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MATH 1314College Algebra

Susan Hord, co-chair; shord@austincc.edu 223-6072Amy Gutierrez, co-chair; aneff@austincc.edu 223-9325

A list of the full committee can be found at http://www.austincc.edu/mthdept5/mman11/cdocs/coursecommittees

FOR THE STUDENT:Text: College Algebra with Modeling and Visualization by Rockswold, 4th edition ISBN# 0-32154230-4Text Bundled with MyMathLab ISBN#0-321-57704-3 hard copy ISBN 0-321-66511-2 Loose leaf.Optional Supplements: Student’s Solution Manual (step-by-step solutions to odd-numbered exercises and chapter review exercises) ISBN#0-321-57702-7, Videotape Series, Digital Video Tutor, MyMathLab Software (CD for Windows) ISBN 0-321-57703-5

▫ You can access the material from the first two weeks online at http://www.austincc.edu/mthdept2/text/ password acc1314

FOR THE INSTRUCTOR: Text: Instructor’s Annotated Edition; Instructor’s Solutions Manual; Instructor’s Testing Manual; TestGen-EQ with QuizMaster-EQ® (Win/Mac), MyMathLab, Addison-Wesley Math Tutor Center (http://www.aw.com/tutorcenter).

MyMathLab, as described below, is a supplement to the Rockswold text and is available online at no cost to students who purchase a new text. Students who purchase used texts may buy access to the programs from Addison Wesley for about $75 from www.mymathlab.com .

MyMathLab is an interactive online course that accompanies the textbook. It contains an online version of the book as well as multimedia learning aids (such as videos and animations) for selected examples and exercises in the text. Students can take tests in MyMathLab that generate a personalized study plan with links to practice exercises for the topics that need more study. Visit www.mymathlab.com for more information.

Instructors can use MyMathLab to assign online homework and tests, track students' results, and create an online community using a variety of course-management tools. Visit www.mymathlab.com for more information. If you choose to set up your own course, you’ll need to give students that unique course number in MyMathLab and tell them to use it instead of the generic ACC course whose access number is given in the standard student handout in this Manual.

Use of MyMathLab for Homework in MATH 1314

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The college algebra course committee sees great advantages in using MyMathLab as a supplement to our course. The committee has a couple of serious concerns, however. We do not feel that the problems contained in the software contain enough conceptual problems of the type offered in the text. In addition, in order to make sure that students can use appropriate mathematical notation, care must be taken to incorporate written work into the course. There are many ways of doing this including supplemental worksheets, quizzes, and homework notebooks. If you should choose to incorporate MML for your course, you should be prepared to describe how you have incorporated other written work in your “How I Taught the Course” essay submitted with your evaluation portfolio.

This course is designed to meet the needs of students in three ways. It fulfills the needs of students required to take College Algebra for their degree, it prepares students for Business Calculus, and it provides algebra and graphing review for students at about the high school Precalculus level. A handout about the Prerequisites for Calculus is included in this section of the Manual. Please give a copy of this handout to all of your students.

TEACHING LEVEL:College Algebra is intended to prepare students for Business Calculus. Some students who are weak in Intermediate Algebra or have just started the course sequence at ACC may be taking the course and planning to take scientific calculus. Some students will be entering a teacher preparation program since College Algebra is now required for that.

The algebra problems and applications in the suggested homework list indicate the levels and types of skills we feel students will need for Business Calculus.

COURSE PURPOSE:The course is designed to teach the functional approach to mathematical relationships that students will need for Business Calculus. This is not the ideal course to fulfill a general mathematics requirement, despite the fact that many colleges list it as an option and some list it as a requirement. Students will generally not know that they may have other options. Students are more likely to succeed in a general mathematics course other than college algebra. Make sure students get information about our other college-level courses (MATH 1332, MATH 1342, MATH 1324) that may satisfy a degree requirement in many situations. (A handout, "Alternatives to College Algebra", about other options is included in this manual at the end of these notes for instructors.) Students are responsible for finding out what alternatives to College Algebra at ACC transfer to their respective colleges.

PREREQUISITE:Instructors need to verify that students have the prerequisite. The prerequisite for College Algebra is MATD 0390, Intermediate Algebra, or current knowledge of high school Algebra II, as measured by an appropriate assessment test. At the current time, there is no universal check of prerequisites before students enroll. The state-generated TSI reports say that students who score 270 or above are qualified to take College Algebra. The THEA, like the SAT I and ACT, is not an algebra placement test. The math department recommends that students take the COMPASS test for a better measure of their algebra skills. Entering students with a COMPASS score of 69 or above can take College Algebra. Entering or current students with a score of 39-68 must take MATD 0390, Intermediate Algebra.

PRETESTS and PREREQUISITE REVIEW ASSIGNMENTS:

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The course committee strongly recommends that you give either a pretest or a review assignment the first week of class, not as a predictor of success but as a wake up call to students. A PREREQUISITE REVIEW page on the prerequisite material is included here. It is not "secure" since it is distributed widely. Feel free to make up your own or use this one. Most of us give the pretest as a homework assignment with the admonition that students pay attention to how much help they need to work the problems as they will need this much help and more when they need to learn the course material. However, we have found no predictive value in pretests. What we have found is that when students are made to take them seriously, it causes the students to focus on what they need to know for the course and it helps them to self-select prerequisite courses when they discover they do not know the prerequisite material. These review assignments can also be very useful in convincing students that they should be able to remember some material on their own, with no class discussion (a boon to instructors). The course committee strongly encourages those students who do not make a reasonable grade on the review assignment and who do not have a current prerequisite background to consider dropping back to Intermediate Algebra.

STUDENTS: Students come into this class with a variety of backgrounds. Some are reviewing the course in preparation for continuing in mathematics. Some had the prerequisite years ago but think they can do it (and some can). Others are fresh from Intermediate Algebra. Some of these Intermediate Algebra students are well prepared while others panic at the increased sophistication of College Algebra. We encourage students who have completed Intermediate Algebra successfully to stay with the course even though they have problems at first. Generally, they can be successful if they set aside the amount of time needed to keep up with the material and if they ask questions as they have difficulties.

ASSESSMENT and EVALUATION: As with all mathematics courses at ACC, you should save copies of your first day handout, all exams and major assignments, and any other supporting materials for evaluation purposes. In addition, every year we will be evaluating the course as regards the Exemplary Educational Objectives (EEOs) and Course Learning Objectives. This evaluation consists of a few test or quiz items that will be provided to you by the course committee during the semester in which we evaluate them. They are to be given on any test or quiz, typically in the last four weeks of the semester. In the past year, problems involving finding and interpreting the long-term behavior of functions in context did not meet the expected standard on the EEO/Course Learning Objective. We wish to emphasize that learning to interpret and use function notation is one of the important objectives of the course. We ask that you do the following:

1. While teaching functions of different types, be sure to emphasize the interpretation of the results as well as the manipulation and evaluation of functional notation.  

