Michael Bowen's VC Course Pages

Math V20, Spring 2018

Introduction and Announcements

Welcome to Math V20 (Precalculus Mathematics) at Ventura College. Michael Bowen (email) will be teaching this course during the spring 2018 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 obtain the book from a source other than the campus bookstore, 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:

1. • Author: R. Narasimhan
   • Title: Precalculus: Building Concepts and Connections, Second Edition with All Access Pass
   • ISBN-13: 978-1630981327
   • Comment: This is the hardcover version, which comes with an All Access Pass (gives students access to videos and an electronic copy).

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.

Holidays

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

• Monday 15 January 2018 (Martin Luther King, Jr., Day)
• Friday 16 February–Monday 19 February 2018 (Presidents' Days)
• Monday 26 March–Friday 30 March 2018 (Spring Break)
• Thursday 26 April–Friday 27 April 2018 (Faculty Training)

Please note that Valentine's Day and St. Patrick's Day are not Ventura College holidays.

Final Examination

Place/date/time:  Room SCI-107, Monday 14 May 2018, 12:30 p.m.

Important Note: This is 30 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 and Supplements	E.C.
(Handout)	Obtain a PDF or DOC (Word) version of the Syllabus Worksheet, answer all 15 questions, and return it to the instructor by the second week of class. (NOTE: This assignment is worth 15 points toward your final score in the class.)
1.1	The Real Number System	47–83 ODD; 90–94 ALL	—
1.2	Exponents, Roots, and Radicals	1–23 ODD; 41–97 ODD; 106–110 ALL	—
1.3	Polynomials and Factoring	51–131 ODD; 139–144 ALL; 146	—
1.4	Rational Expressions	1–57 ODD; 63; 64; 65	—
1.5	Linear and Quadratic Equations	13–81 ODD	—
1.6	Linear Inequalities	19–29 ODD; 44; 45; 46	—
1.7	Equations and Inequalities Involving Absolute Value	1–15 ODD; 29–55 ODD	—
1.8	Other Types of Equations	5–31 ODD; 33; 37; 41; 45; 47; 49	—
2.1	The Coordinate System; Lines and Their Graphs	31–39 ODD; 57; 59; 61; 69–101 EOO	—
2.2	Coordinate Geometry; Circles and Other Equations	5–57 EOO (all odds recommended if time permits); 63–69 ODD; 75–79 ALL	—
2.3	Functions	5–41 ODD; 55–67 ODD; 85	—
2.4	Graphs of Functions	7; 9; 11; 17–53 EOO; 55–64 ALL; 72–78 ALL	—
2.5	Analyzing the Graph of a Function	1–26 ALL; 27–37 ODD (hint: calculate $f\left(-x\right)$, compare with $f\left(x\right)$, and use the even/odd boxes on page 145); 41–53 EOO	—
2.6	The Algebra of Functions	7–31 EOO; 33–51 ODD; 53–69 EOO; 91; 93; 95	—
2.7	Transformations of the Graph of a Function	1–29 EOO; 31–38 ALL; 45–59 ODD	—
2.8	Linear Functions and Models; Variation	35–41 ODD	—
Chapter Test 1 Sections 1.1–1.8 and 2.1–2.8 Wed. 7 Feb. 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 86 (Test): 9–41 ODD Page 203 (Review Exercises): 141 Page 204 (Test): 1–10 ALL; 12; 14; 16; 20(a); 21–26 ALL; 31; 32; 35; 37; 39
		(For students with additional study time) The above plus Page 81 (Review Exercises): 17; 19; 21; 31–45 ODD; 61–109 ODD; 113–141 ODD Page 197 (Review Exercises): 5–13 ODD; 19–29 ODD; 39–49 ODD; 53–61 ODD; 65; 67; 69; 73–79 ALL; 81; 89–109 ODD; 110; 111–121 ODD; 128; 130
3.1	Quadratic Functions and Their Graphs	13–33 ODD; 41–61 EOO	—
3.2	Polynomial Functions and Their Graphs	21–29 ODD; 49–61 EOO; 67–81 ODD; 87–105 ODD	—
3.3	Division of Polynomials; the Remainder and Factor Theorems	1–13 ODD; 21–37; 41; 43	—
3.4	Real Zeros of Polynomials; Solutions of Equations	5–17 EOO (all odds recommended if time permits); 19–22 ALL; 25–57 EOO (all odds recommended if time permits)	—
3.5	Complex Numbers	9–27 ODD (rationalize and/or simplify when appropriate); 33–41 EOO (rationalize and/or simplify when appropriate); 53–75 ODD	—
3.6	The Fundamental Theorem of Algebra; Complex Zeros	17–35 ODD	—
3.7	Rational Functions	5–25 ODD; 29–57 EOO; 59–63 ODD	—
3.8	Quadratic, Polynomial, and Rational Inequalities	1–41 ODD	—
4.1	Inverse Functions	9–33 ODD; 37–61 EOO; 67–74 ALL	—
4.2	Exponential Functions	7–17 ODD; 21–45 EOO; 63–69 ODD	—
4.3	Logarithmic Functions	11–55 ODD; 57–69 EOO	—
4.4	Properties of Logarithms	1–43 ODD; 51–59 ODD	—
4.5	Exponential and Logarithmic Equations	5–25 ODD; 31–51 ODD; 57; 61; 65 (for these last three, use the formula from Example 4on page 370 of the textbook)	—
4.6	Exponential, Logistic, and Logarithmic Models	1–20 ALL; 23(a)(b); 25(a); 27(a)(b)	—
Chapter Test 2 Sections 3.1–3.8 and 4.1–4.6 Wed. 21 Mar. 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 314 (Test): 1–11 ODD; 13 (the problem is really asking you to perform polynomial long division; find the quotient and remainder fraction); 15; 17; 19; 25–35 ODD Page 399 (Test): 3; 5; 7; 8; 9; 10; 11; 17–23 ODD; 27; 28
