EOG REVIEW NOTES - Number Systems

EOG REVIEW NOTES Number Systems

1

Adding Fraction Steps

Adding Fractions

Steps:1) Find a common denominator.

2) Convert the fractions.

3) Add the numerators and keep the denominator.

4) Simplify.

(Equivalent Denominators)

(LCM)

Adding Fraction Examples

Examples of Adding Fractions

2 33 4

+ =

8 912 12

+ =

x 4 x 3

1712 = 5

121

3 35 4

+ =

12 1520 20

+ =

x 4 x 5

2720

= 720

6

66 6 + 1 = 7 720

Subtracting Fraction Steps

Subtracting Fractions

Steps:

1) Find a common denominator.

2) Convert the fractions.

3) Subtract the numerators and keep the denominator. Borrow if necessary.

4) Subtract the whole numbers.

5) Simplify.

(Equivalent Denominators)

(LCM)

Subtracting Fractions with Whole Numbers Example

Subtracting Fractions with Whole Numbers

Subtracting Fractions with Borrowing

5 58 12 =

15 1024 24

=x 3 x 2

524

8

88

1 58 6 =

x 3 x 4

9 5

9 3 2024 245

(Borrow)8 27 2024 245 = 3 7

24

Multiplying Fraction Steps

Multiplying Fractions

Steps:

1) Convert any mixed numbers to improper fractions.

2) Cross reduce if possible.

3) Multiply straight across.

4) Simplify. 4 23

45x =

143

45x = 5615 = 3 11

15

Dividing Fraction Steps

Dividing Fractions

1) Convert any mixed numbers to improper fractions.

2) Keep, Change, Flip (KCF)

Keep the first fraction Change the operation to multiplication, Flip the second fraction to its reciprocal.

3) Follow multiplication rules.

3 5

4 6

K C F

3 6

4 5X

4 23

45 =143

45 =

K C F143

54

x = 7012 = 5 1012 = 5

56


2

Simplifying Fractions

Simplifying FractionsSteps

1) Find the GCF of the numerator & denominator.

2) Divide each number by the GCF.

OR

Use the upside down cake method

1620

Example

=

16 2028 1024 5

ND

(N) (D)

4/51620 16: 1, 2, 4, 8, 16

20: 1, 2, 4, 5, 10, 20

Factors44

45=

Equivalent Fractions

Equivalent FractionsSteps

Multiply or divide the numerator and denominator by the same number to get an equivalent fraction.

34 = 20

?

x 5

Example

34 = 20

?

x 5

x 5(15)

34 = 20

15

34 = 20

?

14x

Equivalent22

= 28

14x 33

= 312

37x 22

= 614

37x 33

= 921

Converting Mixed Numbers to Improper Fractions

Converting Mixed Numbers to Improper Fractions

4 35

x

+

5

(20)23

Steps

1) Multiply the denominator and the whole number.

2) Use that answer and add it to the numerator.

3) Keep your original denominator.

=

6 23

x

+

3

(18)20=

Examples

Converting Improper Fractions to Mixed Numbers

Converting Improper Fractions to Mixed Numbers

Steps

1) Divide the numerator by the denominator.

(That's your whole number)

2) The remainder is your numerator.

3) Keep your original denominator.

4) Simplify final answer.

Examples1248 =

8 1241

844

5

404

r 4

15 48 =15 12

Converting Fractions to Decimals

Converting Fractions to Decimals

Steps:

1) Divide the numerator by the denominator.

Examples:

14 4 1.00

0.25

010820200

35

5 3.00.6

030300

38

8 3.0000.375

03024605640400

Converting Decimals to Fractions

Converting Decimals to Fractions

Steps:

1) Read the number properly.

2) Write exactly how it sounds.

3) Simplify

Examples:

0.4 0.35 0.125 2.5

410 =

25

35100=

720

1251000=

18

510 =

2 122


3

Adding Decimals

Adding Decimals

1. Line up your decimal points.

2. Add in 0's as placeholders

2.Add each number.

3.Drop your decimal point straight down.

Examples:

4.67 + 3.9 = 0.68 + 35.7 = 15 + 8.9

4.67 00.68 15.0+ 3.908.57

1

+ 35.701

36.38+ 08.923.9

1

Subtracting Decimals

Subtracting Decimals

1. Line up your decimal points.

2. Add in 0's as placeholders

2. Subtract each number.

3.Drop your decimal point straight down.

