# Math 0995 Syllabus - USU Canvas

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Math 0995 Syllabus COURSE GOAL: Math 0995 is designed to give students the algebra skills and understanding necessary to fulfill their university QL requirement. TOPICS COVERED: This course is an intermediate course in algebra that begins with a review of introductory algebra concepts. The course is comprised of three units: Manipulating and Simplifying Expressions, Solving Equations and Inequalities, and Graphing Equations and Inequalities. Each unit will consider real-world applications of the associated concepts and procedures and will incorporate the following expression types: linear, quadratic, general polynomial, rational, roots and radicals, exponential, and logarithmic. Specific content objectives are listed at the end of this syllabus. IDEA COURSE OBJECTIVES: This course will involve the following objectives as outlined by USU’s IDEA Center (in decreasing order of emphasis): (Objective 1) Gaining factual knowledge (terminology, classifications, methods, trends). (Objective 2) Learning fundamental principles, generalizations, or theories ASSIGNMENTS AND LESSONS: All lessons are accessed by clicking the Unit tabs on the course homepage in Canvas. There are three units that must be completed for the course. Each unit is made up of lessons that contain a set of notes that can be downloaded and printed and one or more video presentations that have been created and produced by the course instructor. Each lesson will also announce a set of problems that should be completed by accessing MyMathLab, an online platform that will allow you to practice problems and receive feedback. CALCULATORS: Students are encouraged to purchase a graphing calculator. The lessons will be presented using a TI 84+ calculator, but any non-CAS calculator with graphing capabilities will be acceptable for use in the class. You will not need to use a graphing calculator until the last unit so you do not need one right away. CAS calculators such as TI-Nspire CAS, TI-89, Casio FX 2.0, and Casio fx-CP400 are not permitted when taking an exam.

ASSIGNMENTS (HOMEWORK): (50 pts) All assignments (homework) will be done using MyMathLab. You need to follow the lessons that are given on the modules page in Canvas. There are 38 lessons and each lesson tells you which sections you should work on using MyMathLab. If you get stuck on certain problems when you are doing assignments, you can have the software show you examples from the online text that can help you better understand the problem you are working on. It can also show you how to work the problem if you have missed it a couple of times. You will be given four chances to correctly answer any given problem from the homework so if you are careful you should be able to obtain full credit on every assignment. Your score for each assignment will not be recorded in Canvas, but I will enter your total assignment score in Canvas at the end of the semester. Your score will be out of a possible 50 points and will be calculated as followed: Total Points for Quizzes = (Total Percentage of Homework Scores From MyMathLab) × (0.5) For example, if you were to successfully answer 93% of all of the problems on the homework assignments then your total homework score would be (93) ×(0.5) = 46.5 out of 50. There is a gradebook in MyMathLab that will show your progress for the homework assignments. QUIZZES: (100 points) All quizzes will be done using MyMathLab. You need to follow the lessons that are given for each unit in Canvas. After approximately every fourth lesson there will be a quiz that you will take. The quizzes are not proctored and you will work on them similar to how you do assignments in MyMathLab. The main difference is that you will only have one chance to correctly answer each quiz problem. You can, however, retake any quiz as many times as you like (up until the due date) to get a score you are happy with, and only your highest score for each quiz will count. There are 10 quizzes required for the course. Your score for each quiz will not be recorded in Canvas, but I will enter your total quiz score in Canvas at the end of the semester. Your score will be out of a possible 100 points and will be calculated as followed: Total Points for Quizzes = Total Percentage of Quiz Scores From MyMathLab For example, if you were to successfully answer 88% of all of the problems on the 10 quizzes then your total score for quizzes would be 88 out of 100. There is no time limit for quizzes. There is a gradebook in MyMathLab that will show your progress for the quizzes. MIDTERM EXAMS: (100 pts each) Two midterm exams will be given. Exams will be taken online using MyMathLab. Even though the exam is online, you will be required to schedule an appointment to take the exam at a USU distance education center. If you do not live close to a USU distance education center then you need to arrange to take exams with a proctor or use the online proctoring option of Proctorio. There is a link to a page of information on using Proctorio on the homepage of the course in Canvas. The exams will consist of 20 problems that are generated from the same question bank used to create your homework assignments. You will have 90 minutes to complete each midterm exam. No notes are allowed during the exams. The midterm exams are not comprehensive. The material covered on each exam is stated on the course schedule provided later in the syllabus.

