Precalculus: Right Triangle Approach – Beecher, Penna, Bittinger – 4th Edition

R. Basic Concepts of Algebra
R.1 The Real-Number Systemeal Numbers
R.2 Integer Exponents, Scientific Notation, and Order of Operations
R.3 Addition, Subtraction, and Multiplication of Polynomials
R.4 Factoring Terms with Common Factors
R.5 The Basics of Equation Solving
R.6 Rational Expressions
R.7 Radical Notation and Rational Exponents

1. Graphs; Linear Functions and Models
1.1 Introduction to Graphing
1.2 Functions and Graphs
1.3 Linear Functions, Slope, and Applications
1.4 Equations of Lines and Modeling
1.5 Linear Equations, Functions, Zeros, and Applications
1.6 Solving Linear Inequalities

2. More on Functions
2.1 Increasing, Decreasing, and Piecewise Functions; Applications
2.2 The Algebra of Functions
2.3 The Composition of Functions
2.4 Symmetry and Transformations
2.5 Variation and Applications

3. Quadratic Functions and Equations; Inequalities
3.1 The Complex Numbers
3.2 Quadratic Equations, Functions, Zeros, and Models
3.3 Analyzing Graphs of Quadratic Functions
3.4 Solving Rational Equations and Radical Equations
3.5 Solving Linear Inequalities

4. Polynomial and Rational Functions
4.1 Polynomial Functions and Modeling
4.2 Graphing Polynomial Functions
4.3 Polynomial Division; The Remainder and Factor Theorems
4.4 Theorems about Zeros of Polynomial Functions
4.5 Rational Functions
4.6 Polynomial and Rational Inequalities

5. Exponential and Logarithmic Functions
5.1 Inverse Functions
5.2 Exponential Functions and Graphs
5.3 Logarithmic Functions and Graphs
5.4 Properties of Logarithmic Functions
5.5 Solving Exponential Equations and Logarithmic Equations
5.6 Applications and Models: Growth and Decay; Compound Interest

6. The Trigonometric Functions
6.1 Trigonometric Functions of Acute Angles
6.2 Applications of Right Triangles
6.3 Trigonometric Functions of Any Angle
6.4 Radians, Arc Length, and Angular Speed
6.5 Circular Functions: Graphs and Properties
6.6 Graphs of Transformed Sine and Cosine Functions

7. Trigonometric Identities, Inverse Functions, and Equations
7.1 Identities: Pythagorean and Sum and Difference
7.2 Identities: Cofunction, Double-Angle, and Half-Angle
7.3 Proving Trigonometric Identities
7.4 Inverses of the Trigonometric Functions
7.5 Solving Trigonometric Equations

8. Applications of Trigonometry
8.1 The Law of Sines
8.2 The Law of Cosines
8.3 Complex Numbers: Trigonometric Form
8.4 Polar Coordinates and Graphs
8.5 Vectors and Applications
8.6 Vector Operations

9. Systems of Equations and Matrices
9.1 Systems of Equations in Two Variables
9.2 Systems of Equations in Three Variables
9.3 Matrices and Systems of Equations
9.4 Matrix Operations
9.5 Inverses of Matrices
9.6 Determinants and Cramer’s Rule
9.7 Systems of Inequalities and Linear Programming
9.8 Partial Fractions

10. Analytic Geometry Topics
10.1 The Parabola
10.2 The Circle and the Ellipse
10.3 The Hyperbola
10.4 Nonlinear Systems of Equations and Inequalities
10.5 Rotation of Axes
10.6 Polar Equations of Conics
10.7 Parametric Equations

11. Sequences, Series, and Combinatorics
11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 geometric Sequences and Series
11.4 Mathematical Induction
11.5 Combinatorics: Permutations
11.6 Combinatorics: Combinations
11.7 The Binomial Theorem
11.8 Probability