Algebra2-Trig

Welcome to Algebra 2/Trig Trimester 3! =New Procedures:=
 * ======**Test Corrections and Retakes:** These will only be offered if **ALL** homework from a unit is completed. Test corrections and retakes are offered until the next chapter/unit test or assessment.======

=Final Tests = =2nd Period: Thursday, June 9th= =7th Period: Wednesday, June 8th= Final Review Key: NOTES SHEET:

=DO YOU HAVE AN IPOD TOUCH? NEED A GRAPHING CALCULATOR? You can download a FREE graphing calculator app from iTunes. [|Free Graphing Calculator App] = =St. Cloud Math Contest April 7, 2011 = **St. Cloud State Math Contest:** [] The link will take you to some sample tests from past years. Below you will find some of the solutions to select questions from those tests.

For Solutions, see the links below. Keep in mind, these are not official answers, and if you disagree, let's have a discussion. Also, not all problems are completed. Bring any that you solve to me to check over your reasoning if I do not have a solution on my paper. [|2009 SCSU math test.pdf] [|2010 SCSU math test.pdf]

HW8 Basic Trig Identities: [[file:HW8 Basic Trig Identities.doc]]
HW8 Key:

Part 2 Test Tuesday 5/17/2011 (7th Period) Wednesday 5/18/2011 (2nd Period)
Chapter 13 Part 2 Review Key: Graphing Assignment 13.6B Answer Key:
 * Monday 5/9/2011 - Friday 5/13/2011 Graphing Trig Functions**
 * We spent the week exploring how to graph Trig Functions in both degrees and radians.**
 * Basic Graphs: y = sin (x)**
 * Degrees Radians**


 * y = cos (x)**
 * Degrees Radians**

Graphing Notes:

Explore how parameters change a basic graph (shifts, amplitude, and period): []

HOMEWORK 7 KEY:
 * HW7 due 5/16/2011**: [[file:HW7 Graphing Trig Functions.doc]]


 * Friday 5/6/2011 Converting Radians to Degrees**

**Radians Notes:** **Front of HW6 due 5/9/2011 **


 * Test: Tuesday 5/3/2011 (7th Period) Thursday 5/5/2011 (2nd Period)**

**Test Review Key: [[file:13.1-13.3 Review Key.pdf]]**
UNIT CIRCLE (blank):

**Thursday 4/28/2011 Using the Unit Circle to find Trig Values** **sin = y** **cos = x** **tan = y/x** If you know (x, y) for an angle from the unit circle, you know the exact value of the trig function.


 * FINISH HW5 for Monday! **

**Wednesday 4/27/2011 Trig Values for Any Angle** We can use the **terminal** side of the angle to create a right triangle anywhere in the unit circle. The **reference angles** are then the "theta" that we base the trig ratios on. Pay attention to whether x and y are positive or negative for the terminal side. tan = sin / cos = y / x

HW5 #17-23

**Tuesday 4/26/2011 Coterminal and Reference Angles** **Coterminal Angles:** End in the same spot on the unit circle.
 * Reference Angles: **<span style="font-family: 'Comic Sans MS',cursive;">The __acute__ angle between the x-axis and the terminal side of the angle. Ask: Which way is the shortest to the x-axis?


 * <span style="font-family: 'Comic Sans MS',cursive;">HW 5 due Monday 4/2/2011 [[file:HW5 Trig Values for Any Angle.doc]](Problems 1-16) **
 * <span style="font-family: 'Comic Sans MS',cursive;">HW 5 KEY: [[file:HW5 Key.pdf]] **

<span style="font-family: 'Comic Sans MS',cursive;">**Monday 4/25/2011 Solving Right Triangles** <span style="font-family: 'Comic Sans MS',cursive;">**SOH CAH TOA** is our trick for remembering the basic trig functions. <span style="font-family: 'Comic Sans MS',cursive;"> <span style="font-family: 'Comic Sans MS',cursive;">Sine and CoSecant are reciprocals. <span style="font-family: 'Comic Sans MS',cursive;">Cosine and Secant are reciprocals. <span style="font-family: 'Comic Sans MS',cursive;">Tangent and Cotangent are reciprocals. <span style="font-family: 'Comic Sans MS',cursive;">**Triangle Points Project:** <span style="font-family: 'Comic Sans MS',cursive;">You need to collect 20 points. Solving triangles are 2 points a piece. Word problems are 4 points a piece. You must do at least one word problem.

