Michael Bowen's VC Course Pages

# Math V03, Spring 2017

## Introduction and Announcements

Welcome to Math V03 (Intermediate Algebra) at Ventura College. Michael Bowen (email) will be teaching this course during the spring 2017 term.

Important note: This web page is not a substitute for attending class; regular attendance is an expectation of this course. Modifications to homework assignments, and other important news announced in class, may not appear on this page for several days. You are still responsible for all assignments and in-class announcements even if they do not appear here! If you wish to verify information on this page, please contact the instructor.

## Textbook Information

The ISBN number is provided as a convenience if you wish to purchase this item online. The VC bookstore may stock a different ISBN number; either may be used for the course. If you buy from the bookstore, obtain the least expensive version you can find; do not pay extra for MyMathLab, WebAssign, or other software. If you obtain the book from another source, please be sure to obtain the correct edition, as noted below. Older editions are, of course, much less expensive, but the homework problems are different.

Select any one of the following required texts:

• Author: R. Blitzer
• Title: Intermediate Algebra for College Students, Seventh Edition
• ISBN-13: 978-0134178943
• Comment: Use this ISBN if you are purchasing online; this is likely to be the least expensive, provided that you do not wish to use MyMathLab for independent study.
• Author: R. Blitzer
• Title: Intermediate Algebra for College Students, Seventh Edition
• ISBN-13: 978-0134189017
• Comment: This is the standard package available in the VC bookstore; as we will not be using MyMathLab, only purchase this package if nothing else is available OR you want to use MyMathLab on your own for extra study. If you purchase this, do not buy the Package Component.

If you use the Kindle or other digital version, you will want to be able to refer to the information during class, so be sure you own a compatible device (laptop, mobile phone, or e-reader) that you are willing and able to bring to class with you every day.

This additional text is optional: (Note that when there is a conflict between the solution given in the textbook and the solution given in the student solutions manuals, the textbook is usually correct.)

• Author: R. Blitzer
• Title: Student Solutions Manual for Intermediate Algebra for College Students, Seventh Edition
• ISBN-13: 978-0134180137
• Comment: This title may or may not be available at the college bookstore, but it is readily available online.

## Holidays

Classes at Ventura College will meet Monday through Thursday each week of the term, excepting only the dates listed below.

• Monday 16 January 2017 (Martin Luther King Jr.'s Birthday)
• Friday 17 February–Monday 20 February 2017 (Presidents' Day)
• Monday 13 March–Friday 17 March 2017 (Spring Break)
• Thursday 20 April–Friday 21 April 2017 (Faculty In-service Days)

## Homework Club (Office Hours) During Finals Period

• Monday 8 May 2017: 4:00 to 5:00 p.m. in the Tutorial Center
• Tuesday 9 May 2017: 1:00 to 5:00 p.m. in the Tutorial Center
• Wednesday 10 May 2017: 1:00 to 3:30 p.m. in the Tutorial Center
• Friday 12 May 2017: 9:30 to 10:45 a.m. in SCI-350
• Friday 12 May 2017: 1:15 to 3:00 p.m. in SCI-350
• Saturday 13 May 2017: 9:30 a.m. to 12:45 p.m. in the Tutorial Center
• Monday 15 May 2015: 1:00 p.m. to 4:30 p.m. in the Tutorial Center
• You may also contact me by email; you may expect a response within 24 hours.

## Final Examination

Place/date/time:  Room SCI-350, Wednesday 17 May 2017, 8:00 a.m.

Important Note: This is 90 minutes earlier than our usual class meeting time!

Be sure that your big party to celebrate the end of finals occurs after the appropriate date. Requests for administration of early or late finals that require the instructor to reschedule his work or make a special trip to campus are subject to a deduction of points, regardless of the reason for the request.

