Syllabus for Math 115
Textbook: Intermediate Algebra: Connecting Concepts Through Applications by Clark & Anfinson.
Students have the option of purchasing the loose-leaf format bundled with Enhanced WebAssign* Printed Card
Access, or purchasing Enhanced WebAssign Instant Access code with eBook. The electronic option is the cheaper
of the two.
 Instructors are encouraged to use WebAssign for homework. Students tend to complete the homework if it
is counted for part (more than 5%) of their final grade.

Although a graphing calculator is not mandated for this course, students own them. Wherever possible,
instructors may help students to become familiar with, and gain confidence from using, the graphing
calculator. The Department approves the use of a TI 83 or 84. The authors of the textbook offer suggestions
for the use of calculators in the course.

Three in-class exams, equally spaced, throughout the semester, are recommended. Time may be set aside
for review sessions. Instructors must pay keen attention to the pacing of the course.

The textbook has application problems. Instructors should not make these the focus any lesson; however, if
he/she assesses that students have mastered the skills necessary to grapple with these problems, then
application problems should be covered. Students who move on to Math 131 from Math 115 could benefit
from seeing some of the business applications.

Instructors should ensure that students understand the core concepts, before class time is spent covering too
many problems with high levels of difficulty. The idea is quality over quantity and difficulty. Time spent
understanding this example
2
 2 x  2 is worth a lot when students need to take a derivative in a calculus
x2
3
 18m 2 n  2 
 may cause students in the moment is not
course in the future. The trouble an example like 
4 5 
 9m n 
as meaningful as the previous example.

Each section of the textbook has a “Teaching Tip;” instructors should consider them.

Where appropriate, instructors should offer both algebraic and geometric meaning. For example, students
should view solving a 2 x 2 system of linear equations as finding the point where the two lines intersect.
* Enhanced WebAssign is an online learning program that includes problems from the text, tutorial videos, and
ebook. Students receive immediate feedback on their work and have the option to try different versions of the same
problem for additional practice. Tutorial resources such as Master It and Watch It provide step by step guidance to
help students solve problems. Chat About It gives students 300 minutes of 24/7 tutorial assistance with their
homework.
1
Updated 6/25/14
TOPIC
OBJECTIVES
Graphing & Slope
Section 1.3
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Graph equations by plotting points
Calculate the slope of a line given two points
Interpret meaning of slope as a rate of change
Find the midpoint between two points
Distance between two points
Intercepts &
Graphing
Section 1.4
Finding equations of
lines
Section 1.5

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Identify general form of a line
Find and interpret intercepts of a linear
equation
Graph lines using the intercepts
Identify and graph horizontal/vertical lines
Find the equation of a line using slopeintercept form
Find the equation of a line using point-slope
form
Identify (sketch, write equation) parallel and
perpendicular lines (know relationship
between slopes and write equations based on
the relationship).
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Functions & Function
Notation
Section 1.7
Solving Systems of
Equations &
Inequalities
Sections 2.1 – 2.4
Rules for Exponents
Section 3.1
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Identify a function
Apply the vertical line test
Use function notation
Identify domain and range of linear functions
Identify consistent and inconsistent systems
of equations
 Identify dependent lines
 Explain the meaning of a solution of a system
of equations in an application
 Solve a system of equations using the
substitution method
 Solve a system of equations using the
elimination method
 Solve applications using systems of equations
 Solve linear inequalities algebraically
 Meaning of exponent
 Use the rules for exponents to simplify
expressions
 Understand and use negative exponents
Defer discussion on fractional exponents and
radicals until study of radicals later in the
semester.
2
NOTES and
SUGGESTIONS
The textbook does not cover
finding midpoints or distance
between two points in this
section. Instructors may use
examples from a
supplemental source.
It is helpful for students to see
the derivation of the distance
formula, using Pythagorean
theorem.
When the point-slope formula
is introduced, help students to
make the connection with the
formula for slope
Students typically have a hard
time with lines that go
through the origin, for
example, 𝑦 = 2𝑥.
Include function evaluation
here. For example, given
𝑓(𝑥), find 𝑓(7).
Students should know the
geometric meaning of these
systems.
Before giving students rules
for exponents, show why, for
example,
xm
 xmn
xn
Discuss common errors such
as 𝑥 −1 = −𝑥
Avoid saying something like,
“to make the exponent
positive, move it to the
numerator or denominator.”
Show students why
Updated 6/25/14
1
 xn
n
x
Combining
Polynomials
Section 3.2