==

Statistics Chapter 12==

Test Tuesday 4/19/2011
Blank Study Guide Study Guide Key:

<span style="font-family: 'Comic Sans MS',cursive;">HOMEWORK 4 KEY: [[file:HW 4 Key Front.pdf]][[file:HW 4 Key Back.pdf]]
==**Binomial Formula.** Suppose a binomial experiment consists of //n// trials and results in //x// successes. If the probability of success on an individual trial is //P//, then the binomial probability is:==

[[image:http://www.mathnstuff.com/math/spoken/here/2class/90/statpb.gif width="400" height="289"]]
68% of the data is within one standard deviation on either side of the mean 95% is within 2 standard deviations on either side of the mean 99% is within 3 standard deviations on either side of the mean

<span style="font-family: 'Comic Sans MS',cursive;">Monday 4/11/2011
12.4 Measures of Dispersion

<span style="font-family: 'Comic Sans MS',cursive;">Mean Deviation: The average distance from the mean.

 * <span style="font-family: 'Comic Sans MS',cursive;">Find the mean.
 * <span style="font-family: 'Comic Sans MS',cursive;">Find the distance of each data point from the mean.
 * <span style="font-family: 'Comic Sans MS',cursive;">Add up all the distances (no negative values).
 * <span style="font-family: 'Comic Sans MS',cursive;">Divide by the number of data points (n).

<span style="font-family: 'Comic Sans MS',cursive;">Use your calculator.
 * <span style="font-family: 'Comic Sans MS',cursive;">Variance and Standard Deviation: Other measures of how far the average point is from the mean value. **
 * <span style="font-family: 'Comic Sans MS',cursive;">Type all the data points into a list [STAT]
 * <span style="font-family: 'Comic Sans MS',cursive;">Run 1-Var Stats [CALC]
 * <span style="font-family: 'Comic Sans MS',cursive;">The last stat is the standard deviation
 * <span style="font-family: 'Comic Sans MS',cursive;">Square the standard deviation to find the variance

<span style="font-family: 'Comic Sans MS',cursive;">Deck of Cards and Dice Model [[file:Deck of cards.doc]]
<span style="font-family: 'Comic Sans MS',cursive;">OR- Add probabilities for each event <span style="font-family: 'Comic Sans MS',cursive;">AND- Multiply probabilities for each event <span style="font-family: 'Comic Sans MS',cursive;">**Combinations:** Used when the order of an arrangement does not matter. You are simply making a group of items. nCr = n! / (r! (n-r)!)
 * <span style="font-family: 'Comic Sans MS',cursive;">3/25/2011- 3/29/2011 Probabililty Principles **
 * <span style="font-family: 'Comic Sans MS',cursive;">Addition and Independent Events **
 * <span style="font-family: 'Comic Sans MS',cursive;">HW2 due 3/30/2011 [[file:HW2 Probabilities.doc]] **
 * <span style="font-family: 'Comic Sans MS',cursive;">Dependent Events **
 * <span style="font-family: 'Comic Sans MS',cursive;">P(B|A) - **<span style="font-family: 'Comic Sans MS',cursive;">the probability of event B based on A happening. How many options are there for A? This becomes the bottom of the fraction.
 * <span style="font-family: 'Comic Sans MS',cursive;">Dependent Events Activity: [[file:Dependent Events.doc]] **
 * <span style="font-family: 'Comic Sans MS',cursive;">Tuesday 3/22/2011-Thursday 3/24/2011 **
 * <span style="font-family: 'Comic Sans MS',cursive;">Permutations and Combinations **
 * <span style="font-family: 'Comic Sans MS',cursive;">Permutations: **<span style="font-family: 'Comic Sans MS',cursive;">used when the order of an arrangement matters nPr = n!/ (n - r)!

