Week 17: Graphing Sin, Cos, Tan

Notes:
http://www.mathsisfun.com/algebra/trig-sin-cos-tan-graphs.html

Trig Graph:



Graphing Sin and Cos:

Graphing Sin:



Graphing Cos:



Graphing Tan:



Graphing Tan Video:



All:

Week 16: Trig: SohCahToa, Unit Circle, Pythagorean Identity

SohCahToa:
http://www.mathsisfun.com/algebra/sohcahtoa.html

Video..

The Unit Circle:

http://www.mathsisfun.com/geometry/unit-circle.html



Pythagorean Identity:

http://www.coolmath.com/lesson-pythagorean-identities-1.htm

Week 14 & 15: Log vs. Exponential

Exponential/Log Form:





Properties:

Expanding Logs

example:
 




Condensing Logs

 

example:
 



Base of Change Formula:

Week 13: Radical and Rational Expressions

Radical Equations:

with one radical..

with radicals on both side..

Written steps to solving radical equations: http://www.mathsisfun.com/algebra/radical-equations-solving.html

Practice with answer key: http://cdn.kutasoftware.com/Worksheets/Alg1/Radical%20Equations%201.pdf


Rational Expressions:

finding key characateristics and graphing..

 

factoring a rational expression and finding holes...

 

 

 

Practice with answer key: http://cdn.kutasoftware.com/Worksheets/Alg2/Graphing%20Simple%20Rational%20Functions.pdf

Wek 11: Rational Expressions: Adding and Subtracting

Adding and Substracting Rational Expressions Video:

Practice Problems w/ Answer Key: http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Adding+Subtracting%20Rational%20Expressions.pdf

Week 10: Rational Expressions: Multiplying and Dividing

Multiplying and Dividing Rational Epressions:

Practice Problems w/Answer Key (Multiply): http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Multiplying%20Rational%20Expressions.pdf

Practice Problems w/ Answer Key (Divide): http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Dividing%20Rational%20Expressions.pdf

Week 9: How to make an equation using roots?, How to solve a system of equations that consist of a quadratic and a linear & Review

How to make an equation using roots?

Steps from eHow:

http://www.ehow.com/how_5828179_equation-given-its-roots.html

Simplified Steps:


1. Change each root into a factor by changing its signs

Example: roots: 3, -4, -4 ---> changed into factors--->( x - 3=0), (x + 4=0), (x + 4=0)

2. Multiply

Example: (x - 3) (x + 4)= x² +4x – 3x – 12

(x² +4x – 3x – 12)(x + 4)= x³ + 4x²+ 16x – 3x² – 12x – 48

3. Simplify (combine like terms)

x³ + x² +4x – 48


Video:

Class notes:

How to solve a system of equations that consist of a quadratic and a linear

There are two methods: Graphically and Algebraically

To solve graphically:

1.       Graph each function on the same coordinate plane

2.       Identify the points where the two graphs intersect.

3.       These points are the solution to the system of equations

 

Example 1:

1.       Graph each function on the same coordinate plane

 

2.       Identify the points where the two graphs intersect.

( -1, 4) and (3, 8)

3.       These points are the solution to the

system of equations

 

 

To solve algebraically:

1.       Set the functions equal to each other

2.       Solve for x

a.       Move everything to one side of the equation

b.      Factor

c.       Set each factor equal to 0

d.      Solve.

3.       The solution from step 2 is the x value of the solution of the system.

4.       Plug the x into either function to find the y.

5.       Write the solution as an ordered pair.

 

Example 2: 

1.       Set the functions equal to each other
2.       Solve for x
a.       Move everything to one side of the equation
b.      Factor	(x – 3)(x + 1) = 0
c.       Set each factor equal to 0	(x – 3) = 0     (x + 1) = 0
d.      Solve	x = 3             x = -1
4.       Plug the x into either function to find the y.
5.       Write the solution as an ordered pair.	(3, 8) and (-1, 4)

Video:

 

Review: See week 7, 8, & 9

Week 8: End Bx, Intercepts, Solving Polynomials

End Behavior: (Chart)
http://www.purplemath.com/modules/polyends.htm


Intercepts Video (Khan Academy):
http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/graphing_with_intercepts/v/x-and-y-intercepts


X Intercept                                               Y intercept 
 

Steps to Solve                                               Steps to Solve

1.    Factor (find GCF)                                        1. Replace X with ZERO

2.    Set equal to ZERO                                      2. Simply/Solve

3.    Break apart & Set equal to ZERO

4.    Solve equation

Solving Polynomials: (Notes)

http://www.mathsisfun.com/algebra/polynomials-solving.html


Rational Root Theorem Video:
https://www.youtube.com/watch?v=-cZB1lyLlIM#t=35


Synthetic Division Video:

Putting it all together...

Week 7: Complex Numbers

Please use the following link for notes and examples of Complex Numbers:

http://www.mathsisfun.com/numbers/complex-numbers.html


Complex Numbers- Video:

Week 6: Remediation

Expanding polynomials using Pascal's Triangle:

Week 5: Factoring by grouping, Pascal's Triangle, & Complex Numbers

Factoring By Grouping:
http://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-by-grouping/v/factor-by-grouping-and-factoring-completely



Pascal's Triangle:

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

Complex Numbers:

http://www.mathsisfun.com/numbers/complex-numbers.html

Adding, Subtracting and Multiplying Polynomials & Complex Numbers

Adding, Subtracting, Multiplying Polynomials

Vocabulary:
http://quizlet.com/5155393/naming-polynomials-flash-cards/

Naming Practice: (worksheet + answer key)
http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Naming%20Polynomials.pdf


Links:

Adding and Subtracting Polynomials:
http://www.mathsisfun.com/algebra/polynomials-adding-subtracting.html

Adding & Subtracting Video

Multiplying Polynomials:
http://www.mathsisfun.com/algebra/polynomials-multiplying.html

Dividing Polynomials:
http://www.mathsisfun.com/algebra/polynomials-dividing.html

Pascal's Triangle:

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



Complex Numbers:

http://www.mathsisfun.com/numbers/complex-numbers.html

Statistics: Sampling

Key Vocabulary Words:

Population
Sample
Randon Sample
Convenience Sample
Biased Sample
Control Group
Treatment Group
Statistic
Parameter

Formulas:
How to make a prediction about a given population

part of the sample =     x                  
total in sample             total population


Links:
Representative vs Random vs Biased Samples Practice
http://www.ixl.com/math/grade-6/identify-representative-random-and-biased-samples


Videos:

Biased Sampling:

Random Sampling:

Statistics: Z-Score

Videos:
How to calculate Z-score

Formulas:

Z-score

Statistics: Mean, Median & Mode, SD

Key Vocabulary:
Mean
Median
Mode
Range
Dot Plot
Box Plot
Normal Distribution
Standard Deviation


Links:
Variance and Standard Deviation
http://www.ixl.com/math/algebra-2/variance-and-standard-deviation


Videos:
Mean, Median, Mode:

Standard Deviation:
Understanding the concept