MTH 163, Sections 40 & 41 Precalculus I FALL 2015 Instructor Name : Mrs. Donna M. Ratliff Office Number: Room 217 Office Phone Number: (434) 946-2898 Email: dmratliff@amherst.k12.va.us Office Hours: Before school, after school by appointment Credit/Contact Hours: 3 Semester Hours - CVCC Pre-requisites: Placement by Compass/Asset Scores. Students should have successfully completed courses in Algebra I, Algebra II, and Geometry Textbooks/Materials Required: Provided by ACPS ISBN: 978-0-538-73871-2 Title: Precalculus Author: Larson Edition: 8 th Edition Classes Begin: Monday, August 17, 2015 Class Meeting Times: MTWRF - Section 40 (8:40-9:30 AM), Section 41 (10:30-11:20 AM) Classes End: January 11, 2016 Drop Date (with refund): Thursday, September 3, 2015 Withdrawal Date(without penalty): Friday, October 23, 2015 The syllabus attachment is available online at the following address @ http://www.cvcc.vccs.edu/academics/2015fallsemesterinformation.pdf Course Description : This college credit dual enrollment course will move faster than a regular high school class. This course will study concepts including but not limited to: college algebra concepts, matrices, algebraic functions, exponential functions, and logarithmic functions, as well as problem solving strategies. These topics will be covered from the textbook using chapters 1 3 and 7 8. Students will also use scientific calculators in the classroom. Chapter 1: Chapter 2: Chapter 3: Functions and Their Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions SME Division Fall 2015 Page 1
Chapter 7: Chapter 8: Systems of Equations Matrices Policies: Attendance and Missing Assignments. Students are responsible for all material in the course curriculum. Attendance at class is expected. Students should check the homework website to get the assignment when they are absent. Website : http://www.brownbearsw.com/freecal/ratliff_homework Grading Scale and Procedures : There will be four 100 point tests, homework/assignments, quizzes, midterm and a cumulative final exam. Your lowest homework grade will be dropped. No test score will be dropped. Your final grade will be based upon a 10 point scale and will be determined accordingly. Tests.. 40% Quizzes...30% Homework/Assignments. 10% Exam.. 20% Total..100% Your final grade will be based upon a 10 point scale. 90 100. A 80 90... B 70 80... C 60 70 D Less than 60...F Textbook Reading : Students are expected to read and study each section prior to the class lecture. This will enable students to more quickly grasp concepts during the lecture. Homework : Students will be required to complete homework on a regular basis and are expected to work all homework with a pencil in a separate notebook/binder. Please make certain your work is legible; if I cannot read it, then it is wrong. Always copy the original problem and work out your solution; Please keep all your homework throughout the semester; I encourage you to keep a notebook/binder with your homework in it. It will serve as a source of review for quizzes and tests. No late homework will be accepted. Quizzes/Tests : There will be several quizzes during the semester. These quizzes will consist of problems similar to the homework and will be over the material we will have covered during class. Some quizzes will require memorization of rules or theorems, some quizzes will be calculator restricted. No sharing of calculators on quizzes or tests will be allowed. There will be four tests each of them generally will require the entire class time to complete. Tests may be comprised of two parts, one calculator based, one non calculator based. Test dates are listed on the course outline but may be revised by the instructor as necessary. You will be required to do test corrections and this will count as a quiz grade. You will be required to re work the problem and explain what you did wrong/justify your answer. More information about test corrections will be given later. Calculator: Some problems will require the use of calculators. The required calculator is the TI 30XII S, pictured below. You may not use a graphing calculator for any exercise. And you will not be allowed to use a graphing calculator for any tests. Although the use of a scientific calculator is allowed as you study, there will be some calculator restrictions on tests. SME Division Fall 2015 Page 2
