PRECALCULUS
NOTES
TRIG IDENTITIES HANDOUTS: Handout #1 (Basic IDs) … Handout #2 (Advanced IDs)
WEB SITE COMMENTS: Note:
I am always revising these notes; I need to revise the page references after
Chapter 1. These course notes are keyed to Larson's Precalculus, but they can stand alone. 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, San Diego Mesa
College. Email
me … website (other classes; general
Mesa College info).
ALGEBRA NOTES
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
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)
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PRECALCULUS TESTS
Old Exams and Solutions (Fall 2008)
Old Midterm #1
(Prelims, Ch.1) … Solutions (2 hours and 20
minutes) - compatible with Adobe Reader/Acrobat, Version 6.0 and later
Larger files that are compatible with Adobe Reader/Acrobat,
Version 5.0:
Midterm #1
(Prelims, Ch.1) … Solutions (2 hours and 20
minutes)
Old Midterm #2
(Chs.2 and 3) … Solutions (30 minutes for
Part 1; 1 hour and 40 minutes for Part 2)
These files are smaller, but the graphics are
poor:
Midterm #2
(Chs.2 and 3) … Solutions …
Old Midterm #3
(Ch.4) … Solutions (30 minutes for Part 1; 1
hour and 40 minutes for Part 2). If you have trouble downloading, viewing, or
printing this, Email me.
Old Midterm #4
(Chs.5 and 6) … Solutions (50 minutes for
Part 1; 1 hour and 30 minutes for Part 2)
Old Final
(Chs.7-9) … Solutions (2 hours and 20
minutes)