		(For students with additional study time) The above plus Page 309 (Review Exercises): 1–17 ODD; 31–49 ODD; 57–73 ODD; 77–97 ODD; 101–117 ODD Page 395 (Review Exercises): 1–15 ODD; 25; 27; 33–53 ODD; 57–91 ODD; 99; 101(a)(b)
5.1	Angles and Their Measures	21–37 ODD; 51–67 ODD; 77; 79; 81 (start by converting miles per hour to inches per second; angular speed is represented by the variable $\omega$); 85 Note that the textbook is not consistent about whether to convert $\pi$ to a decimal, so if no instructions are provided, write any radians answer in a form that contains $\pi$; if the back of the book gives a decimal answer, don't convert your written answer to a decimal, but check it by using the $\pi$ button on your calculator.	92
5.2	Trigonometric Functions Using the Unit Circle	11–59 ODD; 73–103 ODD	—
5.3	Right Triangle Trigonometry	7–63 ODD	—
5.4	Trigonometric Functions of Any Angle Using Right Triangles	7–13 ODD; 21–97 ODD	—
5.5	Graphs of Sine and Cosine Functions	Please use real graph paper, like this or this or your own, for these problems. 9–33 ODD; 43–53 ODD	—
5.6	Graphs of Other Trigonometric Functions	Please use real graph paper, like this or this or your own, for these problems. 1–11 ODD; 19; 21; 23	—
5.7	Inverse Trigonometric Functions	5–37 ODD	—
6.1	Verifying Identities	21–79 ODD (for the last few problems, note that $\left| {\frac{a}{b}} \right| = \frac{{\left| a \right|}}{{\left| b \right|}}$, and use the logarithm property $\ln \frac{p}{q} = \ln p - \ln q$)	—
6.2	Sum and Difference Identities	9–79 ODD	84; 86
6.3	Multiple-Angle Identities; Sum and Product Identities	9–43 ODD; 77–83 ODD	—
6.4	Trigonometric Equations	9–65 EOO	82
Chapter Test 3 Sections 5.1–5.7 and 6.1–6.4 Mon. 23 Apr. 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 501 (Test): 9–21 ALL; 23; 24; 25; 27; 28 Page 551 (Test): 1–14 ALL; 16–23 ALL; 25 (interpret "first positive value" as "smallest positive value")
		(For students with additional study time) The above plus Page 498 (Review Exercises): 19–39 ODD (ALL recommended if time permits); 45–59 ODD; 63–75 ODD Page 548 (Review Exercises): 1–27 ODD; 30 (use identities to rewrite the given expression in the form $A \sin\left(1000\pi x\right)+B \cos\left(1000\pi x\right)$, where it is your job to determine specific numeric values for $A$ and $B$); 31–34 ALL; 37–57 ODD; 61 (use identities to simplify the equation so it contains only sines or only cosines before you solve it)
7.1	The Law of Sines	9–27 ODD	—
7.2	The Law of Cosines	1–21 ODD	—
7.3	Polar Coordinates	For polar graph paper, you may use this or this. 13–33 ODD	—
7.4	Graphs of Polar Equations	(No assignment)	—
7.5	Vectors	(No assignment)	—
7.6	Dot Product of Vectors	(No assignment)	—
7.7	Trigonometric Form of a Complex Number	(Extra credit only)	40–42
8.1	Systems of Linear Equations and Inequalities in Two Variables	(No assignment)	—
8.2	Systems of Linear Equations in Three Variables	(No assignment)	—
8.3	Solving Systems of Equations Using Matrices	35–51 ODD (please use matrices, not other methods!)	—
8.4	Operations with Matrices	(No assignment)	—
8.5	Matrices and Inverses	(No assignment)	—
8.6	Determinants and Cramer's Rule	29–45 ODD (please use Cramer's rule, not other methods!)	—
8.7	Partial Fractions	(No assignment)	—
8.8	Systems of Nonlinear Equations	1–29 ODD (use elimination or substitution methods; whatever works best)	—
9.1	The Parabola	11–61 ODD	—
9.2	The Ellipse	7–59 ODD	—
9.3	The Hyperbola	7–47 ODD	—
9.4	Rotation of Axes; General Form of Conic Sections	(No assignment)	—
9.5	Polar Equations of Conic Sections	(No assignment)	—
9.6	Pararametric Equations	(No assignment)	—
10.1	Sequences	5–57 ODD	—
10.2	Sums of Terms of Sequences	5–75 ODD	—
10.3	General Sequences and Series	(No assignment)	—
10.4	Counting Methods	(No assignment)	—
10.5	Probability	(No assignment)	—
10.6	The Binomial Theorem	5–41 ODD	44
10.7	Mathematical Induction	(No assignment)	—
Final Examination Chapters 7, 8, 9, 10 Recommended study-guide problems (These are sample exam-like problems for practice purposes; do not turn in with your homework) Bring your Chapter 7/8/9/10 homework to the final for up to 20 points credit! (Not extra credit!) Exam starts at 12:30 p.m. on Monday 14 May		(For students with minimal study time) Page 640 (Test): 1–4 ALL; 6; 7 Page 733 (Test): 5 (solve by using matrices); 11 (solve by using matrices and row operations, not by using the inverse); 12; 13; 14; 17; 18 Page 804 (Test): 1–12 ALL Page 879 (Test): 1–9 ALL; 11; 12(a); 20
		(For students with additional study time) The above plus Page 637 (Review Exercises): 1–7 ODD; 13–19 ODD; 23–32 ALL Page 729 (Review Exercises): 22; 23; 24; 47–54 ALL; 59–62 ALL Page 801 (Review Exercises): 1; 3; 5; 7; 11; 13; 15; 19; 21; 23; 27; 29; 31; 33; 35; 39; 41; 43; 45; 49; 51; 53 Page 875 (Review Exercises): 3; 4; 7; 8; 11–35 ODD; 43(a); 63–70 ALL