2. Assign quiz and test problems that require interpretation of the results of manipulation and evaluation of functional notation. 

It is as important to include a variety of types of interpretations as it is important to include variety in the types of functions and the algebraic complexity of the problems.  

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INTERVENTION:

Insufficient Background: Ideally, students with insufficient background will identify themselves (with help from you) in time to go to adds/drops during the first two class days. For a few days after that (check on dates each semester), your mathematics administrative assistant can move a student to a course at his/her level, if there is space available.

Needing Extra Help: Students who believe that they will need regular extra tutoring are encouraged to register for the Lab Class, MATH 0153. The availability of Lab Classes is fairly limited. Lab Classes are listed in the schedule of classes, or you can give students this information. Walk-in tutoring is available in the Learning/Tutoring Labs at each campus www.austincc.edu/tutor .

Test and Math Anxiety: Links to sites for help with math anxious students are available on the Mathematics Task Force web page.

Panic at the Increased Sophistication from Intermediate Algebra: One of the main ongoing conversations in the Mathematics Task Force is how to minimize this change in level. This problem is not unique to us--all colleges seem to face a similar situation. We do what we can, and that is reflected in our texts and placement advice. But you will still have to deal with quite lot of student frustration at the start of College Algebra. Don't try to convince students that there's not a great change from Intermediate Algebra to College Algebra. There is!! Assure them that this increased sophistication is essential for using mathematics in any substantial way, such as in modeling depreciation of a car or finding the minimum cost of production.

Reality: This course often has a high withdrawal rate. We are not happy with that, but it is true at most other schools as well. Feel free to call one of the chairs of the course committee to discuss any ideas or any concerns you have. It is essential that students who complete the course successfully know how to do problems from all topics in the syllabus.

CALCULATORS: Students do need at least a scientific calculator in order to best use this text. Many of the applications, which are far more realistic than in the past, cannot reasonably be done without a calculator. It is also important that students in College Algebra gain experience using a calculator to do messy arithmetic and to evaluate exponential and logarithmic functions.

GRAPHING CALCULATORS: In addition to the comments below, please refer to the section of this manual that discusses the use of graphing technology in general.

We are still unwilling to require that all students have a graphing calculator; however to fully implement the Rule of 4, we encourage you to check out a set of graphing calculators and overhead graphing calculator to demonstrate and use in class. The administrative assistants on each campus have overhead versions of the TI-84 available for checkout on a semester long basis.

The course committee feels that those students who have graphing calculators should be encouraged to use them correctly. There are continually more sophisticated programs and calculators available, and we feel that students can best be served by giving them guidance in using them to enhance their mathematics education. Students who do not have graphing calculators, but are interested in using them can use the public-domain mathematics software we have available on the computers in the LRS and Learning Lab Computer Centers. There is also shareware for both PCs and for Macs that can be downloaded from the web. Each major campus also has some graphing calculators on reserve in the LRS for student use.

Since we are doing more of our course with calculators, graphing, etc., we feel that it is unreasonable to deny students the use of calculators on tests, with the possible exception of tests on graphing. Some instructors give at least two of the tests with calculator and non-calculator components; other

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instructors try to make tests so that the students consider problems from a graphical, symbolic, numerical and/or verbal perspective. Students who are continuing past College Algebra will use graphing calculators in successive math courses.

It is true that having a graphing calculator and using it appropriately can help students solve equations, etc. However, if students are required to show their work on all problems to receive credit, then they will not be able to rely solely on the calculator. Many of us include the use of graphing calculators in class discussions of various ways to check your solutions -- a discussion well worth having in any mathematics class.

By observing how you operate a graphing calculator, students often learn more quickly how to use their graphing calculators. Many times after you have demonstrated a technique a few times you do not have to do it again. Be aware that Appendix A in the text gives students "just in time" help with keystrokes on the TI-83 and TI-83 Plus graphing calculators. Appendix A is intended not only to help students learn how to use a graphing calculator, but also to save class time for the instructor. Appendix A relieves the instructor from having to frequently remind students how to use their graphing calculators. There are many resources for students to learn how to use a graphing calculator. If you have questions ask one of the co-chairs of the course committee.

One of the most difficult things for students to do with a graphing calculator is to find an appropriate viewing rectangle or window. Sometimes it is important for students to find their own viewing rectangles; other times it can become a major distraction. Finding an appropriate viewing rectangle is essentially the same skill involved in scaling an axis when graphing by hand. Setting a viewing rectangle can lead to a worthwhile discussion about the domains and ranges of functions.

Important Note about Graphing Calculators: Instructors are not allowed to require students to have/purchase a graphing calculator. You may require them for homework problems since they are available for checkout in the library but you cannot have problems on tests that cannot be done without a graphing calculator unless you supply the required calculators. If you have any questions about this please contact one of the co-chairs of the College Algebra committee.

This is a mathematics course, not a graphing calculator course, so be sure the primary focus at all times is on learning mathematical thinking.

HOMEWORK: If you should choose to use MyMathLab for your course please read the statement on the first page of this document. The suggested problems for homework in the manual include even- and odd-numbered problems. If you prefer to assign only odd-numbered problems so that students have the answers to all of the assigned problems, feel free to adapt the homework assignments. Be aware that some of the homework problems in Rockswold may not be as self-explanatory as what we are used to. This is primarily due to the way in which Rockswold incorporates technology. Your students will occasionally need some guidance from you as to how they are supposed to interpret the problems. Some problems in the homework list could involve the use of graphing technology. These are clearly marked in the book. However in many cases, if you prefer NOT to use graphing technology, these problems can be graphed by hand. If this is your first time teaching out of this book it is extremely important that you look over the homework assignments in advance and let your students know what is expected of them. Several of the problems are phrased in such a way that strongly suggests the use of a graphing utility, but can be solved without one. Decide ahead of time what technology requirements you will have of your students, and tailor your homework instructions to that decision.

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TESTING: Your exams are a reflection of what our college algebra syllabus covers and your teaching style. Some of you may include projects (Susan Hord, RVS, has a list of projects that she often includes in College Algebra) and thus have a different percentage for applications on that chapter. The traditional open response, show-the solution test question that is answered individually and without notes is the norm. "Exams must be given in class or the Testing Center. No take-home exams, multiple choice problems and open-notes exams." We discourage the use of multiple choice questions for any substantial portion of a test grade. We do not allow the use of notes or formula sheets for tests. While we encourage alternative forms of assessment (projects, etc) the take-home portion of the final grade including homework and anything else should not exceed 15%. We encourage you to communicate your questions as well as your ideas and suggestions with the college algebra committee.

