Instructor: Vikki Maurer Class: M 1-3, W 1-3, F 1-2

Transcription

1 Math 111 Vikki Maurer SpringTerm 2018 Instructor: Vikki Maurer Class: M 1-3, W 1-3, F 1-2 Course: This course explores relations and linear, quadratic, exponential, polynomial, rational and logarithmic functions. Includes theory of equations, matrices and determinants. Prerequisite: C or better in MTH 95, Intermediate Algebra, or equivalent. Upon completion of the course, the student will be able to: 1. Interpret graphical information, such as identifying types of functions, translations, inverses, intercepts, and asymptotes. 2. Solve a variety of symbolic equations and inequalities, such as rational, absolute value, exponential, radical, logarithmic, and linear systems. 3. Construct appropriate models for real world problems, such as fitting an algebraic function model to a set of data, and system of linear equations. Required for this Course: ALEKS 360 Access Code Regular Internet Access ANY Graphing Calculator (Free App on your phone, Desmos, etc.) Notebook ALEKS COURSE CODE: NW6G9-YQAHM FREE 2-WEEK ACCESS: 04ECB-3969B-73A02-5F47A Phone: but is best. maurerv@linnbenton.edu Office: WOH 119 Office and Advising Hours: M 11:00 to 11:50AM: R 10:00 to 10:50AM F 12:00 to 12:50PM Other times by appointment or drop by. Course Requirements: 20% ALEKS Weekly Homework 5% ALEKS Whole Pie 10% In-Class Assignments and any take home problems or projects 45% Midterm Exams 20% Final Exam Course Grades: Final course grades will follow the standard cut-off A 90%, B 80%, C 70%, D 60% and below 60% earns an F grade. You must earn at least a C grade in Math 111 in order to move on to higher math classes for which Math 111 is a prerequisite. Incomplete Grades: An incomplete grade may be issued for a student who is earning a grade of C or better, but who has failed to complete a major requirement such as the

2 final exam. Any student seeking an incomplete must discuss this option with the instructor and sign an agreement prior to the time when grades are issued. Homework and YOUR Responsibility: The course homework and most of the course learning will be done in an online adaptive learning environment called ALEKS. You will start with an initial knowledge check that assesses what you already know and what you still need to learn. ALEKS then determines a unique lesson plan for you to learn the material of the course. Note: ALEKS tailors its lesson path to your understanding of the course material. You will have more or less work to do in ALEKS to learn the course material, depending on how much of the course material you still need to learn. Every course topic has a lesson from the associated book, College Algebra by Julie Miller and Donna Gerken. You can access an ebook in ALEKS so you don t have to purchase a hard copy unless you want to. Many of the topics also have videos to help you learn the material. You must be prepared to spend at least hours per week on this class, many of those hours working in ALEKS. The first week you must spend at least 5 hours in ALEKS or you will be dropped from the course on Monday of week 2. Note that since this is a 5 credit math class, if you were in a classroom, you would spend 5 hours in class, and 2 hours outside of class for each hour in class. You will want to be working in ALEKS daily or at a minimum 3-4 times a week to complete each weeks objectives. Tip: ALEKS goal is that you understand the course objectives, NOT that you do 20 exercises for that section in the book. (You will have more or less to do depending on whether or not you understand it and can do the math yet.) Recognizing this will help you navigate ALEKS successfully. Missing Class and Late Homework: If you miss class check my website for the lecture notes and any changes to the schedule. The biggest reason why students fail to complete a math class is because of poor attendance. If you miss several of our classes you will find it very difficult to get caught up. Be in class each day. Tests: There are three midterm exams that you will take in class. The dates for these exams are listed on the calendar and will not change. There are no exam retakes or make-ups. If you miss a midterm exam then your final exam percentage will count as the missing test score. In-Class Problems: We will often work in pairs or groups to solve problems during class. These in-class problems will be collected. If you are not in class to work on the problem, then you will not earn credit. There is no way to make up these in-class problems. I will drop 2 of these in-class problems at the end of the term. Final Exam: Your cumulative final exam is worth 150 points. You will be asked not only to demonstrate your mastery of the calculus you learned this term, but you will also be writing about concepts.