As you study, do not become dependent on your calculator. This is a math course, not a calculator use course. No sharing of calculators will be allowed on any evaluation. Graphing calculators will not be allowed. Supplies : 1. 3 ring binder for math notebook with clean loose leaf paper 2. Scientific calculator: Only TI 30XIIs or other scientific calculator may be used in MTH 163. 3. Graph paper 4 5 squares per inch 4. #2 pencils or mechanical pencils. Classroom Expectations : All students are expected to behave in an appropriate manner for college level course work. Promptness and full class attendance are expected. General Course Goals : Objectives/Goals: At the end of this course students will be able to: (1) identify properties of and perform algebraic operations on functions (2) perform transformations on graphs: shifting, resizing, and reflecting (3) find real and complex zeros of polynomials using synthetic and long division (4) graph polynomial and rational functions (5) solve polynomial and rational inequalities (6) apply properties of logarithms (7) solve exponential and logarithmic equations (8) solve systems of linear and nonlinear equations and inequalities (9) solve systems of linear equations using matrix methods Common Student Learning Outcomes : Chapter 1 Functions and their graphs At the end of this unit the student will: 1.1 Rectangular Coordinates a. plot points in the Cartesian plane b. use the distance formula to find the distance between two points c. use the midpoint formula to find the midpoint of a line segment d. use a coordinate plane to model and solve real life problems 1.2 Graphs of linear equations a. sketch graphs of equations b. find x and y intercepts c. use symmetry to sketch graphs of equations d. find equations and sketch graphs of circles e. use graphs of equations in solving real life problems SME Division Fall 2015 Page 3
1.3 Linear equations in two variables a. use slope to graph linear equations in two variables b. find slopes of lines c. write linear equations in two variables d. use slope to identify parallel and perpendicular lines e. use linear equations in two variables to model and solve real life problems 1.4 Functions a. determine whether relations are functions b. use function notation and evaluate functions c. find domains of functions d. use functions to model and solve real life problems 1.5 Analyzing Graphs of functions a. use the vertical line test for functions b. find the zeros of functions c. determine interval of increasing and decreasing for functions d. identify even and odd functions 1.6 A library of functions a. identify and graph linear and squaring functions b. identify and graph cubic, square root and reciprocal functions c. identify and graph piece wise functions d. recognize graphs of common functions 1.7 Transformations of functions shifting, reflecting, and stretching graphs a. use vertical and horizontal shifts to sketch graphs of functions b. use reflections to sketch graphs of functions c. use nonrigid transformations to sketch graphs of functions 1.8 Combinations of functions a. add, subtract, multiply and divide functions b. find the composition of functions c. use combinations of functions to model and solve real life problems 1.9 Inverse functions a. find inverse functions informally b. find inverse functions algebraically c. use the horizontal line test to determine if functions are one to one 1.10 Mathematical Modeling a. write mathematical models for direct, inverse and joint variation b. use the regression feature of a graphing calculator to find equation of least squares regression Chapter 2 Polynomial and Rational Functions At the end of this unit the student will be able to: 2.1 Quadratic functions a. analyze graphs of quadratic functions b. write quadratic functions in standard form and sketch graphs of quadratic functions 2.2 Polynomial functions of higher degree a. use transformations to sketch graphs of polynomial functions SME Division Fall 2015 Page 4
b. use the Leading Coefficient Test to determine the end behavior of graphs of polynomial functions c. use the zeros of polynomial functions as sketching aids d. use the Intermediate value theorem to locate zeros of polynomial functions 2.3 Polynomial and synthetic division a. use long division to divided polynomials by other polynomials b. use synthetic division to divide polynomials by binomials of (x k) c. use the remainder theorem and the factor theorem 2.4 Complex numbers a. use the imaginary unit I to write complex numbers b. add, subtract, and multiply complex numbers c. use complex conjugates to write the quotient of two complex numbers in standard form d. find the complex solutions of quadratic equations 2.5 Zeros of polynomial functions a. use the fundamental theorem of algebra to determine the zeros of polynomial functions b. find the rational