SUGGESTED TEST GUIDELINES:Approximately: 60% on basics

20% applications problems 20% combining basics to test for depth of understanding

New: We ask that you give a test in class on the last day. This test should be comprehensive in that at least 30-40% of it should cover review topics from tests 1-4 with the remainder consisting of newer material.

Because students who are taking this as the only required math course for their discipline tend to panic on the first test, we recommend that you find some way to help them past this hurdle.

One testing technique used by some teachers successfully is to give no partial credit on the first test, but to let students earn up to half the points they missed by correcting the problems afterward. We do not think this is appropriate to do with all the tests, because it sets up inappropriate expectations, but it may be effective on the first test. Bob Quigley, CYP, and Mary Parker, NRG, both have variations of this scheme and will be glad to share.

COMMENTS ON THE COURSE CONTENT:

Text: COLLEGE ALGEBRA through Modeling and Visualization was chosen because of its use of the rule of four and its flexibility. The unifying concept throughout this text is that of a function. The graphing calculator, modeling, and a variety of real-data applications are integrated throughout this text. The rule of four (verbal, graphical, numerical, symbolic) is used to represent mathematical concepts. This text is graphing calculator flexible, which allows instructors to use the graphing calculator as little or as much as desired. Instructors have the flexibility to place more emphasis on graphical and numerical techniques, rather than symbolic techniques. However, instructors can also emphasize symbolic techniques over graphical and numerical techniques if desired.

Applications problems: Applications are integrated throughout this text in both the discussions and the exercises. Many times applications are used to motivate mathematical concepts and help students learn how mathematics is used in our society. It is important to present some applications in class. Students learn by listening and watching how the instructor solves problems. Afterwards they are more comfortable trying to solve application exercises on their own. It is difficult for students to master solving application and modeling exercises if they are not discussed in class. However, applications do not have to be done at the expense of skill-building exercises. You will find that there is time to work examples involving mathematical skills too.

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It is not necessary to assign a large number of applications each day, but it is important to assign at least a couple of applications as part of most assignments. Over time students become more proficient at solving these problems. Select applications that interest you or your students. If you are interested in the application, you will create interest in your students. Strike your own balance between skill-building exercises and exercises that involve applications, modeling, and graphical interpretation. You are an expert and in the best position to judge your students' needs. The rule of four: The rule of four is used throughout this text. It is important in Chapter 1 that students learn what is meant by verbal, graphical, numerical, and symbolic representations of a function. These words will be used in the directions to the homework exercises throughout the rest of the book. Graphical, numerical, and symbolic methods can be used to solve equations and inequalities. (Of these three methods, numerical representations are emphasized the least in this text.) The solution of equations begins in Chapter 2 and continues throughout the text. A basic graphical method for solving equations is the intersection-of-graphs method. This graphical method is explained in Section 2.2 and used throughout the text. The intersection-of- graphs method is quite intuitive for students when solving equations and inequalities involving real applications. There are many examples and exercises that require students to use symbolic techniques to solve equations. Note: This text does not start by reviewing intermediate algebra. (If you would like to start by reviewing prerequisite material, refer to Chapter R.) Chapter 1 is intended to generate student interest and give students a different look at mathematics from the start. Instead of initially concentrating on symbolic manipulation skills from intermediate algebra that students may be weak on, students are introduced to some essential mathematical concepts such as functions and graphs. The motivation behind mathematics is discussed. Skill building is emphasized more after Chapter 1. This chapter is designed to help change students’ attitudes toward mathematics.

If they have them, students should become familiar with their graphing calculators in Chapter 1. If possible, take time to answer questions about graphing calculators. When the questions become repetitive, refer them to Appendix A. You may not know all the answers-that is normal. With the rapid growth in technology, no one can answer every question related to graphing calculators. If you are learning the graphing calculator for the first time, concentrate only on the essential features. The number of calculator skills required in this text is minimal. At the end of the first chapter, students should be able to set a viewing rectangle, graph a function, evaluate mathematical expressions, and make a table, scatterplot or line graph. You may want to have one or more brief quizzes to make sure students are learning all the important concepts in Chapter 1. Changes in the 4th edition ,adoptied fall 2009 Chapter 1 has been expanded from four sections to five sections. Increasing and decreasing

functions, average rate of change, and the difference quotients are discussed in Section 1.5. Circles now appear in Section 1.2 instead of Chapter R.

In Chapter 2, piecewise-linear functions are now discussed earlier in Section 2.1 Complex numbers have been moved to Chapter 3 in a new section. Chapter 4 has been expanded and reorganized from seven to eight sections, making it easier to

cover one section per class. Division of polynomials and real zeros of polynomial functions are now in separate sections.

In Chapter 5 the change of base formula is now presented in Section 5.4. The first two sections in Chapter 6 have been reorganized so that systems of equations are

discussed in Section 6.1. Substitution and elimination are both presented in Section 6.1.

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Changes in the College Algebra curriculum were made by the committee. The changes are as follows: (1) Reduce the time spent reviewing division of polynomials. Since the Intermediate Algebra committee is recommending that this topic be covered in Matd 0390, students should be reasonably proficient at this skill. We also recommend that division of polynomials be included on the pre-test for college algebra.(2) Limit the scope of what we cover concerning graphs of rational functions. Students should be able to sketch the graph of y = 1/xn (where n is a positive integer) and rigid transformations of these types of functions. Students should also be required to state the equations of the vertical and horizontal asymptotes of these functions. The graphing of more general types of rational functions will not be required. Since graphing rational functions is covered extensively in both Pre-Calculus and Business Calculus, students who continue in the mathematics curriculum will be exposed to a more advanced treatment of this topic.(3) Some instructors argue that requiring students to compose functions represented graphically or numerically is a topic for Pre-Calculus, not College Algebra. However, the committee as a whole feels that this topic provides the student with an insight into the concept of function composition not usually gleaned from the mere algebraic derivation of a formula. So we propose that students learn to evaluate (fog)(x) at a given value of x, given either the graphs or numerical tables of the two functions. The student is not expected to graph (fog), given the graphs of f and g. Of course, this does not preclude the requirement that the student find the symbolic representation of (fog)(x). That topic is still among the objectives.(4) When solving systems of linear equations, require Gaussian elimination with back substitution instead of Gauss-Jordan elimination. Systems should have a unique solution and students should be required to reduce the augmented matrix to row echelon form. Reducing the system to reduced row echelon form, or solving systems having infinitely many solutions, will be optional.(5) When solving a system of linear equations via matrix inversion, students should not have to invert the matrix by hand (unless the matrix is a 2 x 2). They can either invert the matrix using technology, or the instructor can give them the inverse of the coefficient matrix. They merely need to understand the concept of the matrix inversion method.

