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Chapter 1: Preparing for Your Journey
Opening 
1.OP 
Chapter Opening 
Section 1.1 
1.1.1 
Interpreting Graphs 

1.1.2 
The Spring Problem 

1.1.3 
Modeling with Functions 

1.1.4 
Rates of Change 

1.1.5 
Setting Up Word Problems 

1.1.6 
Equivalent Expressions 
Section 1.2 
1.2.1 
Inverse Functions 

1.2.2 
Composition of Functions 

1.2.3 
PiecewiseDefined Functions and Continuity 
Section 1.3 
1.3.1 
Radians as a Unit of Measure 

1.3.2 
Radian Measure in the Unit Circle 

1.3.3 
Applications of Radian Measure 
Closure 
1.CL 
Chapter Closure 
Chapter 2: Functions and Trigonometry
Opening 
2.OP 
Chapter Opening 
Section 2.1 
2.1.1 
Characteristics of Functions 

2.1.2 
Transformations of Functions 

2.1.3 
Graphing Rational and Reciprocal Functions 
Section 2.2 
2.2.1 
Special Angles in the Unit Circle 

2.2.2 
Sine and Cosine in the Unit Circle 

2.2.3 
Graphs of Sine and Cosine 

2.2.4 
Transformations of Sine and Cosine 

2.2.5 
Horizontal Stretches of Sine and Cosine Graphs 
Section 2.3 
2.3.1 
Solving Trigonometric Equations 

2.3.2 
Inverse Sine and Cosine 

2.3.3 
Graphs of Tangent and Inverse Tangent 
Closure 
2.CL 
Chapter Closure 
Chapter 3: Algebra and Area Under a Curve
Opening 
3.OP 
Chapter Opening 
Section 3.1 
3.1.1 
Operations with Rational Expressions 

3.1.2 
Rewriting Expressions and Equations 

3.1.3 
Solving Nonlinear Equations and Systems 

3.1.4 
Polynomial Division 

3.1.5 
Solving Classic Word Problems 
Section 3.2 
3.2.1 
Using Sigma Notation 

3.2.2 
Area Under a Curve: Part One 

3.2.3 
Area Under a Curve: Part Two 

3.2.4 
Area Under a Curve: Part Three 
Closure 
3.CL 
Chapter Closure 
Chapter 4: Exponentials and Logarithms
Opening 
4.OP 
Chapter Opening 
Section 4.1 
4.1.1 
Applications of Exponential Functions 

4.1.2 
Stretching Exponential Functions 

4.1.3 
The Number e 
Section 4.2 
4.2.1 
Logarithms 

4.2.2 
Properties of Logarithms 

4.2.3 
Solving Exponential and Logarithmic Equations 

4.2.4 
Graphing Logarithmic Functions 

4.2.5 
Applications of Exponentials and Logarithms 
Closure 
4.CL 
Chapter Closure 
Chapter 5: Triangles and Vectors
Opening 
5.OP 
Chapter Opening 
Section 5.1 
5.1.1 
The Law of Sines and Area 

5.1.2 
The Law of Cosines 

5.1.3 
The Ambiguous Case of the Law of Sines 
Section 5.2 
5.2.1 
An Introduction to Vectors 

5.2.2 
Working with Vectors 

5.2.3 
Applications of Vectors 

5.2.4 
The Dot Product 
Closure 
5.CL 
Chapter Closure 
Chapter 6: Matrices
Opening 
6.OP 
Chapter Opening 
Section 6.1 
6.1.1 
Introduction to Matrices 

6.1.2 
Matrix Multiplication 

6.1.3 
Determinants and Inverse Matrices 

6.1.4 
Solving Systems Using Matrix Equations 
Section 6.2 
6.2.1 
Applications of Matrices 

6.2.2 
Linear Transformations 

6.2.3 
Composition of Transformations 

6.2.4 
Properties of Transformations 
Closure 
6.CL 
Chapter Closure 
Chapter 7: Limits and Rates
Opening 
7.OP 
Chapter Opening 
Section 7.1 
7.1.1 
An Introduction to Limits 