zeros of polynomial functions c. find conjugate pairs of complex zeros d. find zeros of polynomials by factoring e. use Descartes s Rule of Signs and the upper and lower bound rules to find zeros of polynomials 2.6 Rational functions a. find the domains of rational functions b. find the horizontal and vertical asymptotes of graphs of rational functions c. analyze and sketch graphs of rational functions d. how to sketch graphs of rational functions that have slant asymptotes 2.7 Nonlinear Inequalities a. Solve polynomial inequalities b. solve rational inequalities c. use inequalities to model and solve real life problems Chapter 3 Exponential and Logarithmic Functions At the end of this unit the student will be able to: 3.1 Exponential functions and their graphs a. recognize and evaluate exponential functions with base a b. graph exponential functions c. recognize and evaluate exponential functions with base e d. use exponential functions to model and solve real life applications 3.2 Logarithmic functions and their graphs a. recognize and evaluate logarithmic functions with base a b. graph logarithmic functions c. recognize and evaluate natural logarithmic functions d. use logarithmic functions to model and solve real life applications Properties of logarithms a. use the change of base formulas to rewrite and evaluate logarithmic expressions b. use properties of logarithms to evaluate or rewrite logarithmic expressions c. use logarithmic functions to model and solve real life applications 3.4 Exponential and logarithmic equations a. solve simple exponential and logarithmic equations SME Division Fall 2015 Page 5
b. solve more complicated exponential and logarithmic equations c. use exponential and logarithmic equations to model and solve real life applications 3.5 Exponential and logarithmic models a. recognize the five most common types of models involving exponential and logarithmic functions b. use exponential growth and decay functions to model and solve real life problems c. use Gaussian functions to model and solve real life problems d. use logistic growth functions to model and solve real life problems e. use logarithmic functions to model and solve real life problems Chapter 7 Systems of Equations and Inequalities At the end of this unit the student will be able to: 7.1 Linear and Nonlinear Systems of Equations a. use the method of substitution to solve systems of equations in two variables b. use a graphical approach to solve systems of equations in two variables c. use systems of equations to model and solve real life problems 7.2 Two variable linear systems a. use elimination to solve systems of equations in two variables b. interpret graphically the numbers of solutions of systems of linear equations in two variables c. use systems of equations in two variables to model and solve real life problems 7.3 Multivariable linear systems a. use back substitution to solve linear systems in row echelon form b. use Gaussian elimination to solve systems of linear equations c. solve no square systems of linear equations d. use systems of equations in three or more variables to model and solve application problems 7.4 Partial Fractions a. Recognize partial fraction decompositions of rational expressions b. Find partial fraction decompositions of rational expressions 7.5 Systems of Inequalities a. Sketch the graphs of inequalities in two variables b. Solve systems of inequalities c. Use systems of inequalities in two variables to model and solve real life problems 7.6 Linear Programming a. Solve linear programming problems b. Use linear programming to model and solve real life problems Chapter 8 Matrices and Determinants At the end of this unit the student will be able to: 8.1 Matrices and Systems of Equations a. write a matrix and identify its order b. perform elementary row operations on matrices c. use matrices and Gaussian elimination to solve systems of linear equations d. use matrix and Gauss Jordan elimination to solve systems of linear equations 8.2 Operations with Matrices a. decide whether two matrices are equal b. add, subtract and multiply matrices by real numbers c. multiply matrices SME Division Fall 2015 Page 6