Examples:

4.67 ‐ 3.9 = 40.68 ‐ 35.7 = 15 ‐ 8.9

4.67 40.68 15.0‐ 3.900.77

‐ 35.7004.98

‐ 08.906.1

163 3 109

16 4 10014

Multiplying Decimals

Multiplying Decimals

1. Line up your numbers.

2. Multiply without looking at the decimal points.

3.Count how many digits are to the right of each decimal point.

4.Move you decimal to the left that many times.

Example: 3.75 x 2.8 = 3.72.8x0

4

000

61

3057

1

+00501

(2) Digits to rightof decimal(1)

(3) Total

10.5

5

Dividing Decimals Example Problem

Dividing Decimals

1. Format your numbers.

2. Move decimal point in the divisor and dividend to the right until the divisor

3.Divide the numbers.

Example: 20.24 4.6 =

1 4.6 20.24

2 46. 202.4

3

004.4

1841841840

4 4.4Answer: 4.4

is a whole number.

Adding and Subtracting Integers

Adding IntegersSame Signs

1. Add the numbers

2. Use the Same Sign

Different Signs

1.Subtract the smaller # from the larger #

2.Use the sign of the larger number

Subtracting Integers

1.Copy the 1st number

2.Change the subtraction sign to addition

3.Change the 2nd numbers sign to its opposite

4.Follow the rules for adding.

(Copy‐Change‐Change)

Multiplying & Dividing

Multiplying & Dividing

1. Multiply or Divide the number without

looking at the signs.

2. If there is an Even number of negatives

your answer is Positive.

If there is an Odd number of negatives

your answer is Negative.


4

Opposites and Absolute Value

Absolute Value the distance from zero.

I I4 = 4 4 units

I I7 = 7 7 units

Opposites Two numbers that are equal distance from zero on the number line.Opposite of 3 is 3

3 units3 units

10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

Multiplicative Inverse Property & Reflexive Property

Multiplicative Inverse Property

Any number multiplied by its reciprocal is always one.

a = = 1 aa

1a

= = 1 1212

43

34Example:

Reflexive Property a = a The = sign reflects the same value on both sides of the equation.

3 = 312x = 12x

15 = 2x +7 = 2x + 7 = 15Examples:

Distributive Property


a(b + c) = ab + ac

Distribute what is outside of the parenthesis by what is inside the parenthesis.

Examples: 3(x + 4) =

3(x) + 3(4) =

3x + 12

Additive Inverse Property

Additive Inverse Property

a + a = 0

The sum of a number and its opposite is always zero.

Examples: 7 + 7 = 0

5 + 5 = 0

Associative Property

Associative Property

(a + b) + c = a + (b + c)

(a x b) x c = a x (b x c)

No matter how the numbers are grouped, the answer will always be the same.

Examples: (3 + 4) + 5 = 3 + (4 + 5)

(3 x 4) x 5 = 3 x (4 x 5)

Commutative Property

Commutative Property

a + b = b + a

a x b = b x a

Numbers may be added or multiplied together in any order.

Examples: 5 + 6 = 6 + 5

5 x 6 = 6 x 5

EOG REVIEW NOTES Expression and Equations

1


Distributive Property Notes

Different Methods = Same Results

Box Method Arrow Method

4( x + 3) 4( x + 3)

4x 3

Multiply sides

Drop

#'s & Operation

4x 12

4x + 12

Multiply 4(x) + 4(3)

4x + 12

Remember:X + X = 2x X X = X2 , X X X = X3

Combining Like Terms

"Like" terms:• all have the same variable, same power: 3x, x, 12x

• all are constants (numbers): 14, 2.5, 1½, 5

• all have the same variable, same power: 2y2, 6y2, y2

Combining like terms: used to simplify an expression or an equation.

• circle or box the like terms in each expression or equation

• use the number in front of the variable (coefficient) and it’s sign to combine the term

Combining Like Terms Example Problem

4x2 + 6x + 9 + 3x 5

• Circle, box, or underline the like terms in each

expression or equation. Group the operation with the term.

• Use the number in front of the variable (coefficient) and

it’s sign to combine the term.

