NOTE: All assignments are from your textbook (PAN) unless otherwise indicated.

*Exercise Set Handouts are required materials for the course.

Text: Elementary and Intermediate Algebra for College Students, Allen Angel,

ISBN 0-13-013980-7

Optional Supplements:

Shrink-Wrapped Bundle with Student’s Text, Solutions Manual, and

MathPro, ISBN: 0-13-034402-8.

Student’s Solutions Manual, ISBN 0-13-085514-6

Student Study Guide, ISBN 0-13-085513-8

Instructor’s Edition, ISBN 0-13-013991-2

Instructor’s Solutions Manual, ISBN 0-13-085511-1

Printed Test Bank/Instructor’s Resource Guide, ISBN 0-13-085512-X

Videotape Series: ISBN 0-13-040283-4

TestGen – Test Pro4 Bank: Win/Mac Version, ISBN 0-13-040276-1

Math Pro Explorer Tutorial Software: Win/Mac, ISBN 0-13-040279-6

Prentice Hall provides technical support for instructors an 800 number-877-547-4538, M-F 8:00-5:00 CST and e-mail address: 1st@prenhall.com

A half day workshop on MathPro and TestPro will take place for all interested faculty each year.

Testing Schedule: Feel free to schedule the sections in a different order, but give 4 tests and the college wide final exam so that all students have a similar opportunity to learn and show evidence of success.

Additional Notes: The syllabus intends to allow time in the course for each of the following:

(1) deeper investigations into the concepts of mathematics,

(2) group work,

(3) active participation and involvement for all students, and

(4) instruction in study skills.

Some of the problem solving section problems not assigned are excellent group activities. Some of the Group Activities that follow the challenge problems are valuable for encouraging the students to construct their own meanings rather than memorize rules. Most instructors agree on the importance of students understanding the mathematical concepts rather than repeating routine steps and "shortcuts." You will enjoy the many new applications in the text, which will help students connect the meaningfulness of mathematics with their lives. Many faculty members give all or most exams, except the final and perhaps the fourth test, in testing centers in order to allow maximum instruction time in class. When giving exams, it is important to test students’ knowledge and understanding rather than their speed.

We encourage you to use problems from the graphing calculator sections, the Challenge problems, and the group activities as in-class investigations to enrich and enliven your class. Read the discussion about these in the Preface. If you choose to occasionally include some of these in the homework, but be sure your course is consistent with department guidelines. For instance, requiring students to do graphing calculator problems more than occasionally in the homework would, in reality, be requiring them to buy a graphing calculator, which is not acceptable. Also, requiring students to do homework problems from the Challenge problems with more complex algebraic manipulations would result in a course substantially more advanced than is intended. Be sure to provide students with answers to check problems in homework when the answers are not provided in the back of the text.

Problems from the cumulative review exercises are included in the suggested homework with all answers in the text. You may not want to test over these, but encourage students to do the problems in the homework so they will be prepared to use these skills and this knowledge when they need them later in the semester and in later life.

Chapter 1: In a sixteen-week semester, in addition to completing your class introduction and pretest (and pretest review if you choose to review) during the first week of classes, you should fully cover Chapter 1 by the beginning of the third week of classes with special focus on study skills, problem solving and order of operation, sections 1.1, 1.2, and 1.9. Some instructors will want to integrate extra time for 1.1, 1.2, and 1.9 during the first month of instruction. If you are teaching the course in a different length semester (5.5, 8, 11, or 12 weeks), see the weekly schedules in Information for Students to adjust these time periods. Most of Chapter 1 should be review for the student so be sure to refer students who need more time than that scheduled to the learning lab or to the previous course, Basic Mathematics Skills. While helping your students review this material, remember to include short explanations and examples of decimals & percents (Appendix A), finding GCF & LCM (Appendix B), the real # system, its operations and properties (1.4-1.10), inequalities (1.5). A careful, quick review of fractions (1.3) and exponents, parenthesis & order of operations (1.9) is also recommended. If students indicate that they need more than a quick review of this material, talk to them individually to determine which of the following three recommendations to make to each student: (1) stay in MATD 0370, but get additional help immediately by registering for the math lab classes (you may make their attendance in the lab classes a mandatory requirement for allowing them to remain in the course), (2) stay in MATD 0370, but get additional help immediately by visiting the free tutoring center (learning lab) at any ACC campus, or (3) move back a level to Basic Math Skills (MATD 0330) instead. For more information, please refer to the section on Appropriate Course Placement in the Notes for Instructors (on the previous pages in this section of the Math Manual). While reviewing Chapter 1, you may introduce group work by using the group activities.

