Pre-Calculus Mathematics – MATH 2111 – 202
CRN 23578
(Monday, Tuesday, Thursday) (6:00 PM) – (8:45 PM)
Remote
Professor: James McCaughey
Email: jcmccaughey1@ccri.edu or jmccaughey@narrabay.com
Office: N/A
Office Hours: By appointment
Textbook: Larson, 10th Edition, WEBASSIGN, Publisher: CENGAGE L
The Class Key for this course is ccri 5324 6224
Class Materials: computer, calculator, internet access, MS Teams
Course Description (4 credits) Functions and their graphs are discussed with particular attention paid to
polynomial, rational, trigonometric, exponential and logarithmic functions. Determinants, matrices, complex
numbers and analytic geometry are also studied.
Note: Per NEASC standards, for each class hour a student is in class, he or she should expect to work 2 hours
outside of class on the material. This means that you should prepare to spend at least 8 hours each week outside of
class on this course. Schedule your time accordingly.
Learning Outcomes
1. Utilize the complex numbers to obtain all solutions of quadratic equations, and those that are quadratic in form
2. Evaluate functions, including piecewise functions
3. Investigate the domain, range, and symmetry of functions algebraically and graphically
4. Determine the composition of functions
5. Calculate the distance between two points
6. Find the zeros of polynomials by synthetic division or long division
7. Ascertain the vertices and intercepts of functions
8. Identify any asymptotes of rational functions
9. Solve polynomial and rational inequalities and express results as unions or intersections of sets
10. Express the inverse of a relation algebraically and graphically
11. Graph exponential and logarithmic functions
12. Use the properties of logarithms to solve equations
13. Study common and natural logarithms
14. Add and subtract vectors
15. Plot complex numbers in the form a+bi as well as trigonometric form
16. Apply DeMoivre’s Theorem to raise a complex number to a power, and find the nth root of a complex number
17. Solve systems of linear equations using graphing, substitution, elimination, and matrix methods
18. Perform matrix operations and determine inverses and determinants of matrices
19. Solve systems of nonlinear equations in two variables by graphing and substitution
20. Define a conic section and graph parabolas, circles, ellipses, and hyperbolas
21. Identify the foci, center, axes, asymptotes, etc. for parabolas, circles, ellipses, and hyperbolas
22. Study the polar coordinate system and plot polar curves
1
Grading Policy:
Homework:
Exams (3):
Final:
50%
30%
20%
Course Outline
I. FUNCTIONS AND GRAPHS
A. Domain and Range
1. Even and Odd functions
B. Transformations of Functions
1. Reflections
2. Vertical translations
3. Horizontal translations
C. Combinations of Functions
1. Addition/subtraction
2. Multiplication/division
3. Composition
D. Inverse Functions
II. POLYNOMIAL AND RATIONAL FUNCTIONS
A. Linear functions
B. Quadratic functions
C. Polynomial functions of higher degree
D. Synthetic division and zeros of polynomial functions
1. Remainder Theorem
2. Factor Theorem
3. Rational zeros of polynomials
E. Complex numbers and quadratic equations
1. Operations on complex numbers
2. Complex conjugates
F. Rational functions and asymptotes (including slant asymptotes)
G. Polynomial and rational inequalities
III. EXPONENTIAL AND LOGARITHMIC FUNCTIONS
A. Exponential functions and their graphs
B. Logarithmic functions and their graphs
C. Natural and common logarithms
D. Properties of logarithms
E. Change of base formula
F. Exponential and logarithmic equations
G. Exponential and logarithmic models
IV. REVIEW OF TRIGONOMETRY
A. Trigonometric functions
B. Graphs of sine and cosine functions
C. Inverse trigonometric functions
D. Sum/difference, multiple-angle, power-reducing formulas
2
E. Trigonometric equations
F. The Law of Sines
G. The Law of Cosines
V. VECTORS AND COMPLEX NUMBERS
A. Vectors in the plane
B. Vector operations and dot product
C. Polar Coordinates
D. Trigonometric (polar) form of a complex number
E. DeMoivre’s Theorem and finding complex roots
VI. MATRICES AND DETERMINANTS
A. Review of solving systems
1. Graphing
2. Substitution
3. Elimination by adding
B. Matrices and systems of linear equation
1. Augmented matrices
2. Gaussian and Gauss-Jordan elimination
3. Reduced and Row-echelon form of matrices
4. Systems of equations with no, or infinitely many, solutions
C. Operations with Matrices
1. Matrix Addition
2. Matrix Multiplication
D. Inverse Matrices
E. Determinants of Matrices
F. Applications
VII. ANALYTIC GEOMETRY
A. Circles
1. Center, radius, graphs
2. Finding equations
B. Ellipses
1. Foci, vertices, graphs
2. Finding equations
C. Hyperbolas
1. Foci, vertices, graphs
2. Finding equations
D. Parabolas
1. Focus, vertex, graphs
2. Finding equations
E. Polar Coordinates
F. Graphs of Polar Equations
3
Course Schedule:
Week Starting
HW
Monday, July 13, 2020
Topics Covered
I. Functions and Graphs
II. Polynomial and Rational
Functions
III. Exponential and Logarithmic
Functions
IV. Review of Trigonometry
Monday, July 20, 2020
V. Vectors and Complex Numbers
7,8
Monday, July 27, 2020
VI. Matrices and Determinants
9,10
Exam 3
11,12
Final
Monday, June 29, 2020
Monday, July 06, 2020
Monday, August 03, 2020 VII. Analytic Geometry
Exams
Due Date
1
2
Sunday, July 05, 2020
Exam 1
Sunday, July 05, 2020
3,4
5,6
Sunday, July 12, 2020
Exam 2
Sunday, July 12, 2020
Sunday, July 26, 2020
Sunday, July 26, 2020
Thursday, August 06, 2020
Services for Students with Disabilities
Any student with a documented disability may arrange reasonable accommodations. As part of this process,
students are encouraged to contact the office of Disability Services for Students as early in the semester as possible
https://www.ccri.edu/dss/index.shtml
Important Links
Students are responsible for policies set forth in the student handbook. Student Handbook:
https://www.ccri.edu/advising/new_students/student_handbook/
Academic Calendar: (link)
CCRI offers free tutoring at the success center. You can drop in for a tutoring session or set a schedule. Stop by the
success center or visit https://www.ccri.edu/success/
This syllabus is subject to change at the discretion of the instructor. Students are responsible for keeping
current with changes made to this syllabus.
4