7.1.2 
Working With OneSided Limits 

7.1.3 
The Definition of a Limit 

7.1.4 
Limits and Continuity 

7.1.5 
Special Limits 
Section 7.2 
7.2.1 
Rates of Change From Data 

7.2.2 
Slope and Rates of Change 

7.2.3 
Average Velocity and Rates of Change 

7.2.4 
Moving From AROC to IROC 

7.2.5 
Rate of Change Applications 
Closure 
7.CL 
Chapter Closure 
Chapter 8: Extending Periodic Functions
Opening 
8.OP 
Chapter Opening 
Section 8.1 
8.1.1 
Graphing y = asin(b(x – h))+ k 

8.1.2 
Modeling With Periodic Functions 

8.1.3 
Improving the Spring Problem 
Section 8.2 
8.2.1 
Graphing Reciprocal Trigonometric Functions 

8.2.2 
Trigonometric Functions, Geometrically 
Section 8.3 
8.3.1 
Simplifying Trigonometric Expressions 

8.3.2 
Proving Trigonometric Identities 

8.3.3 
Angle Sum and Difference Formulas 

8.3.4 
Double and Half Angle Formulas 

8.3.5 
Solving Complex Trigonometric Equations 
Closure 
8.CL 
Chapter Closure 
Chapter 9: Polar and Parametric Functions
Opening 
9.OP 
Chapter Opening 
Section 9.1 
9.1.1 
Plotting Polar Coordinates by Hand 

9.1.2 
Graphs of Polar Equations 

9.1.3 
Converting Between Polar and Rectangular Forms 

9.1.4 
Families of Polar Functions 
Section 9.2 
9.2.1 
Using the Complex Plane 

9.2.2 
Operations with complex numbers 

9.2.3 
Powers and Roots of Complex Numbers 
Section 9.3 
9.3.1 
Introduction to Parametric Equations 

9.3.2 
Applications of Parametric Equations 
Closure 
9.CL 
Chapter Closure 
Chapter 10: Conics and Series
Opening 
10.OP 
Chapter Opening 
Section 10.1 
10.1.1 
Circles and Completing the Square 

10.1.2 
Ellipses 

10.1.3 
Hyperbolas 

10.1.4 
Parabolas 

10.1.5 
Identifying Conic Sections 

10.1.6 
Conics in Parametric Form 

10.1.7 
Conics in Polar Form 
Section 10.2 
10.2.1 
Arithmetic Series 

10.2.2 
Geometric Series 

10.2.3 
Infinite Geometric Series 

10.2.4 
Applications of Geometric Series 

10.2.5 
The Sum of the Harmonic Series (opt.) 
Closure 
10.CL 
Chapter Closure 
Chapter 11: Precalculus Finale
Opening 
11.OP 
Chapter Opening 
Section 11.1 
11.1.1 
A Race to Infinity 

11.1.2 
Evaluating Limits to Infinity 

11.1.3 
Evaluating Limits at a Point Algebraically 

11.1.4 
Defining The Number e 
Section 11.2 
11.2.1 
Trapping Area with Trapezoids 

11.2.2 
Area as a Function 

11.2.3 
Rocket Launch 
Section 11.3 
11.3.1 
Velocity and Position Graphs 

11.3.2 
Calculating Instantaneous Velocity 

11.3.3 
Writing Slope Functions 

11.3.4 
Definition of a Derivative 

11.3.5 
Slope and Area Under a Curve 
Closure 
11.CL 
Chapter Closure 
Appendix: Statistics
Opening 
S.OP 
Appendix Opening 
Section S.1 
S.1.1 
Mean and Expected Value of a Discrete Random Variable 

S.1.2 
Expected Value and Decision Making 
Closure 
S.CL 
Appendix Closure 