NORTHWEST-SHOALS COMMUNITY COLLEGE

GENERAL COURSE SYLLABUS

 

 

TITLE OF COURSE:  Pre-Calculus Algebra (MTH 112)

 

DIVISION:  Mathematics, Science, and Technology

 

COURSE DESCRIPTION:  This course emphasizes the algebra of functions - including polynomial, rational, exponential, and logarithmic functions. The course also covers systems of equations and inequalities, quadratic inequalities, and the binomial theorem. Additional topics may include matrices, Cramer's Rule, and mathematical induction.
 

HOURS:     Credit:  3       Contact:  3       Lecture:  3      Clinical:  0      Lab:  0     

 

PREREQUISITE(S):  All core mathematics courses in Alabama must have as a minimum prerequisite high school Algebra I, Geometry, and Algebra II with an appropriate mathematics placement score. An alternative to this is that the student should successfully pass with C or higher (S if taken as pass/fail) Intermediate College Algebra, MTH 100.

 

COREQUISITE(S): None

 

REQUIRED TEXTBOOK(S):  Precalculus;  7th Edition; R. E. Larson and R. P. Hostetler with David C. Falvo, Houghton-Mifflin, 2007.

 

SUPPLIES:  Scientific or graphing calculator is highly recommended.

 

GENERAL EDUCATION OBJECTIVE:   All associate degree graduates should be able to use the mathematical concepts, notations, and manipulations needed in their field of study or occupation. (3)

 

COURSE OBJECTIVE(S):  Upon successfully completing Pre-Calculus Algebra, MTH 112, the student should be able to:

 

  1. Solve linear, quadratic, and rational equations in one variable.

 

  1. Solve quadratic inequalities in one variable.

 

3.      Identify and graph basic functions (i.e. constant, identity, linear, absolute value, square root, quadratic, cubic, and reciprocal functions) and transform their graphs for related functions.

  1. Determine domain and range for relations and function; evaluate functions (including piecewise functions), find the inverse of a function; perform operations on functions (including composition.)

  2. Simplify and evaluate expressions containing complex numbers and their operations; find all zeros of higher degree polynomial functions and graph them; use a graph to determine estimations of zeros to solve practical applications.

  3. Identify the domain and asymptotes for rational functions; graph rational functions on a Cartesian coordinate system.

  4. Identify and evaluate logarithmic and exponential functions; solve equations containing logarithmic and/or exponential expressions; solve practical application problems involving logarithms and/or exponentials.

  5. Solve a system of equations or inequalities in two or three variables; develop and solve a system to find solutions for related application problems.

  6. Apply the Binomial Theorem to expand binomials and find specific terms of a binomial expansion.

METHODS OF EVALUATION: 

 

  1. Course Grade Evaluation: (Minimum of 4 measurements)

A comprehensive final exam will be given and counted toward the student’s final average.  Make-up examinations, as such, will not generally be given. 

                        

  1. Evaluation of General Educational Objectives:  Student success on the General Educational Objective (3) is measured by student performance on each of the course objectives, which require use of mathematical concepts, notations, and manipulations.  Performance on each course objective will be evaluated using appropriate problems from the final exam.  Results will be tallied for each course objective.

 

  1. Use of Findings: Instructors will analyze data gathered from the assessment(s) for each course objective and changes will be made based on identified weaknesses.  The math department will meet once every two years to discuss findings and implement strategies to improve department and student performance.

 

OUTLINE OF COURSE TOPICS:

I.   Review Fundamental Concepts of Algebra

            A.  Exponents and Radicals

            B.  Polynomials and Factoring

            C.  Rational Expressions

            D.  Solving Equations and Inequalities (including quadratic inequalities)

           

II.                 Functions and Graphs

            A.  Graphs of Equations

            B.  Linear Equations in Two Variables

            C.  Functions

            D.  Analyzing Graphs of Functions

            E.  Parent Functions and Transformations of Functions

            F.  Combinations of Functions

            G.  Inverse Functions

 

III.       Polynomial and Rational Functions

            A.  Quadratic Functions

            B.  Polynomial Functions of Higher Degree

            C.  Polynomial and Synthetic Division

            D. Complex Zeros and the Fundamental Theorem of Algebra

E.  Zeros of Polynomial Functions

            F.  Rational Functions and Asymptotes

           

IV.       Exponential and Logarithmic Functions

            A.  Exponential Functions and Their Graphs

            B.  Logarithmic Functions and Their Graphs

            C.  Properties of Logarithms

            D.  Exponential and Logarithmic Equations

D.  Exponential and Logarithmic Models

 

V.                 Sequences, Series, and Probability

A. (Optional) Sequences and Series

B. (Optional) Arithmetic Sequences and Partial Sums

C. (Optional) Geometric Sequences and Series

D. (Optional) Mathematical Induction

E. (Required) The Binomial Theorem

F. (Optional) Counting Principles

G. (Optional) Probability

 

VI.       Systems of Equations and Inequalities

            A.  Solving Systems of Equations

            B.  Two Variable Linear Systems

            C.  Multivariable Linear Systems

            D.  Systems of Inequalities

           

VII.      (Optional) Matrices and Determinants

            A.  Matrices and Systems of Equations

            B.  Operations with Matrices

            C.  The Inverse of a Square Matrix

            D.  The Determinant of a Square Matrix

            E.  Applications of Matrices and Determinants

 

AMERICANS WITH DISABILITIES ACT POLICY: It is the policy of Northwest-Shoals Community College to comply with the Americans with Disabilities (ADA) Act. Any student covered under this act needing and desiring reasonable accommodations for this class should notify Linda Waide at 331-5321. See NWSCC catalog for additional details.

 

ATTENDANCE POLICY: Because class attendance is considered to be essential to the accomplishment of course objectives, excessive absences are discouraged. At no time should a student miss more than 20% of the class meetings for a course. These absences also include any absences accrued during late registration. Failure to adhere to the 20% policy may result in a failing grade based on academic performance. Students should discuss with the instructor what is considered “excessive” for a particular course. Any variation of this policy must be approved through the Chief Instructional Officer. A student who is absent due to required participation in a school activity must be allowed to make up work, according to guidelines issued by individual instructors.

 

WITHDRAWAL POLICY:  A student who is unable to complete a course is expected to withdraw from that course by the end of 60% of class meetings.  A student who withdraws by the date published in the schedule will receive a grade of “W” for the course.  This withdrawal is done only by student request.  The grade of “W” is allowed regardless of the student’s grades to the point of withdrawal. 

 

After the designated date of class withdrawal, the approval of the Chief Instructional Officer is required prior to allowing a student to withdraw. The determination of “WP” (withdrawal passing) or “WF” (withdrawal failing) will be made by the instructor for the course and is based on the student’s grades to the point of withdrawal.