4x2 + 9x + 4

6x + 3x = 9x

+9 5 = 4

Steps:

MultiStep Equations

MultiStep Equations Example

Example Problem Completed

4(x 3) + 6x = 16 + 3x

4x 12 + 6x = 16 + 3x1) Distribute

10x 12 = 16 + 3x 4x 12 + 6x = 16 + 3x2) Combine

Like Terms

10x 12 = 16 + 3x3) Variable tosame side 3x3x

7x 12 = 164) Combine

constant terms7x 12 = 16

+12 +127x = 28

5) Solve & Check 7x = 287 7x = 4

Graphing Inequalities

x is less than or equal to 2x ≤ 2 2 ≥ x

x is less than 2x < 2 2 > x

x is greater than or equal to 2x ≥ 2 2 ≤ x

x is greater than 2x > 2 2 < x

InequalitiesGraph the Variable≥ ≤ > <

10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

> Greater Than or equal to > Greater Than < Less Than or equal to < Less than

10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

EOG REVIEW NOTES Expression and Equations

2

Inequalities Helpful Hints

< I I I >1 2 3

* Special Rule *If your variable term is negative you flip your inequality sign.

*Helpful Hints*If your variable is on the left side then your inequality symbol matches the arrow point.

Arrow represents values of the variable.

3 3x < 5

3x > 153x < 15

x > 2 x < 2

< I I I >1 2 3

Translating Words to Equations

Inequality Chart Words to Math Example

Writing word statements as inequalities.Steps:

1) Label the parts of the sentence.

2) Write the inequality.

Example:

+ x <7 15

x + 7 < 15

The sum of a number and 7 is less than 15

Put the operation

where the "and" is.

x + 7 < 157 7x < 8

< I I I >7 8 9

EOG REVIEW NOTES Ratios and Proportions

1

Simple Interest Formula

Simple Interest: I = Prt I = Interest paid (in dollars)P = Principal (the amount of money borrowed)r = rate (change the percent to a decimal)t = time (in years)

Interest: an amount that is collected or paid for the use of money

Simple Interest: Money paid on principal

Principal: the amount of money deposited or borrowed

Rate of Interest: percent charged or earned for the principal

Ratios

What is a Ratio?A ratio is a comparison of two quantities with the same units.

The 3 ways to write a ratio.

Remember that a ratio must always be in simplest form but have two numbers.

Colon Fraction Bar Words

2:3 23

2 to 3

Types of Ratios

Types of Ratios.There are three different types of a ratio.1) Part to Part

2) Part to Whole

3) Whole to Part

White 4 2Black 6 3

= , 2:3, 2 to 3

White 4 2Black 6 3= , 3:2, 3 to 2

White 4 2Total 10 5

= , 2:5, 2 to 5

Black 6 3= , 3:5, 3 to 5Total 10 5

White 4 2Total 10 5= , 5:2, 5 to 2

Black 6 3= , 5:3, 5 to 3Total 10 5

Unit Rates

3 1 8 96 3

1 80 990

Hours is on bottom because it says per hour.

Unit Rate is how many units of the first quantity (numerator) corresponds to one unit of the second quantity (denominator).Examples: $/lb, mi/hr, ft/sec, $/oz, mi/galJayda takes 3 hours to deliver 189

newspapers on her paper route. What is the rate per hour at which she delivers thenewspaper?

NewspapersHours

1893

= 631

Answer: 63NewspapersHour

*Hint

Unit Rate Example

If 3 cookies cost $1.59, the how much does it cost per cookie?

Words Ratio Divide Write Final Answer Cost 1.59 Cookies 3 3 1.59

0.53

150990

$0.53 per cookie

* Remeber the the word "per" shows you what is being compared (Cost per Cookie).

How to determine if each pair of ratios forms a proportion.

How to determine if each pair of ratios forms a proportion.

Examples:

43__ __8

6=

43__ __8

6=

24 = 24

4 x 6 =

8 x 3 =

Yes

46__ __3

5=

46__ __3

5=

18 = 20

4 x 5 =

3 x 6 =

No

23__ __

9=

23__ __6

9=

18 = 18

2 x 9 =

6 x 3 =

Yes

6 53__ __

4=

53__ __7

4=

21 = 20

5 x 4 =

7 x 3 =

No

7


2

How to set up and solve proportion word problems.

How to set up and solve proportion word problems.