<span style="font-family: 'Comic Sans MS',cursive;">Notes from 10.2-10.3 <span style="font-family: 'Comic Sans MS',cursive;">Chapter 10 Notes:
 * <span style="font-family: 'Comic Sans MS',cursive;">HW 1 due 3/25/2011 [[file:HW1 Permuations and Combinations.doc]] **

<span style="font-family: 'Comic Sans MS',cursive;">10.1 Fundamental Counting Principle and Theoretical Probability

<span style="font-family: 'Comic Sans MS',cursive;">Need more examples of the FCM? Go here: [|Fundamental Counting Principle Videos]

<span style="color: #800080; font-family: 'Comic Sans MS',cursive;">Radicals Test Wednesday, February 16th
<span style="color: #800080; font-family: 'Comic Sans MS',cursive;">Review Key:

<span style="font-family: 'Comic Sans MS',cursive;">__Chapter 8 Radical Functions__
<span style="font-family: 'Comic Sans MS',cursive;">**Use an inequality to find the domain. Everything under the root must be __>__0.** <span style="font-family: 'Comic Sans MS',cursive;">***REMEMBER: flip the inequality sign if you multiply or divide by a negative number.**
 * <span style="font-family: 'Comic Sans MS',cursive;">Monday 2/07/2011-Tuesday 2/08/2011: Radical Expressions **
 * <span style="font-family: 'Comic Sans MS',cursive;">Domain: **<span style="font-family: 'Comic Sans MS',cursive;">Radical equations (with a square root sign) are only defined for **postive numbers.**

<span style="font-family: 'Comic Sans MS',cursive;">**Evaluating Expressions:**

<span style="font-family: 'Comic Sans MS',cursive;">**Evaluating Expressions Key: ** <span style="font-family: 'Comic Sans MS',cursive;">***REMEMBER to use PEMDAS!** <span style="font-family: 'Comic Sans MS',cursive;">Simplify the expression down to one number. The number on the outside of the root (index) tells you how many times a factor must appear to come out of the root. <span style="font-family: 'Comic Sans MS',cursive;">1.) Factor the expression under the root. Use the index as a clue for what types of factors you want. <span style="font-family: 'Comic Sans MS',cursive;">2.) Pull out factors that appear the correct number of times (2 for a square root, 3 for a cubed root, etc.) <span style="font-family: 'Comic Sans MS',cursive;">Review how to simplify square roots: [|Simplifying Square Roots]

<span style="font-family: 'Comic Sans MS',cursive;"> <span style="font-family: 'Comic Sans MS',cursive;">**HW12 due 2/11/2011** HW12 Key
 * <span style="font-family: 'Comic Sans MS',cursive;">Graphing: What is the basic shape of a radical? **
 * <span style="font-family: 'Comic Sans MS',cursive;">Use a table to find values for an equation. Remember all graphs should have this basic shape. **

<span style="font-family: 'Comic Sans MS',cursive;">1.) Find a **__common denominator__** and **simplify** to one fraction on both sides of the =. <span style="font-family: 'Comic Sans MS',cursive;">2.) **Cross Multiply**. The denominators will cancel, so the numerators are equal to each other. <span style="font-family: 'Comic Sans MS',cursive;">3.) **Solve** for x. <span style="font-family: 'Comic Sans MS',cursive;">4.) **Check** your solutions. Do they give an error in the denominator?
 * <span style="font-family: 'Comic Sans MS',cursive;">Thursday 2/03/2011: Solving Rational Equations **
 * <span style="font-family: 'Comic Sans MS',cursive;">HW11 due 2/09/2011[[file:HW11 Solving Rational Equations.doc]] **

<span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">Review Key: [[file:Rational Expressions Review Key.doc]]
<span style="font-family: 'Comic Sans MS',cursive;">1.) **Factor** the numerators and denominators of all expressions. <span style="font-family: 'Comic Sans MS',cursive;">2.) **Cancel** any groups which are the same on the top and bottom. <span style="font-family: 'Comic Sans MS',cursive;">3.) **Multiply** across to simplify.
 * <span style="font-family: 'Comic Sans MS',cursive;">Monday 1/24/2011: Multiplying and Dividing Rational Functions **

<span style="font-family: 'Comic Sans MS',cursive;">*If you are dividing, you must **flip** the second fraction (reciprocal) and **multiply**. <span style="font-family: 'Comic Sans MS',cursive;">Adding and Subtracting Rational Functions <span style="font-family: 'Comic Sans MS',cursive;">1.) Make both functions have a **common denominator**. <span style="font-family: 'Comic Sans MS',cursive;">2.) Multiply or **distribute** in each numerator. <span style="font-family: 'Comic Sans MS',cursive;">3.) **Combine like terms** in the numerators. The denominator remains the same. <span style="font-family: 'Comic Sans MS',cursive;">*Watch for signs when you are subtracting the second rational. Change it to an addition problem before carrying out any operations.

