MATH0955: BEGINNING ALGEBRA


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1 MATH0955: Beginning Algebra 1 MATH0955: BEGINNING ALGEBRA Cuyahoga Community College Viewing:MATH0955 : Beginning Algebra Board of Trustees: Academic Term: Subject Code MATH  Mathematics Course Number: 0955 Title: Beginning Algebra Catalog Description: First of two developmental mathematics courses. Topics include simplifying basic algebraic expressions in one variable, solving one variable linear equations, literal equations, linear inequalities in one variable, graphing linear inequalities in one variable, compound inequalities, graphing compound inequalities, determining relation, domain, range of functions graphically and algebraically, performing operations on functions, introducing the rectangular coordinate system, determining equations of lines, graphing lines and two variable inequalities, solving systems of two variable equations and inequalities, performing algebraic operations and simplifying of polynomials involving rules of exponents, and scientific notation. Includes applications and activities to build skills in problem solving. Credit Hour(s): 6 Lecture Hour(s): 6 Requisites Prerequisite and Corequisite MATH0910 Basic Arithmetic and PreAlgebra, or sufficient score on math placement test, or departmental approval. I. ACADEMIC CREDIT Academic Credit According to the Ohio Department of Higher Education, one (1) semester hour of college credit will be awarded for each lecture hour. Students will be expected to work on outofclass assignments on a regular basis which, over the length of the course, would normally average two hours of outofclass study for each hour of formal class activity. For laboratory hours, one (1) credit shall be awarded for a minimum of three laboratory hours in a standard week for which little or no outofclass study is required since three hours will be in the lab (i.e. Laboratory 03 hours). Whereas, one (1) credit shall be awarded for a minimum of two laboratory hours in a standard week, if supplemented by outofclass assignments which would normally average one hour of outof class study preparing for or following up the laboratory experience (i.e. Laboratory 02 hours). Credit is also awarded for other hours such as directed practice, practicum, cooperative work experience, and field experience. The number of hours required to receive credit is listed under Other Hours on the syllabus. The number of credit hours for lecture, lab and other hours are listed at the beginning of the syllabus. Make sure you can prioritize your time accordingly. Proper planning, prioritization and dedication will enhance your success in this course. The standard expectation for an online course is that you will spend 3 hours per week for each credit hour. II. ACCESSIBILITY STATEMENT If you need any special course adaptations or accommodations because of a documented disability, please notify your instructor within a reasonable length of time, preferably the first week of the term with formal notice of that need (i.e. an official letter from the Student Accessibility Services (SAS) office). Accommodations will not be made retroactively. For specific information pertaining to ADA accommodation, please contact your campus SAS office or visit online athttp:// Blackboard accessibility information is available athttp://access.blackboard.com. Eastern (216) Voice
2 2 MATH0955: Beginning Algebra Metropolitan (216) Voice Western (216) Voice Westshore (216) Voice Brunswick (216) Voice OffSite (216) Voice III. ATTENDANCE TRACKING Regular class attendance is expected. TriC is required by law to verify the enrollment of students who participate in federal Title IV student aid programs and/or who receive educational benefits through other funding sources. Eligibility for federal student financial aid is, in part, based on your enrollment status. Students who do not attend classes for the entire term are required to withdraw from the course(s). Additionally, students who withdraw from a course or stop attending class without officially withdrawing may be required to return all or a portion of the financial aid based on the date of last attendance. Students who do not attend the full session are responsible for withdrawing from the course(s). TriC is responsible for identifying students who have not attended a course, before financial aid funds can be applied to students accounts. Therefore, attendance will be recorded in the following ways: For inperson courses, students are required to attend the course by the 15th day of the semester, or equivalent for terms shorter than 5weeks, to be considered attending. Students who have not met all attendance requirements for an inperson course, as described herein, within the first two weeks of the semester, or equivalent, will be considered not attending and will be reported for nonattendance and dropped from the course. For blendedlearning courses, students are required to attend the course by the 15th day of the semester, or equivalent for terms shorter than 5weeks, or submit an assignment, to be considered attending. Students who have not met all attendance requirements for a blendedlearning courses, as described herein, within the first two weeks of the semester, or equivalent, will be considered not attending and will be reported for nonattendance and dropped from the course. For online courses, students are required to login in at least two (2) times per week and submit one (1) assignment per week for the first two (2) weeks of the semester, or equivalent to the 15th day of the term. Students who have not met all attendance requirements for an online course, as described herein, within the first two weeks of the semester, or equivalent, will be considered not attending and will be reported for nonattendance and dropped from the course. At the conclusion of the first two weeks of a semester, or equivalent, instructors report any registered students who have Never Attended a course. Those students will be administratively withdrawn