College Algebra

Math 1314: College Algebra

I am now teaching College Algebra as an online distance learning course.

 

(The material below is from an earlier semester and does not apply to my online course at all.)

Summer 2002

Grading:

There will be 3 or 4 exams and a comprehensive final during the term, each of which will count equally towards your grade. The tests will comprise 85% of your grade. The remaining 15% of your grade will be based on your homework assignments.

You may earn bonus points on each test, except for the final test, by correcting all errors and submitting them to me within one week of receiving the graded test back. If you submit these corrections for every test on which you make less than a 90, then I will replace your lowest test grade with the average of that grade and your grade on the final exam. If you take any test late for any reason, there will be a penalty of 10% off your test grade. However, no late tests will be allowed after I hand the original test back in class (it could be a few days or it could be a week or more).?All tests and assignments must be turned in on or before the last class meeting.

Grades will be assigned as follows:

A

90% or better and a grade of at least 80 on the final

D

60% - 69%

B

80% - 89% and a grade of at least 70 on the final

F

below 60%

C

70% - 79% and a grade of at least 60 on the final

     

W

Withdrawn by student or instructor prior to last withdrawal date on school calendar

I

Incomplete (only given in extenuating circumstances)

Homework:

You should bring your homework to class every day.?It will be collected regularly and graded.?There may also be in-class assignments collected for a grade (as part of your homework grade).

 

Other Important Stuff

Attendance:

It is extremely important for you to attend class regularly. Although I will not take regular attendance, I MAY drop you from the course for excessive absences, although I make no commitment to do so. (If you decide to stop coming, you had best make sure that you drop the course. While I MIGHT do this, it is YOUR responsibility. If you fail to do so, you could receive an F on your permanent record.)

Prerequisites:

Please make sure you have the necessary prerequisites for this course. That means you need a C or better in an Intermediate Algebra (or an equivalent) course or CURRENT knowledge of high school Algebra II as measured by an appropriate grade on placement tests. (Warning:? The TASP, SAT I, and ACT tests are NOT really meant to be placement tests.?We suggest you use the COMPASS tests offered here for placement.)? If I feel you are not prepared for this course, I may choose to withdraw you. If you have any questions about your preparation for the course, please come and talk to me about it.

Keeping up:

Please, try to keep up with the homework and with the lecture in class. There just isn't much time to catch up. This means you have to be sure to allow yourself plenty of time to do the homework and to study.

Ask questions:

Please, please, please, if you don't understand something, or you aren't clear about something, or if you think I (or the book) have made a mistake (it has been known to happen), or if you have any other questions, please ask. Don't let confusion accumulate. If you don't want to ask in class, come to my office hours (or call me) and ask. It is much easier to ask a question now than to miss it on the test.

Always show your work:

It is much more important that you understand the processes involved in solving problems than that you just give me the right answer. If I see from your work that you understand what you are doing, I will usually give partial credit for a problem, even if you made a mistake somewhere along the line. If you don't show your work (unless I believe you could reasonably do it in your head), I may not give you full credit, even if the answer is right. If you can really do something in your head, that's great, but when in doubt, write it down.?It is also very important that you write what you mean. I will correct your notation the first few times, but I will start counting it wrong if you continue to write things incorrectly. In addition, please write clearly and legibly. If I can't read it, I won't grade it.

Cheating:

Don't. In fact, don't even think about it. Do your own work; copying or helping others to copy test questions or answers before, during, or after taking a test is cheating. Cheating is in violation of school rules and is dishonest. Any student found to be involved in cheating may be penalized. The nature of the penalty is at the discretion of the instructor. A report of the incident may be placed in the student's permanent record and the student may also be dismissed from ACC.


Austin Community College Department of Mathematics**

Alternatives to College Algebra

or

?/span>Hints to Help the Beginning Student Distinguish between

First-Level College-Credit Mathematics Courses

Topics in 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 handle the algebraic aspects of the course easily.

Math for Business & Economics (ACC's MATH 1324) (UT's M303D, SWTSU'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, SWTSU'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???? SWTSU = Southwest Texas State University at San Marcos

*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.


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)

i

(B or higher)*
i

i
i

 

i

i

College Algebra**
(MATH 1314)

 

Math for Bus & Eco

(MATH 1324)

College Algebra

(MATH 1314)

i

 

i ????

Trigonometry (MATH 1316)

 

Business Calculus I (MATH 1425)

 

i

 

i

Precalculus (MATH 2412)

 

Business Calculus II (MATH 1426)

i

   

Calculus I (MATH 2413)

   

i

   

Calculus II (MATH 2414)

   

i

   

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 Trig.

