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.
Math 107-FTF: University Mathematics II - A
SUMMER 2013◘ First Time Freshman
Number of Credits: 3
Course Description: Linear functions, equations, inequalities, systems of linear equations, quadratic equations, elementary functions, graphing functions. Effective From: Fall 2012
Prerequisites: None
Textbook: Precalculus - A Right Triangle Approach by Ratti and McWaters, 2nd Edition;bundeled with MyMathLab, ISBN-10: 0-321-64470-0.
Instructor: (for specific course-related information, follow the link below)
Math 107-FTF |
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.
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 deadline will be strictly enforced.
Homework Policy: Every class the professor will assign a few problems to be completed at home and handed in next class.
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.
Quizzes :
There will be several quizzes at least twice a week. There are no make-up quizzes. If a student misses a quiz and has a written excuse, the quiz will be excused, and will not count to the final grade.Midterm Exam: There are NO MAKE-UP EXAMS. The material on the exams will be similar to the problems assigned below. There is one midterm exam on Thursday Thursday, July 25 during the lecture hours. The midterm exam cannot be rescheduled.
Final exam: The final exam is on August 16 during lecture hours. The final exam is cumulative.
Midterm Exam: |
Thursday, July 25 , 2013 |
Final Exam: |
Friday, August 16, 2013 |
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.
Makeup Exam Policy:
There will be
No make-up EXAMS
or Quizzes during the semester. In the event the Final Exam is not taken, under rare circumstances where the student has a legitimate
reason for missing the final exam, a makeup exam will be administered by the math department.
In any case the student must notify the Math Department Office and the Instructor that the exam will
be missed and present written verifiable proof of the reason for missing the exam, e.g., a doctors note,
police report, court notice, etc., clearly stating the date AND time of the mitigating problem.
In the event the Final
Exam is not taken, under rare circumstances where the student has a
legitimate reason for missing the final exam, a makeup exam will be
administered by the math department.
Further Assistance: For further questions, students should contact their Instructor. All Instructors have regular office hours during the week. These office hours are listed at the link above by clicking on the Instructor’s name. Teaching Assistants are also available in the math learning center.
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.
Course Outline and Homework Assignments:
NOTE: The course outline below
specifies which section of the textbook contains the given ALEKS
topic.
Meetings |
ALEKS modules and topics |
Textbook (Ratti) section |
1 to 5 |
Module #1 (43 topics, due
on 07/15/13): |
|
Jul 8 - Jul 12 |
Exponents and integers:
Problem type 1 |
P2 |
|
Exponents and integers:
Problem type 2 |
P2 |
|
Exponents and order of
operations |
P1,P2 |
|
Evaluating a linear
expression in two variables |
P1 |
|
Evaluating a quadratic
expression in one variable |
P1, P2 |
|
Signed fraction addition:
Basic |
P1 |
|
Signed fraction
multiplication: Advanced |
P1 |
|
Complex fractions without
variables: Problem type 2 |
P1 |
|
Plotting a point in the
coordinate plane |
2.1 |
|
Solving a linear equation
with several occurrences of the variable: Variables
on both sides and fractional coefficients |
1.1 |
|
Solving a linear equation
with several occurrences of the variable: Variables
on both sides and distribution |
1.1 |
|
Solving a linear equation
with several occurrences of the variable: Variables
on both sides and two distributions |
1.1 |
|
Solving a linear equation
with several occurrences of the variable: Fractional
forms with binomial numerators |
1.1 |
|
Solving equations with
zero, one, or infinitely many solutions |
1.1 |
|
Simple absolute value
equation |
1.7 |
|
Algebraic symbol
manipulation: Problem type 1 |
1.1 |
|
Algebraic symbol
manipulation: Problem type 2 |
1.1 |
|
Solving a word problem
with two unknowns using a linear equation |
1.1 |
|
Solving a fraction word
problem using a linear equation with the variable on
both sides |
1.1 |
|
Finding the perimeter or
area of a rectangle given one of these values |
1.1,P7 |
|
