Applied Math Final Review

Front 1

Probability

Back 1

A measure of how likely an event is to occur.

Front 2

The probability of an event is written

Back 2

P(event) = number of ways event can occur

total number of outcomes

Front 3

Event

Back 3

An event is a specific result of a probability experiment. (When rolling a number cube, the event of rolling an even number is 3 (you could roll a 2, 4 or 6))

Front 4

Outcomes

Back 4

An outcome is a possible result of a probability experiment. (When rolling a number cube, the possible outcomes are 1, 2, 3, 4, 5, and 6)

Front 5

What is the probability of getting heads when flipping a coin?

Back 5

P(heads) = number of ways = 1 head on a coin = 1

total outcomes = 2 sides to a coin = 2

P(heads)= ½ = 0.5 = 50%

Front 6

Compound event

Back 6

A compound event is when you need to figure the probability for more than one event. It will use either OR or AND.

Front 7

OR probability problems

Back 7

Require obtaining a successful outcome for at least one of the given events. (What is the probability of me rolling a 4 or a 6?1/6+1/6 = 2/6 or 1/3 or 33.3%)

What is the probability of me rolling an even number or a number greater than 4?

2, 4, 6 are even

5, 6 are greater than 4

There are 4 different numbers so 4/6=66.7%

Front 8

OR formula

Back 8

P (A or B) = P (A) + P (B) - P (A and B)

What is the probability that when I pull a number from 1-10 out of a hat it will be odd or greater than 6?

P(odd)=5/10

P(greater than 6)=4/10

P(odd and >6)=2/10

So, P(odd or >6) =5/10 + 4/10 – 2/10

=7/10 or 70% chance the number will be odd or greater than 6.

Front 9

Mutually exclusive

Back 9

Two events that can't happen at the same time.

Front 10

Mutually exclusive equation

Back 10

P (A or B) = P (A) + P (B)

Front 11

Independent event

Back 11

The outcome of one event does not affect the probability of the other event. (Rolling dice, flipping coin, replacing cards in a deck)

Front 12

Dependent events

Back 12

The outcome of an event does affect the probability of the other event. (Card games, bingo, pulling items from a bag)

Front 13

AND problems

Back 13

P (A and B) = P (A) x P (B)

What's the probability of two kings being picked out of a deck of cards if the first card is replaced?

P(K 1) = 4/52

P(K 2) = 4/52

P(K and K) = 4/52 x 4/52

1/13 x 1/13 = 1/169

Front 14

Exponential functions

Back 14

Functions that have the independent variable (x) as an exponent.

Front 15

Exponential equation

Back 15

y=abx where “a” does not equal zero and “x” is bigger than zero

Also written as f(x)=abx

Front 16

Exponential growth

Back 16

y=abx “b” is greater than one (called the growth factor)

Growth factor can be found by taking 1 plus the rate (as a decimal) “a” is the starting amount and “x” is time

The world population in 2016 was 7.4 billion. The annual rate of increase was about 1.26% What’s the growth factor?

1.0126

If this rate stays the same, what’s the population after 20 years? y=7.4(1.0126)20=

Front 17

Exponential decay

Back 17

y=abx “b” is LESS than one (called the decay factor)

Decay factor can be found by taking 1 minus the rate (as a decimal) “a” is the starting amount and “x” is time

Caffeine has a half-life of 5 hours. A French roast coffee has 330 mg per cup. What is the Decay factor? .5

Front 18

Finding an equation from a graph

Back 18

You need to know two points.

Example (0,1) (1,2)

Use the first point to find “a”

1=a(b)0 which makes 1=a

Use the second point to find “b”

2=1(b)1 which makes 2=b

y=1(2)x

Front 19

Standard notation of quadratic equations

Back 19

ax2 + bx + c

a tells if the parabola opens up or down

Positive = opens up and has a minimum Negative = opens down and has a maximum

“c” tells where the parabola crosses the y-axis (y-intercept)

Front 20

Axis of symmetry

Back 20

-b/2aS

Front 21

Graphing quadratic equations

Back 21

Step 1 - Find Axis of Symmetry

Step 2 - Find Vertex

Step 3 - Find Y intercept

Step 4 - Find two more points

Step 5 - Reflect Points and draw line

Front 22

Factoring quadratics

Back 22

First determine ‘a,’ ‘b,’ and ‘c’

What will multiply to equal ‘ac’ and add to equal ‘b’ (find factors)

Use those numbers to rewrite the equation for the middle ‘x’ values.

Leave ‘a’ term and ‘c’ term alone for now

Factor out common parts of first two terms and the second two terms.

What was factored out and what is left in parentheses are your answers

Front 23

Quadratic formula

Back 23

-b + or - squareroot b2

Front 24

Triangles by angle

Back 24

Acute:All angles are less than 90º

Obtuse:One angle measures more than 90o

Right:One angle measures exactly 90o Equiangular:All angles are the same same

Front 25

Triangles by side

Back 25

Scalene:NO sides are the same

Isosceles:2 sides are the same

Equilateral: All sides are the same

Front 26

Exterior angles

Back 26

Exterior angles can also be found by adding the non-adjacent angles.

Front 27

Adjacent

Back 27

Next to the angle

Front 28

Opposite

Back 28

Across from the angle

Front 29

Length inequalities

Back 29

2 sides of a triangle must add up to be more than the biggest side.

Ex. If two sides of a triangle are 5 cm and 7cm, what is the maximum length of the other side?Must be <12 (less than)

What’s the minimum?

Must be >2 (more than)

Written 2

Front 30

Three ways to prove triangles are similar

Back 30

Angle-Angle

Side-Side-Side

Side-Angle-Side

Front 31

a2+b2

Back 31

Obtuse

Front 32

a2+b2>c2

Back 32

Acute

Front 33

Inverse trig angle measures

Back 33

Inverse trigonometry is used to find the measure of an angle.

You must know two sides of the triangle.

Determine if you are using sin, cos, tan.

Put the numbers into your calculator and use sin-1, cos-1, or tan-1.

That is your angle measure. Round to the nearest hundredth.

Front 34

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Back 34

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