## Homework Assignments

• These are listed in chronological order.
• Note: "EOO" (every other odd) means to do problems
1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, etc.
• Note: Please do "E.C." (extra credit) problems on a separate sheet of paper from the regular assignment. These are due at the next exam.
• These are tentative; the instructor may make changes to this list from time to time. Due dates will be announced in class.
• Students must not rely on printed versions of this list; instead, they should check the live online version periodically for possible updates.
• Students who work ahead and complete one or more assignments in advance are taking a risk that the assignment(s) may change before the due date, in which case the advice in the preceding sentence is particularly applicable.
• Students should not expect to earn extra credit for completing tentatively assigned exercises that are later modified or removed from this list.
Overview: This table lists homework assignments and announces examinations. It contains four columns. First row: Column headers. Second and subsequent rows: The homework due for each section covered in the course. Details: The first row is the table header, with column headings describing the data listed in the main body of the table. The second and subsequent rows contain section numbers and titles, assigned problem numbers, and extra credit problems, if any. Column one of these rows contains a section number. Column two of these rows contains the corresponding section title. Column three lists the problem numbers for each section. Column four lists extra credit problems, if any.
§ Title Problems E.C.
Syllabus Worksheet (obtain a copy) (NOTE: This assignment is worth 15 points.)
1.4 (quick review) Solving Linear Equations 7–49 ODD; 55–65 ODD
2.1 Introduction to Functions 1–8 ALL; 9–25 ODD 28; 30
2.2 Graphs of Functions 1–39 ODD 42
2.3 The Algebra of Functions 1–29 EOO; 31–49 ODD
2.4 Linear Functions and Slope (It is recommended that you complete all problem in this section on graph paper, even if some of the problems do not have graphs)
1–13 ODD (find at least three points for each line); 15–39 ODD; 41–61 EOO
2.5 The Point-Slope Form of the Equation of a Line (No assignment)
Chapter Test 1

(Sections 1.4 and 2.1–2.4)

Recommended study-guide problems

(These are sample exam-like problems for practice purposes; do not turn in with your homework)
(For students with minimal study time)
Page 101 (Ch. 1 Test): 23–25 ALL;
Page 174 (Ch. 2 Test): 1–20 ALL
(For students with additional study time) The above plus some or all of
Page 99 (Ch. 1 Review Exercises): 59–73 ODD (true enthusiasts should try 60–74 EVEN also)
Page 172 (Ch. 2 Review Exercises): 1–18 ALL; 20–52 ALL; and
Additional problems taken from the unassigned homework exercises from section 1.4
Additional problems taken from the unassigned homework exercises from sections 2.1–2.4
3.1 Systems of Linear Equations in Two Variables 1–81 ODD
(For problems 1–5, a candidate solution is provided in the form of an ordered pair, so you don't need to graph or solve the system; you just plug in the given ordered pair (preferably using the "woo-hoo" parentheses method) to see whether it is correct, the goal being to give you practice in checking your proposed solution when you are unable to verify it by looking in the back of the book.)
3.2 Problem Solving and Business Applications Using Systems of Equations 3; 11; 15; 19 (if you need extra practice, you may optionally try the remaining ODD problems from 1–17)
(Each of these problems has enough information to produce a system of two equations in two variables; typically each sentence which contains numbers gives rise to a separate equation, so use the sentence-ending periods as a hint to tell you when the information for one equation ends and the information for the next equation begins.)
3.3 Systems of Linear Equations in Three Variables 5–21 ODD; 27; 29
3.4 Matrix Solutions to Linear Systems 1–37 EOO 44 (must be solved using matrix methods to earn credit)
3.5 Determinants and Cramer's Rule (No required problems; extra credit is optional) 34 (must be solved using Cramer's rule to earn credit)
4.1 Solving Linear Inequalities 1–31 ODD; 59; 65
4.2 Compound Inequalities 1–53 ODD
4.3 Equations and Inequalities Involving Absolute Value 1–73 EOO 94 (must include brief interpretation to earn credit)
4.4 Linear Inequalities in Two Variables 1–45 EOO (please use real graph paper for this section!)
4.5 Linear Programming (No required problems; extra credit is optional) 16(a)(b)(c)(d)(e) (all parts must be completed to earn credit)
Chapter Test 2

(Sections 3.1–3.4 and 4.1–4.4)

Recommended study-guide problems

(These are sample exam-like problems for practice purposes; do not turn in with your homework)
(For students with minimal study time)
Page 250 (Ch. 3 Test): 1–6 ALL; 13–16 ALL
Page 310 (Ch. 4 Test): 1–14 ALL; 16–21 ALL
(For students with additional study time) The above plus some or all of
Page 248 (Ch. 3 Review Exercises): 3–15 ALL; 24; 25; 26; 33; 34; 35; 36
Page 308 (Ch. 4 Review Exercises): 1–23 ODD (or ALL if you have time); 25–33 ALL; 35–47 ODD; 48; 49; and
Additional problems taken from the unassigned homework exercises from chapter 3
Additional problems taken from the unassigned homework exercises from chapter 4
5.1 Introduction to Polynomials and Polynomial Functions 1–53 ODD 58; 62
5.2 Multiplication of Polynomials 1–101 EOO (do all the odds if you need extra practice) 116; 144
5.3 Greatest Common Factor and Factoring by Grouping 1–67 ODD
5.4 Factoring Trinomials 1–89 EOO (if you need extra practice with $ac$ method, try some or all of the other odd problems as well)
5.5 Factoring Special Forms 1–93 EOO (if you need extra practice, try some or all of the other odd problems as well)
5.6 A General Factoring Strategy 1–65 EOO (if you need extra practice, try some or all of the other odd problems as well; the bulk of the next exam will seem very similar to the problems in this section)
5.7 Polynomial Equations and Their Applications 1–45 ODD
6.1 Rational Expressions and Functions: Multiplying and Dividing 1–15 ODD (for #7 through #15, the domain consists of all real numbers such that the denominator is not zero); 27–87 EOO (if you need extra practice, you may optionally try the remaining ODD problems from 29–89)
6.2 Adding and Subtracting Rational Expressions 1–65 EOO (if you need extra practice, you may optionally try the remaining ODD problems from 3–63)
Recall that (1) all subtracted numerators must be parenthesized when they are combined over a single denominator, and (2) canceling is not legal if either term has a plus/minus sign near it.