FINAL EXAM: (200 pts) The final exam is a comprehensive review of major topics covered during the semester. There are 40 problems on the final exam. You will be required to schedule an appointment to take the final exam at a USU distance education center or at home using Proctorio. If you do not live close to a USU distance education center then you need to arrange to take exams with a USU approved proctor or at home using Proctorio. The final exam will consist of problems that are generated from the same question bank used to create your homework assignments, quizzes, and your midterm exams. You will have 2.5 hours to complete the final exam. No notes are allowed during the final exam. GRADING: Each midterm exam will be worth 100 points, homework is worth 50 points, Quizzes are worth 100 points, and the final exam is worth 200 points for a total of 550 points. Grades will be assigned according to the following ranges (600 pts maximum): A: 550 – 506 B+: 494 – 484 C+: 439 – 429 D+: 384 – 358 A-: 505 – 495 B: 483 – 451 C: 428 – 396 D: 357 – 300 B-: 450 – 440 C-: 395 – 385 F: 299 and Below COURSE SCHEDULE AND DUE DATES: You are permitted to complete any exam and any assignment as soon as you are ready. You are encouraged to work ahead of schedule. The due dates are the absolute last day that an assignment, quiz, or exam can be completed. If you stay ahead of schedule then you will have some leeway if something unexpected happens where you are not able to complete an assignment as planned. This is an online course and you are at the mercy of technology so plan on technological problems occurring during the semester. Don’t wait until something is due before you finish it because you might be let down by technology. You may complete homework assignments after the given due dates and you will receive 75% credit for the problems completed after the due date.

Suggested Course Schedule: Assignments, Quizzes, and Exams should be completed well in advance of the absolute due date. This date is set to give students time should they experience unforeseen problems when they first attempt to complete an assignment or an exam. No extra time for assignments, quizzes, or exams will be granted to students past the absolute due date for a given assignment, quiz, or exam. Not even a technical problem will serve as an excuse to extend the absolute due date. Students will receive 75% credit for any problems on the homework assignments that are completed after the absolute due date. Assignment Suggested Due Date *Absolute Due Date Lesson 1 May 8 May 13 Lesson 2 May 9 May 13 Lesson 3 May 10 May 13 Lesson 4 May 11 May 20 Quiz 1 May 13 August 10 Lesson 5 May 15 May 20 Lesson 6 May 16 May 20 Lesson 7 May 17 May 20 Lesson 8 May 19 May 27 Quiz 2 May 21 August 10 Lesson 9 May 22 May 27 Lesson 10 May 24 May 27 Lesson 11 May 29 June 3 Lesson 12 May 31 June 3 Quiz 3 June 2 August 10 Lesson 13 June 3 June 10 Lesson 14 June 5 June 10 Lesson 15 June 7 June 10 Lesson 16 June 10 June 17 Quiz 4 June 12 August 10 Lesson 17 June 13 June 17 Lesson 18 June 15 June 17 Lesson 19 June 17 June 24 Quiz 5 June 19 August 10 Exam 1 June 21 June 26 Lesson 20 June 23 July 1

