Algebra II

Graphic Organizers

Slope-Intercept Form Standard Form Point-Slope Form

24

3y x 2 3 6x y 3 2 1y x

Horizontal Line: y = k Vertical Line: x = k

Unit 1: #1

Graphing Lines

Writing the Equation of a LineGiven a point and a slope

Given a point and a parallel line Given a point and a perpendicular line

Given two points

(3,4) 5m

(3,4) parallel to 2 3 7x y

(3,4) (5,1)

(3,4)

4perpendicular to 9

7y x

Unit 1: #2

Substitution Elimination

System of Inequalities

2 3

4 5 29

y x

x y

2 3 4

4 22

x y

x y

3

7

6

y x

y x

x

Unit 1: #3

Solving a System

Unit 1: #4

Solving an Equation

Graphing an Absolute Value FunctionSolving an Inequality

Solving an Inequality

2 3 7 15x 4 7x

26 10

5

x

3 2 5y x

Absolute Value

Factoring Quadratic FormulaCompleting the Square

When to use it?

Unit 2: #1

22 15 7x x 2 6 3 0x x 22 9x x

Solving Quadratic Equations

Unit 2: #2

Standard Form Vertex Form

2y ax bx c 2y a x h k

2 4 3y x x 22 3 5y x

Graphing Quadratic Functions

Unit 2: #3

Quadratic ApplicationsProjectile Motion Optimization Problem

2

A projectile's height at any time

is modeled by this equation:

16 48 80

When does the object hit the ground?

h t t

The perimeter of a rectangle is

60 cm. Call the length x. Come

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

Working with RadicalsMultiplying

SubtractingAdding

Dividing 2

3 2 5

50 828 63

7

5 3

4

7

Unit 3: #2

Rational ExponentsRadical to Exponential Exponential to Radical Properties of Exponents

3

4

3

36

64

81

9

1

2

1

3

3

2

4

3

49

27

16

8

1 3

2 2

43

2

62 1

3 62

x x

y

a b

Unit 3: #3

Solving Radical EquationsThe Basics More difficult Rational Exponents

3

3 7

2 1 4 8

x

x

9 3x x

3

2

2

3

2 27

5 16

x

x

Watch for Extraneous Solutions!!

Unit 3: #4

Graphing Radical Functions3 2y x 3 5 4y x

x y yx

Choose “smart” points

Graphing Exponential FunctionsUnit 4: #1

𝑦=3 (2)𝑥 𝑦=5 (0.4)𝑥

Solving Exponential EquationsUnit 4: #3

Exponential Equations More Difficult Equations

6𝑥=36

4𝑥=8

2𝑥=1

32

32𝑥=9𝑥

Applying Exponential FunctionsUnit 4: #4

Growth: You buy a baseball card for$50. It increases in value at the rateof 12% per year. How much will it beworth in 20 years?

Decay: You buy a car for $15,000. Itdecreases in value at the rate of 16% per year. How much will it be worthin 8 years?

Unit 5: #1

Inverse VariationsAn “inverse variation” or “inverse proportion”

is an equation in the form .

𝑦=12𝑥

x y

What do you notice?

1

2

3

4

612

Graph it!

Unit 5: #2

Graphing Rational Functions𝑦=

6𝑥−2

+3 𝑦=−12𝑥+3

−4

What’s the shortcut for getting points on the graph?

Unit 5: #3 Simplifying RationalExpressions

𝑥2−4𝑥2+6 𝑥+8

Add

DivideMultiply

Subtract

Simplify first!

DomainRestrictions!!

4𝑥

+3𝑦

1𝑥−2

−3

𝑥+2

𝑥2−9𝑥+5

∙𝑥2+7 𝑥+10𝑥2+6 𝑥+9

6 𝑥 𝑦 3

5𝑥+5 𝑦÷

8𝑥4 𝑦2

𝑥+𝑦

Unit 5: #4

Solving Rational EquationsCross-Multiplying Using the common denominator

Watch out for extraneous solutions!

3𝑥+2

=𝑥−1

61𝑥

+56=

72𝑥

Unit 6: #1

SequencesArithmetic – has a common difference Geometric – has a common ratio

𝑎𝑛=𝑎1+ (𝑛−1 )𝑑 𝑎𝑛=𝑎1(𝑟 )𝑛−1

20

30

2,6,10,14,...

Find

Find

a

a

7

11

12,18,27,40.5,...

Find

Find

a

a

Unit 6: #2

SeriesArithmetic Geometric

𝑆𝑛=𝑛2

(𝑎1+𝑎𝑛) 𝑆𝑛=𝑎1 (1−𝑟𝑛)

1−𝑟

20

7 10 13 16 ...

Find S

9

3 6 12 24 ...

Find S

Infinite GeometricSeries

1

If 1,

1

r

aS

r

Find :

100 50 25 12.5 ...

S

Unit 7: #1

Probability

You roll a 6-sided die. What is theprobability that you will roll a number that is greater than 2?

The basics Using a tree diagram

A spinner has spaces (of the samesize) numbered from 1 to 10. If you spin the spinner, what is theprobability that you will land on

a prime number?

You roll two dice. What is theprobability that you will roll a

total of nine?

Unit 7: #2

Permutations/Combinations

Order matters! (Permutation Lock) Order does not matter! (Committee)

In how many ways can a president, vice-president, and secretary be

chosen from a group of 10 people?

In how many ways can a ruling committee of three be chosen

from a group of 10 people?

!

!n r

nP

n r

!

! !n r

nC

r n r

Unit 7: #3

Compound EventsIndependent Events Dependent Events

You flip a coin, then roll a die.What is P(H,4)?

An urn contains 6 red and9 blue marbles. You choose2 marbles with replacement.

What is P(R,B)?

An urn contains 6 red and9 blue marbles. You choose

2 marbles without replacement.What is P(R,B)?

An urn contains 6 red and9 blue marbles. You choose2 marbles with replacement.

What is P(R,R)?