Recipe:
(1) Factor all denominators which are not prime; parenthesize prime denominators. Make a fraction out of any term which is not already a fraction; for example, convert $8$ into $\frac{8}{1}$.
(2) Multiply any fraction containing a "reversed" denominator with a subtraction (example: $(y-x)$ when there is an $(x-y)$ in another denominator) by $\frac{-1}{-1}$.
(3) Find the LCD by playing "who has the most" with the denominators, and write it down.
(4) Multiply each fraction by the necessary $\frac{\text{fudge factor}}{\text{fudge factor}}$ to create matching LCDs in each denominator. (Do not reduce fractions at this stage!)
(5) Parenthesize each numerator and combine (while retaining the parentheses) into a single numerator over the LCD.
(6) "FOIL", distribute, simplify, and combine like terms in the numerator, then factor the numerator if possible; copy the denominator as empty parentheses at each step. (Never "FOIL" the denominator.)
(7) If possible (usually it isn't), cancel matching factors in the numerator and denominator; write remaining answer in full.
6.3 Complex Rational Expressions (No assignment)
6.4 Division of Polynomials 1–11 ODD

6.5 Synthetic Division and the Remainder Theorem (No assignment)
6.6 Rational Equations 1–33 ODD

Recipe:
(1) Factor all denominators which are not prime; parenthesize prime denominators. Make a fraction out of any term which is not already a fraction; for example, convert $x$ into $\frac{x}{1}$.
(2) Multiply any fraction containing a "reversed" denominator with a subtraction (example: $(y-x)$ when there is an $(x-y)$ in another denominator) by $\frac{-1}{-1}$.
(3) Find the LCD by playing "who has the most" with the denominators, and write it down.
(4) Multiply every term or fraction in the equation by $\frac{\text{LCD}}{1}$, but do not FOIL or distribute anything.
(5) Cancel all matching pairs of factors in the numerator and denominator; only cancel factors with a multiplication symbol (possibly an invisible one) next to them.
(6) All denominators should be 1 and disappear, but if they are not, return to step (1) and repeat.
(7) FOIL or distribute everything, then combine like terms.
(8) If the result is linear, solve the equation by isolating the variable. If the result is a polynomial equation (quadratic or higher), then isolate a zero on one side of the equation, then solve by factoring the non-zero side.
(9) (REQUIRED) Substitute each candidate solution into the original equation to verify. Discard any candidate solutions which cause any denominator to become zero. Box the remaining solutions or, if none remain, indicate that the solution is the empty set $\varnothing$.
6.7 Formulas and Applications of Rational Equations 1–13 ODD

Recipe:
(1) Follow steps (1) through (7) from the recipe in section 6.6.
(2) Using addition or subtraction ONLY, move any term containing the "FOR" variable to the left side of the equation, and any term not containing the "FOR" variable to the right side of the equation.
(3) If there is more than one occurrence of the "FOR" variable on the left side of the equation, factor the left side into a distributive with the "FOR" variable in front. If there is only one occurrence of the "FOR" variable on the left side, then continue to the next step.
(4) Divide both sides of the equation by whatever factors remain on the left side of the equation other than the "FOR" variable. This should isolate the "FOR" variable to complete the problem. You do not have to check formula problems.
6.8 Modeling Using Variation (No assignment)
Chapter Test 3

(Sections 5.1–5.7, 6.1–6.4, and 6.6–6.7)

Recommended study-guide problems

(These are sample exam-like problems for practice purposes; do not turn in with your homework)

