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SINCLAIR COMMUNITY COLLEGE DAYTON, OHIO DEPARTMENT TEACHING SYLLABUS FOR COURSE IN MAT 102 - INTERMEDIATE ALGEBRA (5 CREDIT HOURS) 1. PREREQUISITE: MAT 101 - Elementary Algebra or sufficient score on Sinclair Community College Mathematics Placement Test. 2. COURSE DESCRIPTION: Sets, real numbers, polynomials, algebraic fractions, first-degree equations and inequalities in one variable, radical expressions, complex numbers, quadratic equations and inequalities in one variable, graphs in the plane, systems of linear equations, relations and functions. 3. COURSE OBJECTIVES: This course is designed to review and expand the concepts of elementary algebra and to introduce further topics that the student will need to continue the study of mathematics. At the completion of this course, the student will be eligible to enroll in MAT 116 - College Algebra. 4. TEXT: Beginning and Intermediate Algebra, Fourth Edition by Margaret L. Lial, John Hornsby, and Terry McGinnis Pearson/Addison Wesley Publishing; 2008. 5. CALCULATOR: Calculators are permitted in 102, but graphing calculators are not required. Use of calculators on chapter tests is at the option of the instructor. Scientific (but not graphing) calculators will be permitted on the departmental final exam. 6. EXAMS: All exams are to be closed book. No formula sheets allowed on exams. 7. PREPARED BY: Harvey Chew and Jim Willis DATE: Effective: Winter Quarter 2009 SINCLAIR COMMUNITY COLLEGE DAYTON, OHIO CLASS SCHEDULE FOR COURSE IN MAT 102 - INTERMEDIATE ALGEBRA (5 CREDIT HOURS) SECTIONS THAT MEET FIVE TIMES A WEEK WK DAY SECTIONS AND TOPICS OF TEXT M *** Introduction, Diagnostic Test T 5.4 Special Factoring Techniques 1 W 5.4 Summary Exercises on Factoring (p358) R 6.2 Multiplying and Dividing Rational Expressions F 6.4 Adding and Subtracting Rational Expressions M 6.5 Complex Fractions T 6.6 Solving Equations with Rational Expressions 2 W 6.7 Applications of Rational Expressions R 2.6 Ratios and Proportions F 7.1 Review of Graphs and Slopes of Lines* M 7.2 Review of Equations of Lines; Linear Models* T 7.2 Review of Equations of Lines; Linear Models* 3 W REVIEW R TEST ONE (over 5.4, 6.2, 6.4-6.7, 2.6, 7.1, 7.2) F 7.3 Functions M 7.3 Functions T 8.1 Solving Systems of Linear Equations by Graphing 4 W 8.2 Solving Systems of Linear Equations by Substitution R 8.3 Solving Systems of Linear Equations by Elimination F 8.4 Systems of Linear Equations in Three Variables M 8.5 Applications of Systems of Linear Equations T 8.5 Applications of Systems of Linear Equations 5 W 9.1 Set Operations and Compound Inequalities R 9.1 Set Operations and Compound Inequalities F 9.2 Absolute Value Equations and Inequalities M 9.2 Absolute Value Equations and Inequalities T REVIEW 6 W TEST TWO (over 7.3, 8.1-8.5, 9.1, 9.2) R 10.1 Radical Expressions and Graphs F 10.2 Rational Exponents *The Instructor is advised to treat this section as a “New” rather than a “Review” section Note: The Instructor is advised to take full advantage of the “Summary Exercises” included in certain sections. MAT 102 - INTERMEDIATE ALGEBRA SECTIONS THAT MEET FIVE TIMES A WEEK WK DAY SECTIONS AND TOPICS OF TEXT M 10.3 Simplifying Radical Expressions T 10.3 Simplifying Radical Expressions 7 W 10.3 Simplifying Radical Expressions R 10.4 Adding and Subtracting Radical Expressions F 10.5 Multiplying and Dividing Radical Expressions M 10.5 Multiplying and Dividing Radical Expressions Summary Exercises (p676) T 10.6 Solving Equations with Radicals 8 W 10.7 Complex Numbers R REVIEW F TEST THREE (over 10.1-10.7) M 11.1 Solving Quadratic Equations by the Square Root Property T 