Chapter 2: Although most of Chapter 2 should be a review for the student, we recommend that you review each section of this chapter thoroughly. Be sure students recognize the reasons for the differences in the way they work with expressions and equations. As you review the skills in Chapter 2, you should find many opportunities to review/apply problem solving (1.2). Review ratio and proportion (2.6) carefully

Chapter 3: Much of Chapter 3 will be new to the student. Although the formulas in 3.1 may not be new, the applications may be. Instructors from many disciplines stress how important it is for our students to know how to solve formulas for an indicated variable. A careful review of changing application problems into equations (3.2) and solving application problems (3.3) is recommended. Geometric problems (3.4) is reinforced in Appendix C. Motion and mixture problems (3.5) will be new to most students. It is recommended that problems from chapter 3 be used as warm-up/review throughout the rest of the course.

Chapter 4: Graphing linear equations is new to the students. Most students are familiar with bar graphs, line graphs, and circle graphs, but many have never graphed linear equations using a rectangular coordinate system. This is a very important topic and requires special attention. By introducing this topic early in the semester, we are able to include graphing on most, if not all, exams for this course. This chapter presents graphing lines by plotting points and intercepts. It is important for students to understand not only how to graph points and lines but also how to use graphing to solve problems. In 4.2, horizontal and vertical lines are introduced. Support the students in making as many connections as possible in understanding slope. Remind students about rates of change with which they are already familiar and support their expanding their concepts to include the mathematical definition of slope and applications. A careful treatment of section 4.4 (part 6) Compare the Three Methods of Graphing Linear Equations is an excellent introduction to systems of equations in Chapter 9.

Chapter 9: You should cover only part of this chapter in elementary algebra. This will be new material for the student. Solving systems of equations graphically (9.1), by substitution (9.2), and the addition method (9.3) can provoke a good discussion on choosing methods for many sorts of problem solving. You should cover only part of the applications and problem solving section (9.5). Refer to the homework suggested problems. This is another excellent place to talk about problem solving (1.2) and relevant applications (3.5). Note: You should be careful to focus your discussions on applications involving systems of two equations in 9.5.

Chapter 5: It is important that students understand the terminology introduced in this chapter, including polynomial, term, coefficient, and degree. Some students are familiar with collecting like terms, simplifying and/or evaluating algebraic expressions, and multiplying polynomials by a monomial. Zero exponents (5.1) and negative exponents (5.2) will be new to many students. Focus on reasons these make sense in our number system, rather than memorizing rules. Multiplication of a polynomial times a polynomial (5.5) will be new to most. We recommend including scientific notation (5.3) and division of polynomials (5.6) the week before the final exam.

Chapter 6: Factoring is a new concept for most students. We recommend that you teach factoring thoroughly. Try to ensure that they make as many connections as possible for what the word "factor" means as a noun and verb. Stress solving applications using factoring (6.6).

We recommend beginning the review for the final exam as soon as your students finish exam 4 using the review sheet for the final exam along with going back to cover scientific notation (5.3) and division of polynomials (5.6), omitting synthetic division & the remainder theorem.

Quadratic Formula Supplement: You will find a supplement on simple use of the quadratic formula with supporting materials in this manual. Be sure to give 1 or 2 short in-class quizzes on use of the quadratic formula so students will be prepared to determine when to use it and how to use it. It will be listed on the final exam, but they will need to determine on which problems they need to use it.