3 Help: There are many resources available for you if you need help. Ask questions during class or office hours. ALEKS has helpful tutorials and resources. Search YouTube or mathtv.com for the topic of interest and watch a tutorial. Talk with an instructional assistant at the math domain in the Learning Center. Sign up for a FREE tutor in the Learning Center. A Word About the Math Domain in the Learning Center: Originally the math domain was designed to support the developmental math students. Over the years more transfer level math students have come to rely on the math help desk. There is a problem, however, with getting too much help. You end up not learning to think critically on your own; you don t develop confidence in your own abilities; and you end up approaching the math help desk for every little question. Typically students who rely too heavily on the math help desk or on the solutions manual have good homework scores but failing test grades. Be sure you do not go to the math help desk until you have wrestled with the problem first. Read your class notes, check examples in the text, and be sure you have a good handle on what the question is asking you to do. Cheating: Cheating will not be tolerated. If you choose to cheat on an exam and are caught, you will receive a zero grade on your exam, and I will file an incident report. A second episode of cheating will guarantee you an F grade for the course and more severe disciplinary action from the school. If you are having so many problems that you feel the only way out is to cheat, then you need to come talk with me. I am here to help you succeed. There are always ways to work things out for students who are willing to try. Anyone With Special Needs or Circumstances? Students who have issues I should be aware of, have emergency medical information that I should know about, need special arrangements in the event of evacuation, or have documented disabilities who may need accommodations, should talk with me as early as possible, no later than the first week of the term. If additional assistance is required the student should contact the Center for Accessibility Resources in RCH 105 or call LBCC Comprehensive Statement of Nondiscrimination LBCC prohibits unlawful discrimination based on race, color, religion, ethnicity, use of native language, national origin, sex, sexual orientation, gender, gender identity, marital status, disability, veteran status, age, or any other status protected under applicable federal, state, or local laws. For further information see Board Policy P1015 in our Board Policies and Administrative Rules. Title II, IX, & Section 504: Scott Rolen, CC-108, ; Lynne Cox, T-107B, , LBCC, Albany, Oregon. To report: linnbenton-advocate.symplicity.com/public report.

4 Weeks Week 1 April 2 - April 6 Week 2 April 9 April 13 Week 3 April 16 April 20 Week 4 April 23 -April 27 Week 5 April 30 May 4 Week 6 May 7 May 11 Week 7 May 14 May 18 Week 8 May 21 May 25 Week 9 May 28 June 1 Week 10 June 4 June 8 Finals Week June11-June 15 Schedule and Exam Dates First Class is Wednesday, April 4 Sections 2.3 and 2.4 Sections 2.4, 2.5 and begin 2.6 Sections 2.6, 2.7 and 2.8 EXAM 1 Monday, April 23 Section 3.1 and begin 3.2 Sections 3.2, 3.3 and 3.4 Section 3.5 EXAM 2 Friday, May 11 Section 4.1, 4.2 and 4.3 Sections 4.4, 4.5 and 4.6 Monday May 28 NO School Sections 5.1 and 5.2 EXAM 3 Friday, June 1 Section 6.1 and Review for the Final Exam Final Exam, Monday, June 11, 1:00 to 2:50pm ALEKS Topics by Week: Week 1 (25 topics, due on 04/08/2018) Finding x- and y-intercepts of a line given the equation: Basic Finding intercepts of a nonlinear function given its graph Classifying slopes given graphs of lines Finding slope given two points on the line Finding the slope and y-intercept of a line given its equation in the form y = mx+b Graphing a line by first finding its slope and y-intercept Writing the equation of the line through two given points Finding the initial amount and rate of change given a graph of a linear function Identifying functions from relations

5 Vertical line test Evaluating functions: Linear and quadratic or cubic Evaluating a rational function: Problem type 1 Table for a square root function Variable expressions as inputs of functions: Problem type 1 Domain and range from ordered pairs Domain of a rational function: Excluded values Domain of a rational function: Interval notation Domain of a square root function: Basic Finding outputs of a one-step function that models a real-world situation: Function notation Finding inputs and outputs of a two-step function that models a real-world situation: Function notation Finding inputs and outputs of a function from its graph Domain and range from the graph of a discrete relation Domain and range from the graph of a piecewise function Word problem involving average rate of change Domain and range from the graph of a quadratic function Week 2 (29 topics, due on 04/15/2018) Introduction to solving an absolute value equation Solving an absolute value equation: Problem type 2 Solving an absolute value equation: Problem type 3 Solving an absolute value equation: Problem type 4 Solving an absolute value equation of the form ax+b = cx+d Solving an absolute value inequality: Problem type 1 Writing an absolute value inequality given a graph on the number line Solving an absolute value inequality: Problem type 4 Solving an absolute value inequality: Problem type 5 Graphing a vertical or horizontal line Finding the slope and a point on a line given its equation in point-slope form Writing an equation in point-slope form given the slope and a point Writing the equation of the line through two given points Writing the equations of vertical and horizontal lines through a given point Finding slopes of lines parallel and perpendicular to a line given in slope-intercept form Identifying parallel and perpendicular lines from equations Writing equations of lines parallel and perpendicular to a given line through a point Writing and evaluating a function that models a real-world situation: Advanced Interpreting the parameters of a linear function that models a real-world situation Application problem with a linear function: Finding a coordinate given two points Scatter plots and correlation Predictions from the line of best fit Approximating the equation of a line of best fit and making predictions Classifying linear and nonlinear relationships from scatter plots