Assignment Suggested Due Date *Absolute Due Date Lesson 21 June 25 July 1 Lesson 22 June 27 July 1 Lesson 23 June 29 July 1 Quiz 6 July 1 August 10 Lesson 24 July 3 July 8 Lesson 25 July 4 July 8 Lesson 26 July 6 July 8 Quiz 7 July 8 August 10 Lesson 27 July 10 July 15 Lesson 28 July 11 July 15 Lesson 29 July 13 July 15 Lesson 30 July 15 July 22 Quiz 8 July 17 August 10 Exam 2 July 20 July 23 Lesson 31 July 22 July 29 Lesson 32 July 23 July 29 Lesson 33 July 25 July 29 Lesson 34 July 27 August 5 Quiz 9 July 29 August 10 Lesson 35 July 30 August 5 Lesson 36 August 1 August 5 Lesson 37 August 3 August 10 Lesson 38 August 4 August 10 Quiz 10 August 6 August 10 Final Exam August 8 August 10 *I will repeat it again and I will write it in a very big, red font so that you can’t miss this: Assignments, Quizzes, and Exams should be completed well in advance of the absolute due date. This date is set to give students time should they experience unforeseen problems when they first attempt to complete an assignment or an exam. No extra time for assignments, quizzes, or exams will be granted to students past the absolute due date for a given assignment, quiz, or exam. Not even a technical problem will serve as an excuse to extend the absolute due date. Students will receive 75% credit for any problems on the homework assignments that are completed after the absolute due date.

PROCTORED EXAMS: The proctored online exams will be taken on a computer. The job of the proctor is to enter a required password and insure that the instructions specified by the instructor are carried out. Where do I take the Exams? Students located near the main USU campus in Logan should take exams in the campus testing center, located on the south side of the Meril-Cazier Library. Make an appointment by calling (435)797-3617 at least two (2) business days in advance. Students who register for online courses through USU Regional Campuses outside of Cache Valley may schedule exams at their respective centers. Students who do not live near a USU Regional Campus will need to find someone to proctor their exams. Finding a Proctor: Before you can take a proctored exam, you must select a certified proctor. STEP 1: Sign in to the Materials & Testing Services site to select a proctor in your area. STEP 2: Contact the proctor and schedule a time to take your exam(s). STEP 3: YOU'RE DONE! Who can be a Proctor: Examples of acceptable proctors are: • College or professional testing center staff • Full-time school or public librarian • Full-time teacher • School superintendent, principal, or other administrator • Military education director • Embassy education officer Relatives, co-workers (of you or your family), and friends (of you or your family) are not eligible to proctor exams. Current and former USU students are also ineligible. Some proctors may charge a fee for their services. Students are responsible for all fees incurred while taking exams. If you have questions about finding a proctor or proctor requirements, call (435) 797-3617 or (855) 834-2370.

CONTACTING THE INSTRUCTOR: You can contact the instructor by email or by phone. The instructor will respond to emails sent to him within 24 hours Monday through Friday. If you send an email during the weekend then he will respond on the following Monday before 10:00PM. Email Address: greg.wheeler@usu.edu Office Phone: 435-797-2036 USU INCOMPLETE GRADE POLICY: http://www.usu.edu/policies/pdf/Incomplete-Grade.pdf Students are required to complete all courses for which they are registered by the end of the semester. In some cases, a student may be unable to complete all of the coursework because of extenuating circumstances. The term “extenuating” circumstances includes: (1) incapacitating illness which prevents a student from attending classes for a minimum period of two weeks, (2) a death in the immediate family, (3) financial responsibilities requiring a student to alter course schedule to secure employment, (4) change in work schedule as required by employer, (5) judicial obligations, or (6) other emergencies deemed appropriate by the instructor. The student may petition the instructor for time beyond the end of the semester to finish the work. If the instructor agrees, two grades will be given, an I and a letter grade for the course computed as if the missing work were zero. An Incomplete Grade Documentation Form must be filed by the instructor in the departmental office. Students may not be given an incomplete grade due to poor performance or in order to retain financial aid. SPECIAL NEEDS: If you have a disability that will likely require accommodation for this course (relating to pedagogy, exams, alternate format – large print, audio, diskette, Braille, etc.), contact the instructor immediately (first week of class) AND you must document the disability through the Disability Resource Center. All such requests must be discussed with and approved by the instructor.