Section Comments

Chapter 11.1 Numbers, Data, and Problem Solving

Try to use a real-world example that has some personal relevance for students to get them interested in functions on the first day. It will help show students the importance of graphic, numeric, and symbolic representations that are used so much in this book.Chapter 1 in this book is designed to help improve students’ attitudes toward mathematics. Motivate the math by looking at ideas several ways and try not to focus on the symbolic manipulation from other courses that students may be weak on. The essential skill building comes later.

1.2 Visualization and Graphing Data

If you are using graphing calculators this is a good time to have students use them to make scatter plots and to learn the basics of graphing windows. If you aren't using graphing calculators watch out for the exercises that ask for specific viewing rectangles. This section includes the distance and midpoint formulas.

1.3 Functions and Their Representations

This section covers the formal definition of a function along with the domain and range of a function. Expect your students to struggle with these ideas but by this time in the course they will have an intuitive sense of what a function is from prior discussions if you have laid the groundwork in the previous two sections.

1.4 Types of Be sure to emphasize graphic, numeric, and symbolic approaches. Most often,

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Section CommentsFunctions students with different learning styles will latch on to different approaches so it

is worth your time to make the effort.1.5 Functions and Their and Their Rates of Change

Students should be familiar with slope and slope as a rate of change but will find calculating the average rate of change for nonlinear functions symbolically challenging.

Chapter 22.1 Linear Functions and Models

The idea of exact and approximate models is usually new to students. It is worthwhile to bring in data and have students create functions to model the data either as a class or in groups. You can discuss the pros and cons of one model over another once they're created. Students can often be guided to come up with functions that are almost as good a fit to the data as the functions found using regression tools. Use the exercises with small data sets. Students can manage these and they help reinforce the importance of numeric representations. Most students will need to be able to deal with data sets after this course both in real-life and at work. Linear regression is optional

2.2 Equations of Lines

This section should be review for all students. It provides a good opportunity to tie all the loose ends together and to get students’ knowledge of linear functions to the College Algebra level. Watch out for the point-slope equation in the form

, most students have usually seen this equation but not in this form. The form is very useful (especially for functions where the y-intercept is not meaningful and for piecewise-defined functions) and can be easily related to the slope-intercept form of lines and the vertex form of quadratic functions.Direct variation is included in this section and ties in well with slope as a rate of change. After this section, students should have a good grasp of what it means for a function to be linear.

2.3 Linear Equations

This section includes the intersection-of-graphs method. This approach works very well if you are using graphing calculators. You'll need to have handouts or refer students to the appendix. It is nice to emphasize the fact that the y coordinate of the solution point is the same value you get on both sides of the equation when you check the equation by hand. Doing this will help make the connection between the graphic and symbolic approaches.

2.4 Linear Inequalities

Use the graphs of functions to solve inequalities. It is amazing how hard students find this. It is a very useful skill for interpreting graphs in every day life, however, and is extremely important in the next section where the techniques is used to simplify the process of solving absolute value inequalities and equations.

2.5 Absolute Value Equations and Inequalities

For most students, this is the first really hard section in the book. Students will have an intuition about step functions (such as long-distance phone rates) but will find it difficult to grasp how to graph one using the formal definition. Do as many examples as possible. Do enough examples of absolute value function graphs so that students will have an intuitive understanding of why there are two intervals in the solution of absolute value inequalities involving greater than. Note that absolute value inequalities are solved by finding the boundary values

Chapter 33.1 Quadratic Functions and

It would be useful to bring in nonlinear data that is interesting to your students, to draw a scatterplot of the data, and to discuss why a linear model does not fit.

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Section CommentsModels You can find the rates of change between several data points to show that the

rates do not stay constant. The vertex form occurs here. Some instructors have students find values for a, h, and k so that the vertex form fits data that they bring to class. By using the graphing calculator, students can see what changing the values does to the graph, foreshadowing most of the work on transformations that occurs later in the chapter. By asking questions about the graphs, we motivate the discussion on solving quadratic equations in the next section. At this point, students will be able to solve by the intersection-of-graphs method. This leads easily into a discussion of solving quadratic equations.

3.2 Quadratic Equations and Problem Solving

There is less material on factoring here than in traditional books. Students should already be familiar with the quadratic formula. Many students are so used to symbolic manipulation that you might have to remind them to read the directions of the problems that say to solve the equation graphically. You'll have to show students how to use the zero finder at this point if you are using graphing calculators. Make sure students can relate the graph to the equation since this skill will be emphasized throughout the rest of the book.

3.3 Complex Numbers

Not much to say about this section!

3.4 Quadratic Inequalities

If you've laid the foundation properly in the past few sections, this section will not be too difficult. Spend some time relating the graphs of quadratic functions to the quadratic inequality. Try to encourage students to solve every problem both graphically and symbolically to help reinforce the relationship between representations. Watch out for the "hard" inequalities - those of the form a<f(x)<b. These are trivial when done using the intersect function of the calculator but can be difficult when done by hand.

3.5 Transformations of Graphs

Students will find some of this easy if you present several functions (e.g. x^2, x^2+1, x^2+2, etc.) and let them try to deduce how the constant is changing the graph. Students have a tendency to read graphs from left to right rather than up and down consequently they often struggle with vertical stretch (expansion) and vertical shrink (contraction). They will find sketching transformations from the graph more difficult; just make sure they get lots of practice. Don't forget to emphasize numeric representations since they'll help many students who are not as visually oriented to get the point here. The extra practice here will really help them when they study combinations of functions numerically later on.

Chapter 44.1 More Nonlinear Functions and Their Graphs

If you are not using graphing calculators you can still have students find extrema from a given graph.Symmetry is easy for students to see graphically and numerically but they often find the symbolic test difficult – you might ask them to support their work with a graph. There are three different uses of the words odd and even in this chapter - even/odd degree polynomials, even/odd functions, and even/odd multiplicity zeros. It is worthwhile to ask students to use the correct language when discussing these from the beginning. Try to remind them that they are discussing an odd degree polynomial or an odd function and that just using the word odd in any given situation might add to their confusion.

