Precalculus

P. Prerequisites: Fundamental Concepts of Algebra.


Real Numbers and Algebraic Expressions. Exponents and Scientific Notation. Radicals and Rational Exponents. Polynomials. Factoring Polynomials. Rational Expressions. Solving Linear Equations. Solving Quadratic Equations. Solving Inequalities.



1. Graphs, Functions, and Models.


Graphs and Graphing Utilities. Lines and Slope. Distance and Midpoint Formulas; Circles. Basics of Functions. Graphs of Functions. Transformations of Functions. Combinations of Functions; Composite Functions. Inverse Functions. Modeling with Functions.



2. Polynomial and Rational Functions.


Complex Numbers. Quadratic Functions. Polynomial Functions and their Graphs. Dividing Polynomials: Remainder and Factor Theorems. Zeros of Polynomial Functions. Rational Functions and Their Graphs. Polynomial and Rational Inequalities. Modeling Using Variation.



3. Exponential and Logarithmic Functions.


Exponential Functions. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions.



4. Trigonometric Functions.


Angles and Their Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of other Trigonometric Functions. Inverse Trigonometric Functions. Applications of Trigonometric Functions.



5. Analytic Trigonometry.


Verifying Trigonometric Identities. Sum and Difference Formulas. Double-Angle and Half-Angle Formulas. Product-to Sum and Sum-to Product Formulas. Trigonometric Equations.



6. Additional Topics in Trigonometry.


The Law of Sines. The Law of Cosines. Polar Coordinates. Graphs of Polar Equations. Complex Numbers in Polar Form; DeMoivre's Theorem. Vectors. The Dot Product.



7. Systems of Equations and Inequalities.


Systems of Linear Equations in Two Variables. Systems of Linear Equations in Three Variables. Partial Fractions. Systems of Nonlinear Equations in Two Variables. Systems of Inequalities. Linear Programming.



8. Matrices and Determinants.


Matrix Solutions to Linear Systems. Inconsistent and Dependent Systems and Their Applications. Matrix Operations and Their Applications. Multiplicative Inverse of Matrices and Matrix Equations. Determinants and Cramer's Rule.



9. Conic Sections and Analytic Geometry.


The Ellipse. The Hyperbola. The Parabola. Rotation of Axes. Parametric Equations. Conic Sections in Polar Coordinates.



10. Sequences, Induction, and Probability.


Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. The Binomial Theorem. Counting Principles, Permutations, and Combinations. Probability.



11. Introduction to Calculus.


Finding Limits Using Tables and Graphs. Finding Limits Using Properties of Limits. One-Sided Limits; Continuous Functions. Introduction to Derivatives.