Example:

4 cookies cost $6. If you have $15, how many cookies can you buy?

Word Statement(What are you comparing)

CostCookies

Proportion

64

15x

=

Top numbers represent cost and bottom numbers represent cookies.

64

15x

=

60 = 6x66

10 = x10 Cookies

How to solve a proportion with a missing value.

How to solve a proportion with a missing value.

Examples:__ __8 n=3 6

__ __8 n=3 6

3n = 483 3n = 16

Cross Multiply

Solve OneStep Equation

n = 16

__ __5 r=8 6

__ __5 r=8 6

8r = 308 8r = 3.75

r = 3.75

8 30.003.75

24605640400

Part to Whole

Percent Word Problems Part to Whole

Example:

Paul makes a gross salary of $460 each week. If 18% of his salary is withheld for taxes and social security, how much is withheld from his weekly check? How much would be withheld in a month?

Weekly: _______ Monthly: _______

% Part

100 Whole=

=10018

460x

Tax

Tax: *amount of money added to the total cost of a bill

* % = tax

Example:Your cell phone needs a new battery that will cost $10.00 plus tax. If the sales tax is 7%, how much will your total be?

100 cost

Tip

Tip: *amount of money added to the cost of a service

*calculated before tax

* % = tip 100 cost

Tip Example:

You and your friend went to lunch. The bill was $35.00. If you left the server a 15% tip, then how much tip did you leave?

Discount

Discount: *amount of money subtracted from an item or a total

* % = discount

100 cost

Discount Example:Your favorite store is having a sale. The item you buy was originally $30.00, and it is 40% off. How much is the item?


3

Mark Up

An increase in the cost of an item:Mark Up

To make a profit, stores have to charge more for an item than what they paid for it (wholesale amount)

Formula: % Mark Up

100 Wholesale=

Wholesale + MarkUp = Retail Price

Mark Up

Examples: Find the mark up and retail price of the following items.

Wholesale cost of a pen: $0.95

Markup: 60%

Wholesale cost of a computer: $1,850.00

Markup: 75%

Commission

CommissionThe amount of money that an individual receives based on the level of sales he or she has obtained. The sales person is provided a certain amount of money in addition to his/her standard salary based on the amount of sales obtained.

Formula:

% Commission

100 Whole=

Commission

While working at his Uncle's Car Dealership, Dontae sold this $28,194 2012 Mustang and earned a 3% commission.

Percent Change

Percent Change

Percent of change is the amount, stated as a percent, that a number increases or decreases.

Percent Change = Amount of Change

Percent Change = Largest # Smallest #

Percent Change = Difference

Original Amount x 100

Original Amount x 100

Starting AmountI I x 100

Percent Change

Percent Change Steps

1. Subtract to find the difference

2. Divide difference by original number

amount of change

original amount

3. Multiply answer by 100

% of change = amount of changeoriginal amount X 100

EOG REVIEW NOTES Geometry

1

Map Scale Proportion

To solve for missing measurements in a scale drawing you must set up a proportion. Steps:1) Write your word statement.

2) Set Up the proportion

3) Cross multiply

4) Solve the onestep equation.

5) Look at the word statement for your units.

Example: The scale of a drawing is 1/2in = 3ft

Find the measurement for 8 inches.

ftin__ __ __=

1/23

8x

24 = 1/2x__ __1/2 1/2

48 = x

Parts of a Circle

Line segment whose endpoints are the center of a circle and any point on the circle.

Radius

Diameter

Line segment that passes

through the center of a

Chord

Line segment whose endpoints

are any two points on a

circle.

circle and whose endpoints

lie on the circle.

Arc

Part of a circle named

by its endpoints

Area = Radius

Diameter

Circumference

Area and circumference

Area and Circumference of Circles

Use these to help you remember

Circumference Area

Cherry Pie's Delicious Apple Pies are too

Working Area and Circumference Backwards

Working Area and Circumference Backwards

Steps:

1) Write the formula

2) Plug in the information

3) Solve for the variable

4) Answer the question asked

Area of Shaded Regions

Finding the Area of the Shaded Region

Steps:

1) Find the total area of the figure

2) Find the area of the nonshaded figures

3) Find the difference between the areas

4) Answer the question asked

Volume of Prisms

Volume of Prisms

Volume is the amount of three dimensional space an object occupies.

