PRECALCULUS
NOTES and TESTS
WEB SITE 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).
TRIG IDENTITIES HANDOUTS:
Handout
#1 (Basic IDs)
Handout
#2 (Advanced IDs)
ALGEBRA NOTES and TRIG NOTES
ALGEBRA NOTES
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NEW NOTES/BOOK REPLACING PRELIMINARIES AND CHAPTER 1 BELOW
Chapter 0: Preliminary Topics (2-page intro + 99
pages)
BIG FILE: Chapter 0
SMALLER FILES (if you cant get the big file):
Sections
0.1-0.5
Sections 0.6-0.10
Sections 0.11-0.16
Factoring "Handout"
This is already part of the notes (in Section
0.7), but here's a separate file. Factoring.pdf
Chapter 1: Functions (167 pages)
BIG FILES: Chapter
1: Sections 1.1-1.4
Sections 1.5-1.11
SMALLER FILES (if you cant get the big files):
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
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Preliminaries: (3-page intro + 44 pages)
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
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)
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
MINOR CORRECTION:
Section 2.5, Notes 2.55: Factor
over C and find all of its complex zeros.
Section
2.5, Part 3 (New! The QF Method for Factoring Quadratics)
Section
2.6 in Larson: Rational Functions
Section
2.7 in Larson: Nonlinear Inequalities
Chapter 3: Exponential and Log Functions (40 pages)
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)
Section
4.1 in Larson: (Angles); Radian and Degree Measure
Sections 4.2-4.4 in Larson: Trig Functions (Values
and Identities)
Visualizing the Six Basic Trig Functions
TrigSixParts.pdf
(corrected late 2/11/06)
Section 4.5 in Larson: Graphs of Sine and Cosine
Functions
Section 4.6 in Larson: Graphs of Other Trig
Functions
Section
4.7 in Larson: Inverse Trig Functions
Smaller files for older computers:
Section
4.8 in Larson: Applications
Chapter 5: Analytic Trig (61 pages)
Section
5.1 in Larson: Fundamental Identities (IDs)
Section
5.2 in Larson: Verifying Trig IDs
Section 5.3 in Larson: Solving Trig Equations
Sections
5.4 and 5.5 in Larson: More Trig Ids
Handout
#1 (Basic IDs)
Handout
#2 (Advanced IDs)
Chapter 6: Additional Topics in Trig (38 pages of primary notes)
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")
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!
MORE ALGEBRA NOTES; LINEAR ALGEBRA NOTES
Chapter 7: Systems and Inequalities
Sections
7.1-7.3 in Larson: Systems of Equations
Section 7.4 in Larson: Partial Fractions
Sections
7.5-7.6 in Larson: Graphing Inequalities and Linear Programming
Chapter 8: Matrices and Determinants
Section
8.1 in Larson: Matrices and Systems of Equations
Smaller files for older computers:
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
Sections
9.1 and 9.6 in Larson: Sequences, Series, and Counting
Sections
9.2 and 9.3 in Larson: Arithmetic and Geometric Sequences, Partial Sums,
and Series
Section
9.4 in Larson: Mathematical Induction
Section
9.5 in Larson: Binomial Theorem
The Beauty of Pascal's Triangle
The
Magic of Pascal's Triangle (Plinko from The Price is Right and Word Jumbles)
Chapter 10: Conics and Polar Coordinates
(in progress)
Email me
website (other classes; general Mesa
College info).
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PRECALCULUS TESTS
Old Exams and Solutions (Spring 2010)
WARNING: Quiz
1A is keyed to Ch.0 of my new notes/book and (Prelims and 1.1-1.3) of my older
notes. Quiz 1B is keyed to (Section 0.16 on variation and Ch.1) of my new
notes/book and (1.4-1.10) of my older notes.
Quiz
1A (Ch.0 in my new notes/book)
Solutions
(1 hour and 10 minutes)
Quiz
1B (Ch.1 in my new notes/book)
Solutions
(50 minutes)
Midterm
#2 (Chs.2 and 3)
Solutions
(40 minutes for Part 1; 1 hour and 30 minutes for Part 2)
Midterm
#3 (Ch.4)
Solutions
(35 minutes for Part 1; 1 hour and 35 minutes for Part 2).
Midterm
#4 (Chs.5 and 6)
Solutions
(50 minutes for Part 1; 1 hour and 20 minutes for Part 2)
Final
(Chs.7-10)
Solutions
(2 hours and 20 minutes)
Email me
website (other classes; general Mesa
College info).