PRECALCULUS NOTES and TESTS / EXAMS

(ALGEBRA NOTES and TRIG NOTES;

ALGEBRA TESTS / EXAMS and TRIG TESTS / EXAMS)

--------------------------------------------------------------------------------------------------------

 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.

--------------------------------------------------------------------------------------------------------

 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.

 TRIG IDENTITIES HANDOUTS: Handout #1 (Basic IDs)  Handout #2 (Advanced IDs)

--------------------------------------------------------------------------------------------------------

 TUTORING SITES: http://www.tutorvista.com (online tutoring)   http://www.akaritutoring.com (online tutoring)

--------------------------------------------------------------------------------------------------------

EXERCISES

(CONTINUALLY REVISED)

 Chapter 0: Preliminary Topics:

 Chapter 1: Functions

 Chapter 2: Polynomial and Rational Functions

 Chapter 3: Exponential and Logarithmic Functions

#3: HW  Answers  (revised 9/29/18 – minor edits)

 Chapter 4: Trigonometry

#4: HW  Answers  (revised 4/1/17 – minor edits)

 Chapter 5: Analytic Trigonometry

 Chapter 6: Additional Topics in Trigonometry

#5: HW  Answers  (Chs.7-10) (25 points). (revised 5/1/18 – minor edit)

PolarGraphPaper (Ch.10; created using Mathematica with Microsoft Word)

 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.)

--------------------------------------------------------------------------------------------------------

ALGEBRA NOTES

--------------------------------------------------------------------------------------------------------

 Front Matter, Notation, and Chapter 0: Preliminary Topics (99 pages)

BIG FILE: Chapter 0 (revised 1/27/13)

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.

 Quadratic Formula Song! (Section 0.11):

 Chapter 1: Functions (167 pages)

BIG FILES:

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

 Math Dances for Graphing! (Section 1.3):

 http://9gag.com/gag/4419992/do-the-math-dance (correction: x^2 + y^2 = r^2)

 http://i.imgur.com/T4h78XG.gifv (see the dance!)

--------------------------------------------------------------------------------------------------------

 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

--------------------------------------------------------------------------------------------------------

 Chapter 2: Polynomial and Rational Functions (about 82 pages)

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  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:

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)

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

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:

Section 5.1 in Larson: Fundamental Identities (IDs)

Basic Trig IDs (also in Ch.4, 5.1):

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:

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

Khan Academy on Eulers Formula (Do you have emotion?)

--------------------------------------------------------------------------------------------------------

MORE ALGEBRA NOTES;

LINEAR ALGEBRA NOTES

--------------------------------------------------------------------------------------------------------

 Chapter 7: Systems and Inequalities

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:

 CORRECTIONS: Page 8.58 (top): Pierre [not George] Sarrus. Page 8.60 (middle): lower left [not right] corner.

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:

Sections 9.1 and 9.6 in Larson: Sequences, Series, and Counting

 FIBONACCI TED TALK BY PROF. ARTHUR BENJAMIN:

Sections 9.2 and 9.3 in Larson: Arithmetic and Geometric Sequences, Partial Sums, and Series

 QIX AND FILLING IN A BOX (GEOMETRIC SERIES TALK)

 Sample game:

 Winner! (2x)

Section 9.4 in Larson: Mathematical Induction

 THE HEART OF INDUCTION:

 HANDSHAKE PROBLEM:

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)

 The Price is Right / Plinko winner (the Plinko board is in the second half): http://www.youtube.com/watch?v=vuMir11YFPs. What does this have to do with Pascals triangle? See the links above!

http://www.jcu.edu/math/isep/Quincunx/Quincunx.html (This applet's better.)

 Chapter 10: Conics and Polar Coordinates (handwritten; in progress)

BIG FILE:

 ANIMATION ON CONICS

Corrections: (0:48-1:07) The double-nappe cone (or simply cone) here should not be thought of as finite, so there are no bases and there is no base perimeter.  The term directrix is used elsewhere, especially when describing parabolas.

--------------------------------------------------------------------------------------------------------

PRECALCULUS TESTS

(ALGEBRA TESTS and TRIG TESTS)

--------------------------------------------------------------------------------------------------------

Old Exams and Solutions (Fall 2018) – will be deleted in August 2019 (?)

Quiz 1A   Solutions (1 hour and 15 minutes)

 Chapter 0: Preliminary Topics

Quiz 1B   Solutions (45 minutes)

 Chapter 1: Functions

Midterm #2   Solutions (50 minutes for Part 1; 1 hour and 20 minutes for Part 2)

 Chapter 2: Polynomial and Rational Functions

 Chapter 3: Exponential and Logarithmic Functions

Midterm #3   Solutions (40 minutes for Part 1; 1 hour and 30 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]  (Sections 7.5, 7.6 not on Final.)

 Chapter 8: Matrices and Determinants  (Sections 8.3, 8.5 not on Final.)

 Chapter 9: Discrete Math

 Chapter 10: Conics and Polar Coordinates

Current Exams and Solutions (Spring 2019) – will be deleted in January 2020 (?)

Quiz 1A   Solutions (1 hour and 15 minutes)

 Chapter 0: Preliminary Topics

Quiz 1B   Solutions (50 minutes)

 Chapter 1: Functions

Will be listed here as they are done.

--------------------------------------------------------------------------------------------------------

Email me  website (other classes, resources)