MA 131 - Precalculus
Description
Expressions and functions investigated in this course are polynomial, rational, radical, trigonometric, exponential and logarithmic. Applications are introduced throughout the course. Appropriate technology is utilized to enhance understanding and gain insight through explorations. Success in precalculus requires a solid foundation in intermediate algebra skills. This course helps prepare students for the Calculus sequence (MA 133 , MA 134 , MA 255 ).
Credit Hours: 5
Contact Hours: 5
Prerequisites/Other Requirements: MA 107 (C or Higher) or MA 108 (C or Higher) or MA 110 (C or Higher) or ALEKS score of 61 or Higher.
English Prerequisite(s): None
Math Prerequisite(s): None
Course Corequisite(s): None
Academic Program Prerequisite: None
Consent to Enroll in Course: No Department Consent Required
Dual Enrollment Allowed?: Yes
Course Fees: $19.00
Number of Times Course can be taken for credit: 1
Programs Where This Course is a Requirement:
None
General Education Requirement:
Mathematics
General Education Learner Outcomes (GELO):
3. Critical Thinking: Gather and synthesize relevant information, evaluate alternative perspectives, or understand inquiry as a means of creating knowledge, 7. Problem-Solving: Apply theory, calculation, or experimentation to demonstrate effective problem-solving
Course Learning Outcomes:
1. Use appropriate notation to represent mathematical relationships, patterns, and written phrases.
2. Solve various types of equations (including polynomial, radical, rational, exponential, logarithmic, and trigonometric equations) after identifying if they should be solved symbolically, graphically, or numerically.
3. Solve various types of inequalities symbolically, graphically, and numerically.
4. Explore the concept and notation of functions, and inverse functions.
5. Explore complex numbers and solve equations with nonreal solutions.
6. Model functions that describe phenomena using appropriate technology.
7. Utilize problem-solving strategies and/or techniques in mathematical processes and application problems to find quantitative solutions. (GELO 7)
8. Interpret results from quantitative solutions and summarize data and graphs.
9. Apply theorems.
10. Explore, rewrite, and apply identities in various contexts.
11. Explore precalculus topics in algebra and trigonometry.
12. Apply unit circle and right triangle definitions of trigonometric functions.
13. Solve right triangles and oblique triangles.
14. Develop a plan to implement a solution to a problem or issue. (GELO 3)
15. Complete work accurately, with attention to detail.
Course Outline:
I. Function Concept
A. Definition of function
B. Function notation
C. Set notation, interval notation
D. Domain and range
E. Algebra of functions
F. Graphs and transformations
G. Function composition
H. Piecewise-defined functions
II. Geometry
A. Pythagorean theorem and distance formula
B. Angle measurement
C. Arc length and sector area
D. Similar triangles
E. 30-60-90 and 45-45-90 triangles
III. Polynomial and Rational Functions
A. Simplifying polynomial and rational expressions, factoring
B. Polynomial functions (domain and range, end behavior, and relative extrema - including finding the vertex of a parabola)
C. Rational functions (domain and range, asymptotes, end behavior and limits)
D. Inverse functions (one-to-one function)
E. Solving quadratic, radical, and rational equations and inequalities algebraically
F. Using technology to solve quadratic, radical, and rational equations and inequalities
G. Applications and Modeling
IV. Exponentials and Logarithms
A. Exponential functions (domain and range, end behavior, asymptotes)
B. Definition of logarithm as the inverse of an exponential function
C. Simplifying logarithmic expressions
D. Logarithmic functions (domain and range, end behavior, asymptotes)
E. Solving exponential and logarithmic equations algebraically and graphically
F. Applications
V. Other Algebraic Topics
A. Absolute value equations and inequalities
B. Systems of equations
C. Basic conic sections
VI. Trigonometric Functions
A. Right Triangle Definitions
B. Unit Circle Definitions
C. Reference Triangle Definitions
D. Special values of trigonometric functions (multiples of 30 degrees and multiples of 45 degrees)
E. Graphs of basic trigonometric functions (sine, cosine, tangent, secant, cosecant, cotangent)
F. Transformations of sine and cosine
G. Inverse functions for sine, cosine, and tangent
H. Identities
I. Solving trigonometric equations
J. Applications
K. Laws of sines and cosines
Approved for Online and Hybrid Delivery?:
Yes
Instructional Strategies:
Lecture: 0-90%
Facilitated discussion: 0-80%
Mediated instruction: 0-100%
Group work: 0-60%
Mandatory Course Components:
None
Equivalent Courses:
None
Accepted GRCC Advanced Placement (AP) Exam Credit: None
AP Min. Score: NA
Name of Industry Recognize Credentials: None
Course prepares students to seek the following external certification:
No
Course-Specific Placement Test: None
Course Aligned with ARW/IRW Pairing: N/A
Mandatory Department Assessment Measures:
None
Course Type:
General Education- Offering designed to meet the specific criteria for a GRCC Distribution Requirement. The course should be designated by the requirement it fulfills.
Course Format:
Lecture - 1:1
Total Lecture Hours Per Week: 5
People Soft Course ID Number: 101080
Course CIP Code: 27.01
Maximum Course Enrollment: 35
High School Articulation Agreements exist?: No
If yes, with which high schools?: NA
Non-Credit GRCC Articulation Agreement With What Area: No
Identify the Non Credit Programs this Course is Accepted: NA
School: School of STEM
Department: Mathematics
Discipline: MA
Faculty Credential Requirements:
18 graduate credit hours in discipline being taught (HLC Requirement), Master’s Degree (GRCC general requirement)
Faculty Credential Requirement Details:
Master's degree in Mathematics or in a closely related field with at least 18 semester hours of graduate work in mathematics. Teaching experience at the college level is preferred.
Major Course Revisions: General Education Review
Last Revision Date Effective: 20230222T14:23:33
Course Review & Revision Year: 2027-2028
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