V = B hB = Base Areah = height of prism

*Remember the base names the figure.Rectangular

PrismTriangularPrism


2

Working Backwards Steps

Working Backwards with Volume Steps:

1) Read the problem.

2) Write the Formula for the answer given in the problem .

3) Substitute the information given in the problem.

4) Solve for the missing variable.

5) Make sure you have answered what the problem is asking.

Surface Area Foldable

Surface Area

Surface Area is the sum of all the areas of all the shapes that cover the surface of the object.

Steps:1) Label all sides.2) Calculate area of each shape. (Write formula, plug in numbers, then solve)3) Add all areas together.

Triangles Foldable Types of Triangles

Foldable Sum of the Interior Angles of a Triangle

Sum of the Interior Angles of a Triangle

A

B Cm A + m B + m C = 180O< < <

oThe sum of the interior angles of a triangle is always 180.

Example: Find the missing value.

112o

31o

x

31 + 112 + x = 180143 + x = 180143 143

x = 37o


3

Relationship of Exterior Angles with Triangles

o

x

y zw


The sum of the exterior angle and the interior angle is equal to 180 because they make a straight line.

m w + m y = 180O< <


x

y zw


The exterior angle must be equal to the sum of the remote interior angles.

m w = m x + m z< < <

Quick Review

Acute Angle Right Angle Obtuse Angle

Less than 90

Parts of an Angle Naming Angles

o Exactly 90o Greater than 90

Vertex Side: Ray

Side: Ray

Interior: Inside of angle

Exterior: Outside of angle

CommonEndpoint( )

A

B C<ABC or CBA<

* Vertex must always be in the middle

o

Types of Angles

Types of Angles

Complementary Two Angles are Complementary when they add up to 90 degrees (a Right Angle).

Supplementary Two Angles are Supplementary when they add up to 180 degrees.

Vertical Vertical Angles are the angles opposite each other when two lines cross. They are always equal.

Adjacent Two angles are Adjacent when they have a common side and a common vertex (corner point), and don't overlap.

Complementary Angles

Complementary Two Angles are Complementary when they add up to 90 degrees (a

Right Angle).

B<A<

m A + m B = 90< < o

Challenge Question:

If m A equals 43, Find m B.< <o

If m A equals 2x + 4 and m B equals 3x 14, solve for x.

< <

m A + m B = 90< <o

(2x + 4) + (3x 14) = 90

2x + 4 + 3x 14 = 90

5x 10 = 90

5x 10 = 90+ 10 +105x = 1005 5

m A + B = 90< <o

(43)+ B = 9043 43

B = 47 o

ox = 20

Supplementary Angles

Supplementary Two Angles are Supplementary when they add up to 180 degrees.

BAm A + m B = 180< <

o

Challenge Question:

If m A equals 83, Find m B.< <o

If m A equals 3x + 36 and m B equals 7x +14, solve for x.

< <

m A + m B = 180< < o

(3x + 36) + (7x + 14) = 180

3x + 36 + 7x + 14 = 180

10x + 50 = 180

10x + 50 = 180 50 5010x = 13010 10x = 13

m A + m B = 180< <o

(83)+ m B = 18083 83

B = 97 o

o

<


4

Vertical Angles

Vertical Vertical Angles are the angles opposite each other when two lines cross. They are always equal.

B

A

m A = m B < <Challenge Question:

<

If m A equals 6x + 9 and m B equals 81, solve for

<<

m A = m B <

<(6x + 9) = (81 )

C D

m C = m D < <&

o

6x + 9 = 81 9 96x = 726 6x = 12

If m A equals 113, Find m B.<o

m A = m B < <(113) = m B <

o x.

Adjacent Angles

Adjacent Two angles are Adjacent when they have a common side and a common vertex (corner point), and don't overlap.

B<A<

A< B<

B<A<

Common Side

Common Vertex

A< B<C<D<

A is adjacent to ___ & ___ <B is adjacent to ___ & ___

C is adjacent to ___ & ___

D is adjacent to ___ & ___

<

<

<

<

<

<

<

<

<

<

<

D B

A C

D B

A C

EOG REVIEW NOTES Statistics and Probability

1

Mean

Mean

The _____________ of the numbers in a set of data _____________ by the total number of pieces of data.

