NJIT Academic Integrity CODE: All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams. Under the University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.
Number of Credits: 4
Course Description: Linear functions, equations, inequalities, systems of linear equations, quadratic equations, polynomials, rational expressions, expressions involving radicals, partial fraction decomposition, conic sections. Effective From: Summer 2013
Prerequisites: None
Textbook: Precalculus - A Right Triangle Approach by Ratti and McWaters, 2nd Edition, ISBN-10: 0-321-64470-0
Software:
ALEKS www.aleks.com
For ALEKS Help (click here)
Instructor: (for specific course-related information, follow the link below)
Math 108-031 |
Grading Policy: The final grade in this course will be determined as follows:
▪ Quizzes (work at home): |
10% |
▪ ALEKS: |
20% |
▪ Exam: |
70% |
Your final letter grade will be
based on the following tentative scale. To pass this class with a
C or better your overall average must be at least 65% AND you need
to earn at least 60% on
one of the exams.
NOTE: You need to earn a grade of A
in this course to proceed to Math 139
A |
90-100 |
C |
65-74 |
B+ |
85-89 |
D |
55-64 |
B |
80-84 |
F |
0-54 |
C+ |
75-79 |
|
|
Drop Date: Please note that the University Drop Date July 10, 2013 deadline will be strictly enforced.
Format of class: This course meets three times a week namely on Mondays and Thursdays from 9:00 am to 11:00 am and on Wednesday from 9:00 am to 12:00 pm.
ALEKS:
ALEKS
is an online system where students can practice and master
mathematics at www.aleks.com.
There are ten assigned modules where each module contains
problems related to topics of this course. A student must master
the first module to proceed to the second module. A student must
master the second module to move on to the third module and so
on. After completing each module, a student will be given an
ALEKS assessment which will confirm mastery of topics in the
module just taken. Each student has until the end of the
semester to complete all of the modules.
Exams: There are three exams
namely exam 1, exam 2, and the final exam.
Exam 1: |
June 19, 2013 4:15-5:45 pm |
Exam 2: |
July 10, 2013 4:15-5:45 pm |
Final Exam: |
August 8, 2013 3:15-5:45 pm |
The final exam will test your knowledge of all the course
material taught in the entire course. Make sure you read and
fully understand the department's Examination
Policy. This policy
will be strictly enforced. Please note that electronic
devices (such as calculators, cell phones, CD players, etc.)
are not allowed during any exam. Please refer to the
registrar's website for the official date and time of each exam
at http://www.njit.edu/registrar/exams/index.php.
Makeup Exam Policy: There will be NO MAKE-UP EXAMS during the semester. In case because of special circumstances a student cannot take an exam, the student must notify the Math Department Office and the instructor that he/she will miss the exam and present written verifiable proof of the reason for missing the exam, e.g., a doctor’s note, police report, court notice, etc., clearly stating the date AND time of the conflicting circumstances.. In the event the final exam is not taken, under rare circumstances where the student has a legitimate reason for missing the exam, a makeup exam will be administered by the math department.
Attendance: Attendance at all classes (both lecture and recitation) will be recorded and is mandatory. Please make sure you read and fully understand the Department’s Attendance Policy. This policy will be strictly enforced.
Further Assistance: For further questions, students should contact the instructor.
Cellular Phones: All cellular phones and beepers must be switched off during all class times.
MATH DEPARTMENT CLASS POLICIES LINK
All DMS students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly. For DMS Course Policies, please click here.
T |
Full Summer Session Begins |
|
R |
Last Day To Register For Full Semester Course |
|
M |
Memorial Day ~ University Closed |
|
R |
Last Day To Withdraw from this Course |
|
R |
July 4th Holiday ~ University Closed |
|
R |
Final Exam |
ALEKS Course Outline:
Objectives Covered |
Mastery Level |
2. Module #1 |
85% |
3. Module #2 |
85% |
4. Module #3 |
85% |
5. Module #4 |
85% |
6. Module #5 |
85% |
7. Module #6 |
85% |
8. Module #7 |
85% |
9. Module #8 |
85% |
10. Module #9 |
85% |
11. Module #10 |
85% |
A student must meet the
Mastery Level percent for each Objective in order to move on to
the next Objective. For example, if a Mastery Level is set at
90% for the first Objective, students must score 90% or higher
in order to move on to the second Objective. The final day that
Objectives can be completed is 08/08/13.
