# PRECALCULUS, PART 1

## Price: $125 | Credits: One Semester | Dept: Math | Course ID# 225-1

This course is designed to be the first semester of Precalculus. Students will build on previous fundamental concepts from Algebra I, Geometry, and Algebra II or Integrated Math 1, 2, & 3 courses. Students will use the concepts in this course, especially functions to strengthen previous mathematical reasoning and conceptual understanding for mathematical problem solving. Proficiency with these topics is especially important for students who are interested in preparing for college math courses and/or who intend to study Calculus. Precalculus is approved by the University of California A-G as mathematics (category C).

Upon completion of this course, the student is awarded 5 credits. Each credit corresponds to 15 hours of study. Of course, some students work more quickly than others, and some can devote more hours to study, so some students are able to complete the course in an accelerated rate.

### LEARNING OBJECTIVES

In this module, students gain a comprehension of the following:

- Identifying characteristics of algebraic expressions including terms, variables, constants, and coefficients.
- Simplifying and factoring polynomials.
- Simplifying rational expressions using factoring.
- Completing operations of rational expressions using addition, subtraction, multiplication, and division.
- Writing, solving, and graphing linear equations and inequalities.
- Solving systems of linear equations and inequalities.
- Graphing and solving quadratic equations.
- Identifying, evaluating, and performing operations on functions.
- Finding the inverses of functions and what they represent.
- Recognizing the most common parent functions both algebraically and graphically and how they can be transformed.
- Analyzing graphs of functions by their most important characteristics.
- Analyzing and graphing polynomial functions.
- Identifying key characteristics of a polynomial function by using the remainder, factor, and rational roots theorems as well as Descartes rule of signs.
- Analyzing and graphing rational, exponential, and logarithmic functions.
- Solving right triangles using the six basic trigonometric functions.
- Determining the 16-point unit circle and use it to find trigonometric function values.
- Identifying and evaluating inverse trigonometric functions.

Solving oblique triangles and finding their areas. - Graphing trigonometric functions.
- Identifying several trigonometric identities and using them to find trigonometric values, evaluate trigonometric functions and solve trigonometric equations.

### TOPICS COVERED

This course covers the following topics:

- Seeing structure in algebraic expressions.
- Equations and inequalities: writing, solving and graphing.
- Introduction to functions.
- Polynomial, rational, exponential and logarithmic functions.
- Trigonometry