PRECALCULUS NOTES and TESTS

(ALGEBRA NOTES and TRIG NOTES;

 ALGEBRA TESTS and TRIG TESTS)

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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 you’re 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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• TUTORING SITES:

• http://www.tutorvista.com … online tutoring

• http://www.akaritutoring.com … online tutoring

• http://www.ziizoo.com … like Google for tutors

• OTHER RESOURCES:

Click here

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EXERCISES

(CONTINUALLY REVISED)

#1-A: HW … Answers … (Ch.0 in my notes) (9 points) … (revised 1/19/12)

#1-B: HW … Answers … (Ch.1) (6 points) … (revised 1/19/12)

#2: HW … Answers … (Chs.2 and 3) (15 points) … (revised 8/3/11)

#3: HW … Answers … (Ch.4) (15 points) … (revised 1/19/12)

#4: HW … Answers … (Chs.5 and 6) (15 points) … (revised 1/19/12)

#5: HW … Answers … (Chs.7-10) (25 points) … (revised 1/19/12)

Longer version (sections not called “additional”): HW … Answers …

PolarGraphPaper (may help)

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ALGEBRA NOTES

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PrecalcCover

• Chapter 0: Preliminary Topics (2-page intro + 99 pages)

BIG FILE: Chapter 0

SMALLER FILES (if you can’t 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: Sections 1.1-1.4 … Sections 1.5-1.11

SMALLER FILES (if you can’t 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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• Old Versions of Chapters 0 and 1

Preliminaries: (3-page intro + 44 pages)

Part 1: Logic

Part 2: Basic Algebra I

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

Part 3: Basic Algebra II

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 (if you can’t get the big files):

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

• MINOR CORRECTION:

Section 2.5, Notes 2.55: Factor … over C and find all of its complex zeros.

Part 2

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)

BIG FILE: Chapter 3

SMALLER FILES (if you can’t get the big file):

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

SMALLER FILES (if you can’t get the big files):

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

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 (if you can’t get the big files):

Section 5.1 in Larson: Fundamental Identities (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

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 (if you can’t get the big file):

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

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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 (if you can’t get the big file):

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

SMALLER FILES (if you can’t get the big file):

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 (if you can’t get the big file):

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 (handwritten; in progress)

BIG FILE: Chapter 10

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PRECALCULUS TESTS

(ALGEBRA TESTS and TRIG TESTS)

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Exams and Solutions (Fall 2011) – will be replaced in August 2012 (?)

See Math 141 course site for current exams: Click here

Quiz 1A (Ch.0 in my notes) … Solutions (1 hour and 15 minutes)

Quiz 1B (Ch.1 in my notes) … Solutions (45 minutes)

Midterm #2 (Chs.2 and 3) … Solutions (35 minutes for Part 1; 1 hour and 35 minutes for Part 2)

Midterm #3 (Ch.4) … Solutions (30 minutes for Part 1; 1 hour and 40 minutes for Part 2).

Midterm #4 (Chs.5 and 6) … Solutions (40 minutes for Part 1; 1 hour and 30 minutes for Part 2)

Final (Chs.7-9; 10 was skipped in Fall 2011) … Solutions (2 hours and 20 minutes).

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CALCULUS NOTES and TESTS

Email me … website (other classes, resources)