Math 0995 Course Objectives • Be able to determine all of the factors of a given natural number. • Be able to determine the prime factorization for a given natural number. • Be able to determine the least common multiple for a given set of natural numbers. • Be familiar with the basic definition of a set and the notation used to define a set. • Be able to give examples and non-examples of natural numbers. • Understand why no number can be written as a fraction with a denominator of zero. • Be able to write any fraction as a reduced fraction where the numerator and denominator have no common factors other than 1. • Be able to multiply and divide fractions and write the result as a reduced fraction. • Be able to create an equivalent fraction with a given denominator. • Be able to add and subtract fractions and write the result as a reduced fraction. • Be able to write a fraction as a decimal. • Be able to give examples and non-examples of whole numbers. • Be able to give examples and non-examples of integers. • Be able to give examples and non-examples of rational numbers. • Be able to give examples and non-examples of irrational numbers. • Be able to identify problems that can be addressed with each subset of the real numbers. • Be familiar with the basic definition of the absolute value of a real number. • Be able to determine the absolute value of a given real number • Be able to determine the additive inverse of a given number. • Be able to simplify absolute value expressions. • Be able to add and subtract positive and negative integers. • Be able to multiply and divide positive and negative integers. Be able to write a rational number as a decimal. • Be able to convert a rational number from a decimal to a fraction. • Be able to add and subtract rational numbers. • Be able to multiply and divide rational numbers. • Be able to evaluate numerical exponential expressions. • Be able to simplify numerical radical expressions.

• Be able to use the order of operations to evaluate and simplify an expression. • Be able to simplify variable expressions using the algebraic properties of addition and multiplication. • Be able to simplify variable expressions using the distributive property. • Understand and be able to utilize the rules for multiplying and dividing exponential expressions. • Understand and be able to utilize the rule for simplifying the power of an exponential expression. • Understand and be able to utilize the rule for simplifying the powers of products and quotients. • Be able to interpret and simplify an exponential with a zero as an exponent. • Be able to interpret and simplify an exponential with a negative number exponent. • Be able to simplify monomial expressions by using properties of exponents. • Be able to distinguish between polynomial and non-polynomial expressions. • Be able to determine the degree of a polynomial, the leading term, the leading coefficient, and the constant term. Students will also be able to recognize and distinguish between monomials, binomials, and trinomials. • Understand that there are many forms that a polynomial can be expressed in and there are advantages to different forms of a polynomial in different contexts. • Students will learn that the distributive property allows us to change the form of an expression. It is an expression of a relation and should not be understood as a mandate. • Students will learn to change the form of an expression by using the distributive property to expand terms in an expression. • Students will learn how to multiply polynomials and combine like terms to simplify the product. • Students will be able to explain how dividing a polynomial by a polynomial is associated with the process of dividing numbers and writing an improper fraction as a mixed number. • Students will learn to divide a polynomial by a monomial. • Students will be able to use their understanding of addition of fractions to justify the method for dividing a polynomial by a monomial. • Students will learn the algorithm for long division. • Students will learn the algorithm for synthetic division. • Students will learn when it is appropriate to divide polynomials using synthetic division.

