*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 10/27/12)

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
4/24/16)

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

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 (Spring 2017)
– will be deleted in January 2018 (?)**

Quiz 1A
Solutions (1 hour and
15 minutes)

Chapter 0:
Preliminary Topics

Quiz 1B
Solutions (45-50
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 (30-40 minutes
for Part 1; 1 hour and 30-40 minutes for Part 2)

Chapter 4:
Trigonometry

Midterm #4
Solutions (40-45 minutes
for Part 1; 1 hour and 25-30 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]

Chapter 8:
Matrices and Determinants

Chapter 9: Discrete
Math

Chapter 10:
Conics and Polar Coordinates

**Current Exams and Solutions (Fall 2017)
– will be deleted in August 2018 (?)**

Quiz 1A
Solutions (1 hour and
15 minutes)

Chapter 0:
Preliminary Topics

Quiz 1B
Solutions (45 minutes)

Chapter 1:
Functions

Will be listed here as they are done.

Email me website (other classes, resources)