Algebra 1 Common Core Student Edition, Grade 8-9

Division Property of Square Roots

For every num b er a > 0 and b > 0, \/\ = ^vF

Trig o n o m et ric Rat io s

sine o f LA =length of leg opposite length of hypotenuseLA^

cosine o f LA =

tangent o f LA =

length o f leg adjacent to /LA

length o f hypotenuse

length of leg opposite LA

length o f leg adjacent to LA

Ch ap t er 11

and Functions

Rational Expressions

Inverse Variat ion

A n inverse v a ria tio n is a re la tio n s h ip t h a t can be re p re s e n te d

by a function o f the form y = f , where k A 0.

Ch ap t er 12 Data Analysis and Probability

Mean

The m ean o f a set o f d a ta values = t J^ber otdata'values-

St a n d a r d D e v i a t i o n

S ta n d a rd d e v ia tio n is a m e a s u re o f h o w th e valu es in a d a ta

set vary, or deviate from the mean.

Pi

Multiplication Counting Principle
If th e re are m ways to make a first selection and n ways to
make a second selection, there are m • n ways to make the
tw o selections.

Perm u t at io n N o t at io n
The expression nPr represents the number of permutations of
n objects arranged r a t a tim e.
P = n'-
n r (n - r)\

Co m b i n at i o n N o t at i o n

The expression nCr represents the number of combinations

of n objects chosen r a t a tim e.

nQ=

n\

r\(n - r)\

Theoret ical Probabilit y

Pfp vp n t j = number of favorable outcomes

' ' number of possible outcomes

Pr o b ab ilit y o f an Ev en t an d It s Co m p lem en t

P (e v e n t) + P ( n o t e v e n t) = 1, o r

P(not event) = 1 -P(event)

Odds

Odds in favor of an event =

Odds against an event

number of favorable outcomes

number of unfavorable outcomes

number of unfavorable outcomes

number of favorable outcomes

Ex p e r i m e n t a l P r o b a b i l i t y

P(event) =num ber o f tim es t he experim ent is donenumber of times the event occurs

Pr o b ab i l i t y o f M u t u al l y Ex cl u si v e Ev en t s

If A and B are mutually exclusive events, then

P(A o r B) = P {A ) + P (B ).

Pr o b ab ilit y o f Ov er lap p in g Ev en t s

If A and B are overlapping events, then

P(A o r B) = P {A ) + P{B) - P{A and B ).

Pro b ab ilit y o f Tw o In d ep en d en t Even t s

If A and B are independent events, then

P(A a n d B) = P(A) • P{B).

Pr o b ab ilit y o f Tw o D ep en d en t Ev en t s

If A and B are independent events, then

P(A th e n B) = P (A ) • P(B a ft e r A ).

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