4.2 Polynomial Functions and Models

Help students get a solid grasp of what the graphs of polynomials look like for different degrees and leading coefficients. There is a huge payoff later on when they are solving polynomial inequalities. When the long-term behavior is combined with the information about multiplicity of zero from 4.3, students will be able to sketch (or visualize) the graph to solve an inequality.

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Section Comments4.3 Division of Polynomials

This section has been split off from the real zeros section of the 3rd edition.

4.4 Real Zeros of Polynomial Functions

This section has been shortened quite a bit. It will help students if you can do as many examples as possible. It may be useful to completely factor polynomials and to then multiply it out to get the original polynomial. The course committee considers the material on the rational zeros test in this section as optional. Faculty who use graphing calculators can omit this since they can have students find the rational zeros using the graph.

4.5 The Fundamental Theorem of Algebra

It is very useful to use the graphing calculator to check work when performing operations on complex numbers. Students like to see that it is possible to do this; it makes the numbers seem more concrete and less abstract.This section ties all the ideas about factoring and graphs together. It is useful to begin the factoring process by drawing a graph, identifying any rational zeros, and then factoring using synthetic division. Once the polynomial has been reduced by one degree you can continue the process either using the graph or not.Students are often amazed that you can perform synthetic division with complex numbers. This is not too difficult and it is useful to do this since it helps remind students that if a + bi is a zero then its conjugate is also and reinforces operations with complex numbers.

4.6 Rational Functions and Models

Most of this material used to be at the beginning of our previous text. Students struggled and found it very hard. At this point in this text, you’ve related these functions to their graphs and this material seems much easier.You can use numerical representations to help students make sense of horizontal and vertical asymptotes. Choose appropriate values of x and an increment for the table then create a table. Students will be able to see that the values of y are approaching some number or they are growing without bound.

4.7 More Equations and Inequalities

Once again, relate the inequalities to the graphs of the functions.

4.8 Radical Equations and Power

This is where the rules of exponents are reviewed, radicals and rational exponents are covered, and radical equations are solved. Using the approach in this book, students don’t usually find any of this difficult. The applications are interesting especially the ones involving allometric relations.

Chapter 55.1 Combining Functions

It helps when covering this material to start from numeric representations. If you’ve used them earlier, students will pick right up on the idea that (f + g)(2)=f(2)+g(2). Then use graphs to work the same problem, saving the symbolic representation for last. For most students, this is the representation that makes the least sense in this situation.

5.2 Inverse Functions and Their Representations

Introduces one-to-one functions and their inverse functions. This is a good place to start from the verbal representation of a function. If we have a verbal description of some process, how do we describe the inverse of that process using words?If students understand what a function is, it is very easy to use the numeric representation to determine if a function has an inverse or not.

5.3 Exponential Functions and Models

It is worthwhile to explain the multiplicative nature of exponential functions and how this differs from the additive nature of linear functions.Some instructors like to focus on compound interest problems when covering this section. As we look at what happens to an amount as we compound more and more often, students may begin to wonder if the money will grow without bound or if there is a limiting value beyond which it will not grow. This leads naturally into a discussion of the number e.

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Section CommentsIf we ask a question such as “how long would it take $10,000 to grow to $25,000 at 10% compounded annually?” The resulting equation cannot be solved analytically by any of the methods developed in this course so far. This leads us into a discussion of logarithms. (Note: We can solve this equation by the intersection-of-graphs method)

5.4 Logarithmic Functions and Models

This approach to exponential and logarithmic functions might be helpful to students. For example, he makes a connection between something they are familiar with (we hope), the square root function, and the “new” logarithmic function. He uses this to explain when one would use a calculator and when it would be easy to do without one. He also connects the two domains (no negative numbers) in such a way that perhaps students would have a way to remember the information. It may be useful to have students spend quite a bit of time translating from exponential form to logarithmic form and vise versa. Once they truly understand that logarithms are exponents they find the rest of this chapter fairly straight forward. The change-of-base formula is in here but is derived in 5.5.

5.5 Properties of Logarithms

He gives good examples of how to deal with the inverse properties of logs and exponents, including how to “exponentiate” and what that means. He has useful examples of how to model data with logarithms as well as nice descriptions of log properties and why they are true! Emphasize the fact that logarithms are exponents. The basic rules of logarithms follow directly from one of the properties of exponents.

5.6 Exponential and Logarithmic Equations

Watch out for students who think that the equation log(x) = log(y) is solved by dividing both sides of the equation by log! Remind students that log is the name of a function.

Chapter 66.1 Functions and Systems of Equations in Two Variables

Since students learn systems of linear equations in two variables in both Elementary and Intermediate Algebra courses, it may be a good idea for instructors to concentrate on functions, nonlinear systems and variation. A brief review of substitution method with a linear system may be enough to refresh the students’ memory. This material tends to be very easy for students. It is very natural to solve systems by graphing if you solved equations by the intersection-of-graphs method earlier. Traffic Control, problem numbers 81 and 82 are interesting. They have easy to solve equations/inequalities and some thinking is involved.

6.3 Systems of Linear Equations in Three Variables

This section has the applications and systems with three variables..

6.4 Solutions to Linear Systems Using Matrices

Covers matrices, matrix operations and properties. Contains an interesting discussion of how matrices work in digital photography.

6.5 Properties and Applications of Matrices

Covers matrices, matrix operations and properties. Contains an interesting discussion of how matrices work in digital photography.

6.6 Inverses of Matrices/6.7 Determinants

Which section you choose will depend upon your approach. Some of us who use graphing calculators want students to know how to solve systems of equations using inverses. This seems like a logical extension of the study of the structure of mathematical systems. Some of us choose a more symbolic approach to the course and wish to introduce students to finding zeros with the Rational Zeros Theorem and using determinants to solve systems. (Cramer’s rule is optional)

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FINAL NOTE:All of us teaching this course find it challenging because many students are required to take this course and have a great deal of difficulty with the material. Please feel free to call anyone on the course committee with questions or suggestions. We have some teaching tips and are available for support. All instructors do need to finish the syllabus.

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Austin Community College Department of Mathematics**Alternatives to College Algebra

orHints to Help the Beginning Student Distinguish between

First-Level College-Credit Mathematics Courses

College Mathematics (ACC's MATH 1332) (UT’s M302) **

Goal: To broaden the students' repertoire of mathematical problem-solving techniques past algebraic techniques.

This course covers a variety of mathematical topics such as set theory, logic, and probability. Students learn basic college-level techniques in a variety of mathematical areas and learn what types of problems can be solved with each technique. The algebra prerequisite for the course reflects the need for the students to have an understanding of the conceptual aspects of mathematics rather than a need for them to remember the details of how to solve all the types of algebra problems encountered in high school algebra. Students with weaker algebraic manipulative skills should still be able to complete this course successfully.