Solving a linear
inequality: Problem type 2 |
1.6 |
|
Degree and leading
coefficient of a polynomial in one variable |
P3 |
|
Combining like terms:
Advanced |
P3 |
|
Simplifying a sum or
difference of three univariate polynomials |
P3 |
|
Multiplying a monomial
and a polynomial: Univariate with positive leading
coefficients |
P3 |
|
Multiplying binomials
with leading coefficients of 1 |
P3 |
|
Squaring a binomial:
Univariate |
P3 |
|
Multiplying conjugate
binomials: Univariate |
P3 |
|
Multiplying binomials in
two variables |
P3 |
|
Greatest common factor of
two monomials |
P4 |
|
Factoring a quadratic
with leading coefficient 1 |
P4 |
|
Factoring a quadratic
with leading coefficient greater than 1 |
P4 |
|
Factoring a quadratic
polynomial in two variables |
P4 |
|
Factoring a difference of
squares |
P4 |
|
Factoring with repeated
use of the difference of squares formula |
P4 |
|
Factoring out a monomial
from a polynomial: Univariate |
P4 |
|
Factoring a product of a
quadratic trinomial and a monomial |
P4 |
|
Factoring a polynomial by
grouping: Problem type 2 |
P4 |
|
Adding rational
expressions with common denominators |
P5 |
|
Adding rational
expressions with different denominators:
Multivariate |
P5 |
|
Adding rational
expressions with different denominators: ax, bx |
P5 |
|
Adding rational
expressions with different denominators: x+a, x+b |
P5 |
|
Adding rational
expressions with different denominators: Quadratic |
P5 |
6 to 9 |
Module #2 (42 topics, due
on 07/19/13): |
|
Jul 15 - Jul 18 |
Simplifying a ratio of
polynomials: Problem type 1 |
P5 |
|
Simplifying a ratio of
polynomials: Problem type 2 |
P5 |
|
Multiplying rational
expressions: Problem type 1 |
P5 |
|
Multiplying rational
expressions: Problem type 2 |
P5 |
|
Dividing rational
expressions: Problem type 1 |
P5 |
|
Dividing rational
expressions: Problem type 2 |
P5 |
|
Complex fraction: Problem
type 1 |
P5 |
|
Complex fraction: Problem
type 3 |
P5 |
|
Complex fraction: Problem
type 4 |
P5 |
|
Solving a rational
equation that simplifies to a linear equation:
Problem type 1 |
1.1 |
|
Solving a rational
equation that simplifies to a linear equation:
Problem type 2 |
1.1 |
|
Solving a rational
equation that simplifies to a linear equation:
Problem type 3 |
1.1 |
|
Solving a rational
equation that simplifies to a linear equation:
Problem type 4 |
1.1 |
|
Evaluating expressions
with exponents of zero |
P2 |
|
Evaluating numbers with
negative exponents |
P2 |
|
Product rule with
positive exponents |
P2 |
|
Product rule with
negative exponents |
P2 |
|
Quotients of expressions
involving exponents |
P2 |
|
Quotient rule with
negative exponents: Problem type 1 |
P2 |
|
Power rule with positive
exponents |
P2 |
|
Power rule with negative
exponents: Problem type 1 |
P2 |
|
Power rule with negative
exponents: Problem type 2 |
P2 |
|
Using the power and
product rules to simplify expressions with positive
exponents |
P2 |
|
Using the power, product,
and quotient rules to simplify expressions with
negative exponents |
P2 |
|
Square root of a perfect
square monomial |
P6 |
|
Simplifying a radical
expression: Problem type 1 |
P6 |
|
Simplifying a radical
expression: Problem type 2 |
P6 |
|
Square root addition |
P6 |
|
Simplifying a sum of
radical expressions |
P6 |
|
Square root
multiplication |
P6 |
|
Simplifying a product of
radical expressions |
P6 |
|
Simplifying a product of
radical expressions using the distributive property |
P6 |
|
Special products with
square roots: Conjugates and squaring |
P6 |
|
Rationalizing the
denominator of a radical expression |
P6 |
|
Rationalizing the
denominator of a radical expression using conjugates |
P6 |
|
Simplifying a higher
radical: Problem type 1 |
P6 |
|
Simplifying a higher
radical: Problem type 2 |
P6 |
|
Rational exponents: Basic |
P6 |
|
Rational exponents:
Negative exponents and fractional bases |
P6 |
|
Rational exponents:
Products and quotients |
P6 |
|
Rational exponents:
Powers of powers |
P6 |
|
Converting between
radical form and exponent form |
P6 |
10 to 13 |
Module #3 (27 topics, due
on 07/26/13): |
|
Jul 19 - Jul 24 |
Plotting a point in the
coordinate plane |
2.1 |
|
Pythagorean Theorem |
P7 |
|
Area of a triangle |
P7 |
|
Circumference and area of
a circle |
P7 |
|
Area between two
rectangles |
P7 |
|
Area between two
concentric circles |
P7 |
|
Area involving rectangles
and circles |
P7 |
|
Area involving inscribed
figures |
P7 |
|
Volume of a rectangular
