MATH 189: Path to Calculus
Citrus College Course Outline of Record
| Heading | Value |
|---|---|
| Effective Term: | Fall 2025 |
| Credits: | 4 |
| Total Contact Hours: | 72 |
| Lecture Hours : | 72 |
| Lab Hours: | 0 |
| Hours Arranged: | 0 |
| Outside of Class Hours: | 144 |
| Total Student Learning Hours: | 216 |
| Prerequisite: | Intermediate algebra or plane geometry or higher or direct placement based on multiple measures. |
| District General Education: | A3. Mathematics |
| Transferable to CSU: | Yes |
| Transferable to UC: | Yes - Proposed |
| Grading Method: | Standard Letter |
Catalog Course Description
Bridge to calculus; polynomial, rational, exponential, logarithmic, and trigonometric functions; analytic geometry; and systems of equations. Exposure to early calculus themes, such as limits, slopes of tangent lines, and areas under curves. 72 lecture hours.
Course Objectives
- Define all six trigonometric functions in terms of a triangle, the coordinate system and the unit circle.
- Compute angles and sides of triangles in terms of degree or radian measure.
- Graph trigonometric functions and their inverse functions, and discuss the domain, range and properties of these functions.
- Prove trigonometric identities and apply trigonometric identities to solve for exact values, simplify expressions and solve equations.
- Analyze physical problems and create trigonometric relationships involving triangles, the coordinate system, and the unit circle.
- Analyze linear, quadratic, polynomial, rational, absolute value, exponential, logarithmic and piecewise-defined functions as well as inverse functions from a graphic, numeric and analytic perspective.
- Analyze and solve applied problems from various disciplines and involving a variety of equations including but not limited to: linear, quadratic, polynomial, rational, radical, absolute value, exponential and logarithmic equations as well as systems of equations.
- Apply critical thinking and mathematical reasoning skills necessary in collegiate-level algebraic problem solving in related disciplines such as science, business and engineering.
- Observe, interpret and analyze the behavior of graphs of a wide variety of functions and statistical plots.
- Exposure to early calculus themes.
Major Course Content
- Linear, quadratic, polynomial, rational, absolute value, exponential, logarithmic, piecewise-defined and trigonometric functions, graphs and inverses
- Graphic, numeric and analytic methods to solve application problems including linear, quadratic, polynomial, rational, absolute value, exponential, logarithmic, trigonometric equations and systems of equations
- Polynomial and rational functions and equations including the use of graphing utilities and synthetic division to graph
- Trigonometric functions developed from the unit circle using radian and degree measure
- Trigonometric identities
- Graphic, numeric and analytical methods to solve linear and non-linear systems of equations and inequalities
- Historical contributions of number and mathematical theories and concepts from diverse cultures
- Exposure to limits, slopes of tangent lines, and areas under curves.
Suggested Reading Other Than Required Textbook
Reading assignments are required and may include but, are not limited to, the following:
I. Assigned chapters in both the algebra and geometry texts covering those topics included in the course content.
II. Articles from current journals, such as Math Horizons, and newspapers pertaining to applications of radical, exponential, logarithmic and geometric functions.
Examples of Outside Assignments
Outside assignments may include, but are not limited to, the following:
I. Interpreting mathematical principles and using appropriate techniques, such as modeling to solve broader and more difficult problems than those covered in class;
II. Solving a variety of application problems, such as exponential growth and decay, requiring the appropriate use of techniques and theorems learned in class.
III. Making connections between exponential and logarithmic functions.
IV. Reviewing, and where necessary, rewriting class notes;
V. Practicing problems from the appropriate sections;
VI. Preforming computer explorations and tutorials using software and/or the internet
VII. Using DVD’s or online videos to review topics covered in class.
Instruction Type(s)
Lecture, Online Education Lecture