Readiness Topics (11
topics)
·
Solving a decimal word
problem using a linear equation of the form Ax + B = C
·
Solving a linear
inequality: Problem type 3
·
Solving a linear
inequality: Problem type 4
·
Solving a compound linear
inequality: Problem type 1
·
Simplifying a sum or
difference of two univariate polynomials
·
Factoring a polynomial by
grouping: Problem type 1
·
Introduction to the product
rule of exponents
·
Introduction to the power
rule of exponents
·
Cube root of an integer
·
Square root simplification
·
Solving a radical equation
that simplifies to a linear equation: One radical
Module #1 (39 topics)
·
Exponents and integers:
Problem type 1
·
Exponents and integers:
Problem type 2
·
Exponents and order of
operations
·
Evaluating a linear
expression in two variables
·
Evaluating a quadratic
expression in one variable
·
Signed fraction addition:
Basic
·
Signed fraction
multiplication: Advanced
·
Complex fractions without
variables: Problem type 2
·
Degree and leading
coefficient of a polynomial in one variable
·
Combining like terms:
Advanced
·
Simplifying a sum or
difference of three univariate polynomials
·
Multiplying a monomial and
a polynomial: Univariate with positive leading coefficients
·
Multiplying binomials with
leading coefficients of 1
·
Squaring a binomial:
Univariate
·
Multiplying conjugate
binomials: Univariate
·
Multiplying binomials in
two variables
·
Greatest common factor of
two multivariate monomials
·
Factoring a quadratic with
leading coefficient 1
·
Factoring a quadratic with
leading coefficient greater than 1
·
Factoring a quadratic
polynomial in two variables with leading coefficient greater
than 1
·
Factoring a difference of
squares
·
Factoring with repeated use
of the difference of squares formula
·
Factoring out a monomial
from a polynomial: Univariate
·
Factoring a product of a
quadratic trinomial and a monomial
·
Factoring a polynomial by
grouping: Problem type 2
·
Evaluating expressions with
exponents of zero
·
Evaluating numbers with
negative exponents
·
Product rule with positive
exponents
·
Product rule with negative
exponents
·
Quotients of expressions
involving exponents
·
Quotient rule with negative
exponents: Problem type 1
·
Power rule with positive
exponents
·
Power rule with negative
exponents: Problem type 1
·
Power rule with negative
exponents: Problem type 2
·
Using the power and product
rules to simplify expressions with positive exponents
·
Using the power, product,
and quotient rules to simplify expressions with negative
exponents
·
Set builder and interval
notation
·
Union and intersection of
finite sets
·
Union and intersection of
intervals
Module #2 (45 topics)
·
Adding rational expressions
with common denominators
·
Adding rational expressions
with different denominators: Multivariate
·
Adding rational expressions
with different denominators: ax, bx
·
Adding rational expressions
with different denominators: x+a, x+b
·
Adding rational expressions
with different denominators: Quadratic
·
Simplifying a ratio of
polynomials: Problem type 1
·
Simplifying a ratio of
polynomials: Problem type 2
·
Multiplying rational
expressions: Problem type 1
·
Multiplying rational
expressions: Problem type 2
·
Dividing rational
expressions: Problem type 1
·
Dividing rational
expressions: Problem type 2
·
Complex fraction: Problem
type 1
·
Complex fraction: Problem
type 3
·
Complex fraction: Problem
type 4
·
Square root of a perfect
square monomial
·
Simplifying a radical
expression: Problem type 1
·
Simplifying a radical
expression: Problem type 2
·
Square root addition
·
Simplifying a sum of
radical expressions
·
Square root multiplication
·
Simplifying a product of
radical expressions
·
Simplifying a product of
radical expressions using the distributive property
·
Special products with
square roots: Conjugates and squaring
·
Rationalizing the
denominator of a radical expression
·
Rationalizing the
denominator of a radical expression using conjugates
·
Simplifying a higher
radical: Problem type 1
·
Simplifying a higher
radical: Problem type 2
·
Rational exponents: Basic
·
Rational exponents:
Negative exponents and fractional bases
·
Rational exponents:
Products and quotients
·
Rational exponents: Powers
of powers
·
Converting between radical
form and exponent form
·
Pythagorean Theorem
·
Area of a triangle
·
Circumference and area of a
circle
·
Area between two rectangles
·
Area between two concentric