d. use matrix operations to model and solve real life problems 8.3 Inverse of a Square Matrix a. verify that two matrices are inverses of each other b. use Gauss Jordan elimination to find the inverses of matrices c. use a formula to find the inverse of a 2 x 2 matrix d. use inverse matrices to solve systems of linear equations 8.4 Determinants of a Square matrix a. find the determinants of 2 x 2 matrices b. find minors and cofactors of square matrices c. find the determinants of square matrices 8.5 Applications of Matrices and Determinants a. use Cramer s rule to solve systems of linear equations b. use determinants to find the areas of triangles c. use determinants to find the equation of a line d. use determinants to test for collinear points Topics to be covered during course : Chapter 1: Functions and Their Graphs Chapter 2: Polynomial and Rational Functions Chapter 3: Exponential and Logarithmic Functions Chapter 7: Systems of Equations Chapter 8:Matrices Students with Disabilities : If you have a documented physical, mental, or learning disability and you need reasonable accommodations to help you achieve success, please contact Disability Support Services, in the Counseling Center, room 2217 or 2109F, phone: 434.832.7802 or 434.832.7299 or email ADA@cvcc.vccs.edu. To best provide the accommodation you need, make this request as soon as possible, since accommodations cannot be made to change a grade received for any course already completed. SME Division Fall 2015 Page 7
Assignments to be completed : MTH 163 Tentative Outline (Subject to change) Monday Tuesday Wednesday Thursday Friday 17 Intro 1.1 18 1.2 19 1.2 20 1.2/1.3 21 1.3 24 1.3 25 1.4 26 1.4 27 1.5 28 1.5 31 1.6 Sept 1 1.7 2 1.7 3 1.8 4 1.9 7 Labor Day 8 9 10 Test 1 11 2.1 14 2.1 15 2.2 16 2.2 17 2.2/2.3 18 2.3 21 2.3 22 2.4 23 2.4 24 2.5 25 2.5 28 2.5 29 2.6 30 2.6 Oct 1 2.7 2 2.7 5 6 Test 2 7 3.1 8 3.1 9 assessment 3.2 12 13 14 15 16 GP End 3.2 19 TWD 20 21 22 23 26 3.4 27 3.4 28 3.5 29 3.5 30 Nov 2 Test 3 3 TWD 4 7.1 5 7.1 6 7.2 9 7.2 10 7.3 11 7.3 12 7.3 13 7.4 16 7.4 17 7.5 18 7.5 19 7.6 20 7.6 23 8.1 24 8.2 25 26 27 30 8.3 Dec 1 8.3 2 8.4 3 8.5 4 8.5 7 8 Test 4 9 review 10 review 11 CVCC common exam 14 15 16 17 19 SME Division Fall 2015 Page 8
Homework Math 163 Precalculus I SECT PAGES PROBLEMS 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 TEST 1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 8 11 21 23 33 37 48 53 61 65 71 72 78 82 88 91 98 101 7,15,23,39,43,49,53 7,19,23,33,35,39,41,47,55,57,67,69,71,73,77,79,83 9,15,17,23,31,35,47,51,55,59,61,65,67,81,83,87,89,91,93,97,115,129 7,11,13,15,21,23,27,33,43,45,49,51,57,59,65,69,70,71,77,79,81, 93,97,103 11,17,19,21,23,29,39,41,45,57,67,69,75,77,79,83,85,89 13,15,43,45,53,57,63,71 7(a,b),13(a f),15,19,23,25,27,31,37,43,49,55,59,63,65 5,9,13,17,19,23,25,29,37,38,41,45,47,49,51,53,65 7,13,15,17,25,29,35,39,41,49,53,59,63,69,75,95,99 116 120 3,5,17,19,23,29,35,37,39,41,47,49,52,54,55,56,59,60,61,65,66, 69,71,72,73,74,77,79,81,83,85,86,93,95,97,98,101,111,112,115, 119,127,129,131,133,137,139,140,145,147 Chapter 1 132 135 145 149 156 158 164 165 176 180 190 193 201 203 7,9,11,13,15,21,25,29,31,35,41,43,45,47,49,57,63,73,77,79 9,11,15,17,23,27,37,41,45,47,49,53,57,61,69,81,83,91,95 13,23,24,27,31,35,39,47,55(a,b),59,61,63,67,77,81 7,9,13,23,25,31,33,37,41,43,49,53,59,63,67,69,75,79,85 9,13,15,21,25,29,35,41,45,51,57,59,65,67,77,87,91,93,95,99, 101,103,105 11,13,17,19,21,23,25,29,33,35,41,45,55,57,69 7,13,17,21,27,29,33,37,45,53,59,63,71,75 206 209 1,3,5,7,8,9,15,17,19,23,25,27,32,33,35,39,41,43,53,55,59(c,d), 61(a),67,69, 71,73,75,79,85,87,89,91,93,95,97,101,105,107,109, 111,112,113,115,117,121, 125,127,133,135,137,139,143,145,147 TEST 2 3.1 3.2 3.4 3.5 TEST 3 7.1 224 226 234 236 241 243 251 254 262 267 270 272 Chapter 2 7,13,15,23,24,25,27,31,33,41,47,49,51,53,57,59,65,69,70,73 7,9,11,17,19,23,24,25,27,29,33,35,37,39,41,45,47,49,51,57,61, 65,67,69,71,75, 79,83,87,91,97 7,9,15,19,23,29,33,35,37,41,45,47,49,61,63,67,69,71,73,75,77, 81,85,107 5,13,15,19,21,23,27,29,35,43,49,51,57,71,77,81,89,91,95,101, 105,109,110, 119,123,125,129(a) 7,9,11,15,19,23,25,33,37,39,43,47,49,55,61,63,65,69,75,84 1,7,9,11,17,23,27,33,37,41,43,45,49,51,54,55,61,69,71,73,74,75,79,80,83, 85,86,87,89,90,91,93,97,100,101,103,109,111,113,117,119,122,123 Chapter 3 11,13,17,27,29,31,35,39,43,55,57,65,71,81,83 501 504 7.2 513 516 5,9,11,13,17,21,23,25,37,43,45,53 7.3 7.5 7.6 8.1 8.2 8.3 Ch 7 Rev Ch 8 Rev 525 529 545 548 555 557 579 583 594 598 605 607 560 564 630 634 7,11,17,19,21,25,27,31,33,39,41,45,51,61 9,15,17,21,29,35,37,41,43,45,47,49,51,63,65,67,69,71,75,77 7,9,13,15,21,29,31,35,37,39 11,13,17,21,27,35,39,41,43,55,61,65,67,71,77,79,81,95,107,111 7,9,11,13,17,19,29,33,35,39,47,55,59,63 5,9,15 & 43,19 &45,21,35,37,43,45,53,55,57,67 7,10,11,14,19,25,31,32,33,35,38,39,43,51,57,73,75,77,79,83,87,93,95,99,102 1,5,7,13,15,23,24,31,33,39,45,47,51,55,56,59,61,63,73,77,79,85,93,101 TEST 4 Chapter 7 (7.1 7.3, 7.5 7.6) and Chapter 8 (8.1 8.3) SME Division Fall 2015 Page 9