1 LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK MATHEMATICS, ENGINEERING and COMPUTER SCIENCE DEPARTMENT FALL 2015 MAT 096, ELEMENTARY ALGEBRA 6 PERIODS, 5 LECTURES, 1 LAB, 0 CREDITS Catalog Description This course provides a careful treatment of elementary algebra, beginning with linear equations, ending with quadratic equations, and emphasizing the interplay between the algebraic and geometric points of view. Topics include line graphing, systems of linear equations, introduction to functions, exponents, polynomial algebra, factoring, radical expressions, and the quadratic formula. Instructional Objectives During this course, the instructor expects to: 1. Provide students with the skills necessary to construct graphs from linear equations and to deduce linear equations from graphs of straight lines. 2. Enable students to solve systems of linear equations graphically and algebraically and to appreciate the diverse applications involving such systems. 3. Introduce students to the concept of function: elementary examples, tables, the inputoutput model, and evaluating functions. 4. Reinforce students understanding of the laws of exponents in the more general setting of integers. 5. Provide students with the skills required to carry out arithmetic operations on polynomials and factoring. 6. Familiarize students with the arithmetic of radical expressions. 7. Introduce students to quadratic functions and provide them with a powerful tool for finding the zeros of such functions, the quadratic formula.
2 Performance Objectives At the conclusion of this course, students will be able to: 1. Appreciate the interplay of algebra and geometry in drawing graphs of straight lines and deriving linear equations from straight-line data. 2. Solve systems of linear equations and apply skills to solve variety of word problems arising from real-world situations. 3. Understand the power and versatility of the function concept in tabular as well as algebraic settings. 4. Use laws of exponents appropriately in various algebraic settings. 5. Perform arithmetic operations on polynomials, including factoring. 6. Combine and simplify radical expressions. 7. Grasp the basics of quadratic functions and use various methods for solving quadratic equations. Required Text Beginning Algebra, 6th edition (EDUCO International, Inc.) by Man M. Sharma You are required to purchase online access to this text. Evaluation The purpose of a grading system is to give you, the student, and anyone else reading your transcript an accurate record of your performance in this course. The role of the Mathematics Department is to provide a fair, valid, and reliable structure for assessing your achievement. In order to pass this course, you must fulfill the CUNY math proficiency requirements: an overall average of at least 70% AND a score of at least 60 on the CUNY Final Exam. S/R/U grading system: The A/B/C/D/F grading scale is not used in MAT 096. LaGuardia s policy for grading in MAT 096 is as follows: If you meet the above evaluation criteria, you ll receive a passing grade of S. If you don t meet the evaluation criteria, and you don t have any previous R grades in MAT 096, you ll receive an R grade, and you will have to repeat the course. If you don t meet the criteria, and you ve already received one R grade in MAT 096, you ll receive another R, and you will have to repeat the course. If you don t meet the evaluation criteria, and you ve already received two or more R grades in MAT 096, you ll receive a U grade, and you will have to repeat the course. Also, the College s policy concerning grades of W, WN, and WU apply to MAT 096.
3 Grading Categories Online homework 10% Lab work 5% Departmental exams 25% Professor s tests/quizzes 15% Projects 5% Final online pre-test 5% CUNY Final Exam 35% Explanation of Grading Categories 1. Online homework Daily online assignments will be given. It is very important that you do them because they reinforce the concepts learned in that section. Assignments must be completed by the date and time set by your instructor. 2. Lab work You will meet in the Math Lab (MB-44) one hour every week and work on lab sheets containing problems that will enhance your computational skills. A tutor will guide you. You are encouraged to work together and learn from each other. Should you need further assistance, you may ask the lab assistants or bring your questions up with the professor in class. You are required to bring to the tutoring lab a copy of the relevant lab sheet. The lab sheets are available at: www.lagcc.cuny.edu/mec/mat095-and-mat096-lab-sheets/ The completed lab sheets must be submitted to your instructor. He or she will determine when the sheets are due. 3. Departmental exams Two one-hour departmental online examinations will be given. The examinations consist of multiple choice questions, some of which are designed to test algebraic skills, while the others will test conceptual understanding. The second departmental exam will be cumulative.
