PRECALCULUS NOTES and TESTS /
EXAMS
(ALGEBRA NOTES and TRIG NOTES;
ALGEBRA TESTS / EXAMS and TRIG
TESTS / EXAMS)
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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)
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OTHER RESOURCES: Click
here
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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.)
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ALGEBRA NOTES
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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!)
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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
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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
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TRIG NOTES
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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
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MORE ALGEBRA NOTES;
LINEAR ALGEBRA NOTES
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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
CHAPTER 10:
TYPED NOTES ON PARABOLAS (OPTIONAL) AND POLAR CURVES (REQUIRED)
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.
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PRECALCULUS TESTS
(ALGEBRA TESTS and TRIG TESTS)
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Old
Exams and Solutions (Fall 2019) will be deleted in August 2020 (?)
Quiz 1A
Solutions (1 hour and
15 minutes)
Chapter 0: Preliminary Topics
Quiz 1B
Solutions (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 (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 2020) will be deleted in January 2021 (?)
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.
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Email me
website (other classes, resources)