prism |
P7 |
|
Volume of a cylinder |
P7 |
|
Volume of a sphere |
P7 |
|
Surface area of a cube or
a rectangular prism |
P7 |
|
Surface area of a
cylinder |
P7 |
|
Surface area of a sphere |
P7 |
|
Set builder and interval
notation |
P1 |
|
Union and intersection of
finite sets |
P1 |
|
Union and intersection of
intervals |
P1 |
|
Identifying functions
from relations |
2.4 |
|
Determining whether an
equation defines a function |
2.4 |
|
Vertical line test |
2.4 |
|
Evaluating functions:
Problem type 1 |
2.4 |
|
Evaluating functions:
Problem type 2 |
2.4 |
|
Variable expressions as
inputs of functions |
2.4 |
|
Domain and range from
ordered pairs |
2.4 |
|
Domain of a square root
function |
2.4, 2.6 |
|
Domain of a rational
function |
2.4, 3.6 |
|
Finding the domain of a
fractional function involving radicals |
2.4 |
14 |
Midterm Exam –
Thursday, July 25 |
|
|
July 29 – withdrawal
deadline |
|
15 to 18 |
Module #4 (26 topics, due
on 08/01/13): |
|
Jul 26 - Jul 31 |
Graphing a line given its
equation in slope-intercept form |
2.3 |
|
Graphing a line given its
equation in standard form |
2.3 |
|
Graphing a line through a
given point with a given slope |
2.3 |
|
Graphing a vertical or
horizontal line |
2.3 |
|
Finding x- and
y-intercepts of a line given the equation: Advanced |
2.3 |
|
Finding slope given the
graph of a line on a grid |
2.3 |
|
Finding slope given two
points on the line |
2.3 |
|
Finding the slope of a
line given its equation |
2.3 |
|
Writing an equation of a
line given the y-intercept and another point |
2.3 |
|
Writing the equation of a
line given the slope and a point on the line |
2.3 |
|
Writing the equation of
the line through two given points |
2.3 |
|
Writing the equations of
vertical and horizontal lines through a given point |
2.3 |
|
Slopes of parallel and
perpendicular lines: Problem type 1 |
2.3 |
|
Slopes of parallel and
perpendicular lines: Problem type 2 |
2.3 |
|
Finding intercepts and
zeros of a function given the graph |
2.4 |
|
Finding x- and
y-intercepts of the graph of a nonlinear equation |
2.2 |
|
Domain and range from the
graph of a continuous function |
2.4,2.5 |
|
Testing an equation for
symmetry about the axes and origin |
2.2 |
|
Even and odd functions |
2.5 |
|
Writing an equation for a
function after a vertical translation |
2.7 |
|
Writing an equation for a
function after a vertical and horizontal translation |
2.7 |
|
Translating the graph of
a function: One step |
2.7 |
|
Translating the graph of
a function: Two steps |
2.7 |
|
Transforming the graph of
a function by reflecting over an axis |
2.7 |
|
Transforming the graph of
a function by shrinking or stretching |
2.7 |
|
Transforming the graph of
a function using more than one transformation |
2.7 |
19 to 22 |
Module #5 (29 topics, due
on 08/07/13): |
|
Aug 1 - Aug 6 |
Graphing a parabola of
the form y = ax^2 |
2.7, 3.1 |
|
Graphing a simple cubic
function |
2.6,2.7 |
|
Graphing a function
involving a square root |
2.6,2.7 |
|
Graphing an equation
involving absolute value in the plane: Advanced |
2.6,2.7 |
|
Choosing a graph to fit a
narrative |
2.7 |
|
Finding the roots of a
quadratic equation with leading coefficient 1 |
1.4 |
|
Finding the roots of a
quadratic equation with leading coefficient greater
than 1 |
1.4 |
|
Solving a quadratic
equation needing simplification |
1.4 |
|
Solving a rational
equation that simplifies to a quadratic equation:
Problem type 1 |
1.5 |
|
Solving a rational
equation that simplifies to a quadratic equation:
Problem type 2 |
1.5 |
|
Solving a rational
equation that simplifies to a quadratic equation:
Problem type 3 |
1.5 |
|
Completing the square |
1.4 |
|
Solving a quadratic
equation by completing the square |
1.4 |
|
Solving a word problem
using a quadratic equation with rational roots |
1.4 |
|
Solving a word problem
using a quadratic equation with irrational roots |
1.4 |
|
Midpoint of a line
segment in the plane |
2.1 |
|
Distance between two
points in the plane |
2.1 |
|
Graphing a circle given
its equation in standard form |
2.2 |
|
Writing an equation of a
circle given its center and a point on the circle |
2.2 |
|
Writing an equation of a
circle given the endpoints of a diameter |
2.2 |
|
Range of a quadratic
function |
3.1 |
|
Finding the maximum or
minimum of a quadratic function |
3.1 |
|
Word problem using the
maximum or minimum of a quadratic function |
3.1 |
|
Finding the
x-intercept(s) and the vertex of a parabola |