4 Explanation of Grading Categories (continued) 4. Professor s tests/quizzes Your professor will develop and administer two tests and at least three quizzes during the course of the semester 5. Projects Your instructor will assign to you at least ONE of the projects that are either listed in the PQL Sampler (http://ctl.laguardia.edu/pql/sampler) or are similar. 6. Final online pre-test This will be a cumulative online pre-test assigned during the last week of classes. This pre-test will help you prepare for the CUNY final exam. 7. CUNY Final Exam This exam will be given during the final examination week. It will consist of 25 multiple-choice questions that you must complete in 100 minutes. Attendance The maximum number of absences allowed will be 9 hours. Unexcused absences beyond this maximum will result in a grade of WU, R, or U. Academic Integrity This class will be conducted in compliance with LaGuardia Community College s academic integrity policy. IN ORDER TO PASS THIS COURSE, YOU MUST HAVE a) an average total score (computed as stated above) of at least 70, b) a score of at least 60 on the CUNY Final Exam, c) no more than 9 hours of unexcused absences, and d) satisfactorily completed the assignments, quizzes, tests, departmental exams, and lab sheets. Note: Calculators and other electronic devices are NOT allowed in this course.
5 CUNY Final Exam Make-up Policy If you missed your CUNY FINAL EXAM due to a documented reason, then reach out to your professor immediately to request a possible incomplete (INC grade). If your professor decides to grant and submit an INC grade for you, then you have six months to make-up the CUNY FINAL and your overall class grade. Then, see Anthony Pappas (E-223) about the sign-up sheet for a make-up CUNY EXAM. Any student who does not have an INC on their transcript will be removed from the list of eligible students for a make-up. Be aware, you will only be able to make-up your CUNY EXAM one day per semester determined in advance by the LaGuardia testing Office. You are strongly advised to plan ahead. COURSE OUTLINE FOR MAT096, ELEMENTARY ALGEBRA Spring 2015 Text: Beginning Algebra, 6th edition (EDUCO International, Inc.) by Man M. Sharma The following outline is a guide for classroom instruction. It is subject to change based on the College s academic calendar. EDUCO online homework and quizzes are date sensitive and must be activated by the instructor. These assignments should be coordinated with the appropriate classwork material. Week Lesson TOPIC Section Suggested In Class/Homework EDUCO On-Line ASSIGNMENTS 1 Review 1 2 3 4 5 Operations with integers Operations with fractions (including LCD) Translating statements into mathematical expressions Linear equations 1.1 1.2 1.6 2.2 p. 5: 7,9,13,21,39,41,49,61,71,75 p. 15: 1,5,7,11,15,17 p. 51: 5,7,15,17,21,45,51,57 p. 73: 15,21,37,45,85,116,141,153 1.1, 1.2, 1.6, 2.2 2 6 7 8-9 Review More on linear equations Applications of linear equations Literal equations Linear inequalities 2.3 2.4 2.5 2.8 p. 78: 7,11,13,17,19,43,67,75,77 p. 86: 5,7,15,19,23,25,27,31,33 p.93: 1,9,15,23,27,33,35,37 p. 118: 7,9,17,23,27,47,67,79,83 2.3, 2.4, 2.5, 2.8