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 math web page*** or the catalog.

* 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 Intermediate Algebra course, while others need an additional semester of work on algebra, which is done in College Algebra.?Students going directly to Trigonometry from Intermediate Algebra should make sure that they can easily work all problems on the Trig Prerequisite Review.***

** Some students who are very successful in College Algebra are tempted to skip either Trigonometry or Precalculus. That is not acceptable.? 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 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:? Students planning to attend SWTSU should take Math for Business & Economics.?Students who will attend UT may take either Math for Business & Economics or College Algebra to prepare for Business Calculus at ACC.?Students who will transfer to UT before taking Business Calculus should take College Algebra.?

*** For additional information, including prerequisite review sheets for most courses, see <http://www.austincc.edu/math/>


MATH 1314

?/span>College Algebra

Information for Students **

5 1/2 - Week Summer Semester

2002

??????

TEXT: College Algebra, Concepts and Models, 3rd edition, by Larson, Hostetler, & Hodgkins

Optional Supplement: ?tudy and?Solution Guide (step-by-step solutions to selected odd-numbered exercises and review problems and step-by-step solutions to all tests in text)

Optional Supplement: ?raphing Technology Keystroke Guide

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 library.?Graphing calculators are NOT required, but you will use graphing technology in some sections of the book.

Course Purpose:?This course is designed to teach students the functional approach to mathematical relationships that they will need for the business calculus sequence. For students who did not take, or were weak in, Intermediate Algebra (MATD 0390), College Algebra is a good preparation for Trigonometry (MATH 1316).? Other courses, such as MATH 1332 or MATH 1342 are more appropriate to meet a general mathematics requirement, if calculus is not required. Check with your degree plan as to what math course your college requires.

Course Prerequisite: Intermediate Algebra (MATD 0390) or current knowledge of high school algebra as measured by the Assessment Test.?The sections marked (*) in the syllabus/calendar cover material from the prerequisite course.?All the techniques and at least 80% of the problems in them should be review.?The rest of the problems use familiar techniques in more sophisticated ways than before.?Students who have a great deal of difficulty with the material in chapters P and 1 and have not had Intermediate Algebra or its equivalent recently should consider withdrawing and taking Intermediate Algebra.

Videotapes: There is a set of videotapes 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.

Testing, Grading, and Homework:?The testing scheme given with the syllabus and calendar is only one possible scheme.? Your instructor may use a different one.?Your instructor will give you an additional handout with details about testing, grading, and homework for your section of this course.?

Withdrawals and Incompletes:?After the withdrawal date each semester, neither the student nor the instructor may initiate a withdrawal.?It is the student's responsibility to initiate all withdrawals in this course.?The instructor may withdraw students for excessive absences (4) or failure to meet course objectives but makes no commitment to do this for the student.?Attendance is important in this course and expected.?Incomplete grades (I) will be given only in rare circumstances.?Generally, to receive a grade of I, a student must have taken all examinations, be passing, and have a personal tragedy occur after the last date to withdraw which prevents course completion.

Calendar:

Week 1:?1.1* - 1.4*, 1.5, 1.6*, 1.7, 2.*1, 2.4, 2.5

Week 2:?2.2, 2.3, Test 1(Chapter 1, 2.1, 2.4), 3.1-3.3

Week 3: 3.4, 3.5, 4.1, Test 2 (Chapter 2.2, 2.3, Chapter 3), 4.2, 4.3, 4.5, 4.6

Week 4: 4.7, 5.1, Test 3(Chapter 4), 5.2, 5.3

Week 5: 5.4, 5.5, 6.1, 6.2*, Test 4 (Chapter 5), 6.3, 7.1

1/2 week: 7.2, 7.4, Supplement, Test 5 (6.1-7.4) or Final

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


HOMEWORK for College Algebra, 3rd edition, by Larson, Hostetler, & Hodgkins, page 1

If you find that you need help (even changing an answer after you look it up qualifies as help) on more than 25% of these, then you probably should do more homework on that material.?Do problems until you feel comfortable doing them with no more help than you will have on the test.

When you finish the chapter, make up a sample test for yourself from the review problems, take it, and grade it.?Continue to do that until you are pleased with your sample test grade.

Section 2.3 can be done most effectively with graphing technology.?Some problems may suggest a graphing calculator, but these problems are types that we have always done by hand or with a scientific calculator.

The problems in the Appendix were previously in Chapter P.?These are not included in the syllabus, but should be used as needed for review.

