MATH 108 Course Syllabus - SUMMER 2013

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

Prof. Castillo

 

 

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.

May 28, 2013

T

Full Summer Session Begins

May 30, 2013

R

Last Day To Register For Full Semester Course

May 27, 2013

M

Memorial Day ~ University Closed

June 20, 2013

R

Last Day To Withdraw  from  this Course

July 4, 2013

R

July 4th Holiday ~ University Closed

August 8, 2013

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

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