1st Semester Exam Review

PC Exam Review

6.1, 6.2 Law of Sines and Cosines

PC 6.1 Law of Sines PC 6.2 Law of Cosines

4.7 Inverse Trig Functions

PC 4.7 Inverse Trig Functions

Graphing Answers

Tonight's worksheet:
PC Graphing Review Ans And the 4.6 graphing answers:
PC 4.6 Graph Ans

Graphing Trig Functions

I just realized that I never posted notes from 4.5, so they're here too!

PC 4.6 Graphs of Other Trig Functions Notes

PC 4.5 Graphs of Sine and Cosine

4.4 Trig Functions of Any Angle

PC 4.4 Trig Functions of Any L

P.S. - A completed unit circle is here.

Linear and Angular Speed Answers

I did these in a different order than you may have, so watch out! :) PC 4.1 Linear and Angular Velocity

Trig stuff

Some trig resources that you may find helpful:
1.  Trig Definition Sheet (has unit circle, right triangle trig, domains and ranges)
2.  Trig Laws and Identities Sheet (we'll get to these around chapter 5)
3.  Khan Academy videos (It's a guy reteaching what we did in class in case you need to see it again)



Another fun way to help you remember your ordered pairs (aka sin and cos values):
PC The Finger Trick for Trig

The Unit Circle (almost done)

Sorry it's sideways :)

PC Unit Circle

Special Right Triangle Review

PC Spec Rt Triangles

4.1 (cont)

PC 4.1 (cont)

4.1 Radians and Degrees

Trigonometry!  Woo hoo!

PC 4.1 Radians and Degrees

Ch 3 Review Stuff

Here are the (edited) slides that I showed you in class today...

Ch 3 rev trashketball exp logs

View more presentations from Kristen Fouss

And the answers to the review worksheet:
PC Ch 3 Review

3.5 Log and Exponential Models

Sorry for the delay! :)

PC 3.5 Exponential and Log Models

3.4 Solving Exponential and Log Equations

PC 3.4 Solving Exp and Log Eq

Where did logs come from?

The question has come up a few times in the last week or so... where did logs come from? Are natural logs really abbreviated ln because it was the inventor/discoverer's initials? Here are some resources for you to check out if you're so inclined.

1. History of logs
2. wikipedia entry (which says it wasn't until the next century before a connection was made with exponential functions!)
3.  Lots of log stuff

Answers to WS 3.1 - 3

Sorry for my tardiness! :) PC WS 3.1 - 3

3.3 More Properties of Logs

PC 3.3 More Props of Logs

3.2 Logarithmic Functions

PC 3.2 Logarithms

Chapter 2 Review Answers

PC Ch 2 Review

PC Graphing Review PC Graphing Review Ans

2.6 Rational Functions and Asymptotes

PC 2.6 notes

2.5 The Fundamental Theorem of Algebra

PC 2.5 FTA

The cubic pattern

In case you're interested (and someone asked for this, so I know you might be!), here's the pattern we discovered today with the cubic polynomial.

Start with a function.

f(x) = 

Find the zeros.  We picked out 2 and 4 (checked with synthetic division) and ended up with 3/5 as our last.

How can you build the cubic polynomial if you know the zeros (without doing all of the messy binomial multiplication)?  Here we go!

Step 1:  Factor out the 5.  (This only works if the leading coefficient of 1).



Step 2.  Find the product of the zeros. 
                  (Which is the opposite of the constant term.)

Step 3.  Find the sum of the zeros. 
                   (Which is the opposite of the quadratic term.)

Step 4.  Find the sum of the pairwise products which is .
  (Which is the same as the linear term.)

So if you have the zeros of a cubic polynomial with leading coefficient of 1, you can use these patterns to find the polynomial itself.  I thought that was pretty cool! (Could you tell?  :) )

The next problem was to find a cubic polynomial with zeros at 5, . (It ends up being f(x) =  if you're playing along at home.)

Fractals

In case you were totally mesmerized by the Fractal video and would like to see more of it, here's a link.

This is a portion that I think is the coolest - especially the part about the cell phones!  (Which we didn't get to in any of your classes :) ).

Watch the full episode. See more NOVA.