6 Linear relationship and the correlation coefficient Domain and range of a linear function that models a real-world situation Choosing a graph to fit a narrative: Basic Choosing a graph to fit a narrative: Advanced Interpreting the graphs of two functions Week 3 (35 topics, due on 04/22/2018) Simplifying a ratio of factored polynomials: Linear factors Simplifying a ratio of polynomials using GCF factoring Multiplying rational expressions made up of linear expressions Dividing rational expressions involving linear expressions Graphing an absolute value equation of the form y = A x Graphing a cubic function of the form y = ax 3 Determining if graphs have symmetry with respect to the x-axis, y-axis, or origin Evaluating a cube root function Evaluating a piecewise-defined function Finding where a function is increasing, decreasing, or constant given the graph Finding local maxima and minima of a function given the graph Graphing a function of the form f(x) = ax + b: Fractional slope Graphing an absolute value equation in the plane: Basic Graphing a function of the form f(x) = ax 2 + c Graphing a square root function: Problem type 1 Graphing a square root function: Problem type 2 Graphing a cube root function Matching parent graphs with their equations Graphing a piecewise-defined function: Problem type 1 Graphing a piecewise-defined function: Problem type 3 Even and odd functions: Problem type 1 Translating the graph of a parabola: One step Translating the graph of an absolute value function: One step Translating the graph of an absolute value function: Two steps Writing an equation for a function after a vertical translation Translating the graph of a function: Two steps Transforming the graph of a function by reflecting over an axis Transforming the graph of a quadratic, cubic, square root, or absolute value function Writing an equation for a function after a vertical and horizontal translation Sum, difference, and product of two functions Quotient of two functions: Basic Introduction to the composition of two functions Composition of two functions: Basic Expressing a function as a composition of two functions Composition of two functions: Advanced Week 4 (24 topics, due on 04/29/2018) Factoring a quadratic with leading coefficient 1 Factoring a perfect square trinomial with leading coefficient 1 Factoring a difference of squares in one variable: Basic

7 Solving an equation written in factored form Solving a word problem using a quadratic equation with rational roots Solving a word problem using a quadratic equation with irrational roots Graphing a parabola of the form y = (x-h) 2 + k Introduction to the composition of two functions Composition of two functions: Basic Composition of a function with itself Expressing a function as a composition of two functions Composition of two functions: Domain and range Composition of two functions: Advanced Finding the vertex, intercepts, and axis of symmetry from the graph of a parabola Graphing a parabola of the form y = x 2 + bx + c Graphing a parabola of the form y = a(x-h) 2 + k Finding the x-intercept(s) and the vertex of a parabola Rewriting a quadratic function to find its vertex and sketch its graph Finding the maximum or minimum of a quadratic function Word problem involving the maximum or minimum of a quadratic function Word problem involving optimizing area by using a quadratic function Domain and range from the graph of a quadratic function Range of a quadratic function Writing the equation of a quadratic function given its graph Week 5 (31 topics, due on 05/06/2018) Multiplying conjugate binomials: Univariate Squaring a binomial: Univariate Factoring a linear binomial Introduction to the GCF of two monomials Factoring out a monomial from a polynomial: Univariate Solving a word problem using a quadratic equation with rational roots Finding the zeros of a quadratic function given its equation Writing a quadratic function given its zeros Identifying polynomial functions Finding zeros of a polynomial function written in factored form Finding zeros and their multiplicities given a polynomial function written in factored form Finding a polynomial of a given degree with given zeros: Real zeros Finding x- and y-intercepts given a polynomial function Determining the end behavior of the graph of a polynomial function Determining end behavior and intercepts to graph a polynomial function Matching graphs with polynomial functions Inferring properties of a polynomial function from its graph Polynomial long division: Problem type 1 Polynomial long division: Problem type 2 Using the remainder theorem to evaluate a polynomial The Factor Theorem Using a given zero to write a polynomial as a product of linear factors: Real zeros Finding all possible rational zeros using the rational zeros theorem Using the rational zeros theorem to find all zeros of a polynomial: Rational zeros