from that course. However, after the time period in the previous paragraphs, if a student stops attending a class, wants or needs to withdraw, for any reason, it is the student's responsibility to take action to withdraw from the course. Students must complete and submit the appropriate TriC form by the established withdrawal deadline. TriC is required to ensure that students receive financial aid only for courses that they attend and complete. Students reported for not attending at least one of their registered courses will have all financial aid funds held until confirmation of attendance in registered courses has been verified. Students who fail to complete at least one course may be required to repay all or a portion of their federal financial aid funds and may be ineligible to receive future federal financial aid awards. Students who withdraw from classes prior to completing more than 60 percent of their enrolled class time may be subject to the required federal refund policy. If illness or emergency should necessitate a brief absence from class, students should confer with instructors upon their return. Students having problems with class work because of a prolonged absence should confer with the instructor or a counselor. IV. CONCEALED CARRY STATEMENT College policy prohibits the possession of weapons on college property by students, faculty and staff, unless specifically approved in advance as a jobrelated requirement (i.e., TriC campus police officers) or, in accordance with Ohio law, secured in a parked vehicle in a designated parking area only by an individual in possession of a valid conceal carry permit. As a TriC student, your behavior on campus must comply with the student code of conduct which is available on page 29 within the TriC student handbook, available athttp:// must also comply with the College s Zero Tolerance for Violence on College Property available athttp:// documents/ zerotoleranceforviolencepolicy.pdf Outcomes Simplify basic algebraic expressions in one variable. 1. Define and identify variables. 2. Define and identify terms. 3. Define and identify algebraic expressions. 4. Define and identify like terms. 5. Add and subtract like terms. 6. Define and apply the properties of real numbers to algebraic expressions.
3 MATH0955: Beginning Algebra 3 7. Use the Order of Operations to evaluate basic algebraic expressions. 8. Simplify basic algebraic expressions. Solve linear equations and linear inequalities in one variable. 1. Define and use the Addition Property of Equality and the Multiplication Property of Equality to solve linear equations in one variable. 2. Verify solutions to equations. 3. Use the Order of Operations to solve equations. 4. Solve equations that include fractional or decimal coefficients. 5. Solve equations that may have no solution or infinitely many solutions. 6. Translate phrases into algebraic expressions and equations. 7. Solve application problems involving consecutive integers, geometry, percents, and uniform motion with one unknown. 8. Identify and define rates, ratios, and proportions. 9. Solve equations involving proportions. 10. Solve application problems involving rates, ratios, and proportions. 11. Define and solve literal equations. 12. Define and use the Addition Property of Inequality and the Multiplication Property of Inequality to solve linear inequalities in one variable. 13. Write the solution of inequalities using the appropriate inequality symbol, in set builder notation and in interval notation. 14. Graph solutions of linear inequalities on the number line. 15. Determine the intersection and union of two sets. 16. Solve compound inequalities involving and and or and express solutions as inequalities, in interval notation, in setbuilder notation and by graphically on a number line. 17. Solve inequalities in one variable with infinite solutions and no solutions. 18. Translate phrases into algebraic inequalities. 19. Solve application problems involving inequalities. 20. Solve application problems involving compound inequalities in one variable. 21. Identify and define linear equations. Define, evaluate and perform operations on polynomial functions. 1. Define a relation, domain, range, and function. 2. Identify the domain and range of relations and determine whether or not a relation is a function. 3. Evaluate functions algebraically and graphically. 4. Identify the domain and range of functions graphically and algebraically. 5. Use the vertical line test to identify functions. 6. Solve application problems involving functions. Identify components of the rectangular coordinate system, determine the equations of lines, and graph lines and inequalities. 1. Draw the rectangular coordinate system and identify and label the horizontal axis, vertical axis, origin, and quadrants. 2. Read and write the coordinates of points plotted on the rectangular coordinate system. 3. Plot ordered pairs of points in the rectangular coordinate system. 4. Calculate the slope of lines. 5. Describe the meaning of the slope of lines as a rate of change. 6. Identify and determine x and yintercepts algebraically and graphically. 7. Determine equations of lines using the slopeintercept form of an equation. 8. Write equations of lines using function notation. 9. Write equations of lines using the pointslope form of an equation of a line. 10. Write linear equations in standard form. 11. Identify the slope of vertical lines as undefined and determine the equation of vertical lines. 12. Identify the slope of horizontal lines as zero and determine the equation of horizontal lines. 13. Determine the domain and range of vertical linear relations and functions, including horizontal functions. 14. Solve applications involving linear equations and linear function. 15. Graph linear equations using a table. 16. Graph linear equations using the yintercept and the slope of the line. 17. Graph linear equations using the x and yintercepts of the line. 18. Determine the equation of a line parallel to a given line and through a given point.