3.1 |
|
Rewriting a quadratic
function to find the vertex of its graph |
3.1 |
|
Graphing a parabola of
the form y = (x-a)^2 + c |
3.1 |
|
Graphing a parabola of
the form y = ax^2 + bx + c: Integer coefficients |
3.1 |
|
How the leading
coefficient affects the shape of a parabola |
3.1 |
|
Writing the equation of a
quadratic function given its graph |
3.1 |
23 to 25 |
Module #6 (26 topics, due
on 08/12/13): |
|
Aug 7 - Aug 9 |
Solving equations written
in factored form |
3.2 |
|
Finding zeros of a
polynomial function written in factored form |
3.2 |
|
Finding a polynomial of a
given degree with given zeros: Real zeros |
3.2 |
|
Finding x- and
y-intercepts given a polynomial function |
3.2 |
|
Determining the end
behavior of the graph of a polynomial function |
3.2 |
|
Inferring properties of a
polynomial function from its graph |
3.2 |
|
Matching graphs with
polynomial functions |
3.2 |
|
Finding the asymptotes of
a rational function: Problem type 1 |
3.6 |
|
Finding the asymptotes of
a rational function: Problem type 2 |
3.6 |
|
Sketching the graph of a
rational function: Problem type 1 |
3.6 |
|
Sketching the graph of a
rational function: Problem type 2 |
3.6 |
|
Graphing rational
functions with holes |
3.6 |
|
Evaluating an exponential
function that models a real-world situation |
4.1,4.2 |
|
Converting between
logarithmic and exponential equations |
4.3 |
|
Converting between
natural logarithmic and exponential equations |
4.3 |
|
Evaluating a logarithmic
expression |
4.3 |
|
Solving a logarithmic
equation: Problem type 1 |
4.3 |
|
Solving an exponential
equation: Problem type 1 |
4.1,4.2 |
|
Solving an exponential
equation: Problem type 2 |
4.1,4.2 |
|
Solving a word problem
using an exponential equation: Problem type 1 |
4.1,4.2 |
|
Solving a word problem
using an exponential equation: Problem type 2 |
4.1,4.2 |
|
Sketching the graph of an
exponential function: Basic |
4.1,4.2 |
|
The graph, domain, and
range of an exponential function |
4.1,4.2 |
|
Sketching the graph of a
logarithmic function: Basic |
4.3 |
|
The graph, domain, and
range of a logarithmic function |
4.3 |
|
Sketching the graph of a
logarithmic function |
4.3 |
|
Translating the graph of
a logarithmic or exponential function |
4.1,4.2,4.3 |
26 to 29 |
Module #7 (29 topics, due
on 08/16/13): |
|
Aug 12 - Aug15 |
Converting between degree
and radian measure: Problem type 1 |
5.1 |
|
Converting between degree
and radian measure: Problem type 2 |
5.1 |
|
Sketching an angle in
standard position |
5.3 |
|
Reference angles: Problem
type 1 |
5.3 |
|
Reference angles: Problem
type 2 |
5.3 |
|
Special right triangles |
5.2 |
|
Sine, cosine, and tangent
ratios |
5.2 |
|
Finding trigonometric
ratios given a right triangle |
5.2 |
|
Using a trigonometric
ratio to find a side length in a right triangle |
5.2 |
|
Using trigonometry to
find distances |
5.2 |
|
Using a trigonometric
ratio to find an angle measure in a right triangle |
5.2 |
|
Using trigonometry to
find angles of elevation or depression |
5.2 |
|
Solving a right triangle |
5.2 |
|
Trigonometric functions
and special angles: Problem type 1 |
5.3 |
|
Trigonometric functions
and special angles: Problem type 2 |
5.3 |
|
Trigonometric functions
and special angles: Problem type 3 |
5.3 |
|
Finding values of
trigonometric functions given information about an
angle: Problem type 1 |
5.3 |
|
Finding values of
trigonometric functions given information about an
angle: Problem type 2 |
5.3 |
|
Finding values of
trigonometric functions given information about an
angle: Problem type 3 |
5.3 |
|
Amplitude and period of
sine and cosine functions |
5.4 |
|
Amplitude, period, and
phase shift of sine and cosine functions |
5.4 |
|
Sketching the graph of a
sine or cosine function: Problem type 1 |
5.4 |
|
Sketching the graph of a
sine or cosine function: Problem type 2 |
5.4 |
|
Sketching the graph of a
sine or cosine function: Problem type 3 |
5.4 |
|
Classifying systems of
linear equations from graphs |
8.1 |
|
Solving a simple system
using substitution |
8.1 |
|
Solving a system of
linear equations using elimination with
multiplication and addition |
8.1 |
|
Solving a system that is
inconsistent or consistent dependent |
8.1 |
|
Solving a word problem
involving a sum and another simple relationship
using a system of linear equations |
8.1 |
30 |
Final Exam –
August 16 |
|
Prepared By: Prof. Victor Aranda Barreto
Last revised: July 1, 2013