11.2 Solving Quadratic Equations by Completing the Square 9 W 11.3 Solving Quadratic Equations by the Quadratic Formula R 11.4 Equations Quadratic in Form F 11.5 Formulas and Further Applications M 11.6 Graphs of Quadratic Functions T 11.7 More about Parabolas and their Applications 10 W 11.7 More about Parabolas and their Applications R 11.8 Quadratic and Rational Inequalities F REVIEW M TEST FOUR (over 11.1-11.8) T REVIEW 11 W REVIEW R FINAL EXAM (Comprehensive) IMPORTANT NOTE: The final exam will be in two parts. One part will be prepared by the department in the Fall, Winter, and Spring quarters. It will be a 20 question, 40 minute, multiple choice test. It will be sent to the instructor in the mail. Another part is to be prepared by the instructor. It may be of any format, but should be 15 minutes long. The instructor should count the departmental part for 80% of the final exam score and the other part for 20%. The final exam score should count for about 20% of the final course grade. The instructor will be asked to report the scores on the departmental part and the final course grades back to the department. CLASS SCHEDULE FOR COURSE IN MAT 102 - INTERMEDIATE ALGEBRA (5 CREDIT HOURS) SECTIONS THAT MEET TWICE A WEEK WK DAY SECTIONS AND TOPICS OF TEXT 1 M/T *** Introduction, Diagnostic Test 5.4 Special Factoring Rules 5.4 Summary Exercises on Factoring (p358) 6.2 Multiplying and Dividing Rational Expressions W/R 6.4 Adding and Subtracting Rational Expressions 6.5 Complex Fractions 6.6 Solving Equations with Rational Expressions 2 M/T 6.7 Applications of Rational Expressions 2.6 Ratios and Proportions W/R 7.1 Review of Graphs and Slopes of Lines* 7.2 Review of Equations of Lines; Linear Models* 3 M/T 7.2 Review of Equations of Lines; Linear Models* REVIEW W/R TEST ONE (over 5.4, 6.2, 6.4-6.7, 2.6, 7.1, 7.2) 7.3 Functions 4 M/T 8.1 Solving Systems of Linear Equations by Graphing 8.2 Solving Systems of Linear Equations by Substitution W/R 8.3 Solving Systems of Linear Equations by Elimination 8.4 Systems of Linear Equations in Three Variables 5 M/T 8.5 Applications of Systems of Linear Equations 9.1 Set Operations and Compound Inequalities W/R 9.2 Absolute Value Equations and Inequalities REVIEW *The Instructor is advised to treat this section as a “New” rather than a “Review” section Note: The Instructor is advised to take full advantage of the “Summary Exercises” included in certain sections. MAT 102 - INTERMEDIATE ALGEBRA SECTIONS THAT MEET TWICE A WEEK - CON'T WK DAY SECTIONS AND TOPICS OF TEXT 6 M/T TEST TWO (over 7.3, 8.1-8.5, 9.1,9.2) 10.1 Radical Expressions and Graphs W/R 10.2 Rational Exponents 10.3 Simplifying Radical Expressions 7 M/T 10.4 Adding and Subtracting Radical Expressions 10.5 Multiplying and Dividing Radical Expressions W/R 10.5 Multiplying and Dividing Radical Expressions 10.6 Solving Equations with Radicals 8 M/T 10.7 Complex Numbers REVIEW W/R TEST THREE (over 10.1-10.7) 11.1 Solving Quadratic Equations by the Square Root Property 11.2 Solving Quadratic Equations by Completing the Square 9 M/T 11.3 Solving Quadratic Equations by the Quadratic Formula 11.4 Equations Quadratic in Form W/R 11.5 Formulas and Further Applications 11.6 Graphs of Quadratic Functions 10 M/T 11.7 More about Parabolas and their Applications 11.8 Quadratic and Rational Inequalities W/R REVIEW, TEST FOUR (over 11.1-11.8) 11 M/T REVIEW, FINAL EXAM (Comprehensive) IMPORTANT NOTES: The syllabus for the “twice a week section” provided above is based on twenty-one meetings or classes. Twenty-one is the minimum number of class meetings during a quarter when a holiday occurs on a class day. The instructor is advised to find