This chapter reviews many of the fundamental algebra skills that students should have mastered in Algebra 1 and Algebra 2. Students are encouraged to take the time to go over these sections to ensure they are ready for the more advanced concepts later in the course.

Sections:

• 1.1 One Step Equations
• 1.2 Solving Two Step Equations
• 1.3 Solving Multi-Step Equations
• 1.4 Formulas and Literal Equations
• 1.5 Linear Inequalities
• 1.6 Compound Inequalities
• 1.7 Introduction to Absolute Value
• 1.8 Solving Absolute Value Equations
• 1.9 Absolute Value Inequalities
• 1.10 Graphing Absolute Value Equations
• 1.11 Graphing Lines with One Variable
• 1.12 Graphing Lines with Two Variables
• 1.13 The Slope of a Line
• 1.14 Slope Intercept Method
• 1.15 XY Intercept Method
• 1.16 Writing the Equations of Lines -Using Slope-Intercept Form
• 1.17 Writing the Equations of Lines -Using Point-Slope intercept
• 1.18 Writing the Equations of Lines -Given the Slope and a Point
• 1.19 Writing the Equations of Lines -Given Two Points
• 1.20 Standard Form of Linear Equations
• 1.21 Best Fitting Lines and Scatter Plots
• 1.22 Linear Models/Word Problems
• 1.23 Graphing Linear Inequalities in Two Variables

Functions and relations transcend all through mathematics. The first part of this chapter reviews core concepts at the Algebra 1/2 level. The second part of this chapter covers more advanced study of the topic of functions and relations. Time is taken to explain the difference between a function and relation and introduce the student to the language of functions to include the domain, range and linear/nonlinear functions.

Students will also learn function operations, composite functions and graphing. Lastly, students will learn how to transform functions as well as doing a detailed analysis of the domain and range of functions.

Sections:

• 2.1 Introduction to Functions and Relations
• 2.2 Function Operations
• 2.3 Inverse Functions
• 2.4 Graphing Functions
• 2.5 Linear and Nonlinear Functions
• 2.6 Special Functions
• 2.7 Composite Functions
• 2.8 Interval and Set Builder Notation
• 2.9 Function Symmetry
• 2.10 Transformations of Functions
• 2.11 Function and Relation Analysis (Finding Domain/Range)

The first part of the chapter reviews all the concepts and skills to solve second-degree polynomials which are quadratic functions. Next, the student will learn advanced techniques and concepts to solve a polynomial equation of any degree. Lastly, the chapter covers rational functions to include graphing a rational function and solving a rational inequality.

Sections:

• 3.1 Introduction to Quadratic Equations
• 3.2 Solving Quadratic Equations by Square Roots
• 3.3 Graphing Quadratic Equations
• 3.4 The Quadratic Formula
• 3.5 Solving Quadratic Equations by Factoring
• 3.6 The Discriminant – Types of Roots
• 3.7 Completing the Square
• 3.8 Quadratic Equation Word Problems
• 3.9 Graphing Quadratic Inequalities
• 3.10 Complex and Imaginary Numbers
• 3.11 Graphing Polynomials
• 3.12 Solving Polynomial Equations by Factoring
• 3.13 Polynomial Division (Long and Synthetic Division)
• 3.14 Remainder and Factor Theorem
• 3.15 Rational Root Theorem (Rational-Zero Test)
• 3.16 Solving n-degree Polynomials (Fundamental Theorem of Algebra)
• 3.17 Descartes’ Rule of Signs and Bounds
• 3.18 Graphing Rational Functions (Vertical and Horizontal Asymptotes)
• 3.19 Rational Inequalities

For most students this chapter will be their first introduction to logarithms. As such the chapter focuses on teaching the basic core concepts of a logarithm and its relationship to an exponential function. Students will learn how to covert between a logarithm/exponential equation.

Additionally, the chapter defines the properties of logarithms and how to condense and expand logarithmic expressions. The Natural Base e and Natural logarithms are explored with explanations of how to use the “log and ln” functions on a scientific calculator. Finally, the chapter covers the methods and procedure to solve exponential and logarithmic equations.

Sections:

• 4.1 Exponential Growth and Decay Functions
• 4.2 Introduction to Logarithms
• 4.3 Properties of Logarithms
• 4.4 The Natural Base e
• 4.5 Natural Logarithms
• 4.6 Solving Logarithmic Equations
• 4.7 Solving Exponential Equations

This very important chapter introduces the student to advanced trigonometry. Concepts involving the trigonometric ratios, sin, cos, tan, radians are explored. Next, the chapter focuses on evaluating trigonometric functions and finding the inverse of a trigonometric function. Lastly, students learn to graph sin, cos, tan, csc, sec, and cot graphs. Special note: students will need their graphing calculators for the chapter practice problems.

