(Note: Chapters 2-13 end with Chapter Review, Chapter Projects, and Cumulative Review.)
R. Review.
Classification of Numbers. Algebra Review. Geometry Review. Polynomials. Factoring Polynomials. Polynomial Division; Synthetic Division. Rational Expressions. nth Roots; Rational Exponents. Chapter Review.
1. Equations and Inequalities.
Linear Equations. Quadratic Equations. Quadratic Equations in the Complex Number System. Radical Equations; Equations Quadratic in Form. Solving Inequalities. Equations and Inequalities Involving Absolute Value. Applications: Interest, Mixture, Uniform Motion, Constant Rate Jobs. Chapter Review. Chapter Projects.
2. Graphs.
Rectangular Coordinates. Graphs of Equations. Circles. Lines. Parallel and Perpendicular Lines. Scatter Diagrams; Linear Curve Fitting. Variation.
3. Functions and their Graphs.
Introduction to Functions. The Graph of a Function. Properties of Functions. Library of Functions; Piecewise-Defined Functions. Graphing Techniques: Transformations. Mathematical Models: Constructing Functions.
4. Polynomial and Rational Functions.
Quadratic Functions and Models. Polynomial Functions. Rational Functions I. Rational Functions II: Analyzing Graphs. Polynomial and Rational Inequalities. The Real Zeros of a Polynomial Function. Complex Zeros; Fundamental Theorem of Algebra.
5. Exponential and Logarithmic Functions.
Composite Functions. Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms. Logarithmic and Exponential Equations. Compound Interest. Growth and Decay; Newton's Law; Logistic Models. Logarithmic Scales.
6. Trigonometric Functions.
Angles and Their Measure. Right Triangle Trigonometry. Computing the Values of Trigonometric Functions of Given Angles. Trigonometric Functions of General Angles. Unit Circle Approach; Properties of the Trigonometric Functions. Graphs of the Sine and Cosine Functions. Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions. Phase Shift; Sinusoidal Curve Fitting.
7. Analytic Trigonometry.
The Inverse Sine, Cosine, and Tangent Functions. The Inverse Trigonometric Functions. Trigonometric Identities. Sum and Difference Formulas. Double-angle and Half-angle Formulas. Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations I. Trigonometric Equations II.
8. Applications of Trigonometric Functions.
Applications Involving Right Triangles. Law of Sines. Law of Cosines. Area of a Triangle. Simple Harmonic Motion; Damped Motion; Combining Waves.
9. Polar Coordinates; Vectors.
Polar Coordinates. Polar Equations and Graphs. The Complex Plane; DeMoivre's Theorem. Vectors. The Dot Product.
10. Analytic Geometry.
Conics. The Parabola. The Ellipse. The Hyperbola. Rotation of Axes. Polar Equations of Conics. Plane Curves and Parametric Equations.
11. Systems of Equations and Inequalities.
Systems of Linear Equations: Substitution and Elimination. Systems of Linear Equations: Matrices. Systems of Linear Equations: Determinants. Matrix Algebra. Partial Fraction Decomposition. Systems of Nonlinear Equations. Systems of Inequalities. Linear Programming.
12. Sequences; Induction; The Binomial Theorem
Sequences. Arithmetic Sequences. Geometric Sequences; Geometric Series. Mathematical Induction. The Binomial Theorem.
13. Counting and Probability.
Sets and Counting. Permutations and Combinations. Probability of Equally Likely Outcomes.
APPENDIX GRAPHING UTILITIES.
The Viewing Rectangle. Using a Graphing Utility to Graph Equations. Using a Graphing Utility to Locate Intercepts and Check for Symmetry. Using a Graphing Utility to Solve Equations. Square Screens. Using a Graphing Utility to Graph Inequalities. Using a Graphing Utility to Solve Systems of Linear Equations. Using a Graphing Utility to Graph Polar Equations. Using a Graphing Utility to Graph Parametric Equations.
Answers.
Index
