*PRECALCULUS NOTES and TESTS / EXAMS*

**(ALGEBRA NOTES and TRIG NOTES;**

** ****ALGEBRA TESTS / EXAMS and TRIG TESTS
/ EXAMS)**

**--------------------------------------------------------------------------------------------------------**

* Printing Suggestions for Typed Files*

I recommend two-page-to-a-side and/or double-sided printing to
save paper. If the typed print is too small, try something like Page Setup:
Scale: 110% or 105%, unless print gets cut off (100% may be better for handwritten
notes). Color printing is nice, but B&W printing is cheaper.

These
are pdf files. You can get the free Adobe Reader at http://www.adobe.com. Get a version that is
compatible with your system!

**--------------------------------------------------------------------------------------------------------**

**
WEBSITE COMMENTS:**** **Link
to these web pages, not individual pdf files! I am
always revising these notes; I need to revise the page references after Chapter
1. These course notes are currently keyed to Larson's *Precalculus*, but
they can stand alone, and they will be formed into an independent book
(complete with exercises) later. The revolutionary "Frame Method" for
graphing trig functions was inspired by Tom Teegarden
and Karl Smith's *Trigonometry* text. Suggestions are welcome! - Thanks
Ken Kuniyuki (B.S., M.S. *Stanford* / M.A. *UCSD*), Professor: *San
Diego Mesa College*. Email me
website (other classes; general Mesa
College info).

Creative Commons License: For
attribution, simply mention my name and/or web URL somewhere if youre using
huge chunks of the notes. I simply want due credit.

**
PRECALCULUS COURSE WEBSITE: **Click
here

**
TRIG IDENTITIES HANDOUTS: **Handout
#1 (Basic IDs)
Handout #2
(Advanced IDs)

**--------------------------------------------------------------------------------------------------------**

** TUTORING**** SITES:**** **http://www.tutorvista.com
(online tutoring)
http://www.akaritutoring.com (online
tutoring)

**
OTHER RESOURCES: **Click here

**EXERCISES**

**(CONTINUALLY REVISED)**

#1-A:
HW
Answers
(revised 1/19/16)

Chapter 0: Preliminary Topics:

#1-B:
HW
Answers
(revised 9/3/15)

Chapter 1: Functions

#2:
HW
Answers
(revised 9/16/16 – answer to 2.2, #4)

Chapter 2: Polynomial and Rational Functions

Chapter 3: Exponential and Logarithmic Functions

#3:
HW
Answers
(revised 9/29/18 – minor edits)

Chapter 4: Trigonometry

#4:
HW
Answers
(revised 4/1/17 – minor edits)

Chapter 5: Analytic Trigonometry

Chapter 6: Additional Topics in Trigonometry

#5:
HW
Answers
(Chs.7-10)
(25 points). (revised 5/1/18
– minor edit)

PolarGraphPaper
(Ch.10; created using *Mathematica*
with *Microsoft Word*)

Chapter 7: Systems of Equations and Inequalities

Chapter 8: Matrices and Determinants

Chapter 9: Discrete Math

Chapter 10: Conics and Polar Coordinates (Ch.10 is mostly handwritten.)

**ALGEBRA NOTES**

* Front Matter, Notation, and Chapter 0: Preliminary Topics (99
pages)*

**BIG FILE:**** **Chapter 0 (revised 1/27/13)

**SMALLER FILES (for faster download): **Sections
0.1-0.5
Sections
0.6-0.10
Sections
0.11-0.16

**Factoring
"Handout": **Factoring.pdf: This is already
part of the notes (in Section 0.7), but here's a separate file.

** CORRECTED ON 1/27/13: **On the bottom of page 0.2.2, when the converse
is declared to be false, **Z** and **Q** should be switched.

** Quadratic Formula Song! (Section 0.11): **https://www.youtube.com/watch?v=IfpkQVyqK7c

* Chapter 1: Functions (167 pages)*

**BIG FILES:**** **Sections
1.1-1.4
Sections
1.5-1.11

**SMALLER FILES (for faster download): **Sections
1.1-1.2
Sections
1.3-1.4
Sections
1.5-1.7
Sections 1.8-1.9
Sections
1.10-1.11

** CORRECTION to 1.2.3! **In the middle of page 1.2.3, -9 (instead of 9)
is not in the domain of *f*.

**
Math Dances for Graphing! (Section 1.3):**

http://9gag.com/gag/4419992/do-the-math-dance
(correction: x^2 + y^2 = r^2)

http://www.seyedrezabazyar.com/fa/math-dances/

http://i.imgur.com/T4h78XG.gifv
(see the dance!)

