Transcript Graphic Organizers for the course

Algebra II
Graphic Organizers
Unit 1: #1
Slope-Intercept Form
2
y  x4
3
Horizontal Line: y = k
Standard Form
2x  3y  6
Point-Slope Form
y  3  2  x  1
Vertical Line: x = k
Unit 1: #2
Given a point and a slope
(3, 4)
m5
Given a point and a parallel line
(3, 4)
Given two points
parallel to 2 x  3 y  7
(3, 4)
(5,1)
Given a point and a perpendicular line
(3, 4)
4
perpendicular to y  x  9
7
Unit 1: #3
Substitution
Elimination
y  2x  3
4 x  5 y  29
2x  3y  4
System of Inequalities
y  x3
y  x  7
x6
4 x  y  22
Unit 1: #4
Solving an Equation
Solving an Inequality
2 x  3  7  15
Solving an Inequality
x2
5
 6  10
x4 7
Graphing an Absolute Value Function
y  3 x  2 5
Unit 2: #1
Factoring
Completing the Square
Quadratic Formula
2 x 2  15  7 x
x2  6x  3  0
2x2  x  9
When to use it?
Unit 2: #2
Standard Form
Vertex Form
y  ax  bx  c
y  a  x  h  k
y  x  4x  3
y  2  x  3  5
2
2
2
2
Unit 2: #3
Projectile Motion
Optimization Problem
A projectile's height at any time
is modeled by this equation:
The perimeter of a rectangle is
60 cm. Call the length x. Come
h  16t 2  48t  80
When does the object hit the ground?
up with a formula for the area of
the rectangle. Then find the vertex
of the parabola. What information
does the vertex give you?
Unit 3: #1

32 5

28  63
2
Multiplying
Adding
4
7
50  8
Dividing
Subtracting
7
5 3
Unit 3: #2
Radical to Exponential
1
2
49 
36 
3
Exponential to Radical
Properties of Exponents
 12   32 
 x  x  
  
1
3
64 
27 
4
 32 
y  
 
4
81 
3
2
16 
6
 9
3

4
3
8 
 23 16 
 2a b  


Unit 3: #3
The Basics
More difficult
x9  x3
x 3  7
2 3 x 1  4  8
Rational Exponents
 x  2
3
2
 27
 x  5
2
3
 16
Watch for Extraneous Solutions!!
Unit 3: #4
y  x3  2
y  3 x5 4
Choose “smart” points
x
y
x
y
Unit 4: #1
𝑦 = 3(2)𝑥
𝑦 = 5(0.4)𝑥
Unit 4: #3
Exponential Equations
6𝑥 = 36
4𝑥 = 8
More Difficult Equations
2𝑥
1
=
32
32𝑥 = 9𝑥
Unit 4: #4
Growth: You buy a baseball card for
$50. It increases in value at the rate
of 12% per year. How much will it be
worth in 20 years?
Decay: You buy a car for $15,000. It
decreases in value at the rate of 16%
per year. How much will it be worth
in 8 years?
Unit 5: #1
An “inverse variation” or “inverse proportion”
𝑘
is an equation in the form 𝑦 = .
𝑥
12
𝑦=
𝑥
x
y
1
2
3
4
6
12
What do you notice?
Graph it!
Unit 5: #2
6
𝑦=
+3
𝑥−2
−12
𝑦=
−4
𝑥+3
What’s the shortcut for getting points on the graph?
Unit 5: #3
Add
4 3
+
𝑥 𝑦
Subtract
1
3
−
𝑥−2 𝑥+2
Simplify first!
𝑥2 − 4
𝑥 2 + 6𝑥 + 8
Divide
Multiply
𝑥 2 − 9 𝑥 2 + 7𝑥 + 10
∙
𝑥 + 5 𝑥 2 + 6𝑥 + 9
Domain
Restrictions!!
6𝑥𝑦 3
8𝑥 4 𝑦 2
÷
5𝑥 + 5𝑦 𝑥 + 𝑦
Unit 5: #4
Cross-Multiplying
Using the common denominator
3
𝑥−1
=
𝑥+2
6
1 5
7
+ =
𝑥 6 2𝑥
Watch out for extraneous solutions!
Unit 6: #1
Arithmetic – has a common difference
Geometric – has a common ratio
𝑎𝑛 = 𝑎1 + 𝑛 − 1 𝑑
𝑎𝑛 = 𝑎1 (𝑟)𝑛−1
2, 6,10,14,...
12,18, 27, 40.5,...
Find a20
Find a7
Find a30
Find a11
Unit 6: #2
Arithmetic
Geometric
𝑛
𝑆𝑛 = 𝑎1 + 𝑎𝑛
2
𝑎1 1 − 𝑟 𝑛
𝑆𝑛 =
1−𝑟
7  10  13  16  ...
3  6  12  24  ...
Find S 20
Find S9
Infinite
Geometric
Series
If r  1,
S
a1
1 r
Find S :
100  50  25  12.5  ...
Unit 7: #1
The basics
You roll a 6-sided die. What is the
probability that you will roll a
number that is greater than 2?
A spinner has spaces (of the same
size) numbered from 1 to 10. If
you spin the spinner, what is the
probability that you will land on
a prime number?
Using a tree diagram
You roll two dice. What is the
probability that you will roll a
total of nine?
Unit 7: #2
Order matters! (Permutation Lock)
In how many ways can a president,
vice-president, and secretary be
chosen from a group of 10 people?
n Pr 
n!
 n  r !
Order does not matter! (Committee)
In how many ways can a ruling
committee of three be chosen
from a group of 10 people?
n Cr 
n!
r ! n  r  !
Unit 7: #3
Independent Events
Dependent Events
You flip a coin, then roll a die.
What is P(H,4)?
An urn contains 6 red and
9 blue marbles. You choose
2 marbles without replacement.
What is P(R,B)?
An urn contains 6 red and
9 blue marbles. You choose
2 marbles with replacement.
What is P(R,B)?
An urn contains 6 red and
9 blue marbles. You choose
2 marbles with replacement.
What is P(R,R)?