Pre-Calculus

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In American mathematics education, Pre-Calculus, an advanced form of secondary school algebra, is a foundational mathematical discipline. It is also called introduction to Analysis, or Math Analysis. In many schools, Pre-Calculus is actually two separate courses: Algebra and Trigonometry. Pre-Calculus does not prepare students for calculus as Pre-Algebra prepares students for Algebra I. While Pre-Algebra teaches students many different fundamental algebra topics, Pre-Calculus does not involve calculus, but explores topics that will be applied in calculus.

You will, however, receive an introduction to Calculus by way of the study of Limits and Exceptions at the end of the course.

Click on the following link to download the course syllabus: Pre-Calculus Course Syllabus

Course Outline

The following are the units and the sections that will be covered this year in the Pre-Calculus course.

1. Fundamental Concepts of Algebra
   1. Properties of Real Numbers
   2. Exponents and Radicals
   3. Rational Expressions
   4. Solving Equations
   5. Linear Inequalities in One Variable
2. Functions And Their Graphs
   1. Functions
   2. Analyzing Graphs of Functions
   3. Transformations of Functions
   4. Composite Functions
   5. Inverse Functions
3. Polynomial and Rational Functions
   1. Continuity and Even/Odd Functions
   2. Polynomials and Factoring
   3. Quadratic Functions and Models
   4. Polynomial Functions of Higher Degree
   5. Polynomial and Synthetic Division
   6. Complex Numbers
   7. Zeros of Polynomial Functions
   8. Rational Functions
   9. Non-Linear Inequalities
4. Exponential and Logarithmic Functions
   1. Exponential Functions and Their Graphs
   2. Logarithmic Functions and Their Graphs
   3. Properties of Logarithms
   4. Exponential and Logarithmic Equations
   5. Exponential and Logarithmic Models
5. Trigonometry
   1. Radian and Degree Measures
   2. Trigonometric Functions & The Unit Circle
   3. Right Triangle Trigonometry
   4. Trigonometric Functions of Any Angle
   5. Graphs of Sine & Cosine Functions
   6. Graphs of Other Trig. Functions
   7. Inverse Trig. Functions
6. Analytic Trigonometry
   1. Using Fundamental Identities
   2. Verifying Trig. Identities
   3. Solving Trigonometric Equations
   4. Law of Sines
   5. Law of Cosines
   6. Vectors & The Dot Product
7. Systems of Equations & Inequalities
   1. Linear & Nonlinear Systems of Equations
   2. Two-Variable Linear Systems
   3. Mulitvariable Linear Systems
   4. Partial Fractions
   5. Systems of Inequalities
8. Matrices & Determinants
   1. Matrices & Systems of Equations
   2. Operations With Matrices
   3. Inverse of a Square Matrix
   4. Determinant of a Square Matrix
   5. Applications of Matrices
9. Sequences, Series, and Probability
   1. Sequences & Series
   2. Arithmetic Sequences and partial Sums
   3. Geometric Sequences and Series
   4. Mathematical Induction
   5. The Binomial Theorem
   6. Counting Principles
   7. Probability
10. Analytic Geometry
    1. Lines
    2. Ellipses
    3. Hyperbolas
    4. Conics
    5. parametric Equations
    6. Polar Coordinates
11. Analytic Geometry in Three-Dimensions
    1. The Three-Dimensional Coordinate System
    2. Vectors in Space
    3. Cross Product of Two Vectors
    4. Lines and Planes in Space
12. Limits and and Introduction to Calculus
    1. Intro to Limits
    2. Techniques for Evaluating Limits
    3. The Tangent Line Problem
    4. Limits at Infinity and Limits of Sequences
    5. The Area Problem