Chapter 5: We recommend 5.3 scientific notation and 5.6 (parts 1-4 only) division of polynomials the week before the final exam along with an integrated review of the course. Support students in connecting division of polynomials with their understanding of the long division algorithm for whole numbers.

ELEMENTARY ALGEBRA SUGGESTED HOMEWORK (Angel)

The square roots of a number are the values which, when squared, result in that number.

If is a square root of k, then ()= k: ()= (3)= 9, ()= 5, etc.

Every positive number has two square roots, one positive and the other negative. For example, the number 25 has two square roots, 5 and –5, because the square of each of these is 25. The radical symbol, , is used to indicate the positive (or principal) square root of a number: = 5. The negative square root is represented by taking the opposite of the positive root, e.g., the negative square root of 25 is written –= –5. The number under the radical symbol, in this case 25, is called the radicand.

0 has a single square root (= 0) and negative numbers have no real number square roots since this would require the square of some real number to be negative. For example, is not a real number.

Perfect squares are numbers such as 0, 1, 4, 9, 16, etc., which are the square of a whole number. That is, 0= 0, 1= 1, 2= 4, 3= 9, 4= 16, etc. Thus, the square roots of perfect squares are integers: = 0; = 1; = 2; = 3; = 4; etc.

Not all square roots are equal to integers. The square roots of numbers like 5 (which is not a perfect square) are irrational numbers. The only way to represent them exactly is by using a radical, . For calculation purposes, however, we often use a calculator to get a decimal approximation: = 2.236067977... or, rounded to three places, 2.236.

Even without a calculator, we can get a rough approximation of such square roots by making use the fact that if a < b < c, then < < (square roots preserve the order.)

Since 4 < 5 < 9, then < < . Thus, lies between 2 and 3 (i.e., between and .)

More generally, to approximate , locate k between successive perfect squares. Then must lie between their square roots. An example follows:

Between which two consecutive integers does lie?

Many square roots of non-perfect-squares may be rewritten in simpler form. If k is not a perfect square, but k = a•b where a or b is a perfect square other than 0 or 1, then we may simplify by making use of the following rule for square roots:

For non-negative real numbers a and b, =

Example: Since 28 = 4•7, = = = 2

Thus, to simplify the square root of a positive number which is not itself a perfect square, we try to find a perfect square (4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, etc.) other than 0 or 1 which divides evenly into the radicand. If we find such a perfect square factor, we rewrite the radicand as a product of two factors (the perfect square and the number we get when we perform that division). Now, use the rule above to rewrite the square root as a product of two square roots. Take the square root of the perfect square, and either write it in front of the other square root or multiply it by any number immediately in front of the roots. Leave the other factor, which is not a perfect square, under its radical. Check to see if any perfect squares other than 0 or 1 divide evenly into the factor remaining under the radical. If so, repeat the process. If not, then you are finished simplifying the square root. Here are some additional examples:

a. = = = 3

b. 7= 7= 7= 7•5= 35

c. 2= 2= 2= 2•3= 6

d. = = = 3= 3= 3= 3•2 = 6

The Quadratic Formula is a formula by which any quadratic equation can be solved, including even those which cannot be solved by factoring.

If a quadratic equation is written in standard form, ax+ bx + c = 0, where a ¹ 0, then its solution(s) can be obtained by substituting the values of a, b, and c into the formula

x =

Note that a, b, c are the coefficients of the x, x, and constant terms.

Example 1: Solve using the quadratic formula: 4x= 6 – 5x

4x= 6 – 5x 4x+ 5x – 6 = 0

Rewrite in standard form so that we can determine the values of a, b, and c: Move all terms to one side of the equation, written by descending degree, equal to 0.

x = = = =

This gives two answers: x = = = , or

x = = = –2

4x+ 5x – 6 = 0 (4x – 3)(x + 2) = 0 4x – 3 = 0 x + 2 = 0 x = x = –2

Factor the trinomial. Set each factor = 0. Solve each linear equation.

