Analytical Mathematics/MTH 112 Dual Enrollment





Precalculus Algebra

Math 112 Section 9

(Dual Enrollment)


Instructor:  Jennifer E. Collins; Gaston High School;; (256) 547-8828

*Please note that the official mode of communication between the College and students is the Gadsden State Email system and Blackboard.


Office Hours:  Monday – Friday 7:30 a.m. – 3:00 p.m.

Academic Division Information:

Division of Mathematics and Engineering

Dr. Susan Williams Brown


Dean of Academic Programs and Services

Dr. Leslie Worthington


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.

Pre-requisite(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) MTH 100 Intermediate College Algebra.  Any student not meeting the prerequisites for this class may be administratively withdrawn. It is the students’ responsibility to make sure that all prerequisites have been met.

Placement Exam Score (COMPASS OR ACCUPLACER):

COMPASS Algebra (AL) 66-100, College Algebra (CA) 0-45, ACT Minimum of 22 on math portion, or ACCUPLACER Elementary Algebra (EA) 80-120, College Level Math (CLM) 50-79.

Required Textbook/s:  College Algebra, 7th Edition

ISBN Loose-Leaf Text:  9780134469164, Author:  Blitzer, Publisher:  Pearson Education

(Textbook PowerPoints are available for Instructor use.)

Optional/Additional books, supplies, materials, or software:  Scantron Answer Sheet #19641, 3 ring binder, use of calculator allowed at Instructor’s discretion, but NO CELL PHONES!


Important Websites: 

Last Day to Withdraw:  November 26, 2018
Withdrawing can adversely affect financial aid, especially if done before completing 60% of the term.

Final Examination:  December 10-14, 2018

Course Objectives:  The objective of this course is to provide an understanding of concepts, develop competent skills, and demonstrate applications in the following areas:

  1. analytic and geometric interpretation of algebraic, exponential, and logarithmic functions
  2. analytic and geometric interpretation of systems of equations and inequalities


While building on the manipulative skills from algebra this course strives to develop analytic skills as a preparation for further mathematical applications or courses in mathematics requiring knowledge of algebraic and transcendental functions.


SACS Student Learning Outcomes:

  1. Demonstrate the ability to evaluate algebraic functions.
  2. Demonstrate the ability to evaluate composite functions.
  3. Demonstrate the ability to find the difference quotient of a function.
  4. Demonstrate competent skills in exponential functions by exhibiting the ability to evaluate an exponential function.
  5. Demonstrate the ability to evaluate a logarithmic function.
  6. Demonstrate the ability to transform a logarithmic function into exponential form.
  7. Demonstrate the ability to apply the properties of logarithmic functions.
  8. Demonstrate the ability to evaluate a logarithm using the change-of-base formula.
  9. Demonstrate competent skills in analytic and geometric interpretation of systems of equations by exhibiting the ability to solve a system of 2 equations with 2 unknowns.
  10. Demonstrate competent skills in analytic and geometric interpretation of inequalities by exhibiting the ability to solve a quadratic inequality.


Assignments and Assessment:



All assignments and/or Chapter Tests

80 %

Final Exam



Grade Averages:

Percentage Grade

Letter Grade











*Students must achieve a C – 70% or higher in this course to proceed to the next level math course.


Make-up Policy: Make up work MAY be provided at the discretion and convenience of the instructor. You must have an EXCUSED absence in order to make up any missed assignments and/or tests.   

Blackboard Information: If you need assistance with Blackboard, please submit a request to the Help Desk at or call 256-549-8341 during business hours.

Blackboard Guides:


Computer System Requirements:

Academic Misconduct: Academic misconduct such as cheating and plagiarism is not permitted. Suspected cases of academic misconduct or dishonesty will be reported to the appropriate dean and may result in the student receiving a failing grade for the course.

College General Regulation:

Attendance and Withdrawal:

Harassment and Discrimination Policy:

Disability Services (ADA):

Copyright Information:

It is illegal to download music through the College computer network system.  Students who are found to be illegally downloading music will be subject to federal and state laws pertaining to such acts.  Additionally, Gadsden State Community College Catalog and Student Handbook states the following: “Any use of College technology resources for illegal, inappropriate, or obscene purposes, or in support of such activities is prohibited.  Respect for intellectual property or copyright, ownership of data, security measures, and personal right and privacy must always be demonstrated.”

General Student Services:

Student Support Services:

Complaint Processes:


Course Schedule (Tentative Daily Schedule)
The course schedule is subject to change at the discretion of the instructor.


