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COURSE OUTLINE FOR COLLEGE MATHEMATIC

A. COURSE NUMBER
AND TITLE:
MT125 – COLLEGE MATHEMATICS
B. CURRICULUM: Mathematics/Computer Science Unit Offering
C. CATALOG
DESCRIPTION:
(C, N, S) (4, 0) 4 Credits
The first course in a two-semester sequence of college algebra
and trigonometry. The sequence is preparatory for an introductory
or survey level of calculus. Basic Algebra skills are reviewed and
extended. Functions, in general, and their inverses are studied
along with the properties, graphs and transformations of linear,
quadratic absolute value, radical rational, logarithmic and
exponential functions. Equations of the above functions as well as
linear systems of equations and linear and absolute value
inequalities are solved. Related application problems are
incorporated throughout. Prerequisite: MT007 or MT013 or
equivalent, and appropriate mathematics level code. Level code is
determined by Mathematics Department placement test and/or
successful completion of mathematics courses.
   
D. DURATION OF
INSTRUCTIONAL
PERIOD:
Two hundred minutes per week for fifteen (15) weeks.
E. ACADEMIC
CREDIT HOURS:
Four (4) credit hours.
F. SUGGESTED TEXT/
COURSE MATERIALS:
See individual campus Book Specific Outline. A scientific
Calculator with yx and logarithmic functions will be required. Use of
a graphing calculator will be optional.
G. COURSE OUTCOMES: Upon completion of this course, the student will be able to:

1. Apply the concepts of the real number system and the
properties of real numbers.
2. Simplify and perform the fundamental operations (addition,
subtraction, multiplication, and division) on real numbers,
polynomials, and radical expressions; and simplify complex
fractions.
3. Solve linear, quadratic, (inc. imaginary roots), absolute
value, radical, exponential and logarithmic equations.
4. Solve linear and absolute value inequalities.
5. Interpret, set up and solve problems involving direct, inverse
and joint variation.

6. Define function and determine whether a given relation is a
function.
7. Evaluate a given function, use function notation, perform
operations on functions, and the composition of functions.
8. Ascertain when a function has an inverse and be able to
compute the inverse when it exists.
9. Graph, interpret the graph of functions and transformation of
functions—including linear, absolute value, quadratic, cubic,
radical, simple rational, exponential and logarithmic.
10. Solve systems of equations in 2 and 3 variables
11. Interpret and apply the properties of exponential and
logarithmic functions.
12. Solve word problems that involve the use of linear,
quadratic, exponential and logarithmic functions and
systems of linear equations.
13. TECHNOLOGY OBJECTIVES:
Students will be able to demonstrate proficiency with a
scientific calculator in performing the following skills:
a. Evaluating functions, various roots and exponents
b. Find Log x, Lnx and ex
c. Solve exponential and logarithmic equations

   
H. PROGRAM
COMPETENCIES:
(SEE J. ECC GRADUATE LEARNING OUTCOMES)
I.  SUNY General Education
Ten Knowledge Areas:
• Interpret and draw inferences from mathematical models
such as formulas, graphs, tables and schematics
Related Course Outcomes: 5, 6, 8, 9, 10, 11, 12

• Represent mathematical information symbolically, visually,
numerically and verbally
Related Course Outcomes: 3-9, 11, 12

• Employ quantitative methods such as arithmetic, algebra,
geometry, or statistics to solve problems
Related Course Outcomes: 1-5, 7, 8, 10, 12, 13

• Estimate and check mathematical results for
reasonableness
Related Course Outcomes: 3, 5, 8, 12

• Recognize the limits of mathematical and statistical
methods
Related Course Outcomes: 3, 6, 8, 10, 11
   
J. ECC Graduate Learning
Outcomes (GLO):
1. Apply appropriate mathematical procedures and quantitative
methods
Related Course Outcomes: 1-13
K. ASSESSMENT OF
STUDENT LEARNING:
Assessment of the individual student learning outcomes will be
measured by:

1. Minimum of four 50-minute tests that measure the
objectives.
2. Optional final exam that tests the course objectives.
L.  LIBRARY RESOURCES: Option of the instructor.
M. TOPICAL OUTLINE: INSTRUCTIONAL
PERIODS:
  I. Real Number System

a. Basic concepts of real numbers
b. Fundamental operations (addition, subtraction,
multiplication, and devision) of real numbers
c. Properties of real numbers

0.5 week
 
  II. Exponents and Radicals

a. Rules of exponents
b. Fundamental Operations of radicals
c. Relationship between exponents and roots
d. Operations with complex numbers

1.5 weeks
 
  III. Fundamental Algebraic Operations

a. Factoring and fundamental operations
involving polynomials
b. Simplification of rational expressions
and complex fractions
c. Fundamental operations involving rational
expressions
2 weeks
 
  IV. Equations

a. Linear
1. Solving Linear equations
2. Solving linear inequalities
3. Applications
i. Word problems
ii. Formulas

b. Quadratic
1. Methods of Solving Quadratic Equations
i. Factoring
ii. Completing the square
iii. Quadratic formula
2. Applications

c. Miscellaneous Equations
1. Solving radical equations
2. Solving Equations in quadratic form
3. Solving equations with rational exponents

d. Absolute value equations and Inequalities

3.5 weeks
 
  V. Functions

a. Concept of a function
b. Operations involving functions
1. Fundamental operations
2. Composition
3. Inverse
c. Variation
d. Symmetry
e. Graphing and transformations (shifting,
stretching, shrinking and reflecting of the
basic graphs)
1. Linear functions
i. slope perpendicular and parallel
ii. intercepts
2. Quadratic and Cubic Functions
3. Reciprocal Function
4. Square Root Functions
5. Absolute Value Functions
6. Piece-wise Functions

3 weeks
 
  VI. Exponential and Log Functions

a. Definition of exponential and log functions
b. Properties of exponential and log functions
c. Graphing of exponential and log functions
d. Fundamental operations involving log functions
e. Exponential and logarithmic equations
f. Applications of exponential and log equations

2.5 weeks
 
  VII. Systems of Linear Equations

a. Solve linear equations in two variables
algebraically and graphically
b. Solving linear equations in three variables
algebraically
c. Cramer’s Rule (optional)
d. Applications to word problems

1 week
 
  VIII. Evaluation 1 week
N. PREPARED BY: C. Curley, D. Malczewski, L. Kuroski, J. Pirie, D. Doucette, S. Metwali