Example 2: Solve using the quadratic formula: m– m – 2 = 4m – 5

m– m – 2 = 4m – 5 m– 5m + 3 = 0

Rewrite in standard form: Move all terms to one side of the equation, collect like terms, write by descending degree, and set equal to 0.

Then a = 1, b = –5, and c = 3. Substitute these values into the quadratic formula:

Example 3: Solve using the quadratic formula: y+ 6y – 2 = 5(y– 1)

y+ 6y – 2 = 5(y– 1) y+ 6y – 2 = 5y– 5 0 = 5y– 5 – y– 6y + 2   0 = 4y– 6y – 3

Distribute the 5. Move all terms to one side of the equation and set equal to 0. We moved them to the right so that the lead coefficient, 4, would be positive, which is optional. Collect like terms and write by descending degree.

y = = ± = ±

Example 4: Solve using the quadratic formula: x+ 6x + 9 = 0.

Note that in this case (involving a perfect square trinomial) we get only one answer.

Doing the same problem by factoring shows us that there actually are two answers

but they are not different. We just get the same answer twice.

x+ 6x + 9 = 0 (x + 3)= 0 x + 3 = 0 x + 3 = 0 x = –3 x = –3

Factor the trinomial. Set each factor = 0. Solve each linear equation.

Example 5: Solve using the quadratic formula: n+ n + 1 = 0.

Between which two consecutive integers do each of the following square roots lie?

1.

2.

3.

4.

Simplify each of the following square roots.

Solve the quadratic equations below either by factoring or by using the quadratic formula. Give exact answers, and where appropriate, give approximations rounded to three decimal places.

(revised May 2001)

The following objectives are listed in a sequence ranging from the simple to the more complex. As such, this document should not be viewed as a chronological guide to the course, although some elements naturally will precede others. These elements should be viewed as mastery goals which

will be reinforced whenever possible throughout the course.

Overall objectives:

1. Students will feel a sense of accomplishment in their increasing ability to use mathematics to solve problems of interest to them or useful in their chosen fields. Students will attain more positive attitudes based on increasing confidence in their abilities to learn mathematics.
2. Students will learn to understand material using standard mathematical terminology and notation when presented either verbally or in writing.
3. Students will improve their skills in describing what they are doing as they solve problems using standard mathematical terminology and notation.

1. Description and classification of whole numbers, integers, and rational numbers using sets and the operations among them.

1. identify and use properties of real numbers
2. simplify expressions involving real numbers
3. evaluate numerical expressions with integral exponents
4. simplify square roots of perfect square whole numbers

1. Polynomials.

1. distinguish between expressions that are polynomials and expressions that are not
2. classify polynomials in one variable by degree and number of terms
3. simplify polynomials
4. add, subtract, multiply, and divide polynomials (including the use of long division techniques and the distributive law)
5. factor polynomials (including factoring out the greatest common factor, factoring by grouping, factoring trinomials in which the leading coefficient is one, factoring trinomials in which the leading coefficient is not one, factoring the difference of two squares, factoring the sum or difference of two cubes)
6. understand and use the exponent laws involving integer exponents
7. convert numbers into and out of scientific notation and perform multiplication and division with numbers written in scientific notation

1. Solve linear equations in one variable involving integral, decimal, and fractional coefficients and solutions

 

 

 

 

 

 

2. Application problems.

1. write and evaluate linear expressions from verbal descriptions
2. solve application problems which lead to one of the following types of equations: linear equations in one variable, systems of two linear equations in two variables, quadratic equations
3. solve literal equations for a specified variable using only addition and multiplication principles
4. solve application problems using ratio and proportion
5. use given data to estimate values and to evaluate geometric and other formulas
6. solve problems involving the Pythagorean Theorem