Elementary Statistics (ACC's MATH 1342) (UT's M316 or UT's STA309) **

Goal: To teach the student to do basic statistical analyses and to enable the student to be an "intelligent user" of standard statistical arguments.

The focus of this course is on using conceptual mathematical skills to solve a particular type of applications problems. Algebraic manipulation is not a major part of this course; however, students will be required to use formulas extensively. (A "pretest" indicating the level of skill expected is available from the mathematics department.) Enough explanation will be given that students who once learned algebra, but have forgotten many of the details, will be able to handle the algebraic aspects of the course easily.

Math for Business & Economics (ACC's MATH 1324) (UT's M303D,Texas State’s M 1319) **

Goal: To teach the student some applications of algebra to business and economics problems and to provide a minimal level of algebraic foundation for the first semester of business calculus.

The focus of this course is on the applications problems, with algebra skills from the first two years of high school algebra used as necessary. Students who are not able to demonstrate all the skills from high school Algebra II just before beginning the course will probably find this course very difficult.

College Algebra (ACC's MATH 1314) (UT's M301, Texas State's M 1315) **

Goal: To provide the student with the algebraic foundation for calculus.The student is expected to be currently confident and skilled in all topics from the first two

years of high school algebra or from MATD 0390, Intermediate Algebra, and the new material will build on that foundation with little or no review. Students who are not able to demonstrate all the skills from high school Algebra II just before the beginning of the course will probably find this course very difficult.

UT = University of Texas at Austin *Additional information about ACC's mathematics curriculum and faculty is available on the Internet at http://www.austincc.edu/math/

** It is the student's responsibility to determine if these courses are applicable to a specific degree plan at ACC or at another institution.

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Prerequisites for Calculus

There are two calculus sequences at ACC (and at most colleges) -- Business Calculus and Calculus. The prerequisite sequence is different for these. Depending on background, students may start the prerequisite sequence at different places

Intermediate Algebra (MATD 0390) Intermediate Algebra (MATD 0390)

College Algebra**(MATH 1314)

Math for Bus &

Eco(MATH 1324)

College Algebra

(MATH 1314)*Trigonometry (MATH 1316)

Business Calculus I (MATH 1425)Precalculus (MATH 2412)

Business Calculus II (MATH 1426)

Calculus I (MATH 2413)

Calculus II (MATH 2414)

Calculus III (MATH 2415)

Where to start: The only way that students may skip courses in a sequence is to begin higher in the sequence, based on current knowledge of material from high school courses. 1. A student who needs a review of high school Algebra II will start in

Intermediate Algebra (or below.) 2. A student who completed high school Algebra II, but no higher, and whose

assessment test score indicates that he/she remembers that algebra, will start in College Algebra or Math for Business & Economics. A substantially higher assessment test score enables the student to start in Trigonometry.

3. A student who completed some precalculus, elementary analysis, or trigonometry in high school, and whose assessment test score indicates that he/she remembers algebra, is eligible to start higher in the sequence than College Algebra. Check the catalog or the math web page.***

* The material in the Trigonometry course requires that students are quite adept with the skills from high school Algebra II (Intermediate Algebra). Some students will achieve that level of skill in the College Algebra course if their placement score is high enough, while others need an additional semester of work on algebra that is done in two courses, Intermediate Algebra and College Algebra.

** Some students who are very successful in College Algebra are tempted to skip either Trigonometry or Precalculus and enroll in Calculus I. That is not acceptable. Trigonometry topics are essential to success in Calculus, and while it is true that the topic list for Precalculus has only a few additions from the topic list for College Algebra, the level of sophistication of the presentation

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and the problems on all topics is greater in Precalculus. That increased sophistication is necessary for an adequate background for the Calculus sequence. ***

Notes about the Business sequence: Texas State University requires Math for Business and Economics and Business Calculus I. Students who will attend the UT College of Business must complete the entire Business Calculus sequence before transferring. For more information, including requirements for UT economics students, see http://www.austincc.edu/mthdept2/notes/1425.html

*** For additional information, including prerequisite review sheets for most courses, see http://www.austincc.edu/math/ Suggested Homework: College Algebra through Modeling and Visualization

Section - Problems1.1: 9, 19, 23, 25, 39, 43, 53, 57, 63, 65, 79, 81, 85, 951.2: 21, 25, 43, 49, 55, 61, 63, 65, 69, 71, 73, 77, 85, 87, 91, 93*1.3: 1, 3, 5, 7, 15, 19, 23, 25, 27, 32, 37, 43, 45, 47, 50*, 61, 67, 75, 77, 79, 81, 83, 87, 89, 91, 93, 95, 971.4: 1, 9, 17, 19, 21, 27, 29, 31, 35, 37, 43, 531.5: 1, 5, 9, 13, 17, 21, 25, 29, 31, 35, 37, 43*, 47, 55, 61, 73, 77

2.1: 1, 3, 5, 9, 11, 15, 19, 25, 33, 37, 38, 39, 40, 41, 49, 53, 63, 67, 69, 73, 772.2: 5, 7, 9, 11, 15, 19, 31, 39, 41, 43, 47, 49, 51, 65, 71, 81, 87, 101, 103 2.3: 5, 13, 19, 21, 35, 47, 57, 61, 75, 79, 86, 87, 93, 101, 103, 105, 1072.4: 1, 3, 5, 7, 9, 11, 13, 17, 23, 27, 37, 43, 47, 59, 63, 83, 87, 892.5: 1, 3, 7, 9, 13, 15, 16, 17, 18, 28, 35, 53, 61, 65, 71, 73, 75

3.1: 1, 3, 5, 7, 9, 11, 13, 17, 19, 25, 35, 39, 47, 51, 55, 59, 61, 63, 79, 81, 83, 85, 86, 87, 883.2: 1, 9, 15, 19, 25, 33, 39, 41, 45, 49, 53, 61, 63, 65, 68, 71, 83, 85, 87, 89, 93, 104, 1153.3: 1, 3, 5, 7, 9, 11, 23, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 57, 61, 62, 63, 66, 753.4: 1, 3, 5, 7, 9, 11, 13, 21, 29, 31, 33, 43, 45, 47, 49, 51, 55, 61, 653.5 1, 3, 5, 7, 9, 11, 13, 21, 29, 31, 33, 37, 45, 47, 49, 51, 55, 65, 75, 79, 89, 93, 95

