Mathematics 115 - College Algebra

At $3.69 per gallon, 10 gallons of gas will cost $36.90. But how much will it cost to fill that 23 gallon tank on
your SUV? If you are getting 18 miles per gallon, 10 gallons of gas will take you 180 miles. Thus, $36.90 will be
the cost of driving 180 miles. But how much gas (and, hence, what will be the cost of) a 450‐mile trip? When
things are turned around a bit and simple arithmetic is not enough to get the desired result, we get into the
realm of algebra.

In a laboratory experiment, you might measure the temperature at various time intervals. Plotting those data
points on a coordinate system gives a picture of the data, and you can then go on to model the behavior with a
straight line or some other curve. Being able to decide upon best‐fitting linear or nonlinear models, as well as
writing down a formula for these that may be used for further purposes, are additional places for the methods
of algebra.

In algebra, the primary techniques you learn, through investigation, practice, and application, are (1) graphing,
(2) using variables to represent quantities yet to be determined, (3) determining linear and nonlinear models,
and (4) manipulating the algebraic expressions resulting from such models. Because of the vast range of uses
for these techniques, to be successful in virtually any field of study, some ability with algebra is essential.

We will spend time doing practice problems, allowing you to acquire skill with the techniques. It is equally
important that you also have opportunities to experiment and get a better sense of why things work the way
they do. The simple question of why we add fractions the way we do is an example of where this is helpful.
Since this class is coordinated with your Chem 108 class, we will have a great opportunity to develop the algebra
in parallel with applications of interest from your other class. As the term progresses, it is possible you will
additionally see topics from both Math 115 and Chem 108 being integrated with your writing for Eng 111.

In class, we spend time working on example problems, as well as attempting investigations and applied
problems designed to increase your understanding of the mathematics. Outside of class, you will be expected
to complete the material on “hippocampus.org” and further develop ability with pre‐requisites for this class by
working with “ALEKS” in the Mathematics Achievement Center. You will have assigned work in your textbook
and other problems as introduced in class. In order to better quantify your gains, we will use a National Science
Foundation program‐developed diagnostic as a pre‐ and post‐test. Finally, I will employ surveys and other
“affective” measurements to collect your input on the design of the class, my performance in helping you be
successful, and so on.

Material to be covered:
• Course text – Chapters 1‐4, 9
• ALEKS preparatory program
• Hippocampus program; login to “jeffpde” or use the link on Math 115 web page.

Final Grade: You will be graded according to performance on homework, projects, quizzes, and exams. Relative
weights for each and assignment of final course grades will be as follows.
 

A 90‐100%, B 80‐89%, C 70‐79%, D 60‐69%, F 0‐59%

Course Policies
1. Homework and Projects: Daily homework will be assigned, but not all of it will be collected for grading. Projects will
sometimes take the form of extended problem sets from the book and, at other times, consist of an application which
requires you to utilize ideas and techniques learned while completing homework problems.

2. Quizzes and Exams: Unless otherwise announced, all quizzes/exams will be closed book and generally consist not only
of problems similar to the homework, but also problems which test your comprehension of the material. The final
exam will be comprehensive. Calculators may be used, but use of any graphics, symbolic manipulation, and/or
advanced programming capabilities is not allowed unless announced otherwise beforehand.

3. Extension of due dates for homework/projects and make‐up exams may be granted only in the following instances:
• Extreme illness (your own). Let me know about your condition as soon as possible. We will arrange necessary
make‐up work as your good health returns.
• Emergencies (i.e., car accident, death in the family). Again, get in touch with me as soon as possible, and we’ll
make suitable arrangements.
• Excused absences (i.e., athletic events which are excused by university officials). Make‐up work must be arranged
and completed in advance.