4 4 MATH0955: Beginning Algebra 19. Determine the equation of a line perpendicular to a given line and through a given point. 20. Solve applications involving realworld linear equations and linear functions. 21. Graph linear inequalities in two variables. 22. Solve applications involving linear inequalities by graphing Solve systems of linear equations and inequalities in two variables. 1. Determine whether or not given ordered pairs are solutions to linear systems of equations. 2. Solve systems of linear equations by the Method of Graphing. 3. Use graphing to identify lines as parallel and the system as inconsistent with no solution. 4. Use graphing to identify systems of equations as dependent with infinite solutions. 5. Use graphing to identify systems as independent with a unique ordered pair as a solution. 6. Solve systems of linear equations by the Method of Substitution. 7. Use the Method of Substitution to identify lines as parallel and the system of equations as inconsistent with no solution. 8. Use the Method of Substitution to identify systems of equations as dependent with infinite solutions. 9. Use the Method of Substitution to identify systems of equations as independent with a unique ordered pair as a solution. 10. Solve systems of linear equations by the Method of Addition including equations with fractional and decimal coefficients. 11. Use the Method of Addition to identify lines as parallel and the system of equations as inconsistent with no solution. 12. Use the Method of Addition to identify systems of equations as dependent with infinite solutions. 13. Use the Method of Addition to identify systems as independent with a unique ordered pair as a solution. 14. Determine the most efficient method for solving linear systems. 15. Solve systems of linear inequalities in two variables by graphing. 16. Solve application problems involving linear systems using the Methods of Graphing, Substitution, and Addition including mixture and simple interest problems. 17. Solve application problems involving systems of linear inequalities in two variables using the graphing method. Simplify, evaluate, and perform operations on polynomials and expressions involving exponents. 1. Solve application problems using scientific notation. 2. Define polynomial, standard form, degree, coefficient, monomial, binomial, trinomial, and degree of polynomial in one variable. 3. Evaluate polynomials in several variables given values for each variable. 4. Perform addition and subtraction with polynomials in one or more variables. 5. Multiply monomial expressions. 6. Identify and use the product rule for exponents. 7. Identify and use the powertopower rule for exponents. 8. Identify and use the productstopowers rule for exponents. 9. Multiply monomials and polynomials. 10. Multiply two polynomials with neither being a monomial. 11. Determine the product of two general binomials. 12. Determine the product of conjugate binomials. 13. Determine the square of a binomial sum. 14. Determine the square of a binomial difference. 15. Multiply general binomials or use the specialproduct formulas with multiple variables. 16. Divide monomial expressions. 17. Identify and use the quotient rule for exponents. 18. Identify and use the quotientstopowers rule. 19. Identify and use the zeroexponent rule. 20. Identify and use the negative exponent rule. 21. Divide polynomials by a monomial. 22. Simplify expressions with exponents involving multiple properties of exponents. 23. Solve applications involving polynomials. 24. Define and identify scientific notation of numbers. 25. Define and identify expanded form of numbers. 26. Perform conversions from scientific notation to decimal notation. 27. Perform conversions from decimal notation to scientific notation. 28. Use properties of exponents to perform computations with numbers in scientific notation. Methods of Evaluation: A. Exams
5 MATH0955: Beginning Algebra 5 B. Quizzes C. Homework D. Projects E. In class collaborative work F. Comprehensive final exam G. Online coursework H. Class participation Course Content Outline: 1. Algebraic expressions in one variable a. Definition of variable b. Definition of a term. c. Definition of algebraic expression d. Definition of like terms e. Addition and subtraction of like terms f. Properties of real numbers and expressions g. Order of Operations to evaluate expressions h. Simplify expressions. 