Factoring
Polynomials
Section 3.4-3.5
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Quadratic
Functions/Polynomial
functions
Sections 4.1, 4.4, 4.5,
4.6
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Rational Functions
Polynomial Division
Add/Subtract
Rational Exp.
Sections 7.1 – 7.4
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Solving Rational
Equations
Sections 7.5
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Perform arithmetic operations with
polynomials
Combine functions (+/-/x)
Combine functions within an application
Factor out GCF (include binomial GCF)
Factor by grouping
Factor quadratics using grouping
Factor perfect square trinomials
Factor difference of two squares
Factor difference and sum of cubes
Identify a quadratic function; determine
whether it has a maximum or minimum
point. Identify vertex and tell when graph is
increasing or decreasing by reading a
quadratic graph. Omit discussion about
vertex form of a quadratic.
Solve a quadratic equation using:
o Factoring
o Square root property
o Completing the square
Quadratic Formula
Sketch a quadratic function by finding the
roots and plotting other points
Rational Functions (omit discussion on
variation)
Identify a rational function
Find the domain of a rational function
Simplify rational expressions using factoring
x/÷ of Rational functions
Division by a monomial
Long division (Omit synthetic division)
Add rational expressions (with like/unlike
denominators)
Subtract rational expression (with like/unlike
denominators)
Simplify Complex Fractions
Solve rational equations
3
Discuss common errors such
as (𝑎 + 𝑏)2 = 𝑎2 + 𝑏 2
Students should be able to
write and simplify an
expression for one function
composed with another. For
example, 𝑓(𝑥 + 1). They
may even see 𝑓(𝑎 + ℎ) or
𝑓(𝑥 + ℎ) to prepare them for
the difference quotient and
further, the definition of the
derivative.
Students should work with
prime polynomials, and
understand that not all
polynomials are factorable
using real, rational numbers.
-Use completing the square to
derive the Quadratic formula.
-Because simplifying radicals
shows up later, students may
use the calculator to evaluate
radicals, and round answers.
-Students should also
understand that the solutions
(roots, zeroes) to these
equations are the x-intercepts.
Therefore no real solutions
imply no x-intercepts.
Discuss common errors such
𝑎+1
𝑎
𝑎−1
as
= , and
= −1
𝑏+1
𝑏
𝑎
Students should learn how to
simplify complex fractions—
the kind that resembles the
difference-quotient formula
that they will need for
calculus.
Students should know when a
“solution” is outside of the
domain of the expressions in
the equation. This is another
opportunity for students to
solve literal equations (i.e.,
Updated 6/25/14
Rational
Exponents/Radical
Notation
(Section 3.1)
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Radical Functions
Sections 8.1-8.2
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Multiply/Divide
radical expressions
8.3
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Solving Radical
Equations 8.4
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Parabolas and Circles
9.1
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Use the rules for exponents to simplify
expressions with rational/fractional
exponents
Understand the relationship between rational
exponents and radical expressions.
Write expressions with rational exponents in
radical notation/write expressions written in
radical notation with rational exponents
Find the domain of radical functions
Sketch the graph of basic radical functions
Simplify radical expressions (according to
the conditions for when a radical is
simplified)
Add and subtract radical expressions
(combine like terms)
Multiply and divide radical expressions
Rationalize denominators
Use conjugates to rational denominators
Simplify solutions that result from using the
quadratic formula
Solve radical equations involving one or
more square roots
Solve radical equations involving higher
roots
Circles and Parabolas
4
where one variable is solved
for in terms of other
variables). This is needed to
find inverse functions in precalc.
Examples should also include
negative exponents.
Omit discussion on higher
order radicals here.
Updated 6/25/14