Examination is scheduled for Monday 17 April
(For students with minimal study time)
Page 401 (Ch. 5 Test): 6–13 ALL; 16–37 ALL
Page 499 (Ch. 6 Test): 2–11 ALL; 14; 15; 16; 20; 21; 23
(For students with additional study time) The above plus some or all of
Page 398 (Ch. 5 Review): 1–3 ALL; 11–89 ODD; 93–97 ODD
Page 496 (Ch. 6 Review): 1–27 ODD; 35; 36; 49–55 ODD; 57; 59; 61; and
Additional problems taken from the unassigned homework exercises from chapter 5
Additional problems taken from the unassigned homework exercises from chapter 6
7.1 Radical Expressions and Functions 1–89 ODD; problems 27–31 require graph paper (if you need extra practice, you may optionally try 91–94 ALL)
7.2 Rational Exponents 1–111 EOO (if you need extra practice, you may optionally try the remaining ODD problems from 3–109)

How to determine whether an expression containing exponents is fully simplifed:
1. All parentheses have been processed and removed
2. Coefficients are fully reduced to lowest terms, and contain no decimals or fractions
3. The resulting expression contains at most one negative sign (and it must precede the expression, not appear in an exponent)
4. Each variable (letter) appears no more than once (exception: "small" variables appearing in exponents are not limited)
5. Each and every exponent is positive (exponents of 1 are customarily omitted from the final result)
7.3 Multiplying and Simplifying Radical Expressions 1–81 EOO
7.4 Adding, Subtracting, and Dividing Radical Expressions 1–61 EOO; 63; 65 (if you need extra practice, you may optionally try the remaining ODD problems from 3–59)
7.5 Multiplying with More Than One Term and Rationalizing Denominators 1–89 EOO
7.6 Radical Equations 1–37 EOO 44; 46
7.7 Complex Numbers 1–91 ODD
8.1 The Square Root Property and Completing the Square 1–61 EOO

Recipe for completing the square:
(0) If the problem is an expression, write it in the form $y=ax^2 + bx + c$; if it is an equation, write it in the form $0=ax^2 + bx + c$.
(1) Add or subtract the $c$ term as needed to remove it from the right side of the equation (it will show up next to $y$ or the $0$ on the left).
(2) Divide the entire equation (each term) by $a$; if there is a negative in front of the $x^2$ term, multiply or divide each term by $-1$. This step may create fractions; do not be alarmed.
(3a) In the margin, multiply the coefficient of the $x$ term (last term on the right) by $\frac{1}{2}$ and call the result $h$ (for "half"); make a note of it.
(3b) In the margin, square $h$ (that is, find the value of $h^2$) and write it also.
(4) Return to the main calculation and add $h^2$ to both sides of the equation (simply append "$+ h^2$" to the other terms already present).
(5) Concurrently simplify the left side as needed (this may require using an LCD), and factor the right side into a perfect square of the form $\left(x + h\right)^2$. The value of $h$ from step (3a) will always be the number next to the $x$ inside the parentheses (it's mathemagical).
(6) If the original problem was an expression, then isolate $y$ on the left side by adding or subtracting a term (if needed) and then clearing fractions (if needed), in that order. If the original problem was an equation, then take the square root of both sides of the equation (always insert a $\pm$), and take additional steps as needed to isolate $x$. In either case, never "FOIL" or distribute the parentheses from step (5).
8.2 The Quadratic Formula 1–53 EOO

Recall that the "discriminant" is given by the value of the expression ${b^2} - 4ac$.

Never use the quadratic formula until the equation is free of parentheses and there is a zero on one side of the equation.
9.1 Exponential Functions 1–11 ODD; 17–23 ODD
9.3 Logarithmic Functions 1–19 ODD (use the rearrangement mechanism with the understanding that $b^n=p$ is equivalent to ${\log _b}n=p$);
21–41 ODD (hang "$=x$" onto the right side of the equation, then solve using the rearrangement mechanism);
53–71 ODD (use the properties summarized on the bottom of page 698 of the textbook, or try the rearrangement mechanism);
Recall that $\ln x$ is always equivalent to ${\log _e}x$; convert all radicals to fractional powers before working any logarithm problem
9.4 Properties of Logarithms 1–35 ODD (an expanded answer contains no products, quotients, radicals, or exponents);
37–59 ODD (a condensed answer contains no plus or minus signs and no coefficients, and "log" or "ln" appears no more than one time);
61–67 ODD (use the change-of-base formula and your calculator to obtain a decimal approximation rounded to the nearest ten-thousandth)
9.5 Exponential and Logarithmic Equations 1–63 ODD
Final Examination

(Chapters 7–9)

Recommended study-guide problems

(These are sample exam-like problems for practice purposes; do not turn in with your homework)

Bring your Chapter 7/8/9 homework to the final for up to 20 points credit! (Not extra credit!)

