PRECALCULUS NOTES
Note
: I am always revising these; 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).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
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: This Trig IDs handout will be handed out in class. It is critical!
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!
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)
---------------------------------------------------------------------------
OLD EXAMS AND SOLUTIONS (Fall 2007)
Midterm #1 (Prelims, Ch.1) … Solutions (2 hours and 20 minutes)
Midterm #2 (Chs.2 and 3) … Solutions (55 minutes for Part 1; 1 hour and 15 minutes for Part 2)
Broken apart for older computers: Solutions Part 1 … Solutions Part 2
Midterm #3 (Ch.4) … Solutions (35 minutes for Part 1; 1 hour and 35 minutes for Part 2)
Broken apart for older computers: Solutions Part 1 … Solutions Part 2
Midterm #4 (Chs.5 and 6) … Solutions (50 minutes for Part 1; 1 hour and 20 minutes for Part 2)
Broken apart for older computers: … Solutions (1st half) … Solutions (2nd half)
Final (Chs.7-10) … (2 hours and 20 minutes)
Due to the fires, we are expected to skip 9.4 and Ch.10.
Solutions (big file)
Part 1 … Part 2 … (in smaller parts)