Outline of Concepts and Sections

Tentative Homework Problems


1.2 – Linear Equations and Rational Equations

P.120 (1-9odd, 31-47odd, 61-73odd)


1.4 – Complex Numbers

P.146 (29, 31)


1.5 Part 1 – Quadratic Equations

P.167 (1-33odd, 47-73odd, 91, 105)


1.6 – Other Types of Equations

P.185 (1-27odd, 31, 35, 49-55odd)


1.7 – Linear Inequalities and Absolute Value Inequalities

P.203 (27, 31, 33, 41, 51)


3.6 – Polynomial and Rational Inequalities

P.440 (3, 5, 11, 15, 17, 35)


1.5 Part 2 – Quadratic Equations

P.167 (109, 113) Find x and y intercepts


2.1 Part 1 – Basics of Functions and Their Graphs

P.230 (39-47odd)


2.8 – Distance and Midpoint Formulas; Circles

P.332 (1, 19, 31-39odd, 41-51odd)


2.3 – Linear Functions and Slope

P.267 (1-33odd, 39, 40, 45, 46, 49-71odd)


2.4 – More on Slope

P.278 (5-11odd, 31, 32)


2.1 Part 2 – Basics of Functions and Their Graphs

P.230 (11-17odd, 27-32all, 55-64all)


2.2 – More on Functions and Their Graphs

P.251 (53-57odd, 71-81odd)


2.6 – Combinations of Functions; Composite Functions

P.310 (1-5odd, 31-35odd, 51-55odd, 61, 73)


2.7 – Inverse Functions

P.321 (1, 3, 11-17odd, 29-33odd, 39)


2.5 – Transformations of Functions

P.294 (53-59odd, 67, 69, 81-89odd, 95, 99)


3.1 – Quadratic Functions

P.360 (9-15odd, 17-29odd Find vertex, intercepts, and graph)


3.3 – Dividing Polynomials; Remainder and Factor Theorems

P.392 (1-23odd, 41, 43)


3.4 – Zeros of Polynomial Functions

P.406 (1-17odd)


3.5 – Rational Functions and Their Graphs

P.426 (1-5odd, 21-43odd, 57, 67, 81-85odd)


4.1 – Exponential Functions

P.474 (1-9odd, 11, 12, 15, 27, 28, 35, 37, 43, 47, 53)


4.2 – Logarithmic Functions

P.489 (1-19odd, 21-29odd, 43, 53, 55, 65, 81-89odd)


4.3 – Properties of Logarithms

P.501 (1-31odd, 41-65odd, 71-76all)


4.4 – Exponential and Logarithmic Equations

P.514 (1-5odd, 19, 20, 27, 37, 53-71odd)


5.1 – Systems of Linear Equations in Two Variables

P.555 (1-33odd)


5.2 – Systems of Linear Equations in Three Variables

P.566 (1-9odd)


5.4 – Systems of Nonlinear Equations in Two Variables

P.587 (29-33odd)


5.6 – Linear Programming (additional topic)

P.608 (5-10all)


8.5 – The Binomial Theorem (additional topic)

P.796 (9-15odd, 23)




Remaining Topics for ALCOS Algebra II w/Trig

Matrix Operations and Applications:

  1. Use matrix notation.
  2. Understand what is meant by equal matrices.
  3. Add and subtract matrices.
  4. Perform scalar multiplication.
  5. Solve matrix equations.
  6. Multiply matrices.
  7. Model applied situation with matrix operations.

8, 9, 10, 11, 26

The Ellipse and The Hyperbola:

  1. Graph ellipses centered at the origin.
  2. Write equations of ellipses in standard form.
  3. Graph ellipses not centered at the origin.
  4. Solve applied problems involving ellipses.
  5. Locate the hyperbola’s vertices and foci.
  6. Write equations of hyperbolas in standard form.
  7. Graph hyperbolas centered at the origin.
  8. Graph hyperbolas not centered at the origin.
  9. Solve applied problems involving hyperbolas.


Trigonometry Concepts & Applications (Supplemental):

  1. Understand radian measure
  2. Convert between degrees and radians
  3. Understand the unit circle
  4. Define the six trig functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions.

30c, 37, 38, 39, 40

Probability/Statistics (Supplemental):

  1. Compute empirical probability.
  2. Compute theoretical probability.
  3. Find the probability that an event will not occur.
  4. Find the probability of one event or a second event occurring.
  5. Find the probability of one event and a second event occurring.
  6. Use the Fundamental Counting Principle.
  7. Use the permutations formula.
  8. Distinguish between permutation problems and combination problems.
  9. Use the combinations formula.