<span style="font-family: 'Comic Sans MS',cursive;">1.) **Factor** the top and bottom of the function. <span style="font-family: 'Comic Sans MS',cursive;">2.) **Find the holes**. If something on the bottom cancels with something on the top, it creates a hole in the graph at the x-value that makes it a zero. <span style="font-family: 'Comic Sans MS',cursive;">3.) **Find the vertical asymptotes**. Any groups left on the bottom should be set to zero. Find the x-values which make zero in the denominator. <span style="font-family: 'Comic Sans MS',cursive;">4.) **Find the horizontal asymptotes.** Use table below to compare the **degrees** of the first terms. <span style="font-family: 'Comic Sans MS',cursive;">5.) **Draw** in the asypmptotes on the graph. Use a calculator to find the basic shape of the curve around the asymptotes.
 * <span style="font-family: 'Comic Sans MS',cursive;">HW10 due Thursday 1/27/2011: [[file:HW10 Rational Function Operations.doc]] **
 * <span style="font-family: 'Comic Sans MS',cursive;">HOMEWORK 10 KEY: [[file:HW10 Key.doc]] **
 * <span style="font-family: 'Comic Sans MS',cursive;">Thursday 1/20/2011: Graphing Rational Functions **


 * **If the degrees of the numerator are....** || **the horizontal asymptote is....** ||
 * Smaller than the denominator || y=0 ||
 * Equal to the denominator || divide the coefficients of the first terms ||
 * Bigger than the denominator || no horizontal asymptote ||

<span style="font-family: 'Comic Sans MS',cursive;">1.) Find k (the constant of variation) <span style="font-family: 'Comic Sans MS',cursive;">2.) Plug k in to the standard formula and find the missing value for the information given.
 * <span style="font-family: 'Comic Sans MS',cursive;">HW9 due Monday 1/24/2011 [[file:HW9 Graphing Rational Functions.doc]] **
 * <span style="font-family: 'Comic Sans MS',cursive;">Tuesday 1/18/2011: Inverse and Joint Variation **

<span style="font-family: 'Comic Sans MS',cursive;">Inverse Variation: y = k/x (division) Joint Variation: z = kxy (multiplication)
 * <span style="font-family: 'Comic Sans MS',cursive;">HW8 due 1/20/2011 [[file:HW8 Variation.doc]] **

<span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">Test on Chapter 7: Thursday 1/13

 * Polynomials Review Key [[file:Polynomials Review Key.doc]]**

Steps for Finding Zeros: 1.) Factor the Polynomial so each term is in the form (ax + b) (use factoring, graphs, and division to find the factors) 2.) Set each factor equal to 0 and solve for x. ax + b = 0 Remember: There are the same number of roots as the degree of the polynomial (highest power).
 * <span style="font-family: 'Comic Sans MS',cursive;">Monday 1/10/2011: Finding the Zeros of a Polynomial **

HW 7 KEY :
 * Homework 7 due 1/12**[[file:HW7 Solving Polynomial Equations.doc]]

<span style="font-family: 'Comic Sans MS',cursive;">There are several ways to factor polynomials: <span style="font-family: 'Comic Sans MS',cursive;">
 * <span style="font-family: 'Comic Sans MS',cursive;">Wednesday 1/05/2011: Mulitplying and Factoring Polynomials **


 * <span style="font-family: 'Comic Sans MS',cursive;">Look for a **Greatest Common Factor** (something all terms have in common).
 * <span style="font-family: 'Comic Sans MS',cursive;">If there are four terms, try grouping. Put the first two terms together and the last two together. Find the GCF and see if you can factor further.
 * <span style="font-family: 'Comic Sans MS',cursive;">Use Sum and Difference of Cubes Formulas.

<span style="font-family: 'Comic Sans MS',cursive;">or <span style="font-family: 'Comic Sans MS',cursive;">

<span style="font-family: 'Comic Sans MS',cursive;">Graphing Calculator will help you to find minimums and maximums. <span style="font-family: 'Comic Sans MS',cursive;">The **standard form** of a polynomial is to list terms from highest degree to lowest. We call the highest power the **degree** of the polynomial.
 * HW 6 Multpilying and Dividing Polynomials** [[file:HW6 Factoring and Multiplying Polynomials.doc]]
 * <span style="font-family: 'Comic Sans MS',cursive;">Monday 1/03/2011: Intro to Polynomials **
 * <span style="font-family: 'Comic Sans MS',cursive;">Homework 5 due 1/06/2011[[file:HW5 Intro to Polynomials.doc]] **