out ahead whether the number of classes to be taught is twenty-two rather than twenty-one. If so, the instructor is advised to make any necessary adjustments to the syllabus above in order to take advantage of the additional class meeting. The final exam will be in two parts. One part will be prepared by the department in the Fall, Winter, and Spring quarters. It will be a 20 question, 40 minute, multiple choice test. It will be sent to the instructor in the mail. Another part is to be prepared by the instructor. It may be of any format, but should be 15 minutes long. The instructor should count the departmental part for 80% of the final exam score and the other part for 20%. The final exam score should count for about 20% of the final course grade. The instructor will be asked to report the scores on the departmental part and the final course grades back to the department. TO THE INSTRUCTOR To ensure consistency, at some minimum level, regarding which formulas students are required to learn in each of its courses, the Mathematics Department has developed the attached list for this course. PREREQUISITE FORMULAS are formulas of special importance that students are expected to know upon entering this course. (If PREREQUISITE FORMULAS are not listed, separate COURSE FORMULA lists for prerequisite courses are available in the Mathematics Department Office.) COURSE FORMULAS are those that students are required to learn (and required to demonstrate that they have learned) as the formulas are presented in the course. Requiring students to learn more than those listed is the instructor’s option. Please note that only formulas are listed. Students are also expected to learn definitions, theorems and procedures that will allow them to meet course objectives. If you have questions regarding this matter, please contact your course coordinator. Math 102 Formulas Prerequisite Formulas Formulas of special importance that students are expected to know upon entering this course: - Geometric Formulas Area Perimeter Square A s2 P 4s Rectangle A lw P 2l 2w 1 Triangle A (bh) P a bc 2 - Sum of the Angles in a Triangle A B C 180 - Square of a Binomial: (x + y)2 = x2 + 2xy + y2 (x – y)2 = x2 – 2xy + y2 - Pythagorean Theorem a2 + b2 = c2 x if x 0 - Absolute Value of x | x| x if x 0 Course Formulas Formulas that students are required to memorize in this course: Chapter 5 - Difference of Squares x2 – y2 = (x + y)(x – y) - Sums and Differences of Cubes x3 + y3 = (x + y)(x2 – xy + y2) x3 – y3 = (x – y)(x2 + xy + y2) Chapter 6 - Multiplying and Dividing Rational Expressions P R PR P R P S PS (Q 0, S 0) (Q 0, R 0, S 0) Q S QS Q S Q R QR - Adding and Subtracting Rational Expressions P R PR P R PR (Q 0) (Q 0) Q Q Q Q Q Q - Distance, Rate, Time d rt , r d / t , t d / r - Rate of Work 1 If a job can be completed in t units of time, then the rate of work is job per unit of t time. Chapter 7 rise change in y y 2 y1 - Slope of a Line m x1 x 2 run change in x x 2 x1 - Forms of Linear Equations Point-slope form y y1 m( x x1 ) Slope-intercept form y mx b General form Ax By C Horizontal line yb Vertical line xa x1 x 2 y1 y 2 - Midpoint Formula , 2 2 Chapter 9 - Absolute Value Equations and Inequalities If k, p, and q are real numbers with k 0, then | ax + b | = k ax + b = k or ax + b = - k | ax + b | k ax + b k or ax + b - k | ax + b | k - k ax + b k | ax + b | = | cx + d | ax + b = cx + d or ax + b = -(cx + d) Chapter 10 - Principal Square Root of a 2 a2 a If n is an even positive integer n an a If n is an odd positive integer n an a - Fractional Exponents 1 a n a n m 1 a m 1 a a n am m n n n am n m 1 a n m (a 0) n a - Laws of Radicals n a n b n ab n