* Old Versions of Chapters 0 and 1*

**Preliminaries:
(3-page intro + 44 pages) **
** **Part 1: Logic** **
** **Part 2: Basic Algebra I
Part 3: Basic Algebra II
**Factoring
"Handout": **This is already part of the notes, but here's the
handout as a separate file. Section A.3: Factoring problems: Factoring.pdf

**Chapter
1: Functions and Their Graphs (108 pages) **
** **Sections 1.1, 1.2, and 1.3 in
Larson: Rectangular Coordinates; Graphs of Equations and Circles; Graphs
and Lines** **
** **Section 1.4 in Larson:
Functions** **
Sections 1.5
in Larson: Analyzing Graphs of Functions: Part 1
Part 2
Part 3** **
** **Section 1.6 in Larson: A
Library of Parent Functions** **
**
**Section 1.7 in Larson:
Transformations**
**Section
1.8 in Larson: Combining Functions** **
** **Sections
1.9 and 1.10 in Larson: Inverse Functions; Mathematical Modeling and
Variation

* Chapter 2: Polynomial and Rational Functions (about 82 pages)*

**BIG FILES:**** **Sections
2.1-2.4
Sections
2.5-2.7** **

**SMALLER FILES (for faster download):**

Section 2.1 in Larson:
Quadratic Functions (and Parabolas)

Section 2.2 in Larson:
Polynomial Functions of Higher Degree

Section 2.3 in Larson: Long and
Synthetic Polynomial Division

Section 2.4 in Larson: Complex
Numbers

Section
2.5 in Larson: Finding Zeros of Polynomial Functions

Part 1
Part 2
Section 2.5, Part 3 (New!
The QF Method for Factoring Quadratics)

** MINOR CORRECTION: **Section 2.5, Notes 2.55: Factor
over **C**
and find all of its ** complex** zeros.

Section 2.6 in Larson: Rational
Functions

Section 2.7 in Larson:
Nonlinear Inequalities

* Chapter 3: Exponential and Log Functions (40 pages)*

**BIG FILE:**** **Chapter 3

**SMALLER FILES (for faster download):**

Section 3.1 in Larson:
Exponential Functions and Their Graphs

Section 3.2 in Larson: Log
Functions and Their Graphs

Section 3.3 in Larson: (More)
Properties of Logs

Sections 3.4 and 3.5 in Larson:
Exponential and Log Equations and Models

**TRIG NOTES**

* Chapter 4: Trigonometry (Intro) (93 pages)*

**BIG FILES:**** **Sections
4.1-4.4
Sections
4.5-4.6
** **Sections
4.7-4.8
Handout
#1 (Basic IDs)

**SMALLER FILES (for faster download):**

Section 4.1 in Larson:
(Angles); Radian and Degree Measure

Sections
4.2-4.4 in Larson: Trig Functions (Values and Identities): Part 1
Part 2

**Basic
Trig IDs (handout in class): **Basic Trig IDs
(also in 5.1 notes)

**Visualizing
the Six Basic Trig Functions: **http://www.kkuniyuk.com/TrigSixParts.pdf
(corrected late 2/11/06)

Section
4.5 in Larson: Graphs of Sine and Cosine Functions: Part 1
Part 2

Section
4.6 in Larson: Graphs of Other Trig Functions: Part 1
Part 2

Section 4.7 in Larson: Inverse
Trig Functions

Smaller
files for older computers: Part
1
Part 2

Section 4.8 in Larson:
Applications

* Chapter 5: Analytic Trig (61 pages)*

**BIG FILES:**** **Sections 5.1-5.3
Sections
5.4-5.5 and IDs** **

**SMALLER FILES (for faster download):**

Section 5.1 in Larson:
Fundamental Identities (IDs)

