**MATH 141 -
PRECALCULUS**

**
NOTES FOR THE FINAL**

**
OUTLINE FOR THE FINAL:****
**Math141OutlineFinal.pdf

**BIG
FILES:****
**Chapter 7
Chapter 8
Chapter 9 (see
Pascal Triangle Links below)
Chapter 10 (mostly
handwritten)

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

**VIDEOS
AND WEB LINKS: SEE BELOW**

**SMALLER
FILES (if you cant get the big files)**

**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

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

** FIBONACCI TED TALK BY PROF. ARTHUR BENJAMIN: **https://www.youtube.com/watch?v=SjSHVDfXHQ4

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

** HANDSHAKE PROBLEM: **https://www.youtube.com/watch?v=dIejOnMP20c

** KHAN ACADEMY ON INDUCTION: **https://www.khanacademy.org/math/algebra-home/alg-series-and-induction/alg-induction/v/proof-by-induction

Section 9.5 in Larson: Binomial
Theorem

**The
Beauty of Pascal's Triangle**

http://www.mathsisfun.com/pascals-triangle.html

See
also __Chaos and Fractals__ by Peitgen, et al.

http://en.wikipedia.org/wiki/Pascal's_triangle

The Magic of Pascal's
Triangle (Plinko from *The Price is Right*
and Word Jumbles)

**QUINCUNX ("PLINKO") APPLETS AND SITES**

**
***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 Pascals triangle? See the links above!

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

http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html

http://en.wikipedia.org/wiki/Bean_machine** **(Wikipedia article)

http://en.wikipedia.org/wiki/Quincunx** **(Wikipedia article)

**Chapter
10: Conics and Polar Coordinates**

** ANIMATION ON CONICS**

https://www.youtube.com/watch?v=HO2zAU3Eppo

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.

Chapter 10 in Larson: Ellipses
(handwritten) and Hyperbolas (typed)

Section 10.4 in Larson:
More on Hyperbolas (handwritten)

Sections 10.7 and 10.8 in Larson:
Polar Coordinates and Polar Graphs (handwritten)