Bucks County Community College
Newtown, PA 18940
Distance Learning PreCalculus
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Course Information Sheet |
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Instructor: Dr. E. Fitt
Office: Founders 123
Phone: 215 968 8260
Email: fitte@bucks.edu
I. Course Description
An introduction to the foundations of analysis designed to precede the calculus sequence with emphasis on functions and graphs. Topics include properties of absolute value, polynomial, rational, exponential, logarithmic and trigonometric functions; techniques for solving equations and inequalities and an introduction concept of limits and the difference.
Prerequisite: MATH ATP Level 9 or MATH122 with a grade of C or better, or
MATH120 and High School trigonometry.
II.
Required Course Content and Direction
A.
Learning Goals
Course Specific:
The student will be able to:
1. Apply and extend algebraic skills.
2. Analyze calculus-related concepts such as limits, tangent to a curve and the difference quotient.
3. Apply the properties of functions such as finding the domain and range and develop the skill to graph them.
4. Accurately use a graphics calculator to find phase shifts, reflecting and stretching graphs of functions.
5. Perform operations of functions; addition, subtraction, multiplication, division and composition of functions.
6. Find the inverse function and graph.
7. Construct mathematical models with functions using real-world applications or formulas.
8. Find zeros of a function, determining symmetries of a function, using limits to determine end behavior of a function.
9. Solve problems involving maximizing and minimizing a quadratic function both algebraically and graphically.
10. Find vertical, horizontal and slant asymptotes for rational functions and graph.
11. Graph exponential and logarithmic functions, and use the properties of logarithms and the definition of e.
12. Solve exponential and logarithmic equations and application problems using exponents and logarithms.
13. Define trigonometric functions using the unit circle and right triangle definition.
14. Graph trigonometric functions, find the inverse trigonometric functions and verify trigonometric identities and formulas.
15. Solve trigonometric equations and solve applications problems using real-world applications.
Course Learning Goals:
Category I:
Math or Science: the students will be able to:
1. develop the ability to analyze, interpret, and apply quantitative information.
Core Learning Objectives:
Category I
Math
or Science: the student will be able to:
1. accurately translate descriptive problems into mathematical formulas and solve them. (1)
Category III:
CRITICAL THINKING/PROBLEM SOLVING
The students will be able to:
Demonstrate an understanding of solving problems by:
a. recognizing the problem
b. reviewing information about the problem
c. developing plausible solutions
d. evaluating the results
B. Planned Sequence of Topics and/or Learning Activities:
The following is a list of the minimum amount of course material to be covered by the instructor. Accompanying each topic is an approximate number of lessons required to study the topic.
1. Review Topics (10 lessons)
a) exponents & Scientific notation
b) radicals & rational exponents
c) polynomials
d) factoring polynomials
e) rational expressions
f) linear equations
g) quadratic equations
h) linear inequalities
2. Graphs, Functions, and Models (9 lessons)
a) graphs& graphing utilities
b) lines and slopes
c) distance & midpoint formulas, circles
d) basic functions
e) graphs of functions
f) transformations of functions
g) combinations of functions, composite functions
h) inverse functions
i) modeling with functions
3. Polynomial & Rational Functions (9 lessons)
a) Complex numbers
b) Quadratic Functions & Applications
c) Polynomials Functions, Application & Graphs
d) Dividing Polynomials; Remainder and Factor Theorem
e) Zeros of Polynomial Functions
f) Rational Functions and Graphs Polynomial & Rational Inequalities
4. Exponential & Logarithmic Functions (5 lessons)
a) exponential functions
b) logarithmic functions
c) properties of logarithms
d) exponential & logarithmic equations
e) optional; modeling with exponential and logarithmic functions
5. Trigonometric Functions & Analytical Trigonometry (10 topics)
a) angles and their Measure
b) trigonometric functions; the unit circle
c) right triangle trigonometry
d) trigonometric functions of any angle
e) graphs of sine and cosine functions
f) graphs of other trigonometric functions
g) inverse trigonometric functions
h) applications of trigonometric functions
i) verifying trigonometric identities
j) sum and difference formulas
k) double angle and half angle identities
6. Additional Topics in Trigonometry (5 topics)
a) optional: product to sum and sum to product formulas
b) trigonometric equations
c) the law of sines
d) the law of cosines
C.
Assessment Methods for Core Learning Goals
All critical thinking and problem solving, college level mathematics or science, and discipline-specific course objectives will be assessed as follows:
The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment such as oral communication among students and between teacher and student(s), and formal assessment using open-ended questions reflecting theoretical and applied situations.
III. Withdraw
If you should find it necessary to withdraw, College policy states that “Withdraw during the first 10 weeks carries a W grade.” Check the College catalog for the withdraw date specific to the semester in which you are enrolled.
If you do not take the tests and do not withdraw you will receive an F.
IV. Extra Help if you find you are having difficulty with any concepts is always available.
My office hours are posted on my door – Founders 123
If you cannot be available during scheduled hours, we can schedule a time that is mutually convenient.
Tutoring help is available free of charge in the Learning Center, L121
Supplementary study materials are available in CourseCompass.
Do not wait to get extra help. Contact me by phone or by email at the first sign of difficulty.