1. Linear equations in two variables.

1. identify the relationship between the solution of a linear equation in two variables and its graph on the cartesian plane
2. understand and use the concepts of slope and intercept
3. graph a line given either two points on the line or one point on the line and the slope of the line
4. identify the equations of the line in the standard, point-slope, or slope-intercept forms and graph their solutions
5. write an equation of a line given its graph or description (including one point on the line and the slope of the line, or two points on the line)
6. solve systems of linear equations

6. Quadratic equations.

1. find solutions to quadratic equations and equations of higher degree using the technique of factoring
2. recognize a need to use the quadratic formula to solve quadratic equations and solve quadratic equations by using the quadratic formula when simplification of square roots other than perfect squares is not needed

7. Description and classification of irrational numbers.

1. simplify perfect square radical expressions
2. simplify perfect square radical expressions
3. use decimal approximations in applications that involve radical expressions

8. Geometry

1. Understand the difference between perimeter and area and be able to use formulas for these appropriately.
2. Understand the concept of volume and be able to use formulas appropriately for a variety of 3-dimensional figures.
3. Solve problems involving similar figures

Important Information: The textbook contains three CDs and is wrapped in cellophane. Do not buy a book NOT wrapped in cellophane. Do NOT open the cellophane covering the book until after you have verified with your instructor that you are in the correct course. Once the package is opened, you may NOT return the book to the bookstore. The cellophane has a sticker on it which reads: "STOP! DO NOT OPEN until you have checked with your instructor." The price of the book includes the cost of your license for using the computer software. The sticker on the book is your proof of purchasing the software license. You must save the cellophane wrapping with the sticker (your proof of purchase), and turn it in to your instructor with your first homework assignment.

Text: Academic Systems' Interactive Mathematics Elementary Algebra Personal Academic Notebook

Supplemental Materials: Paper, Pencils, Erasers, Scientific Calculator, Graph Paper

** If you are unsure whether or not this warning applies to you, see an ACC advisor immediately.

In Progress grades (IP) are also rarely given. In order to earn an "IP" grade the student must

*Additional info about ACC's Math Dept. is available at <http://www2.austin.cc.tx.us/math/>.

This special section of the course uses the Academic Systems Interactive Mathematics computer software package. The software provides visual explanations and includes an audio component so that you may listen to the explanations. It is called "interactive" because you are continually being prompted for input. This program is successfully used at over 250 schools in the United States.

In this class, you will be in charge of your learning in a way that is different from a traditional lecture class. The format of the course is somewhat self-paced, which means you may complete the material before the end of the semester. It also means that you may spend less time on familiar topics and more time on troublesome topics. In order to complete the course within the semester, you must generally keep up with the weekly schedule and test schedule provided. In order to succeed in this class, you should plan to spend about 9 to 15 hours each week (or more, if necessary) working on the material, depending on how much of the material is already review for you. The program is available all day everyday except when it is being backed up. Backups are scheduled for 1 AM every day, and should only very rarely take more than 2 hours to complete.

Please be careful with the CDs in your book. They hold lots of information and are very sensitive. Please handle them with care. If they become dirty or scratched, you may get error messages while using the software. If you receive an error message while working outside of ACC, print or copy the error message. Then try cleaning the CD with rubbing alcohol on a lint-free cloth. If that doesn't work, please call the free Academic Systems technical support line listed below, and wait on the line to get help for your error message. If they are unable to help you, please ask your instructor for help.

For more information about using Interactive Mathematics, please visit the Academic Systems web site <http://www.academiconline.com> and explore the pages called "Getting Started" and "Interactive Mathematics Resources." This web site contains the latest information about computer requirements as well as instructions for installing and using the Interactive Mathematics software.

In order to use this program, you will need a computer with the following minimum requirements:

Computer (PC): Windows 95, 98, SE, ME, 2000**, or Windows NT Workstation 4.0

[NOTE: The math program will not run on MacIntosh computers.]

