Pre Cal Notes

These are the notes from the latest textbook series.



For more detailed notes - see the below downloadable PDF files.

The below notes are from Professor Ken Kuniyuki's Web Page and they follow along with our material. 

• Old Versions of Chapters 0 and 1

Preliminaries: (3-page intro + 44 pages) Part 1: Logic Part 2: Basic Algebra IPart 3: Basic Algebra IIFactoring "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)


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 1.1-1.4Sections 1.5-1.11

SMALLER FILES (for faster download):

Sections 1.1-1.2 … Rectangular Coordinates; Graphs of Equations and Circles

Sections 1.3-1.4 … Graphs and Lines ; Functions

Sections 1.5-1.7 … Analyzing Graphs of Functions; A Library of Parent Functions; Transformations

Sections 1.8-1.9 … Combining Functions; Inverse Functions

Sections 1.10-1.11 ... Mathematical Modeling and Variation

Sections 1.1, 1.2, and 1.3 in Larson: ;

Section 1.4 in Larson:

Sections 1.5 in Larson: Analyzing Graphs of Functions: Part 1Part 2Part 3

Section 1.6 in Larson: A Library of Parent Functions

Section 1.7 in Larson:

Section 1.8 in Larson

Sections 1.9 and 1.10 in Larson: ;

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

BIG FILES: Sections 2.1-2.4Sections 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 1Part 2Section 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 4.1-4.4Sections 4.5-4.6 Sections 4.7-4.8Handout #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 1Part 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 1Part 2

Section 4.6 in Larson: Graphs of Other Trig Functions: Part 1Part 2

Section 4.7 in Larson: Inverse Trig Functions

Smaller files for older computers: Part 1Part 2

Section 4.8 in Larson: Applications

• Chapter 5: Analytic Trig (61 pages)

BIG FILES: Sections 5.1-5.3Sections 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 1Part 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

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

https://www.youtube.com/watch?v=mgNtPOgFje0

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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 1Part 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 1Part 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

• FIBONACCI SCULPTURE: http://sfglobe.com/2015/01/14/3d-printed-sculptures-look-alive-when-spun-under-a-strobe-light/

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: https://www.youtube.com/watch?v=Wvzyd0OZg1I

• Winner! (2x) https://www.youtube.com/watch?v=RGSPj3vlR6M

Section 9.4 in Larson: Mathematical Induction

• THE HEART OF INDUCTION: https://www.youtube.com/watch?v=p_E3feHZtZM

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 (Spring 2016) – will be deleted in January 2017 (?)

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 (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]



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


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

SMALLER FILES (for faster download): Sections 0.1-0.5Sections 0.6-0.10Sections 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 1.1-1.4Sections 1.5-1.11

SMALLER FILES (for faster download): Sections 1.1-1.2Sections 1.3-1.4Sections 1.5-1.7Sections 1.8-1.9Sections 1.10-1.11



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Subpages (3): Chapter 1 Chapter 2 Chapter 3
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