4.1: 1, 3, 5, 7, 9, 11, 15, 23, 25, 31, 35, 47, 53, 65, 69, 73, 81, 85, 91, 95*4.2: 1, 3, 5, 8, 9, 15, 16, 25, 31, 35, 41, 45, 55, 67, 75, 77, 854.3: 7, 9, 13, 15, 21, 29, 32, 37, 39, 41, 43, 46, 47, 49, 514.4 1, 3, 7, 11, 13, 17, 21, (27, 29, 30 if using graphing calculator option) , 31, 35, 39, 43, 47, 55, (57, 59, 61 if non GC option) 71, 79, 87, 95, 1104.5: 1, 3, 5, 11, 15, 17, 21, 25, 29, 39, 414.6: 1, 7, 10, 15, 21, 24, 31, 33-36, 37, 45, 47, 49, 51, 53, 81, 85, 93, 964.7: 3, 5, 9, 11, 13, 17, 23, 25, 28, 29, 37, 40, 43, 47, 49, 57, 65, 71, 75, 84, 91, 93, 95, 103, 105, 108 4.8: 1, 5, 9, 13, 17, 18, 23, 27, 31, 33, 35, 45, 46, 53, 57, 63, 65, 67, 77, 83, 85, 87

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5.1: 1, 3, 5, 7, 9, 12, 17, 23, 33, 35, 37, 39, 41, 53, 57, 61, 65, 72, 73, 77, 85, 975.2: 1, 3, 5, 7, 13, 15, 19, 23, 24, 29, 39, 41, 45, 49, 55, 56, 63, 71, 77, 81, 93, 95, 101, 105, 107, 121, 123, 1295.3: 1, 3, 5, 7, 9, 11, 13, 16, 17, 19, 21, 25, 27, 29, 37, 39, 41, 45, 47, 53, 55, 59, 61, 65, 69, 71, 72, 87, 925.4: 1, 3, 5, 7, 11, 17, 19, 21, 23, 31, 33, 35, 37, 45, 49, 53, 57, 61, 69, 73, 75, 79, 83, 83, 99, 101, 103, 105, 107, 117, 119, 121, 123, 1255.5: 1, 5, 7, 11 13, 15, 23, 25, 26, 31, 32, 43, 45, 47, 52, 53, 65, 67, 75, 83, 905.6: 1, 3, 5, 9, 14, 17, 21, 27, 33, 37, 45, 49, 53, 55, 61, 69*, 72, 73, 75, 79, 83, 86, 93, 95, 101

6.1: 1, 3, 11, 21, 25, 29, 31, 32, 35, 37, 38, 43, 47, 51, 53, 58, 67, 71, 76, 81, 89, 113, 116, 122, 131, 133, 139, 1416.3: 1, 3, 5, 7, 9, 13, 17, 23, 27, 31, 33, 35, 37, 39 6.4: 1, 3, 5, 7, 9, 10, 11, 17, 19, 21, 23, 25, 27, 33, 39, 51, 57, 60,73, 75, 836.5: 1, 5, 10, 11, 13, 16, 21, 25, [27,29opt], 31, 34, 35, 37, 39, 41, 44, 55*, 65, 676.6: Matrix Inverse, Optional6.7: Determinants, OptionalYou are to choose one of two options: 1)Rational Zeros in 4.4 and 6.7: Determinants

or 2) Finding Zeros of Polynomial graphically in 4.4 and 6.6: Matrix Inverses

First Day Handout for StudentsMATH 1314, College Algebra Semester/Session

Section Number & synonym Campus, Room #, Time of day

Instructor's Name: Office Hours:Phone Number: Information on how conferencese-mail: outside of office hours can be scheduled.Web site, if applicable

TEXT: College Algebra with Modeling and Visualization by Gary Rockswold, 4th ed. ISBN# 0-32154230-4Text bundled with MyMathLab, 0-32-157704-3 Hard copy ISBN 0-32-166511-2 Loose LeafYou can access the material from the first two weeks online at http://www.austincc.edu/mthdept2/text/ password acc1314

MyMathLab is an optional interactive online course that accompanies the text. You may purchase access to MyMathLab online from AddisonWesley for $75.00 at: www.mymathlab.com/buying.htmlMyMathLab includes:

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▫ Online access to all pages of the textbook▫ Multimedia learning aids (videos & animations) for select examples and

exercises in the text▫ Practice tests and quizzes linked to sections of the textbook▫ Personalized study guide based on performance on practice tests and

quizzesVisit www.mymathlab.com for more information. To use MyMathLab, you'll need:

▫ Course ID*:acc34248▫ Student access number: provided with purchase of MyMathLab access.

* If your instructor has set up a different course ID for your class, he or she will let you know. If so, use the course ID provided by your instructor.

Videotapes: There is a set of video DVDs keyed to the text by section in the Learning Resource Center of each campus. Students who miss class or who need extra review may find these useful. Also, with the bundled text with MyMathLab is a set of video tutorials.

COURSE DESCRIPTIONMATH 1314 COLLEGE ALGEBRA (3-3-0). A course designed for students majoring in business, mathematics, science, engineering, or certain engineering-related technical fields. Content includes the rational, real, and complex number systems; the study of functions including polynomial, rational, exponential, and logarithmic functions and related equations; inequalities; and systems of linear equations and determinants. Prerequisites: MATD 0390 or satisfactory score on the ACC Assessment Test. (MTH 1743)

Course Prerequisite: Intermediate Algebra (MATD 0390) or current knowledge of high school algebra as measured by the Assessment Test. Students who have a great deal of difficulty with the Pretest and/or review and have not had Intermediate Algebra or its equivalent recently should consider withdrawing and taking Intermediate Algebra.

Calculator: Students need either a scientific or business calculator. (Has log or ln key.) If a student cannot purchase one, calculators are available from the LRS. Graphing calculators are not required, but you will use graphing technology in most sections of the book. Graphing calculators are also available in the LRS. Most ACC faculty are familiar with the TI family of graphing calculators. Hence, TI calculators are highly recommended for student use.  Other calculator brands can also be used.  Your instructor will determine the extent of calculator use in your class section.

INSTRUCTIONAL METHODOLOGYThis course is taught in the classroom primarily as a lecture/discussion course. 

COURSE RATIONALEThis course is designed to teach students the functional approach to mathematical relationships that they will need for a business calculus sequence.

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Other courses, such as MATH 1332, or MATH 1342 are more appropriate to meet a general mathematics requirement. Check with your degree plan as to what math course your college requires.

 COMMON COURSE OBJECTIVESCommon course objectives are attached. They can also be found at:

http://www.austincc.edu/mthdept2/tfcourses/obj1314.htm Note: include these in your syllabus.