Exam starts at 8:00 a.m. on Wednesday 17 May
(For students with minimal study time)

Page 578 (Ch. 7 Test): 1–23 ALL; 25–30 ALL

Page 626 (8.3 homework): 18–38 EVEN (use a graphing calculator, or Meta-calculator, to check your graphs; to use Meta-calculator, click on "Graphing Calculator", type your equation in box 1 [#17 would be "y=(x‑4)^2‑1" without the quotes], and click the "Graph" tab)

Page 659 (Ch. 8 Test): 1–5 ALL; 9–12 ALL; 16; 17
You may wish to print the handout "Quadratic Functions: Questions and Answers" to help with your review of Chapter 8.

Page 753 (Ch. 9 Test): 1; 4; 5(a); 6; 7; 9; 10; 11; 14–26 ALL
(For students with additional study time) The above plus some or all of

Page 576 (Ch. 7 Review): 1–75 ODD; 81; 83; 87–101 ODD

Page 657 (Ch. 8 Review): 1; 3; 5; 8; 9; 10; 14; 15; 16; 21; 23; 25; 33; 34; 35; 36

Page 749 (Ch. 9 Review): 1; 2; 14–40 ALL; 46; 47; 48; 53–81 ODD

Additional problems taken from the unassigned homework exercises from chapter 7
Additional problems taken from the unassigned homework exercises from chapter 8
Additional problems taken from the unassigned homework exercises from chapter 9

## Course Handouts and Study Aids

• PDF (Adobe® Acrobat Reader™) is the best format to use if you want to print on paper (for example, to replace a lost copy).
• HTML files are not, for the most part, printer-friendly; this is the best format for on-screen reading, and if you can read these words, you already have the software!
• DOC and DOCX files are in the native Microsoft® Word format; if you do not have Word, use this Word Viewer from the Microsoft web site (this software can display Word files, but cannot modify them).
• PPT files are PowerPoint® presentations; if you do not have PowerPoint, use this PowerPoint Viewer, again from the Microsoft web site.

## Will You Succeed or Fail in Mathematics?

This checklist is adapted from a handout prepared by math and philosophy instructor Steve Thomassin. It will allow you to compare your approach to a mathematics course to the approaches taken by successful … and unsuccessful … students.

Overview: This table lists typical attributes of successful and unsuccessful mathematics students. It contains three columns. First row: Column headers. Second and subsequent rows: Student attributes. Details: The first row is the table header, with column headings describing the data listed in the main body of the table. The second and subsequent rows describe specific attributes that contribute to success or failure. Column one of these rows specifies whether the attribute is related to attitude, class work, homework, or getting help. Column two of these rows contains attributes of successful students. Column three of these rows contains attributes of unsuccessful students.
Attribute Type Predictor of Success Predictor of Failure
Attitude Focus on things that are under your control. Blame things that are out of your control (the text, the instructor, or "the system") for your difficulties.
Be optimistic. Believe that you can do it. Be pessimistic. Convince yourself that you will fail.
Be positive. Find ways to make math interesting and fun. Be negative. Find ways to make math dull and painful.
Be open. See the uses, power, patterns, and magic of mathematics. Be closed. Blind yourself to math's uses and its practical and esthetic value.
Be practical. Make yourself aware of the doors that passing each math class opens to you. Be impractical. Ignore the doors that open when you pass a math class.
Class Work Attend every class. Aim for perfect attendance, even if you already know it all. Be absent often. Dig a hole so deep that you cannot climb out except by dropping the course.
Be focused. Concentrate on the math topic at hand. Be mentally elsewhere. Daydream. Talk. Distract and annoy neighboring students.
Take good notes. Solve problems along with the instructor. Avoid participating in the discussion. Just watch the instructor.
Be inquisitive. Ask questions so that the instructor knows what you would like to learn more about. Be uninterested. Make the instructor guess what it is that you might be confused about.
Homework Be regular. Always do at least some homework before the next class, and finish by the due date. Be sporadic. Do homework only when it easily fits your schedule.
Invest time. Spend double to triple the amount of in-class time. Invest little time. Spend less time doing homework than you spend in class.
Review notes; read text; do all assigned problems (maybe even more), and check the answers. Ignore notes and text explanations; try a few problems, and don't bother checking to see if they are right.
Getting Help When needed, take advantage of all opportunities: study groups, tutors, instructor office hours. Even when lost, never seek assistance.

Michael Bowen's VC Course Pages: Math V03, Spring 2017