Average or Equal Share

Example: 18, 19, 21, 22

Mean = ___________

sumdivided

Sum = 18 + 19 + 21 + 22 = 80Divide by 4 = 80/4 = 20

20

Median

Median

The number in the _____________ of a set of data when the data are arranged in order.

If there are two numbers the

median is their average.

Example: 10, 11, 13, 15, 19

Example #1 Median = ___________

middle

* Mark out the ends as pairs13

Example #2: 10, 11, 13, 14, 15, 19 Find the average: (13+14)/2 = 13.5

Example #2 Median = ___________13.5

Mode

Mode

The number that occurs __________ often.

Example: 75, 78, 80, 80, 90, 100, 101

Mode = ___________

most

80

Range

Range

_____________ between the maximum and the minimum.

Example: 18, 19, 21, 22

Range = ___________

Difference

22 18 = 4

4

Outlier

Outlier

A number in a data set that is ____________ smaller or larger than the other numbers.

Example: 55, 80, 75, 90, 85, 95, 100, 100

Outlier = ___________

significantly

55

Variation

Variation

A measure of how ______________ a set of data is.

Example: 75, 78, 80, 80, 90, 100, 101

There is a cluster around _____________.

A gap is from _____________.

The range is _____________.

spread out

75 80

80 90

26


2

Completed Box and Whisker Plot

2, 3, 5, 6, 8, 9, 12, 12, 13Median

of entire setLeast Value

GreatestValue

Median of lower half Median of upper half

4 12

Lower Quartile Upper Quartile

2 4 6 8 10 12 14*If the median falls between two numbers you have to average them. (Add and divide by 2)

Completed Box and Whisker Plot

2, 3, 5, 6, 8, 9, 9, 12, 12, 13

Medianof entire set

Least Value

GreatestValue

Median of lower half Median of upper half

5 12Lower Quartile Upper Quartile

2 4 6 8 10 12 14

8.5

*If the median falls between two numbers you have to average them. (Add and divide by 2)

Identifying Information on a Box and Whisker Plot

Lower Extreme The ______ number in the data set.

1st Quartlie The middle number of the _________ half of the data.

2nd Quartile The middle number of the data set. Also know as the _________.

3rd Quartile The middle number of the _________ half of the data.

Upper Extreme The _______ number in the data set.

Interquartile Range (IQR) The range of the ______

(between the _____ and the ____ quartiles.)

smallest

1st/lower

median

2nd/upper

largest

box

1st 3rd

MAD Notes

Mean Absolute Deviation

The mean absolute deviation or MAD of a set of data is the average distance between each data value and the mean.

Steps to find the MAD:

1. Find the mean of the data.

2. Find the distance (absolute value) between each data value and the mean.

3. Add the distances together and divide by the number of data points. This answer is the MAD.

Experimental Probability

Experimental Probability

Favorable Outcome

What does happen?

Example: You toss a die 10 times. You record the number. You want to find the experimental probability of getting a 3.

If 3 occurred 6 times, the probability is

Number of Trials Conducted

610 = 3

5

Theoretical Probability

Theoretical Probability

Favorable Outcome

What should happen?

Example: There are 6 numbers on a die. You want to find the theoretical probability of getting a 3.

The probability of rolling a 3 =

When tossing a die you should get a 3 one sixth of the time.

Total Possible Outcomes

16


3

Outcomes

Determining OutcomesSteps:

1) Divide the items into groups.

2) Determine how many items are in each group.

3) Multiply.

Fundamental Counting Principle (FCP)

If an event has m possible outcomes and another independent event has n possible outcomes, then there are mn possible outcomes for the two events together

Outcomes

OutcomesA restaurant offers dinner specials consisting of a main course, one vegetable and one dessert.If there are 2 main courses, 3 vegetables, and 2 desserts, how many dinner specials are possible?

FCP = 2 3 2

12 outcomesM1

V1

V2

V3

D1 M1V1D1D2 M1V1D2D1 M1V2D1D2 M1V2D2D1 M1V3D1D2 M1V3D2

M2

V1

V2

V3

D1 M2V1D1D2 M2V1D2D1 M2V2D1D2 M2V2D2D1 M2V3D1D2 M2V3D2

Simple and Compound Events

Simple Compound

EOG REVIEW NOTES - Number Systems

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