functions

5.3 The Exponential Function and Natural Logarithms

5.4 Exponential/Logarithmic Equations and Applications

5.5 Applications from Business, Finance and Physical Science

5.6 Exponential, Logarithmic, and Logistic Regression Models

6 Systems of Equations and Inequalities

6.1 Linear Systems in Two Variables with Applications

6.2 Linear Systems in Three Variables with Applications

6.3 Systems of Linear Inequalities and Linear Programming

6.4 Systems and Absolute Value Equations and Inequalities

6.5 Solving Linear Systems Using Matrices and Row Operations

6.6 The Algebra of Matrices

6.7 Solving Linear Systems Using Matrix Equations

6.8 Matrix Applications: Cramers Rule, Partial Fractions and More

7 Conic Sections and Non-Linear Systems

7.1 The Circle and the Ellipse

7.2 The Hyperbola

7.3 Nonlinear Systems of Equations and Inequalities

7.4 Foci and the Analytic Ellipse and Hyperbola

7.5 The Analytic Parabola

8 Additional Topics in Algebra

8.1 Sequences and Series

8.2 Arithmetic Sequences

8.3 Geometric Sequences

8.4 Mathematical Induction

8.5 Counting Techniques

8.6 Introduction to Probability

8.7 The Binomial Theorem