Course Handouts and Study Aids

The documents listed below are available for viewing or download. The list below provides links to download free software to read the file formats of the various documents.

• 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.

Course Handouts

• Course Information (HTML)
  Course Information (PDF)
• Course Requirements and Grading, Side 1 (HTML)
  Course Requirements and Grading, Side 1 (PDF)
• Course Requirements and Grading, Side 2 (HTML)
  Course Requirements and Grading, Side 2 (PDF)
• Tips for Success (HTML)
  Tips for Success (PDF)
• Standards of Student Conduct and Classroom Rules (HTML)
  Standards of Student Conduct and Classroom Rules (PDF)
• Syllabus Worksheet (DOC)
  Syllabus Worksheet (PDF)
• Instructor's Schedule (HTML)
  Instructor's Schedule (PDF)

Study Aids

• Multiplication Tables (DOC)
  Multiplication Tables (PDF)
• Divisibility Rules (DOC)
  Divisibility Rules (PDF)
• Sieve of Eratosthenes (PDF) with directions (HTML) (finds prime numbers)
• Powers of Ten Tutorial (HTML) (off-site; requires Java™ Runtime Environment [free download] to be installed and enabled on your computer)
• Translating English Phrases into Algebraic Expressions (DOCX)
  Translating English Phrases into Algebraic Expressions (PDF)
• Multilingual Vocabulary for Mathematics (possibly helpful for students whose first language is not English) (HTML)
• Basic Algebra Review (DOC)
  Basic Algebra Review (PDF)
• Basic Geometry Review (PPT)
  Basic Geometry Review (PDF)
• Rectangular Graph Paper:
  • 4 grids per sheet (PDF)
  • Full-sheet grid, 5 squares to the inch (PDF)
  • Full-sheet grid, 2.5 squares to the inch (PDF)
• Quadratic Functions: Questions and Answers (DOC)
  Quadratic Functions: Questions and Answers (PDF)
• Transformations of Functions (HTML) (may require downloading and installation of free software to view all portions; see the page itself for details)
• Essential Trigonometric Identities for Physics & Calculus (DOC)
  Essential Trigonometric Identities for Physics & Calculus (PDF)
• Polar Graph Paper:
  • 15-degree markings (PDF)
  • 10-degree markings (PDF)

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.