• Students will learn what a factor is and what it means to factor an expression. Building on their experiences with factoring integers, students will be able to determine the factors for a given monomial expression. • Students will learn to change the form of an expression by using the distributive property to factor terms in an expression. • Students will be able to identify the greatest common factor for all terms of an expression and will be able to factor out the greatest common factor to create a factored form of the expression. • Students will be able to identify examples and non-examples of expressions that are written in a factored form and those that are not. They will be able to identify the individual factors of an expression in a factored form. • Students will learn the method of factoring by grouping. • Students will learn the method of factoring a trinomial where the leading coefficient is 1. • Students will learn the method of factoring a trinomial where the leading coefficient is not 1. • Students will learn to recognize and factor difference of squares binomials. • Students will learn to recognize and factor perfect square trinomials. • Students will learn the importance of factoring expressions as a prerequisite for reducing a fraction. The students will first review the idea of reducing non-variable fractions by determining factors and then progress to reducing rational expressions. • Students will learn why it is inappropriate to cancel like terms that exist in the numerator and denominator of a fraction. • Students will learn that the domain of a rational expression often changes when a rational expression is reduced. • Students will learn their work with rational expressions is not considered completely simplified unless all of the factors of all of the numerators and denominators are identified and that no numerators and denominators have a common factor. • Building on their experiences with multiplying rational numbers, students will progress to multiplying rational expressions. • Students will learn the benefits of writing the numerators and denominators of rational expressions in factored form when multiplying or dividing. • Students will be exposed to different products that can exist in rational expressions and will be able to combine the factors of a given product and reduce the resulting fractions.

• Students will review the idea that division is the same as multiplying by a reciprocal. • Building on their experiences with adding rational numbers, students will progress to adding rational expressions. • Students will learn the benefits of writing the numerators and denominators of rational expressions in factored form when adding or subtracting. • Students will learn that an exponential expression with a rational exponent is equivalent to a radical expression. • Students will learn that positive real numbers have two real square roots and that negative real numbers do not have real square roots. • Students will learn that most principle nth roots of real numbers are irrational and that any decimal representation of an irrational number is an approximation. • Students will learn and be able to justify the properties associated with multiplying and dividing radicals. • Students will learn to reduce a radical. • Students will learn to simplify expressions by combining radical terms that are alike. • Students will learn to rationalize the denominator of an expression.-Students will learn why it is often beneficial to rationalize the denominator of an expression that contains a radical. • Students will learn the relationship between logarithms and exponents. • Students will learn to simplify logarithms that are equal to rational numbers. • Students will learn to model real-world scenarios using expressions. • Students will be able to recognize variables, constants, and operations expressed verbally or in written language. • Students will learn set notation as a way to describe a set of numbers, both finite and infinite, that satisfy a given condition. • Students will learn interval notation as a way to describe continuous sets. • Students will be able to graph a set of numbers on the real number line. • This lesson will emphasize that graphs of equations are visual descriptions of solution sets. This is stressed in such a way that students will have the same understanding when they learn to graph sets of ordered pairs and two-variable equations. • Students will learn that equations are expressions of a relation and they indicate two forms of the same thing.

• Students will learn examples of conditional equations, identities, and contradictions. • Students will determine the solutions of equations of many different forms that are sufficiently simplified so that the solutions can be determined without the need to manipulate an equation. These equations should include linear, polynomial, rational, radical, and exponential equations. • Students will learn that solving an equation is an exercise in simplifying an equation to a form where the values required to satisfy the equals relation can be determined. • By manipulating equations, students will learn and will be able to justify the following properties of equations: addition/subtraction property, multiplication/division property, zero-factor property, nth-roots property, powers property, and the absolute value property. • Students will be able to solve linear equations that require distributing, combining like terms, arithmetic with fractions. • Students will be able to identify linear equations that are identities and contradictions. • Students will understand that a linear equation can be solved without carrying the simplification to the point where the unknown is isolated. Students will understand that solving an equation is not the process of getting x by itself; it is the process of doing whatever is necessary to determine the values of x. • Students will be able to solve equations that can be simplified to a form that includes a single absolute value term that is equal to a real number. • Students will be able to identify absolute value equations that are contradictions. • Students should be able to justify when and why we can rewrite an absolute value equation as two equations associated with a positive and negative value for the argument of the absolute value. • Students will be able to be able to use the zero factor property to solve polynomial equations that can be factored by factoring out a common factor, factoring trinomials, and difference-of- squares binomials. • Students will be able to solve polynomial equations that require factored terms to be expanded and like terms combined, in order to use the zero-factor property. • Students will be exposed to equations that have imaginary solutions. Imaginary numbers will be mentioned as a topic of future study. Students will learn that such polynomials have no real number solutions, and depending on the context we then must determine if it is prudent to determine the imaginary solutions.