circles
·
Area involving rectangles
and circles
·
Area involving inscribed
figures
·
Volume of a rectangular
prism
·
Volume of a cylinder
·
Volume of a sphere
·
Surface area of a cube or a
rectangular prism
·
Surface area of a cylinder
·
Surface area of a sphere
Module #3 (26 topics)
·
Solving a linear equation
with several occurrences of the variable: Variables on both
sides and fractional coefficients
·
Solving a linear equation
with several occurrences of the variable: Variables on both
sides and distribution
·
Solving a linear equation
with several occurrences of the variable: Variables on both
sides and two distributions
·
Solving a linear equation
with several occurrences of the variable: Fractional forms with
binomial numerators
·
Solving equations with
zero, one, or infinitely many solutions
·
Simple absolute value
equation
·
Algebraic symbol
manipulation: Problem type 1
·
Algebraic symbol
manipulation: Problem type 2
·
Solving a word problem with
two unknowns using a linear equation
·
Solving a fraction word
problem using a linear equation with the variable on both sides
·
Finding the perimeter or
area of a rectangle given one of these values
·
Solving a linear
inequality: Problem type 2
·
Solving a rational equation
that simplifies to a linear equation: Problem type 1
·
Solving a rational equation
that simplifies to a linear equation: Problem type 2
·
Solving a rational equation
that simplifies to a linear equation: Problem type 3
·
Solving a rational equation
that simplifies to a linear equation: Problem type 4
·
Finding the roots of a
quadratic equation with leading coefficient 1
·
Finding the roots of a
quadratic equation with leading coefficient greater than 1
·
Solving a quadratic
equation needing simplification
·
Solving a rational equation
that simplifies to a quadratic equation: Problem type 1
·
Solving a rational equation
that simplifies to a quadratic equation: Problem type 2
·
Solving a rational equation
that simplifies to a quadratic equation: Problem type 3
·
Completing the square
·
Solving a quadratic
equation by completing the square
·
Solving a word problem
using a quadratic equation with rational roots
·
Solving a word problem
using a quadratic equation with irrational roots
Module #4 (34 topics)
·
Plotting a point in the
coordinate plane
·
Identifying functions from
relations
·
Determining whether an
equation defines a function
·
Vertical line test
·
Evaluating functions:
Problem type 1
·
Evaluating functions:
Problem type 2
·
Variable expressions as
inputs of functions
·
Domain and range from
ordered pairs
·
Domain of a square root
function
·
Domain of a rational
function
·
Finding the domain of a
fractional function involving radicals
·
Graphing a line given its
equation in slope-intercept form
·
Graphing a line given its
equation in standard form
·
Graphing a line through a
given point with a given slope
·
Graphing a vertical or
horizontal line
·
Finding x- and y-intercepts
of a line given the equation: Advanced
·
Finding slope given the
graph of a line on a grid
·
Finding slope given two
points on the line
·
Finding the slope of a line
given its equation
·
Writing an equation of a
line given the y-intercept and another point
·
Writing the equation of a
line given the slope and a point on the line
·
Writing the equation of the
line through two given points
·
Writing the equations of
vertical and horizontal lines through a given point
·
Slopes of parallel and
perpendicular lines: Problem type 1
·
Slopes of parallel and
perpendicular lines: Problem type 2
·
Finding intercepts and
zeros of a function given the graph
·
Finding x- and y-intercepts
of the graph of a nonlinear equation
·
Domain and range from the
graph of a continuous function
·
Testing an equation for
symmetry about the axes and origin
·
Midpoint of a line segment
in the plane
·
Distance between two points
in the plane
·
Graphing a circle given its
equation in standard form
·
Writing an equation of a
circle given its center and a point on the circle
·
Writing an equation of a
circle given the endpoints of a diameter
Module #5 (13 topics)
·
Even and odd functions
·
Writing an equation for a
function after a vertical translation
·
Writing an equation for a
function after a vertical and horizontal translation
·
Translating the graph of a
function: One step
·
Translating the graph of a
function: Two steps
·
Transforming the graph of a
function by reflecting over an axis