8 Using the rational zeros theorem to find all zeros of a polynomial: Irrational zeros Multiplying expressions involving complex conjugates Finding a polynomial of a given degree with given zeros: Complex zeros Using a given zero to write a polynomial as a product of linear factors: Complex zeros Using the rational zeros theorem to find all zeros of a polynomial: Complex zeros Linear factors theorem and conjugate zeros theorem Week 6 (22 topics, due on 05/13/2018) Restriction on a variable in a denominator: Linear Solving a rational equation that simplifies to linear: Denominator x Solving a rational equation that simplifies to linear: Denominator x+a Solving a rational equation that simplifies to linear: Denominators a, x, or ax Solving a rational equation that simplifies to linear: Denominators ax and bx Solving a rational equation that simplifies to linear: Like binomial denominators Solving a rational equation that simplifies to linear: Unlike binomial denominators Solving a rational equation that simplifies to linear: Factorable quadratic denominator Solving a rational equation that simplifies to quadratic: Binomial denominators and numerators Solving a rational equation that simplifies to quadratic: Factorable quadratic denominator Finding the intercepts, asymptotes, domain, and range from the graph of a rational function Finding the asymptotes of a rational function: Constant over linear Finding the asymptotes of a rational function: Linear over linear Finding horizontal and vertical asymptotes of a rational function: Quadratic numerator or denominator Finding the asymptotes of a rational function: Quadratic over linear Graphing a rational function: Constant over linear Graphing a rational function: Linear over linear Transforming the graph of a rational function Graphing a rational function: Quadratic over linear Matching graphs with rational functions: Two vertical asymptotes Graphing a rational function with more than one vertical asymptote Writing the equation of a rational function given its graph Week 7 (26 topics, due on 05/20/2018) Horizontal line test Determining whether two functions are inverses of each other Inverse functions: Quadratic, square root Inverse functions: Cubic, cube root Graphing the inverse of a function given its graph Finding, evaluating, and interpreting an inverse function for a given linear relationship Table for an exponential function Graphing an exponential function and its asymptote: f(x)=b x

9 Graphing an exponential function and its asymptote: f(x) = a(b) x Translating the graph of an exponential function The graph, domain, and range of an exponential function Transforming the graph of a natural exponential function Evaluating an exponential function that models a real-world situation Using a calculator to evaluate exponential expressions involving base e Introduction to compound interest Finding a final amount in a word problem on exponential growth or decay Finding the final amount in a word problem on compound interest Converting between logarithmic and exponential equations Converting between natural logarithmic and exponential equations Evaluating logarithmic expressions Translating the graph of a logarithmic function Graphing a logarithmic function: Basic The graph, domain, and range of a logarithmic function Domain of a logarithmic function: Advanced Finding the final amount in a word problem on continuous compound interest Finding the final amount in a word problem on continuous exponential growth or decay Week 8 (23 topics, due on 05/27/2018) Finding the initial amount and rate of change given an exponential function Writing an equation that models exponential growth or decay Choosing an exponential model and using it to make a prediction Solving an equation of the form logba = c Basic properties of logarithms Using properties of logarithms to evaluate expressions Expanding a logarithmic expression: Problem type 1 Expanding a logarithmic expression: Problem type 2 Writing an expression as a single logarithm Change of base for logarithms: Problem type 1 Solving a multi-step equation involving a single logarithm: Problem type 1 Solving a multi-step equation involving natural logarithms Solving an equation involving logarithms on both sides: Problem type 1 Solving an exponential equation by finding common bases: Linear exponents Solving an exponential equation by using natural logarithms: Decimal answers Solving an exponential equation by using logarithms: Decimal answers, advanced Finding the time in a word problem on compound interest Finding the time given an exponential function with base e that models a realworld situation Finding the initial amount in a word problem on continuous compound interest Finding the rate or time in a word problem on continuous exponential growth or decay Finding half-life or doubling time Writing and evaluating a function modeling continuous exponential growth or decay given doubling time or half-life

10 Writing and evaluating a function modeling continuous exponential growth or decay given two outputs Week 9 (18 topics, due on 06/03/2018) Identifying solutions to a system of linear equations Classifying systems of linear equations from graphs Graphically solving a system of linear equations Solving a system of linear equations using substitution Solving a system of linear equations using elimination with addition Solving a system of linear equations using elimination with multiplication and addition Solving a system of linear equations with fractional coefficients Solving a system of linear equations with decimal coefficients Solving a 2x2 system of linear equations that is inconsistent or consistent dependent Solving a word problem involving a sum and another basic relationship using a system of linear equations Solving a word problem using a system of linear equations of the form Ax+By = C Solving a word problem using a system of linear equations of the form y = mx + b Solving a value mixture problem using a system of linear equations Solving a percent mixture problem using a system of linear equations Solving a distance, rate, time problem using a system of linear equations Solving a tax rate or interest rate problem using a system of linear equations Introduction to solving a 3x3 system of linear equations Solving a 3x3 system of linear equations: Problem type 1 Week 10 (8 topics, due on 06/10/2018) Identifying the operations used to create equivalent systems of equations Solving a 3x3 system of linear equations: Problem type 1 Solving a 3x3 system of linear equations: Problem type 2 Solving a 3x3 system of linear equations that is inconsistent or consistent dependent Solving a word problem using a 3x3 system of linear equations: Problem type 1 Completing Gauss-Jordan elimination with a 2x2 matrix Gauss-Jordan elimination with a 2x2 matrix Completing Gauss-Jordan elimination with a 3x3 matrix