• Students will learn the importance of recognizing the domain of a rational equation as they solve rational equations. • Students will be able to determine the least common multiple of the denominators of a given rational equation. • Students will use the multiplication principle to rewrite a rational equation into an equivalent form with no fractions. Students will be able to identify the assumptions that are made about the domain of the equivalent non-fractional form. • Students will be able to simplify and solve rational equations that can be simplified into linear and polynomial equations. • Students will be able to solve radical equations that can be written in a form where a single radical term is equal to a real number or a linear equation. • Students will be able to justify the need to check for extraneous solutions after an equation is simplified by raising both sides of the equal sign to a power. • Students will be informed that many formulas and equations require a term of the form (x-h)^2. Examples of such equations will be presented. • Students will be able to rewrite a quadratic function into the form (x-h)^2=b using the completing-the-square algorithm. • Students will solve the general quadratic equation ax^2+bx+c=0 • Students will be able to use the quadratic formula to solve quadratic equations that are originally presented in many different forms. • Students will be able to solve linear inequalities that require distributing, combining like terms, arithmetic with fractions. • Students will be able to justify the need to change the direction of the inequality when multiplying or dividing by a negative number. • Students will justify and rewrite inequalities that can be written in the form |f(x)|A where A is a positive number. • Students will identify absolute value equations with no solutions and infinite solutions. • Students will describe some of the solutions to two-variable equations using only ordered pairs. • Students will be able to determine if a given ordered pair is or is not a solution to a given equation. • Review of the Cartesian plane.

• Students will learn to plot the solutions of two variable equations as points in the Cartesian plane. • Students will be able to determine if a given point is or is not a point on the graph of a given equation. • The lesson will emphasize the graph of an equation as a continuous set of points, each of which is a solution to the equation. • Students will learn that the intercepts of an equation are solutions to the equation that correspond to a value of zero for the corresponding unknown. • Students will learn that the solutions of linear equations all belong to a given line. • Students will be able to determine examples and non-examples of linear equations. • Students will learn to summarize all of the solutions to a linear equation by identifying two solutions. • Students will be able to determine the x-intercept and y-intercept of the graph of a given linear equation. • Students will learn that the solutions of an equation of the form y=a is the set of points on a horizontal line that all have a y-coordinate of a. • Students will learn that the solutions of an equation of the form x=b is the set of points on a vertical line that all have a x-coordinate of b. • Students will be able to determine the slope of a line given two points on the line. • Students will be able to determine the slope of a line given the equation of the line—in any form—by first determining two solutions to the equation. • Students will be able to determine the slope of a line by converting the equation to slope- intercept form. • Students will find the equation of a line given enough information to determine the slope and a point on the line. • Students will learn the relationship between parallel/perpendicular lines and their slopes. • Students will learn to graph equations on their calculators. • Students will learn to use tables to evaluate equations at different values on their calculator. • Students will learn to use trace and zoom on their calculators. • Students will be able to find x-intercepts on their calculators. • Students will learn to find intersections of two graphs on their calculators.

• Students will learn that solving the equation f(x)=g(x) is equivalent to finding the x-intercepts of the equation y=f(x)-g(x) or y=g(x)-f(x) • Students will solve a one-variable equation by graphing an appropriate two-variable equation and interpreting the graph. • Students will solve a one-variable inequality by graphing an appropriate two-variable equation and interpreting the graph. • Students will learn to model real-world scenarios using equations and graphs of equations. • Students will solve problems by interpreting graphs. • Students will be able to determine if a given ordered pair is or is not a solution to a 2x2 system of equations. • Students will be able to use the method of substitution and elimination to solve a 2x2 system of linear equations. • Students will be able to use the graphs of equations to solve a 2x2 system of linear equations. • Students will be able to graphically describe the equations and the solutions to a dependent or inconsistent 2x2 system of linear equations.

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