a n a n b b kn a km n a m - Distance Formula d ( x 2 x1 ) 2 ( y 2 y1 ) 2 - Imaginary Unit i 1 (i 2 1) b i b Chapter 11 - Square Root Property x2 = k x= k or x = k - Quadratic Formula b b 2 4ac If ax bx c 0, then 2 x (a 0) 2a - Forms of Quadratic Functions General Form f x ax 2 bx c F x a x h k , vertex (h, k) 2 Standard Form b - Line of Symmetry for a Parabola x (a 0) 2a b b - Vertex Formula 2a , f 2a (a 0) Important! Many instructors have seen improved student performance from incorporating Math Lab assignments into their course structure. These could be given as required assignments, optional assignments, or extra credit assignments. You can create your own Math Lab assignments or you can use the ones created by the Math Lab that are attached to this syllabus. There is one assignment for each test. Each assignment represents at least 2 to 3 hours of Lab work. Please contact the Math Lab (room: 1315; phone: 512-2286) with any questions. MATH LAB NAME___________________ ROOM 1315 LAB ASSIGNMENT 0 READ THESE DIRECTIONS! Show this paper to the Lab Assistant when you sign in. Have the Lab Assistant initial and stamp this paper when you sign out. You must watch BOTH of these videos. These tapes will help you do better on your exams! It is highly recommended that you watch the first tape before your first exam and the second tape as soon after your first exam as possible. Bring your graded exam with you when you watch the second tape. Lab Initials and Stamp VDC Heath “Preparation and Test Taking Skills” ___________________ (about 40 min) VDC Heath “Analyzing Results and Improving Performance” (about 20 min) ___________________ MATH LAB NAME___________________ ROOM 1315 LAB ASSIGNMENT 1 (MATH 102) Go to: www.interactmath.com READ THESE DIRECTIONS! Show this paper to the Lab Assistant when you sign in. Have the Lab Assistant initial and stamp this paper when you sign out. Show your work neatly on a separate sheet of paper. You do NOT have to complete this in one session. WHEN you have completed all materials, staple your work to the back of this sheet and turn in to your instructor. Lab Initials and Stamp InterAct Chapter 5 Section 4 “Special Factoring Rules” Exercises 19,25,43,45,59,61,71,77 ____________________ InterAct Chapter 6 Section 2 “Multiplying and Dividing Rational Expressions” Exercises 17,29,41,47,55,61 ____________________ InterAct Chapter 6 Section 4 “Adding and Subtracting Rational Expressions” Exercises 35,65,67,69 ____________________ InterAct Chapter 6 Section 5 “Complex Fractions” Exercises 11,23,33,35 ____________________ InterAct Chapter 6 Section 6 “Solving Equations with Rational Expressions” Exercises 17,31,47,49,83 ____________________ InterAct Chapter 6 Section 7 “Applications of Rational Expressions” Exercises 3,21,33,39 ____________________ InterAct Chapter 2 Section 6 “Ratios and Proportions” Exercises 39,63,65 ____________________ InterAct Chapter 7 Section 1 “Review of Graphs and Slopes of Lines” Exercises 7,49,57,59,69,73,83,91,97,99 ____________________ InterAct Chapter 7 Section 2 “Review of Equations of Lines; Linear Models” Exercises 5,21,25,45,49,51,63,67,75 ____________________ MATH LAB NAME___________________ ROOM 1315 LAB ASSIGNMENT 2 (MATH 102) Go to: www.interactmath.com READ THESE DIRECTIONS! Show this paper to the Lab Assistant when you sign in. Have the Lab Assistant initial and stamp this paper when you sign out. Show your work neatly on a separate sheet of paper. You do NOT have to complete this in one session. WHEN you have completed all materials, staple your work to the back of this sheet and turn in to your instructor. Lab Initials and Stamp InterAct Chapter 7 Section 3 “Functions” Exercises 5,11,13,25,33,41,53,69 ____________________ InterAct Chapter 8 Section 1 “Solving Systems of Linear Equations by Graphing” Exercises 33,35,37 ____________________ InterAct Chapter 8 Section 2 “Solving Systems of Linear Equations by Substitution” Exercises 3,7,13,17,19 ____________________ InterAct Chapter 8 Section 3 “Solving Systems of Linear Equations by Elimination” Exercises 9,13,19,31,35,37 ____________________ InterAct Chapter 8 Section 4 “Systems of Linear Equations in Three Variables” Exercises 3,17,25,29 ____________________ InterAct Chapter 8 Section 5 “Applications of Systems of Linear Equations” Exercises 23,33,39 ____________________ InterAct Chapter 9 Section 1 “Set Operations and Compound Inequalities” Exercises 7,13,17,22,31,43,47,55,57 ____________________ InterAct Chapter 9 Section 2 “Absolute Value Equations and Inequalities” Exercises 27,31,41,45,65,77,81,93 ____________________ MATH LAB NAME___________________ ROOM 1315 LAB ASSIGNMENT 3 (MATH 102) Go to: www.interactmath.com READ THESE DIRECTIONS! Show this paper to the Lab Assistant when you sign in. Have the Lab Assistant initial and stamp this paper when you sign out. Show your work neatly on a separate sheet of paper. You do NOT have to complete this in one session. WHEN you have completed all materials, staple your work to the back of this sheet and turn in to your instructor. Lab Initials and Stamp InterAct Chapter 10 Section 1 “Radical Expressions and Graphs” Exercises 13,21,25,41,47,69,73,77,105,107,111 ____________________ InterAct Chapter 10 Section 2 “Rational Exponents” Exercises 3,5,13,31,35,79,83 ____________________ InterAct Chapter 10 Section 3 “Simplifying Radical Expressions” Exercises 15,35,39,41,49,61,71,79,91,99,107 ____________________ InterAct Chapter 10 Section 4 “Adding and Subtracting Radical Expressions” Exercises 7,9,21,33 ____________________ InterAct Chapter 10 Section 5 “Multiplying and Dividing Radical Expressions” Exercises 9,11,23,43,49,63,69,75,103 ____________________ InterAct Chapter 10 Section 6 “Solving Equations with Radicals” Exercises 9,17,27,47,49,55,65 ____________________ InterAct Chapter 10 Section 7 “Complex Numbers” Exercises 1,3,9,17,23,31,45,47,53,61,73 ____________________ MATH LAB NAME___________________ ROOM 1315 LAB ASSIGNMENT 4 (MATH 102) Go to: www.interactmath.com READ THESE DIRECTIONS! Show this paper to the Lab Assistant when you sign in. Have the Lab Assistant initial and stamp this paper when you sign out. Show your work neatly on a separate sheet of paper. You do NOT have to complete this in one session. WHEN you have completed all materials, staple your work to the back of this sheet and turn in to your instructor. Lab Initials and Stamp InterAct Chapter 11 Section 1 “Solving Quadratic Equations (Square Root Property)” Exercises 9,21,25,37,57,65 ____________________ InterAct Chapter 11 Section 2 “Solving Quadratic Equations (Completing the Square)” Exercises 21,41,49 ____________________ InterAct Chapter 11 Section 3 “Solving Quadratic Equations (Quadratic Formula)” Exercises 7,11,29,39,41,45 ____________________ InterAct Chapter 11 Section 4 “Equations Quadratic in Form” Exercises 15,33,49,61,69,75 ____________________ InterAct Chapter 11 Section 5 “Formulas and Further Applications” Exercises 5,9,19,33,37,49 ____________________ InterAct Chapter 11 Section 6 “Graphs of Quadratic Equations” Exercises 1,5,9,13,25,29,33 ____________________ InterAct Chapter 11 Section 7 “More About Parabolas; Applications” Exercises 5,7,13,23,35 ____________________ InterAct Chapter 11 Section 8 “Quadratic and Rational Inequalities” Exercises 7,13,21,29,37 ____________________