A.3??7, 9, 11, 17, 25, 27, 29, 33, 39, 51, 53, 55

A.4??17, 18, 27, 31, 35, 37, 41, 43, 45, 47, 49, 53, 55, 59, 61, 65

A.5 ??7, 19 ,23, 25, 29, 31, 35, 39, 41, 45, 47, 49, 51

A.6??3, 5, 7, 11, 13, 15, 19, 21, 23, 27, 35, 37, 39, 43, 47

A.7??7, 9, 13, 15, 21, 23, 27, 29, 35, 37, 41, 43, 44, 47, 49, 59

Additional algebra problems:?Simplify and write the answer with no negative exponents.

1.? ????.? ?????3.? ?????4.?

1.1? 1, 5, 19, 23, 25, 37, 45, 47,? 53,?63, 65, 69, 71, 73, 74

1.2? 19, 21, 23, 25, 27, 29, 33, 35, 37, 39, 41, 43, 47, 49, 53, 55, 61, 63, 69, 70, 75, 76, 79, 81

1.3??1, 12, 13, 15, 21, 23, 25, 31, 33, 37, 39, 41, 51, 55, 59, 61,63,65,67,69, 77, 79, 81

1.4 ?5,7,9,13,19,27,29,31,37,39,41,43,45,46,51,55,57,59, 60, 61, 63, 65, 71, 73

1.5??, 7, 11, 13, 23, 27, 31, 35, 41, 45, 51, 53, 65, 71, 72

1.6? 17, 23, 25, 31, 33, 35, 37, 39,?40, 55, 59, 61, 65

1.7? 3, 7, 11, 15, 17, 19, 23, 27, 29, 33, 37,?38, 45, 53, 55

2.1 ?13, 19, 23, 29, 35, 49, 51

2.2??, 4, 7, 9, 10, 15, 16, 19, 21, 23, 25, 27, 28, 29, 31, 33, 35, 37, 41,45, 47, 53, 55,?57, 58, 59, 60,?61, 63,

????????????71, 73, 75

2.3? 1-10, 11, 13, 15, 17, 19, 21, 25, 31, 33, 35, 37, 39, 43, 45,?47, 49, 51, 52

2.4? 1, 5, 7, 13, 15, 17, 19, 21, 23, 25, 27, 29, 33, 35, 43, 45, 47, 48,?51, 57, 61, 63, 69, 71

2.5??4, 17, 20, 23, 25, 27, 29, 31, 32, 33, 48

3.1? 1, 3, 8, 9, 10, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 36, 37, 39, 44, 55, 59,63, 65, 66, 75

3.2? 1, 3, 5, 7, 9, 12, 15, 17, 21, 23, 25, 29, 33, 35, 37-41, 43, 45, 47, 49, 59, 65, 67, 69

3.3      1, 3, 7, 9-12, 15, 16, 18, 18, 23, 25, 27, 39, 40, 41, 43, 45, 47-49, 51, 55ab, 57, 59

3.4      1, 5, 9, 13, 17, 20, 25, 27-29, 33, 35-37, 39, 41, 43, 45, 55, 57, 59(optional), 61(optional)

3.5      2, 3, 5-7, 9, 11, 13, 23, 30, 33, 41, 47, 50, 59,?61

4.1? 1-9, 11, 12, 15, 17, 19, 21, 23, 25, 27, 31, 33, 35, 37, 43, 45, 47, 49, 53

4.2? 1-7, 12-15, 19, 21, 23, 25, 27, 31, 35-41, 43-45, 47, 49-51, 53, 55, 57, 59, 61

4.3? 1, 3, 9, 10, 13, 15, 17, 21, 27, 31, 33, 35, 39, 41, 49-53, 55, 59, 63a

4.5? 7, 11, 13, 19, 21, 27, 29, 31, 33, 35, 41, 43, 45, 59, 61, 63, optional exercises 67, 69, 73, 75

4.6? 1, 3, 5, 27, 31, 33, 35, 37, 39, 41, 43

4.7? 1, 3, 5, 9-22, 27, 31, 33, 35, 41, 43, 49, 55, 57, 59, 61

5.1? 1, 3, 5, 9, 11-18, 19, 21, 23, 25, 29, 31, 33, 35, 39, 43, 45, 51, 53, 55, 57, 60

5.2? 1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 25, 29, 33, 35, 37, 38, 39-47, 49, 53, 55, 65, 67

5.3? 9, 11, 13, 17, 19, 23, 27, 33, 37, 39, 41, 51, 53, 57, 65, 67, 69, 73, 75, 79, 81(optional)

