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Apr 20, 2024
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MA 120A - Precalculus Mathematics4 lecture hours 0 lab hours 4 credits
Course Description
This course provides a review of the aspects of algebra, trigonometry, and analytic geometry that are necessary for success in calculus for the benefit of students with slight deficiencies in any of these areas. It is not intended as a substitute for a rigorous course in any of these topics. The ‘A’ designation after the course number indicates this is a special section taught with extra math lab hours built in as a requirement for successful completion if the course. We typically run this course in the winter term for those students who were not successful in passing MA 120 in the fall. (prereq: MA 127 or equivalent)
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
- Be proficient with exponential expressions including the laws of exponents and negative and rational exponents
- Factor simple polynomial expressions
- Simplify rational expressions including products, sums, and complex rational expressions
- Solve rational equations including consideration of the domain by means of linear approach and quadratic approach (solving by factoring and/or quadratric formula)
- Be able simplify radical expressions including rationalizing the numerator or denominator
- Solve radical equations (optional)
- Understand the concept of a function, its range and domain, and its graph
- Be proficient with linear functions and models including recognizing that the slope represents rate of change
- Know the graphs of common equations
- Transform the graphs of functions graphically and algebraically
- Understand piecewise-defined functions
- Use operations of functions including composition of functions on calculus concepts such as difference quotients
- Understand exponential functions, their domain and range, and graphs
- Understand logarithmic functions, their domain and range, and graphs
- Be proficient with the properties of logarithms including solving exponential equations
- Understand the measure of an angle including radians and degrees
- Understand the definition of the six trigonometric functions including their relation to the geometry of the unit circle and right triangles
- Evaluate the trigonometric functions both approximately, by using the calculator, and exactly, by using reference angles of common angles
- Apply trigonometric properties to applications
- Know the graphs of the three of sine, cosine and tangent. Recognize the remaining three trigonometric graphs
- Be proficient with basic trigonometric identities including reciprocal identities, ratio identities and Pythagorean identities
- Be familiar with other trigonometric identities (double angle and reduction or half-angle identities)
- Understand the definition of the inverse trigonometric functions and be able to evaluate to find common angles
- Solve basic trigonometric equations
Prerequisites by Topic
Course Topics
- Properties of exponents (2 classes)
- Factoring and simplifying polynomials, rational and radical expressions (4 classes)
- Solving quadratics and trigonometric functions (3 days)
- General functions and their properties: linear, basic graphs, piece-wise (6 classes)
- Trigonometric functions and their properties (11 classes)
- Exponential and log functions (4 classes)
- Reviews and exams (7 classes)
Coordinator
Gina Moran, Lecturer
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