Answers to grid review

PC Connect 4 Review

2.3 Real Zeros of Poly Functions

PC 2.3 notes

2.2 (Continued)

PC 2.2 Notes Day 2

2.2 Polynomial Functions of a Higher Degree (Day 1)

PC 2.2 notes

2.1 Quadratic Functions

PC notes 2.1

Chapter 1 Review stuff

In the domain for #3, both 3's should have negatives. (-inf, -3) U (-3, 9) U (9, inf) PC Chapter 1 Review 2011 PC Ch 1 Trashketball

Piecewise functions

PC Piecewise Fns

Parent Functions

PC Parent Function Chart

Open House slides

Precalc open house

View more presentations from Kristen Fouss.

Characteristics of Functions

PC Characteristics of Functions

Additional Information

I'd like you all to fill out this survey for me by Friday, August 26th (don't worry - I'll remind you about it in class!). This will take care of the information that teachers normally collect from you the first day.

If you don't know what period you'll be in my class yet, please wait to do the survey until then. I'd like to organize them by classes. If you're just dying to know what period you'll have precalc, email me and I'll let you know. :)

We're nearly there!

I hope you all are having a great summer! If it's anything like mine, it's going waaaaay too quickly.

Here are the answers to the summer work. Please keep in mind that I make dumb mistakes just like everyone else, so if something isn't working out for you, shoot me an e-mail and I'll check it for you.

Please have these problems done and ready to turn in when you come to class the first day! We'll go over any problems that you had and take our quiz on that Friday.

Summer Work Answers

11.4 Limits at Infinity

PC 11.4 Limits at Infinity

11.2 - 3 Review Stuff

The slides from today's game:
11.2 - 3 review slides

The answers to WS 11.2 - 3:
PC WS 11.2 - 3

And a blank copy if you want one:
PC WS 11.2 - 3 blank

11.3 Notes

Day 1:  PC 11.3 Tangent Line to a Graph

Day 2:  PC 11.3 Derivatives

11.2 Notes

Day 1: Dividing and Rationalizing Techniques

PC 11.2 Dividing and Rationalizing

Day 2: Using Technology and the Difference Quotient

PC 11.2 Tech and Diff Quot

11.1 Finding Limits Numerically

PC 11.1 Finding a Limit Numerically

Limits!

8.5 The Binomial Theorem

PC 8.5 Binomial Theorem

8.4 Mathematical Induction

PC 8.4 Mathematical Induction

8.4 Proof by Induction

Top Ten Algebra Mistakes

#10. Squaring the negative. A minus a squared unless it’s been snared: 

#09. Logarithms: The log of the sum ain’t the sum of the log: 

#08. Shifting function: Add to y go high, add to x go west: 

#07. Inequality: Multiplying the inequality by a negative flips the inequality: 

#06. On exponents: When in doubt, write it out: 

#05. Fractional exponent: Don’t flip over the root. 

#04. Subtraction: Don’t forget to share the minus and the negativity. 

#03. Cancellation: Cancel factors, not individual terms. 

#02. Quadratics: Remember exponents 2, answers 2. 

#01. Squaring: Don’t forget to FOIL. .

8.3 Geometric Sequences

PC 8.3 Geometric Sequences

8.2 Arithmetic Sequences

In case you "need" some notes for 8.2....

PC 8.2 Arithmetic Sequences & Series

8.1 Sequences and Series

Welcome back!

PC 8.1 Sequences and Series

PC 4th Quarter Plan

WS 6.1 - 2

PC WS 6.1-2

6.1 and 6.2 notes

PC 6.1 Law of sines

PC 6.2 Law of Cosines

Happy pi day!

I didn't have the chance to show this in class, but it's pretty cool so I wanted you all to see it. :)

Regulators!

This is for Kyle....

5.5 Double- and Half-Angle Formulas

PC 5.5 Double and Half Angle Formulas

5.4 Sum and Difference Formulas

PC 5.4 Sum and Difference Formulas

9.5 - 6, 6.5 Review Stuff

Slides from today's game (with answers... I think they're all right!)

PC 9.5 - 6, 6.5 game

Answers from WS 9.5 - 6, 6.5
PC WS 9.5 - 6, 6.5

A blank version of the review sheet:
WS 9.5 - 6, 6.5 (blank)

6.5 Powers and Roots of Complex Numbers in Trig Form

PC 6.5 Powers and Roots

And Multiplying and Dividing from the day before:

PC 6.5 Multiplying and Dividing in Trig Form