Precalculus

1. ALGEBRA: THE FUNDAMENTALS. The Real Numbers. Operations with Real Numbers. Polynomials and Rational Expressions. Exponents and Radicals. The Complex Numbers. First-Degree Equations and Inequalities to One Variable. Absolute Value Equations and Inequalities. Quadratic Equations and Equations in Quadratic Form. Quadratic and Rational Inequalities. Substitution. Chapter Summary. Review Exercises. Practice Test. 2. FUNCTIONS AND GRAPHS: PART I. The Cartesian Coordinate System: Graphing Straight Lines Functions and Circles. Slope. Equations of a Line. Relations and Functions. Function Notation. Relating Equations to Their Graphs. Introduction to Graph Sketching: Symmetry. Chapter Summary. Review Exercises. Practice Test. 3. FUNCTIONS AND GRAPHS: PART II. Basic Graphing Principles. More Graphing Principles: Types of Functions. Mathematical Modeling: Extracting Functions from Real-Life Situations. Quadratic Functions. Operations in Functions. Inverse Functions. Chapter Summary. Review Exercises. Practice Test. 4. POLYNOMIAL, RATIONAL AND RADICAL FUNCTIONS. Polynomial Functions. More Polynomial Functions and Mathematical Models. Polynomial Division, Roots of Polynomials; The Remainder and Factor Theorems. More on Roots of Polynomial Equations; The Rational Root Theorem and Descartes's Rule of Signs. Radical Functions. Variation. Chapter Summary. Review Exercises. Practice Test. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Logarithmic Functions. Properties of Logarithms: Logarithmic Equations. Common and Natural Logarithms: Exponential Equations and Change of Base. Applications. Chapter Summary. Review Exercises. Practice. 6. TRIGONOMETRY. Angle Measurement and Two Special Triangles. The Trigonometric Functions of a General Angle. Right Triangle Trigonometry and Applications. The Trigonometric Functions as Functions of Real Numbers. Chapter Summary. Review Exercises. Practice Test. 7. THE TRIGONOMETRIC FUNCTIONS. The Sine and Cosine Functions and Their Graphs. The Tangent, Secant, Cosecant, and Contangent Functions and Their Graphs. Basic Identities. Trigonometric Equations. The Inverse Trigonometric Functions. Chapter Summary. Review Exercises. Practice Test. 8. MORE TRIGONOMETRY AND ITS APPLICATIONS. The Addition Formulas. The Double-Angle and Half-Angle Formulas. The Law of Sines and The Law of Cosines. Vectors. The Trigonometric Form of Complex Numbers and DeMoivre's Theorem. Polar Coordinates. Chapter Summary. Review Exercises. Practice Test. 9. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES. Elimination and Substitution: 2 X 2 Linear Systems. Elimination and Gaussian Elimination: 3 X 3 Linear Systems. Solving Linear Systems Using Augmented Matrices. The Algebra of Matrices. Solving Linear Systems Using Matrix Inverses. Determinants and Cramer's Rule: 2 X 2 and 3 X 3 Systems. Properties of Determinants. Systems of Linear Inequalities. An Introduction to Linear Programming: Geometric Solutions. Chapter Summary. Review Exercises. Practice Test. 10. CONIC SECTIONS. Conic Sections: Circles. The Parabola. The Ellipse. The Hyperbola. Identifying Conic Sections: Degenerate Forms. Translations and Rotations of Coordinate Axes. Nonlinear Systems of Equations and Inequalities. Chapter Summary. Review Exercises. Practice Test. 11. SEQUENCE, SERIES AND RELATED TOPICS. Sequences. Series and Sigma Notation. Arithmetic Sequences and Series. Geometric Sequences and Series. Mathematical Induction. Permutations and Combinations. The Binomial Theorem. Chapter Summary. Review Exercises. Practice Test.