PRECALCULUS NOTES and TESTS / EXAMS

(ALGEBRA NOTES and TRIG NOTES;

 ALGEBRA TESTS / EXAMS and TRIG TESTS / EXAMS)

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• Printing Suggestions for Typed Files

I recommend two-page-to-a-side and/or double-sided printing to save paper. If the typed print is too small, try something like Page Setup: Scale: 110% or 105%, unless print gets cut off (100% may be better for handwritten notes). Color printing is nice, but B&W printing is cheaper.

These are pdf files. You can get the free Adobe Reader at http://www.adobe.com. Get a version that is compatible with your system!

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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)

• OTHER RESOURCES: Click here

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EXERCISES

(CONTINUALLY REVISED)

#1-A: HW … Answers … (revised 7/28/14)

• Chapter 0: Preliminary Topics:

#1-B: HW … Answers … (revised 2/9/14)

• Chapter 1: Functions

#2: HW … Answers … (revised 2/21/14)

• Chapter 2: Polynomial and Rational Functions

• Chapter 3: Exponential and Logarithmic Functions

#3: HW … Answers … (revised 10/27/12)

• Chapter 4: Trigonometry

#4: HW … Answers … (revised 4/6/13)

• Chapter 5: Analytic Trigonometry

• Chapter 6: Additional Topics in Trigonometry

#5: HW … Answers … (revised 4/29/13)

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

PolarGraphPaper (may help)

• 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.

• Chapter 1: Functions (167 pages)

• CORRECTION to 1.2.3! In the middle of page 1.2.3, -9 (instead of 9) is not in the domain of f.

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

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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

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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

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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Old Exams and Solutions (Fall 2013) – will be deleted in August 2014 (?)

Quiz 1A …  Solutions (1 hour and 15 minutes)

• Chapter 0: Preliminary Topics

Quiz 1B …  Solutions (45 minutes)

• Chapter 1: Functions

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

• Chapter 2: Polynomial and Rational Functions

• Chapter 3: Exponential and Logarithmic Functions

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

• Chapter 4: Trigonometry

Midterm #4 …  Solutions (45 minutes for Part 1; 1 hour and 25 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

• Chapter 8: Matrices and Determinants

• Chapter 9: Discrete Math

• Chapter 10: Conics and Polar Coordinates [as time permits]

Current Exams and Solutions (Spring 2014) – will be deleted in January 2015 (?)

Quiz 1A …  Solutions (1 hour and 15 minutes)

• Chapter 0: Preliminary Topics

Quiz 1B …  Solutions (45 minutes)

• Chapter 1: Functions

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

• Chapter 2: Polynomial and Rational Functions

• Chapter 3: Exponential and Logarithmic Functions

Midterm #3 …  Solutions (35 minutes for Part 1; 1 hour and 35 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

• Chapter 8: Matrices and Determinants

• Chapter 9: Discrete Math

• Chapter 10: Conics and Polar Coordinates [as time permits]

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CALCULUS NOTES and TESTS

Email me … website (other classes, resources)