Pre-Calculus

Review of Fundamental Concepts of Algebra

•   Real Numbers and Their Properties
• Exponents (Introduction, Rules, and Scientific) and Radical Basic Rules, Radicals using rational exponents , Radicals Same Root, Radicals Different Root
•  Factoring
•   Rational Expressions (Multiplying and Dividing), (Adding and Subtracting)
•  Solving Equations
•  Linear Inequalities in One Variables

Functions and Their Graphs 

1.1 Rectangular Coordinates

1.2 Graphs of Equations

1.3  Linear Equations in Two Variables

1.4  Functions , Domain and Range

1.5 Analyzing Graphs of Functions

1.6 Parent Functions

1.7 Transformations of Functions

1.8 Combinations of Functions:  Composite Functions

1.9  Inverse Functions

Polynomial and Rational Functions

2.1 Quadratic functions and Models

2.2  Polynomial Functions of Higher Degree

2.3 Long Division and Synthetic Division

2.4 Complex Numbers

2.5 Zeros of Polynomial Functions

2.6 Rational Functions (Asymptotes)

2.7 Non-linear Inequalities

Trigonometry

SOH CAH TOA- basic right triangle trigonometry: Sine, Cosine, and Tangent, inverse functions

4.1 Radian and Degree measure

4.2 The Unit Circle

4.3 Right Triangle Trigonometry

4.4 Trigonometric Functions of Any angle

4.5 Graphs of Sine and Cosine Functions

4.6 Graphs of Other Trigonometric Functions

4.7 Inverse Trigonometric Functions

4.8 Applications and Models

Analytic Trigonometry

5.1 Using Fundamental Identities

5.2 Verifying Trigonometric Identities

5.3 Solving Trigonometric Equations

5.4 Sum and Difference Formulas Sine, Cosine

5.5 Multiple-Angle and Product-to-Sum Formulas

Additional Topics in Trigonometry

6.1 Law of Sines

6.2 Law of Cosines

       Heron's Area

6.3 Vectors in the Plane

6.4 Vectors and Dot Products

Exponential and Logarithmic Functions

3.1 Exponential Functions and their Graphs

3.2 Logarithmic Functions and Their Graphs

3.3 Properties of Logarithms

       Product Rule

       Quotient Rule

       Power Rule

       Change of Base

3.4 Exponential and Logarighmic Equations

3.5 Exponential and Logarithmic Models

Systems of Equations and Inequalities

7.1 Linear and Nonlnear Systems of Equations

7.2 Two variable Linear Systems

7.3 Multivariable Lnear Systems

7.4 Partal Fractions

7.5 Systems of Inequalities

7.6 Linear Programming

Matrices and Determinants

8.1 Matrices and Systems of Equations

8.2 Operations with Matrices

8.3 The Inverse of a Square Matrix

8.4 The Determinant of a Square Matrix

8.5 Applications of Matrices and Determinants

Sequences, Series and Probability

9.1 Sequences and Series

9.2 Arithmetic Sequences and Partial Sums

9.3 Geometrc Sequences and Series

9.4 Mathematcal Induction

9.5 The Binomial Theorem

9.6 Counting Principles

9.7 Probablility

Topics in Anaytic Geometry

10.1 Lines

10.2 Introduction to Conics: Parabolas; Circles

10.3 Ellipses

10.4 Hyperbolas

10.5 Rotation of Conics

10.6 Parametric Equations

10.7 Polar Coordinates

10.8 Graphs of Polar Equations

10.9 Polar Equations of Conics

Limits and an Introduction to Calculus

12.1 Introductions to Limits

12.2 Techniques for Evaluating Limits

12.3 The Tangent Line Problem

12.4 Limits at Infinty and Limits of Sequences

12.5 The Area Problem

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