CPU: Intel Pentium Processor

RAM: 32 MB Minimum (64 MB Recommended)

Video Card: Capable of High Color (16-Bit) with 800 x 600 Minimum Recommended Resolution

Sound Card: Amplified, Windows Compatible [NOTE: Must be amplified]

Internet Access: Internet Dial-Up (Minimum 28.8 Modem) or 10 BaseT Ethernet Connection

[NOTE: ACC does not provide internet accounts for students. You must have your own.]

Browser: Netscape Navigator 4.x or Higher, or Microsoft Internet Explorer 4.x or Higher

[NOTE: Netscape 6 is currently not supported.]

CD-ROM: 4X CD-ROM Drive (or Higher) with 32-Bit Drivers

Hard Drive: 150 MB Uncompressed Free Space

*For Free Technical Support (24 hours a day, 7 days a week), please call 1-800-681-4357.

**REVISED NOTE ABOUT WINDOWS 2000: The new Installer CD (Version 8.1) works with all versions of Windows. If your computer has Windows 2000 and your book has CD Version 8.0, please borrow Version 8.1 from your instructor. This CD is used only once to install the program.

Academic Systems Software: The software for the course is divided into Topics. Each Topic is divided into Lessons. Within each Lesson are some or all of the following six Modules:

OVERVIEW: · Brief summary of prerequisite skills for the lesson

· Pretest (may only be taken once)

EXPLAIN: · Mathematics instruction

· Check for understanding problems with feedback

· Help line: Red Phone icon gives hints or simplified explanation

· Glossary Words: Click on any underlined word for the on-line definition

APPLY: · Practice problems to apply the skills learned in Explain

· Link to Explain: Icon with Sun (like Explain) will link from Apply

· Explanation of the Expression Editor, if needed

EXPLORE: · Optional module available with some lessons

· More challenging problems to explore and discover mathematics

EVALUATE: · Quiz for the lesson (up to three versions may be taken for each lesson)

· Homework and Practice Test in the book should be completed before

· Up to three attempts are allowed on the quiz; highest grade is recorded

Your textbook is the Personal Academic Notebook (PAN). Refer to this book when completing homework assignments, reviewing for tests, or taking the Practice Test to prepare for the Pretest (in Overview on the computer) or the Quiz (in Evaluate on the computer). In addition to taking Practice Tests from the book and Pretests and Quizzes on the computer, you will be taking Tests, either in class or in the Testing Center. You will also take a comprehensive departmental final exam. More information about ACC’s Testing Centers is available at <http://www2.austin.cc.tx.us/testctr/>.

Your instructor will provide you with at least three additional handouts: (1) a list of homework problems, (2) a schedule indicating which lessons to complete each week, when tests are to be taken, and what those tests will cover, and (3) a handout detailing your instructor’s testing, homework, and grading procedures. If you have not received these handouts, please ask your instructor for them..

To make the best use of your time on the computer, you may use the following guidelines:

Your grade on the lesson will be the highest of three attempts on the Evaluate Quiz, unless you score 95 or more on the Overview Pretest and save that Pretest grade as your Quiz grade for the lesson.

This weekly schedule and schedule of exams is provided to help you pace yourself so that you may take tests on time and complete the course during the semester. You may work ahead and finish early. If you get behind this schedule, speak to your instructor about how to get caught up.

Additional Help: Free tutoring is available at the Learning Labs at most ACC campuses. For more info about the Learning Labs, please visit the web site <http://www2.austin.cc.tx.us/rvslab/ll.html>.

Speak to your instructor if you have any questions or concerns about participating in this class. If, for any reason, you would prefer to attend a traditional lecture class, please ask your instructor to help you make a schedule change. These changes should be done as early in the semester as possible.

*Lessons 1.1, 2.3, 3.1, 4.1, and 10.1 have additional Exercise Sets that are required for this course.

Information for Students** page 1 of 2

2001-2002

**Additional information about ACC's mathematics curriculum and faculty is available on the Internet at <http://www2.austin.cc.tx.us/math/>

Information for Students page 2 of 2

2001-2002

Information for Students page 2 of 2

2001-2002