Algebra and Trigonometry - Text Only - 5th edition

Note: Each chapter contains a Summary, Review Exercises, and a Test.

An Introduction to Graphing Utilities.
P. Prerequisites.

P.1 Real Numbers.
P.2 Exponents and Radicals.
P.3 Polynomials and Special Products.
P.4 Factoring.
P.5 Rational Expressions.
P.6 Errors and the Algebra of Calculus.
P.7 Graphical Representation of Data.

Project: Numerically Finding a Maximum Volume.

1. Equations and Inequalities.

1.1 Graphs of Equations.
1.2 Linear Equations in One Variable.
1.3 Modeling with Linear Equations.
1.4 Quadratic Equations.
1.5 Complex Numbers.
1.6 Other Types of Equations.
1.7 Linear Inequalities.
1.8 Other Types of Inequalities.

Project: Finding Falling Times Numerically.

2. Functions and Their Graphs.

2.1 Linear Equations in Two Variables.
2.2 Functions.
2.3 Analyzing Graphs of Functions.
2.4 Shifting, Reflecting, and Stretching Graphs.
2.5 Combinations of Functions.
2.6 Inverse Functions.
Project: A Graphical Approach to Maximization.

Cumulative Test for Chapters P - 2.

3. Polynomial Functions.

3.1 Quadratic Functions.
3.2 Polynomial Functions of Higher Degree.
3.3 Polynomial and Synthetic Division.
3.4 Zeros of Polynomial Functions.
3.5 Mathematical Modeling.

Project: Finding Points of Intersection Graphically.

4. Rational Functions and Conics.

4.1 Rational Functions and Asymptotes.
4.2 Graphs of Rational Functions.
4.3 Partial Fractions.
4.4 Conics.
4.5 Translations of Conics.

Project: Graphical Approach to Finding Average Cost.

5. Exponential and Logarithmic Functions.

5.1 Exponential Functions and Their Graphs.
5.2 Logarithmic Functions and Their Graphs.
5.3 Properties of Logarithms.
5.4 Exponential and Logarithmic Equations.
5.5 Exponential and Logarithmic Models.

Project: Graphical Approach to Compound Interest.
Cumulative Test for Chapters 3 - 5.

6. Trigonometry.

6.1 Angles and Their Measures.
6.2 Right Triangle Trigonometry.
6.3 Trigonometric Functions of Any Angle.
6.4 Graphs of Sine and Cosine Functions.
6.5 Graphs of Other Trigonometric Functions.
6.6 Inverse Trigonometric Functions.
6.7 Applications and Models.

Project: Analyzing a Graph.

7. Analytic Trigonometry.

7.1 Using Fundamental Identities.
7.2 Verifying Trigonometric Identities.
7.3 Solving Trigonometric Equations.
7.4 Sum and Difference Formulas.
7.5 Multiple-Angle and Product-to-Sum Formulas.

Project: Projectile Motion.

8. Additional Topics in Trigonometry.

8.1 Law of Sines.
8.2 Law of Cosines.
8.3 Vectors in the Plane.
8.4 Vectors and Dot Products.
8.5 Trigonometric Form of a Complex Number.

Project: Adding Vectors Graphically.
Cumulative Test for Chapters 6 - 8.

9. Systems of Equations and Inequalities.

9.1 Solving Systems of Equations.
9.2 Two-Variable Linear Systems.
9.3 Multivariable Linear Systems.
9.4 Systems of Inequalities.
9.5 Linear Programming.

Project: Fitting Models to Data.

10. Matrices and Determinants.

10.1 Matrices and Systems of Equations.
10.2 Operations with Matrices.
10.3 The Inverse of a Square Matrix.
10.4 The Determinant of a Square Matrix.
10.5 Applications of Matrices and Determinants.

Project: Solving Systems of Equations.

11. Sequences, Series, and Probability.

11.1 Sequences and Series.
11.2 Arithmetic Sequences and Partial Sums.
11.3 Geometric Sequences and Series.
11.4 Mathematical Induction.
11.5 The Binomial Theorem.
11.6 Counting Principles.
11.7 Probability.

Project: Exploring Difference Quotients.
Cumulative Test for Chapters 9 - 11.

Appendices.
A. Proofs of Selected Theorems.
B. Concepts in Statistics.

B.1 Representing Data.
B.2 Measures of Central Tendency and Dispersion.
B.3 Least Squares Regression