5.4? 1, 5, 9, 11, 13, 15, 17, 21, 25, 29, 35, 41, 43, 45, 51, 53, 55, 59, 61,?65,?67ab, 73

5.5      1, 3, 7, 10, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 41, 45ac


HOMEWORK for College Algebra, 3rd edition, by Larson, et. al.,?page 2

6.1? 1, 3, 5, 7, 9, 13, 19, 27, 41, 45, 47, 51, 55

6.2? 3, 5, 7, 13, 15, 23, 31, 33, 35, 39, 41, 45

6.3? 1, 3, 5, 13, 19, 27, 31, 33, 35, 39, 41

7.1? 1, 3, 5, 13, 17, 20, 21, 23, 29, 31, 37, 39, 43, 45, 49, 51, 59

7.2? 1, 5, 7, 16, 19, 39, 41

7.4? 3, 9, 11, 17, 23, 29, 31, 33, 35

Supplement:?For each of the following systems with a unique solution, solve it using Cramer’s Rule:

?? 7.2: 31, 33;??7.1: 41, 47

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Cramer’s Rule for Solving Systems of Linear Equations

????? If a system of linear equations with the same number of equations as unknowns has a unique solution, that solution may be found using ratios of various determinants.?The following example of a 3 by 3 system illustrates the rule.

To solve this system, where , , and are variables and all other letters represent known real numbers???

consider the following four determinants.? (Evaluate determinants using the methods of 7.4.)

???? ????sub> ????sub>

If , the system does not have a unique solution.? If , the solution to the system of equations is ,? , and .

Example:?Solve?

, ,

Thus, the solution of the system is , , .


Errata in Larson's College Algebra, Concepts and Models, 3rd edition

Section 1.4, p. 43, 59 & 61: refer to Ex 6 in text on p. 41.?You might clarify that -2.7 and -16 characterize gravitational forces on the moon and the earth, respectively.

Section 1.6, p. 67, problem 59.?Should read "find the minimum number of weeks..." instead of maximum number.

Section 2.3, p. 116, prob. 51: answer in back of text is wrong, should be $.69

Section 3.1, pg. 161, prob. 27: answer in back of text is wrong, it should be "all real numbers".

Section 3.2, P. 173, prob 17:?answer should be: ...behavior changes at (0,0) and at (-2,4)

Section 3.2, p. 175, probs. 67 and 69.?Example 6 on Pg 169 uses the model "for calls up to 1 minute,...".?Using a similar model for problems 67 and 69,?problem 67 should read: "for calls up to 1 minute, the cost is $.75" and for problem 69, "for packages up to one pound, cost is $10.75".

Pg 181: Caution: the graphs (transformations) are NOT drawn to the same scale, thus not allowing visual comparisons.

Pg 190, graph shown as a solution to Example 7, is incorrect. It should be a step function.?(Elections are only once every two years for house, so number will stay the same throughout the two year period unless appointments are made).

Pg. 233, Exercise 4.2: #8 b) is not right since graph is not correct

Pg 242: Example 7.?P = ?hould be? ?since P is per cent.?Graph is also in decimals instead of

???????per cent, as labeled:?1.00 should be 100 on vertical scale for graph b) since it is labeled %.

Pg. 244, Sect 4.3: Prob 55 & 59.?Instructions better stated: Simplify by division or reduce to lowest terms.?Answer in back needs a restriction on "x" for each for the expressions to be equal.

Pg. 286, Prob 13:?in graph c, the horizontal asymptote, y=1, is omitted.? Also, the zero for 13c, x = -4,?is off the graph.

Pg 306, Section 5.1, problem 25: answer in back of text is wrong.?Graph should be a smooth, decreasing exponential graph going through points (-2,14), (-1,2), (0,-1), (1, -1.75), with asymptote: y = -2

Page 323, Example 9,?asks students to find "an equation that expresses y as a function of x," however the example expresses the answer equation as? .?So, to complete and solve for y:? .

Pg. 347, Problem 25.?Population reaches 150K during 2013, but if consider whole years, would be 2014.

Pg 369, Problem 55.?Same as in 25 above.?Overtakes during 1996, but if consider whole years, would be 1997.

Solutions Guide errors:

Section 2.1, p. 97, prob 35: answer should be: x = -9, 15

Section 2.2, p. 108, prob 71: answer should be: C = 6

Section 6.1.?Problem 55.?sign wrong from second equation in the first step of the solution.


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It was last updated on September 8, 2012 .