Sections:

• 5.1 Trigonometric Ratios
• 5.2 Angles of Rotation and Radian Measure
• 5.3 Evaluating Trigonometric Functions
• 5.4 Inverse Trigonometric Functions
• 5.5 Graphs of Sine and Cosine Functions
• 5.6 Graphs of Other Trigonometric Functions 

This chapter continues to explore more topics in trigonometry – the focus of this chapter is trigonometric identities. Students will learn how to use and verify trigonometric identities.

Students will also learn how to solve a trigonometric equation. A wide of variety of trigonometric identities will be covered to include the fundamental identities, sum and difference, double and half angle, and product and sum identities.

Sections:

• 6.1 Trigonometric Identities
• 6.2 Solving Trigonometric Equations
• 6.3 Sum and Difference Identities
• 6.4 Double-Angle and Half-Angle Identities
• 6.5 Product and Sum Identities

This chapter explores many applications of trigonometry at an advanced level. Students will learn how to solve non-right triangles using the Laws of Sine and Cosine. Next, the chapter will focus on polar (trigonometric) forms of complex numbers and how to take the powers and roots of complex numbers using trigonometry. Additional related topics are explored to include vectors and parametric equations.

Sections:

• 7.1 Laws of Sine and Cosine
• 7.2 Polar Equations
• 7.3 Trigonometric Form of Complex Numbers
• 7.4 Powers and Roots of Complex Numbers (De Moivre’s Theorem)
• 7.5 Vectors
• 7.6 Parametric Equations

This chapter explores the shapes that can be constructed from various sections of a cone – hence the name of the chapter is called “conic sections”. Students will learn the equations and related terminology of circles, parabola, ellipses and hyperbolas. Lastly, students will learn the how identify conic sections given various forms of equations and the techniques to translate conic sections graphically.

Sections:

• 8.1 Circles (Conic Sections)
• 8.2 Parabolas (Conic Sections)
• 8.3 Ellipses (Conic Sections)
• 8.4 Hyperbolas (Conic Sections)
• 8.5 Translations of Conic Sections

The first part of this chapter reviews techniques to solve linear systems – skills covered in Algebra 1 & 2. Students will also explore special systems, word problems and systems of linear inequalities. The topic of Linear Programming will be reviewed, as well. The second part of the chapter covers advanced system topics such as partial fractions and solving 3-variable and non-linear systems.

Sections:

• 9.1 Solving Systems by Graphing
• 9.2 Solving Systems Substitution Method
• 9.3 Solving Systems by Elimination/Linear Combination
• 9.4 Solving Linear Systems Word Problems
• 9.5 Special Linear Systems
• 9.6 Solving Systems of Linear Inequalities
• 9.7 Linear Programming
• 9.8 Partial Fractions – Part 1
• 9.9 Partial Fractions – Part 2
• 9.10 Three Variable and Nonlinear Systems

   

This chapter introduces the core concepts of matrices and determinants to students. Time is taken to teach terminology and common applications of matrices. Students will learn how to perform various matrix operations to include matrix addition, subtraction, multiplication, and scalar multiplication.

Additionally, students will learn the steps to find determinants and inverse of a matrix. The chapter also focuses on how matrices can be used to solve linear systems by using an inverse matrix or Cramer’s Rule.

Sections:

• 10.1 Introduction to Matrices
• 10.2 Matrix Operations
• 10.3 Matrix Multiplication
• 10.4 Determinants
• 10.5 Identity and Inverse Matrices
• 10.6 Solving Systems using Inverse Matrices
• 10.7 Solving Systems using Cramer’s Rule

The first part of this chapter is a deep look into sequence and series. Sections in this part of the chapter include an introduction to sequence and series concepts, arithmetic sequence and series and geometric sequence and series. Also, included is a section on infinite geometric series.

The next part of the chapter covers basic concepts of probability to include a discussion into the Law of Large Numbers and a section on more advanced concepts like independent, dependent and mutually exclusive events. In addition to probability there is a section on counting theory which will look at how to count using trees and the Fundamental Principle of Counting.

Lastly, the chapter will look into counting arrangements using combinations and permutations.

Sections:

• 11.1 Introduction to Sequence and Series
• 11.2 Arithmetic Sequence and Series
• 11.3 Geometric Sequence and Series
• 11.4 Infinite Geometric Series
• 11.5 The Binomial Theorem
• 11.6 Introduction To Probability
• 11.7 Counting Theory
• 11.8 Probability of Independent, Dependent and Mutually Exclusive Events
• 11.9 Permutations and Combinations