Learning OutcomesUpon successful completion of this course, students will be able to do at least 70% of the following:

1. Demonstrate understanding and knowledge of properties of functions, which include domain and range, operations, compositions and inverses.

2. Recognize and apply polynomial, rational, exponential, logarithmic functions and solve related equations.

3. Apply graphical, symbolic and numeric techniques.

4. Evaluate all roots of higher degree, polynomial and rational functions.

5. Recognize, solve and apply systems of linear equations using matrices. 

COURSE EVALUATION/GRADING SCHEMEGrading criteria must be clearly explained in the syllabus. The criteria should specify the number of exams and other graded material (homework, assignments, projects, etc.). Instructors should discuss the format and administration of exams. Applications (recognizing and using) are an important part of college algebra. Tests will include application/word problems, possibly 20%. Guidelines for other graded materials, such as homework or projects, should also be included in the syllabus.

COURSE POLICIES Include Your Missed Exam Policy statementInclude your Homework Policy, including your policy about late workInclude your statement on Class Participation expectationsReinstatement policy (if applicable)

 ACC Policies: ACC has a series of policies that the syllabus must contain. These policies include statements on

Attendance, * Withdrawal, * Incomplete Grades, * Scholastic Dishonesty, Students Rights and Responsibilities, * Safety, * Use of ACC Email, Academic Freedom, * Testing Center, * Student Services, * Students with

DisabilitiesYour First Day Handout must have a statement for each of these headings.

Insert the full text of those statements, not just a link, in your First Day Handout.To find the policies Go to www.austincc.edu/mthdept5/mman12/statements.html

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These are the ACC recommended statements, except for the Incomplete Grade statement. The included Incomplete Grade statement is a combination of the ACC recommended statement and the Math Dept recommended statement which we have used for many years.

Attendance Policy (if no attendance policy, students must be told that)The recommended attendance policy follows. Instructors who have a different policy are required to state it. Attendance is required in this course. Students who miss more than 4 classes may be withdrawn.  Withdrawal Policy (include the withdrawal deadline for the semester) It is the student's responsibility to initiate all withdrawals in this course. The instructor may withdraw students for excessive absences (4) but makes no commitment to do this for the student. After the withdrawal date, neither the student nor the instructor may initiate a withdrawal. Incomplete Grade PolicyIncomplete grades (I) will be given only in very rare circumstances. Generally, to receive a grade of "I", a student must have taken all examinations, be passing, and after the last date to withdraw, have a personal tragedy occur which prevents course completion. 

Course-Specific Support ServicesSections of MATH 0153(1-0-2) are sometimes offered. This lab class is designed for students currently registered in COLLEGE Algebra, MATH 1314. It offers individualized and group setting to provide additional practice and explanation. This course is not for college-level credit. Repeatable up to two credit hours. Students should check the course schedule for possible offerings of the lab class.ACC main campuses have Learning Labs, which offer free first-come, first-serve tutoring in mathematics courses. The locations, contact information and hours of availability of the Learning Labs are posted at: http://www.austincc.edu/tutor  

Include the following policies that are listed at beginning of Math Manual. Go to www.austincc.edu/mthdept5/mman11/statements.html

Statement on Scholastic Dishonesty

Statement on Scholastic Dishonesty Penalty

Statement on Student Discipline

Statement on Students with Disabilities

Statement on Academic Freedom

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TESTING CENTER POLICY: ACC Testing Center policies can be found at:http://www.austincc.edu/testctr/

STUDENT SERVICES: The web address for student services is: http://www.austincc.edu/support The ACC student handbook can be found at: http://www.austincc.edu/handbook

Suggested timelines/breaks for test:Calendar for 16 week session:Week 1: 1.1, 1.2, 1.3Week 2: 1.4, 1.5Week 3: 2.1, 2.2, 2.3Week 4: 2.4 – 2.5 Test 1 (Ch 1, 2.1-2.4)Week 5: 3.1, 3.2, 3.3Week 6: 3.3, 3.4, 3.5Week 7: 4.1, 4.2Week 8: 4.3, 4.4, 4.5 Test 2 (2.5, Ch 3, 4.1, 4.2)

Week 9: 4.6, 4.7, 4.8Week 10: 5.1, 5.2Week 11: 5.3, 5.4Week 12: 5.5, 5.6 Test 3 (4.3-5.4)Week 13: 6.1, 6.3Week 14: 6.4, 6.5Week 15: 6.6 or 6.7 (choose one), Test 4 (5.5-6.?)Week 16: Review, Final Exam

Calendar for 12 week session:Week 1: 1.1, 1.2, 1.3, 1.4Week 2: 1.5, 2.1-2.3Week 3: 2.4 – 2.5, Test 1Week 4: 3.1-3.4Week 5: 3.5, 4.1,4.2Week 6: 4.3, 4.4, Test 2

Week 7: 4.5-4.8, 5.1Week 8: 5.2-5.5Week 9: 5.6, Test 3Week 10: 6.1,6.3Week 11: 6.4, 6.5, 6.6 or 6.7 (choose one)Week 12: Test 4, Review, Final Exam

Calendar for 8 week session:Week 1: 1.1, 1.2, 1.3, 1.4, 1.5

Week 5: Test 2, 4.6 – 5.1

Week 2: 2.1 - 2.5 Week 6: 5.2 - 5.5Week 3: Test 1, 3.1 - 3.5 Week 7: 5.6, Test 3, 6.1-6.5Week 4: 4.1-4.5 Week 8: 6.6 or 6.7 (choose one), Test 4, Review, Final Exam

Calendar for 6-week sessionWeek 1 Introduction, Sections 1.1 –

2.3Week 4 Sections 4.7 – 5.4 Test 3

Week 2 Sections 2.4 – 3.5 Test 1 Week 5 Sections 5.5 – 6.5 Test 4Week 3 Sections 4.1 – 4.6 Test 2 Week 6 Sections 6.6 or 6.7 (choose

one), Review, Final

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Calendar for 11- Week SessionWeek 1: 1.1, 1.2, R.2, 1.3Week 2: 1.4, 2.1- 2.3Week 3: 2.4, 2.5, Test 1Week 4: 3.1 - 3.4Week 5: 4.1 - 4.3Week 6: 4.4, Test 2, 4.5, 4.6

Week 7: 4.7, 4,8, 5.1Week 8: 5.2 - 5.5Week 9: 5.6, Test 3, 6.1, 6.3Week 10: 6.4, 6.5, 6.6 or 6.7 (choose one)Week 11: Test 4, Review, Final Exam

**Additional information about ACC's mathematics curriculum and faculty is available on the Internet at http://www.austincc.edu/math/