4. Office Hours in the Mathematics Achievement Center – Phelps Hall Gym: These are times when you have the
opportunity to meet with me outside of class to discuss problems, progress, etc. It is also a good idea to use these
times to work on ALEKS, and all scheduled ALEKS assessments may take place only during these times or by other
special arrangement. You are also welcome to contact me via email. The most important this is to get your questions
answered.

5. A Note about Study Habits: A good rule of thumb is to spend 2‐3 hours of study time outside of class for each hour of
class time. This time should be spent in diligent study, but should not be done in blocks of time exceeding an hour or
so per study session. 15‐30 minute blocks of otherwise down time, interspersed throughout the day, can become very
productive if used to work on a small group of problems. Keep a record of questions that come up in your studies and
get them answered either by yourself, a fellow student, a tutor, or by me.

Studying with a friend or in a group can be a very positive thing, provided that all participants are contributing.
Since not all assigned homework will be collected for grading, it is very important that you make a special effort to
complete daily assignments in a timely fashion.

6. In all graded materials, sufficient work must always be shown which supports your results. Answers alone, with no
supporting work, will almost never receive full credit. Your submitted work must be neat, clearly presented, stapled,
and have your name written legibly on it. Learning to take pride in the presentation of your work is almost as
important as learning the actual material of a course itself.

7. You are always responsible for all information given during the class period. Additionally, any work done in class for
grade may not be made up due to absence from class (unless excusable as listed above).

Mathematics 115 – College Algebra is a Basic Skills in Mathematics Course

Catalog Course Description: This course will give students a rigorous preparation in algebra. Topics include
review of basic algebraic concepts, functions and graphs, polynomial, radical, rational, exponential and
logarithmic functions; equations, inequalities, systems of equations and inequalities; applications. This is a
University Studies course which satisfies the Basic Skills in Mathematics.
Basic Skills in Mathematics: The purpose of the Mathematics requirement in University Studies is to help
students develop an appreciation of the uses and usefulness of mathematical models of our world, as applied in
a variety of specific contexts. Mathematics 115 contains requirements and learning activities that promote
students' abilities to...

I. use logical reasoning by studying mathematical patterns and relationships;
This is an integral part of nearly every topic in the course. One of the main focuses of the course is the
function concept, where we examine the relationship between y and x through the function f(x). Students
will be asked to graph basic function types such as linear, quadratic, polynomial, and rational functions.
Another main focus of the course is the solution of equations. These will either be those presented to the
student to solve or equations that are set‐up by the student as part of the solution of a application
(word/story) problem.

II. use mathematical models to describe real‐world phenomena and to solve real‐world problems ‐ as well as
understand the limitations of models in making predictions and drawing conclusions;
Nearly all course topics have an application component to them, where students will need to use them to
solve real‐world problems. Many of these are word problems which force students to critically analyze
given information and extract the important elements in order to construct algebraic expressions and
equations that can then be solved.

III. organize data, communicate the essential features of the data, and interpret the data in a meaningful way;
Solving word problems forces students to extract from given information (or data), the important elements
that can then be used to set up equations that allow them to solve the problem. When graphing polynomial
functions, students will need to identify and communicate important features of the function, e.g. maxima,
minima, regions where the function is increasing, where it is decreasing, and concavity changes.

IV. extract correct information from tables and common graphical displays, such as line graphs, scatter plots,
histograms, and frequency tables;
Graphing is very important component of algebra. In this courses students will be graphing linear equations;
solving linear inequalities graphically; graphing quadratics & higher order polynomials, radical functions,
rational functions, exponential, and logarithmic functions. Also students will be working with relationships
between two variables from a data table.

V. express the relationships illustrated in graphical displays and tables clearly and correctly in words; and/or
Identification of important features of graphs and where those features come from mathematically is
stressed. When these graphs represent real‐world phenomenon being to able express in words what they
show is stressed.

VI. use appropriate technology to describe and solve quantitative problems.
Use of appropriate technology such a graphing calculators and computer‐based learning resources will be
prevalent throughout the course.