Algebra II

Graphic Organizers

Slope-Intercept Form Standard Form Point-Slope Form

2 43

y 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 97

y x

Unit 1: #2

Substitution Elimination

System of Inequalities

2 34 5 29y xx y

2 3 44 22x yx y

37

6

y xy xx

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

5x

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 timeis modeled by this equation:

16 48 80When does the object hit the ground?h t t

The perimeter of a rectangle is60 cm. Call the length x. Comeup with a formula for the area ofthe rectangle. Then find the vertexof the parabola. What informationdoes the vertex give you?

Unit 3: #1

Working with RadicalsMultiplying

SubtractingAdding

Dividing 23 2 5

50 828 63

75 3

47

Unit 3: #2

Rational ExponentsRadical to Exponential Exponential to Radical Properties of Exponents

3

4

3

36

64

81

9

12

13

32

43

49

27

16

8

1 32 2

432

62 13 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

32

23

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=132

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

23

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−

3𝑥+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−16

1𝑥 +

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

aSr

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 rnPn r

!! !n rnC

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)?