·
Transforming the graph of a
function by shrinking or stretching
·
Transforming the graph of a
function using more than one transformation
·
Graphing a parabola of the
form y = ax2
·
Graphing a simple cubic
function
·
Graphing a function
involving a square root
·
Graphing an equation
involving absolute value in the plane: Advanced
·
Choosing a graph to fit a
narrative
Module #6 (21 topics)
·
Range of a quadratic
function
·
Finding the maximum or
minimum of a quadratic function
·
Word problem using the
maximum or minimum of a quadratic function
·
Finding the x-intercept(s)
and the vertex of a parabola
·
Rewriting a quadratic
function to find the vertex of its graph
·
Graphing a parabola of the
form y = (x-a)2 + c
·
Graphing a parabola of the
form y = ax2 + bx + c: Integer coefficients
·
How the leading coefficient
affects the shape of a parabola
·
Writing the equation of a
quadratic function given its graph
·
Solving equations written
in factored form
·
Finding zeros of a
polynomial function written in factored form
·
Finding a polynomial of a
given degree with given zeros: Real zeros
·
Finding x- and y-intercepts
given a polynomial function
·
Determining the end
behavior of the graph of a polynomial function
·
Inferring properties of a
polynomial function from its graph
·
Matching graphs with
polynomial functions
·
Finding the asymptotes of a
rational function: Problem type 1
·
Finding the asymptotes of a
rational function: Problem type 2
·
Sketching the graph of a
rational function: Problem type 1
·
Sketching the graph of a
rational function: Problem type 2
·
Graphing rational functions
with holes
Module #7 (15 topics)
·
Evaluating an exponential
function that models a real-world situation
·
Converting between
logarithmic and exponential equations
·
Converting between natural
logarithmic and exponential equations
·
Evaluating a logarithmic
expression
·
Solving a logarithmic
equation: Problem type 1
·
Solving an exponential
equation: Problem type 1
·
Solving an exponential
equation: Problem type 2
·
Solving a word problem
using an exponential equation: Problem type 1
·
Solving a word problem
using an exponential equation: Problem type 2
·
Sketching the graph of an
exponential function: Basic
·
The graph, domain, and
range of an exponential function
·
Sketching the graph of a
logarithmic function: Basic
·
The graph, domain, and
range of a logarithmic function
·
Sketching the graph of a
logarithmic function
·
Translating the graph of a
logarithmic or exponential function
Module #8 (19 topics)
·
Converting between degree
and radian measure: Problem type 1
·
Converting between degree
and radian measure: Problem type 2
·
Sketching an angle in
standard position
·
Reference angles: Problem
type 1
·
Reference angles: Problem
type 2
·
Special right triangles
·
Sine, cosine, and tangent
ratios
·
Finding trigonometric
ratios given a right triangle
·
Using a trigonometric ratio
to find a side length in a right triangle
·
Using trigonometry to find
distances
·
Using a trigonometric ratio
to find an angle measure in a right triangle
·
Using trigonometry to find
angles of elevation or depression
·
Solving a right triangle
·
Trigonometric functions and
special angles: Problem type 1
·
Trigonometric functions and
special angles: Problem type 2
·
Trigonometric functions and
special angles: Problem type 3
·
Finding values of
trigonometric functions given information about an angle:
Problem type 1
·
Finding values of
trigonometric functions given information about an angle:
Problem type 2
·
Finding values of
trigonometric functions given information about an angle:
Problem type 3
Module #9 (5 topics)
·
Amplitude and period of
sine and cosine functions
·
Amplitude, period, and
phase shift of sine and cosine functions
·
Sketching the graph of a
sine or cosine function: Problem type 1
·
Sketching the graph of a
sine or cosine function: Problem type 2
·
Sketching the graph of a
sine or cosine function: Problem type 3
Module #10 (5 topics)
·
Classifying systems of
linear equations from graphs
·
Solving a simple system
using substitution
·
Solving a system of linear
equations using elimination with multiplication and addition
·
Solving a system that is
inconsistent or consistent dependent
·
Solving a word problem
involving a sum and another simple relationship using a system
of linear equations
Prepared By: Prof. Carlos Castillo
Last revised: June 11, 2013