2. Linear equations and linear inequalities a. Definition of linear equations b. Addition and Multiplication Properties of Equality c. Verification of solutions d. Order of Operations in equations e. Equations with fractional or decimal coefficients f. Equations with no solution or infinite solutions g. Translate phrases to equations h. Applications including consecutive Integer, geometry, percent and uniform motion i. Definition of rates, ratios, and proportions j. Solve proportions k. Applications with rates, ratios, and proportions l. Literal equations m. Addition and Multiplication Properties of Inequalities n. Solutions as inequality statements, set builder notation and interval notation o. Graph inequalities p. Intersection and union q. Compound inequalities r. Inequalities with infinite solutions or no solution s. Inequality applications t. Compound inequality applications u. Translate phrases to inequalities 3. Functions a. Define relation, domain, range, function b. Domain and range of relation and determine relation or function c. Evaluate algebraically and graphically d. Domain and range of functions e. Vertical line test f. Applications 4. Rectangular Coordinate System, equations of lines, graph lines and inequalities a. Rectangular Coordinate System b. Coordinates of points c. Plot ordered pairs d. Calculate slope e. Slope as a rate of change f. Slopeintercept form of an equation g. Linear functions h. Pointslope form of an equation i. Standard form of an equation
6 6 MATH0955: Beginning Algebra j. Slope and equations of vertical lines k. Slope and equation of horizontal lines l. Domain and range of vertical linear relations and functions, include horizontal functions m. Applications of linear equations and functions n. Tables to graph lines o. Yintercept and slope to graph lines p. X and yintercepts to graph lines q. Parallel lines r. Perpendicular lines s. Realworld applications of linear equations and functions t. Graph linear inequalities u. Applications of linear inequalities 5. Systems of linear equations and inequalities a. Order pairs as solutions b. Solve by graphing method c. Graphing to identify parallel lines as inconsistent systems with no solution d. Graphing to identify as dependent systems with infinite solutions e. Graphing to identify as independent systems with unique solution f. Solve by substitution method g. Substitution Method to identify parallel lines as inconsistent systems with no solution h. Substitution Method to identify as dependent systems with infinite solutions i. Substitution Method to identify as independent systems with unique solution j. Solve by Addition Method include fractional and decimal coefficients k. Addition Method to identify parallel lines as inconsistent systems with no solution l. Addition Method to identify as dependent systems with infinite solutions m. Addition Method to identify as independent systems with unique solution n. Efficient methods for solving systems o. Systems of inequalities p. Applications of systems including mixture and simple interest q. Application of systems of inequalities 6. Simply, evaluate and operations on polynomials and expressions with exponents a. Define polynomials and descriptive terminology b. Evaluate multivariable polynomials c. Addition and subtraction of polynomials d. Multiply monomials e. Exponent product rule f. Exponent powertopower rule g. Exponents productstopower rule h. Multiply monomial and polynomials i. Multiply polynomials, neither monomial j. General binomial products k. Product of conjugates l. Square of binomial sum m. Square of binomial difference n. General binomial and specialproduct formulas with multiple variables o. Divide monomials p. Exponent quotient rule q. Exponent quotienttopower rule r. Zero exponent rule s. Negative exponents t. Divide polynomial by monomial u. Multiple properties of exponents within a problem v. Applications of polynomials w. Definition of scientific notation x. Definition of expanded form y. Scientific notation to decimal z. Decimal to scientific notation
7 MATH0955: Beginning Algebra 7 aa. Computation with scientific notation bb. Application of scientific notation Resources Blitzer, Robert.Introductory and Intermediate Algebra for College Students.4th ed. Boston, MA: Pearson Education, Rockswold, Gary and Terry Kreiger.Beginning and Intermediate Algebra with Applications and Visualizations.3rd ed. Boston, MA: Pearson Education, Tussy, Alan R. and David Gustafson.Elementary and Intermediate Algebra.5th ed. Belmont, CA: Cengage, Wright, D. Franklin.Introductory and Intermediate Algebra.6th ed. Mt. Plasant, SC: Hawkes Learning Systems, Resources Other 1. Software provided through publisher corresponding to textbook 2. Software and Ebook Top of page Key: 2819
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