Precalculus

1. FOUNDATIONS AND FUNDAMENTALS. The Real Number System. Exponents and Radicals. Algebraic Expressions. Graphs of Equations. Techniques for Solving Equations. Inequalities. Lines. 2. FUNCTIONS AND THEIR GRAPHS. Functions. Graphs of Functions. Combinations of Functions. Inverses of Functions. Selected Functions. Modeling with Functions and Variation. 3. POLYNOMIAL AND RATIONAL FUNCTIONS. Polynomial Functions. Division of Polynomials. Zeros and Factors of Polynomials. Real Zeros of Polynomials. Rational Functions. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Logarithmic Functions. Logarithmic Identities and Equations. Exponential Equations and Applications. Modeling with Exponential and Logarithmic Functions. 5. TRIGONOMETRIC FUNCTIONS. Angles and Their Measurements. Trigonometric Functions of Acute Angles. Trigonometric Functions of Real Numbers. Graphs of Sine and Cosine. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. 6. TRIGONOMETRIC IDENTITIES AND EQUATIONS. Fundamental Trigonometric Identities. Sum and Difference Identities. Double-Angle and Half-Angle Identities. 7. APPLICATIONS OF TRIGONOMETRY. The Law of Sines. The Law of Cosines. Trigonometric Form of Complex Numbers. Powers and Roots of Complex Numbers. Polar Coordinates. Vectors. 8. RELATIONS AND CONIC SECTIONS. Relations and Their Graphs. Parabolas. Ellipses. Hyperbolas and Classification of Conic Sections. Rotation of Axes and General Conic Sections. Parametric Equations. 9. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Equations. Matrices. Linear Systems and Matrices. Gaussian and Gauss-Jordan Elimination. Inverses of Square Matrices. Determinants and Cramer?s Rule. Systems of Inequalities. Linear Programming. 10. INTEGER FUNCTIONS AND PROBABILITY. Sequences. Series. Permutations and Combinations. Probability. The Binomial Theorem. Mathematical Induction.