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P. Preliminary Concepts | |
The Real Number System | |
Integer and Rational Number Exponents | |
Polynomials | |
Factoring | |
Rational Expressions | |
Complex Numbers | |
Equations and Inequalities | |
Linear and Absolute Value Equations | |
Formulas and Applications | |
Quadratic Equations | |
Other Types of Equations | |
Inequalities | |
Variation and Applications | |
Functions and Graphs | |
A Two Dimensional Coordinate System and Graphs | |
Introduction to Functions | |
Linear Functions | |
Quadratic Functions | |
Properties of Graphs | |
The Algebra of Functions | |
Modeling Data Using Regression | |
Polynomial and Rational Functions | |
The Remainder Theorem and the Factor Theorem | |
Polynomial Functions of Higher Degree | |
Zeros of Polynomial Functions | |
The Fundamental Theorem of Algebra | |
Graphs of Rational Functions and Their Applications | |
Exponential and Logarithmic Functions | |
Inverse Functions | |
Exponential Functions and Their Applications | |
Logarithmic Functions and Their Applications | |
Properties of Logarithms and Logarithmic Scales | |
Exponential and Logarithmic Equations | |
Exponential Growth and Decay | |
Modeling Data with Exponential and Logarithmic Functions | |
Trigonometric Functions | |
Angles and Arcs | |
Right Triangle Trigonometry | |
Trigonometric Functions of Any Angle | |
Trigonometric Functions of Real Numbers | |
Graphs of the Sine and Cosine Functions | |
Graphs of the Other Trigonometric Functions | |
Graphing Techniques | |
Harmonic Motion--An Application of the Sine and Cosine Functions | |
Trigonometric Identities and Equations | |
Verification of Trigonometric Identities | |
Sum, Difference, and Cofunction Identities | |
Double- and Half-Angle Identities | |
Identities Involving the Sum of Trigonometric Functions | |
Inverse Trigonometric Functions | |
Trigonometric Equations | |
Applications of Trigonometry | |
The Law of Sines | |
The Law of Cosines and Area | |
Vectors | |
Trigonometric Form of Complex Numbers | |
De Moivre's Theorem | |
Topics in Analytic Geometry | |
Parabolas | |
Ellipses | |
Hyperbolas | |
Rotation of Axes | |
Introduction to Polar Coordinates | |
Polar Equations of the Conics | |
Parametric Equations | |
Systems of Equations and Inequalities | |
Systems of Linear Equations in Two Variables | |
Systems of Linear Equations in More than Two Variables | |
Nonlinear Systems of Equations | |
Partial Fractions | |
Inequalities in Two Variables and Systems of Inequalities | |
Linear Programming | |
Matrices | |
Gaussian Elimination Method | |
The Algebra of Matrices | |
The Inverse of a Matrix | |
Determinants | |
Cramer's Rule | |
Sequences, Series, and Probability | |
Infinite Sequences and Summation Notation | |
Arithmetic Sequences and Series | |
Geometric Sequences and Series | |
Mathematical Induction | |
The Binomial Theorem | |
Permutations and Combinations | |
Introduction to Probability | |
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