College Algebra
Mr. Frentrop
Room 102
2015-2016
Course Description: A sophisticated study of relations, functions, and their graphs, ratios, proportion,
variation, linear equations, problem solving, quadratic and quadratic form equations, theory of higher
degree equations, systems of equations, inequalities, and determinants. Students may earn three hours of
college credit through the Metropolitan Community Colleges system if they meet MCC requirements. One
honor point may be earned for successful completion of the course for college credit at the end of the
semester. The MCC fee is required for college credit and must be paid within the first week of the
semester. If a student elects to take the dual credit class for no college credit, he/she must still meet district
requirements.
Class Procedure: Students are REQUIRED to keep a notebook. The notebook will consist of a three ring
binder and loose leaf notebook paper or a spiral. All class notes, book assignments, and any other
assignments will be kept in the notebook. Homework and notes are to be done on separate sheets of paper.
(May not do homework on back of notes) Notebooks are to be kept current at all times and will be
randomly checked. On homework, tests, and quizzes ALL WORK MUST BE SHOWN to receive full
credit. There will be at least one test per chapter. All unit tests are closed book. If desired a student may
want to obtain a graphing calculator. (TI-83 or 84 is recommended)(Calculators are optional) Calculators
will be allowed on most tests and on the Final Exam. We also have TI-83 calculators that may be checked
out.
No late homework accepted and no late tests or quizzes will be given. If you are having trouble with the
material it is your responsibility to get extra help before the test is given.
I am in room 102 with 4th hour plan period.
I usually arrive at school at least 45 minutes early and will be available to offer extra help. I can only stay
after school with advanced notification.
E-Mail:
jfrentrop@bssd.net
Phone:
224-1315 ext 50683
Grading:
Notebook
Tests and Quizzes
Final Exam
10%
65%
25%
Class Rules: Students are expected to abide by all rules contained in the student handbook.
All tests will be completed during allotted time, NO extra time given.
If absent the day of a test, then the test must be made up no later than
one week after returning
Course Outline:
I.
Review of the Fundamental Concepts in Algebra
1. The Real Number System
2. Basic Rules of Algebra
3. Radicals and Rational Exponents
4. Polynomials and Special Products
5. Factoring
6. Fractional Expressions
II.
Algebraic Equations and Inequalities
1. Linear Equations
2. Linear Equations and Modeling
3. Quadratic Functions
4. The Quadratic Formula
III.
Complex Numbers
1. Complex Numbers
2. Other Types of Equations
3. Linear Inequalities
4. Other Types of Inequalities
IV.
Functions and Graphs
1. The Cartesian Plane
2. Graphs of Equations
3. Lines in the Plane
4. Functions
5. Graphs of Functions
6. Combinations of functions
7. Inverse Functions
V.
Polynomial Functions: Graphs and Zeros
1. Quadratic Functions
2. Polynomial Functions of Higher Degree
3. Polynomial Division and Synthetic Division
4. Real Zeros of Polynomial Functions
5. The fundamental Theorem of Algebra
VI.
Rational Functions
1. Rational Functions
VII.
Exponential and Logarithmic Functions
1. Exponential Functions
2. Logarithmic Functions
3. Properties of Logarithms
4. Solving Exponential and Logarithmic Equations
5. Exponential and Logarithmic Applications
VIII. Systems of Equations and Inequalities
1. Systems of Equations
2. Systems of Linear Equations in 2 Variables
3. Linear Systems in more than 2 Variables
4. Systems of Inequalities
IX.
Matrices and Determinants
1. Matrices and Systems of Linear Equations
2. Operations with Matrices
3. The Inverse of a Square Matrix
4. The Determinant of a Square Matrix
OBJECTIVES
The student will be able to do the following:
1. To solve quadratic equations by:
a. Factoring
b. Using the definition of square root
c. Completing the square
d. Using the quadratic formula
2. To add, subtract, multiply, divide, and find powers of complex numbers
3. To solve equations of quadratic form
4. To solve radical equations
5. To identify the type of symmetry on the graph
a. Symmetry about the y-axis
b. Symmetry about the x-axis c. Symmetry about the origin
6. To find the equation of a line given a point and the slope, or given 2 points
7. To find the slope of a parallel line or perpendicular line
8. To identify equations which represent functions of x
9. To identify functions from the graphs
10. To evaluate functions
11. To find the domain of a function from the equation or from the graph
12. To identify odd and even functions from the equation or from the graphs
13. To find the sum, difference, product, and quotient of 2 functions
14. To form the composition of 2 functions
15. To find the inverse of a function
16. To transform a quadratic function into standard form and identify the vertex
17. To sketch the graphs of polynomial equations using the x-intercepts, y-intercepts, and the leading
coefficient test
18. To find the quotient and remainder of a polynomial division using either long division or synthetic
division
19. To find the upper and lower bound of the real zeros of a polynomial
20. To list the possible rational zeros of a polynomial
21. To determine the possible number of positive and negative real zeros of a polynomial using Descartes’
Rule of Signs
22. To find the real and imaginary zeros of a polynomial by using objectives 18 – 21
23. To identify the horizontal and vertical asymptotes of a rational function
24. To solve linear, quadratic, and rational inequalities and express the answers with number line graphs
and interval notation
25. To graph the following:
a. Absolute value equations
b. Linear equations
c. Quadratic equations
d. Third and fourth degree polynomial equations
e. Rational equations
f. Circles
g. Exponential equations
26. To solve a system of equations in 2 variables using substitution
27. To solve a system of linear equations in 2 or 3 variables
28. To evaluate second and third order determinants
29. To solve a system of linear equations in 2 or 3 variables using Cramer’s Rule
30. To simplify expressions involving logarithms
31. To solve exponential equations and applications of exponential equations (compound interest,
population growth, etc..)