**Basic
Trig IDs (also in Ch.4, 5.1): **Basic Trig IDs

Section 5.2 in Larson:
Verifying Trig IDs

Section
5.3 in Larson: Solving Trig Equations: Part 1
Part 2

Sections 5.4 and 5.5 in Larson:
More Trig Ids

**Trig IDs:** Handout #1 (Basic
IDs)
Handout #2
(Advanced IDs)

* Chapter 6: Additional Topics in Trig (38 pages of primary
notes)*

**BIG FILE:**** **Chapter 6

**SMALLER FILES (for faster download):**

Section 6.1 in Larson: The Law
of Sines

Section 6.2 in Larson: The Law
of Cosines

**Flowchart
for Sections 6.1 and 6.2** (better for practical use than actual
"memorization"): M1410601Chart.pdf

Section 6.3 in Larson: Vectors
in the Plane

Section 6.4 in Larson: Vectors
and Dot Products

Section 6.5 in Larson: Trig
Form of a Complex Number

**Related
"Handout"**
(not handed out in class, though; print it!): M1410605Handout.pdf

**Khan
Academy on Eulers Formula** (Do you have emotion?)

https://www.youtube.com/watch?v=mgNtPOgFje0

**MORE ALGEBRA NOTES;**

** LINEAR ALGEBRA NOTES**

* Chapter 7: Systems and Inequalities*

**BIG FILE:**** **Chapter 7

**SMALLER FILES (for faster download):**

Sections 7.1-7.3 in Larson:
Systems of Equations

Section
7.4 in Larson: Partial Fractions: Part 1
Part 2

Sections 7.5-7.6 in Larson:
Graphing Inequalities and Linear Programming

* Chapter 8: Matrices and Determinants*

**BIG FILE:**** **Chapter 8

** CORRECTIONS: **Page 8.58 (top): Pierre
[not George] Sarrus. Page 8.60 (middle): lower left
[not right] corner.

**SMALLER FILES (for faster download):**

Section 8.1 in Larson: Matrices
and Systems of Equations

Smaller
files for older computers: Part
1
Part 2

Section 8.2 in Larson: Matrix
Operations

Section 8.3 in Larson: Matrix
Inverses

Section 8.4 in Larson:
Determinants

Section 8.5 in Larson: Applications
of Determinants

* Chapter 9: Discrete Math*

**BIG FILE:**** **Chapter 9

**SMALLER FILES (for faster download):**

Sections 9.1 and 9.6 in Larson:
Sequences, Series, and Counting

** FIBONACCI SCULPTURE: **http://sfglobe.com/2015/01/14/3d-printed-sculptures-look-alive-when-spun-under-a-strobe-light/

** FIBONACCI TED TALK BY PROF. ARTHUR BENJAMIN: **https://www.youtube.com/watch?v=SjSHVDfXHQ4

Sections 9.2 and 9.3 in Larson:
Arithmetic and Geometric Sequences, Partial Sums, and Series

** QIX AND FILLING IN A BOX (GEOMETRIC SERIES TALK)**

** Sample game: **https://www.youtube.com/watch?v=Wvzyd0OZg1I

** Winner! (2x) **https://www.youtube.com/watch?v=RGSPj3vlR6M

Section 9.4 in Larson: Mathematical
Induction

** THE HEART OF INDUCTION: **https://www.youtube.com/watch?v=p_E3feHZtZM

** HANDSHAKE PROBLEM: **https://www.youtube.com/watch?v=dIejOnMP20c

** KHAN ACADEMY ON INDUCTION: **https://www.khanacademy.org/math/algebra-home/alg-series-and-induction/alg-induction/v/proof-by-induction

Section 9.5 in Larson: Binomial
Theorem

**The
Beauty of Pascal's Triangle**

http://www.mathsisfun.com/pascals-triangle.html

See
also __Chaos and Fractals__ by Peitgen, et al.

http://en.wikipedia.org/wiki/Pascal's_triangle

The Magic of Pascal's
Triangle (Plinko from *The Price is Right*
and Word Jumbles)

**QUINCUNX ("PLINKO") APPLETS AND SITES**

**
***The Price is Right / Plinko** *winner (the Plinko board is in the second half): http://www.youtube.com/watch?v=vuMir11YFPs.
What does this have to do with Pascals triangle? See the links above!

http://www.jcu.edu/math/isep/Quincunx/Quincunx.html** **(This applet's better.)

* Chapter 10: Conics and Polar Coordinates (handwritten; in
progress)*

**BIG FILE:**** **Chapter 10

** ANIMATION ON CONICS**

https://www.youtube.com/watch?v=HO2zAU3Eppo

Corrections: (0:48-1:07) The double-nappe cone (or simply cone) here should not be thought of
as finite, so there are no bases and there is no base perimeter. The term directrix
is used elsewhere, especially when describing parabolas.

**PRECALCULUS TESTS**

**(ALGEBRA TESTS and TRIG TESTS)**

**Old Exams
and Solutions (Fall 2018) – will be deleted in August 2019 (?)**

Quiz 1A
Solutions (1 hour and
15 minutes)

Chapter 0: Preliminary Topics

Quiz 1B
Solutions (45 minutes)

Chapter 1: Functions

Midterm #2
Solutions (50 minutes
for Part 1; 1 hour and 20 minutes for Part 2)

Chapter 2: Polynomial and Rational Functions

Chapter 3: Exponential and Logarithmic Functions

Midterm #3
Solutions (40 minutes
for Part 1; 1 hour and 30 minutes for Part 2)

Chapter 4: Trigonometry

Midterm #4
Solutions (40 minutes
for Part 1; 1 hour and 30 minutes for Part 2)

Chapter 5: Analytic Trigonometry

Chapter 6: Additional Topics in Trigonometry

Final
Solutions (2 hours
and 20 minutes). Material covered in later terms may differ.

Chapter 7: Systems of Equations [and Inequalities] (Sections 7.5, 7.6 not on Final.)

Chapter 8: Matrices and Determinants
(Sections 8.3, 8.5 not on Final.)

Chapter 9: Discrete Math

Chapter 10: Conics and Polar Coordinates

**Current
Exams and Solutions (Spring 2019) – will be deleted in January 2020 (?)**

Quiz 1A
Solutions (1 hour and 15
minutes)

Chapter 0: Preliminary Topics

Quiz 1B
Solutions (50 minutes)

Chapter 1: Functions

Will be listed here as they are done.

Email me
website (other classes, resources)