6 3 Lab Sheet # 1 10 Professor s Test I 11 12 13 14-15 Linear Equations Linear equations in two variables Graphing linear eqs./intercepts Slope Equations of a line 3.1 3.2 3.3 3.4 p. 134: 3,5,7,9,17,21,31,33,47,48,59 p. 141: 1,3,11,15,17,21,25,31,37,49 p.151: 1,5,11,15,19,21,23,45,53,59 p. 161: 7,9,13,17,25,29,33,39,43,49, 55,59,67,69,71,73 3.1, 3.2, 3.3, 3.4 4 16 17 18 19 Lab Sheet # 2 Solving Systems of Linear Equations Graphically Substitution method Addition method Applications 4.1 4.2 4.3 4.5 p. 192: 3,11,19,21,39,43,45,47,51,55 p. 197: 3,5,7,11,31,43,45 p. 203: 5,7,13,21,23,37 p. 213: 1,3,5,7,9,13,15,23,25,29 4.1, 4.2, 4.3, 4.5 5 6 Lab Sheet # 3 20 Departmental Exam I Introduction to Functions 21-22 Functions: Evaluating functions using function notation, input-output model, tables of values Exponents & Polynomials 23 Rules of exponents 24-25 26 27-28 29 30 Integer exponents Lab Sheet # 4 Exponents & Polynomials Polynomial addition & subtraction Polynomial multiplication Special products Division: by monomials only 3.6 5.1 5.5 5.2 5.3 5.4 5.6 p. 175: 1,3,7,9,11,13,15,20,31,33, 35,39,43,45,47,55 p. 224: 3,5,13,15,21,23,27,37,61,65, 81,89 p. 245: 5,9,11,13,17,19,23,27,29,33 37,43,45 p. 230: 31,35,39,41,51,57,67,71,77 p. 235: 5,17,25,29,31,41,51,53,65,67 p.239: 1,7,23,25,31,45 p. 249: 3,5,11,15,25,27 3.6, 5.5 5.2, 5.3, 5.4, 5.6 7 8 31 32 33 34-35 36 37-38 39-40 Lab Sheet # 5 Factoring Greatest common factor (GCF) & Factoring by grouping Factoring trinomials Special factorizations (difference of two squares, perfect square trinomials) Lab Sheet # 6 Solving Quadratic Equations By factoring (zero principle) Applications Review 6.1 6.2 6.3 6.4 6.5 p. 264: 3,7,13,17,29,33,45,57,59, 73,77 p. 271: 3,5,13,17,39,49,51,55,57,63 65,77 p. 278: 1,7,9,17,27,37,41,43,47,55, 79,89 p. 284: 7,17,23,29,31,37,43,47,65 p. 288: 1,3,11,15,17,21,23,27,31 6.1,6.2, 6.3 6.4,6.5 9 Lab Sheet # 7 41 Departmental Exam II Roots (square roots only) 42 What roots mean and finding roots 43 Multiplication and division of roots 44-45 Addition and subtraction of roots 8.1 8.2 8.3 p. 367: 3,5,29,39,43,53,55,57 p. 372: 3,15,17,19,25,29,33 35, 39, 51,53,63,69 p. 377: 5,17,29,31,35,37,39,41,47 8.1, 8.2, 8.3 Lab Sheet # 8
7 10 46 47 48-49 Roots (square roots only) Rationalizing the denominator Solving Quadratic Equations (again) Square root property Solution by formula 8.4 9.1 9.3 p. 382: 3,9,15,37,43,47,55,61,63,67 p. 400: 3,9,13,17,19,21,27,31 p. 417: 3,9,13,17,21,29 8.4, 9.1, 9.3 11 Lab Sheet # 9 50 Professor s Test II 51 52 53 54 Review Decimal numbers Percents Ratios and proportions Scientific notation (including word problems) Lab Sheet # 10 1.3 1.4 2.6 5.7 p. 22: 3,7,8,12,13,14 p. 27: 1,2,3,4,8,11,13,15 p. 100: 11,17,35,47,57,63,65,73,79 p. 253: 7,17,21,23,31,37,48,49,50 1.3, 1.4, 2.6, 5.7 12 55-59 Cumulative review for the CUNY Final Exam Problem sets and sample tests to be assigned by the instructor. 60 Final Online Pre-test