Flashcards in Need to Know Deck (85):

1

## The Commutative Property

### a+b=b+a ; a*b=b*a

2

## The Associative Property

### (a+b) +c = a+(b+c) ; (a*b)*c = a*(b*c)

3

## The Distributive Property

### a*(b+c) = ab+ac

4

## The Commutative and Associative Properties do not work with

### Subtraction or Division

5

## Prime Numbers

### 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 and 59

6

## Factorization for 21

### 3 and 7 are prime factors

7

## Greatest Common Factor (GCF) of 56 and 70

###
The factorization of 56 is = 2*2*2*7

The factorization of 70 is = 2*5*7

The two largest numbers in both is 2*7 = 14

8

## Least Common Factor (LCF) of 9 and 15

###
The factorization of 9 is = 3*3

The factorization of 15 is = 3*5

Multiply the shared primes (3*3) by the unshared primes (5) = 45

9

## The absolute value is...

### The positive form of the number

10

## |x| and |-x| are equal to

### x

11

## To find some part of a whole use

###
Part Percent

-------- = -----------

Whole 100

12

## Percent Change

###
(Change * 100)

%change = ---------------------

Original

13

##
Exponent Laws:

A B

x * x equals

###
(A+B)

x

14

##
Exponent Laws:

A

X

---------

B

X equals

###
(A-B)

X

15

##
Exponent Laws:

B

A

X equals

###
(A*B)

X

16

## 1 raised to any power is

### 1

17

## 0 raised to any nonzero power is

### 0

18

## Any number raised to the power of 0 is

### 1

19

##
Fractions as Exponents:

1/2

x equals

###
__

√ x

20

##
Fractions as Exponents:

2/3

x equals

###
_____

1 | 2

√ x

21

##
Negative Exponents:

(-1)

x equals

###
1

--

x

22

##
Negative Exponents:

(-2)

x equals

###
1

-----

2

x

23

## A negative number raised to an even power is

### positive

24

## A negative number raised to an odd power is

### negative

25

##
Odd/Even Exponents:

3

x = 8 means x =

### 2

26

##
Odd/Even Exponents:

4

x = 16 means x =

### 2 or it can equal -2

27

##
Simplifying Expressions:

(6xy + 5x) - (4xy - 3y)

###
You are able to subtract the like variables and keep the other variables the same.

This equals = 2yx+5x+3y

28

##
Multiply Monomials:

3 2

5y * 6y equals

###
5

30y

29

##
Multiplying Polynomials:

(x+2) (x+7) =

###
Use the FOIL (First, Inner, Outer, Last) Method:

2

x +9x + 14

30

##
Factoring Using GCF:

3 2

6x + 12x +33x =

###
2

3x(2x +4x +11)

31

##
Solving Equations:

What you do to one side

###
You must also do to the other.

32

##
Eliminating Fractions:

a b

---- * -----

b a is equal to

### 1

33

##
Eliminating Fractions:

2

---- x = 8

5

###
Multiply the fraction to make it one. What you do to one side must also be done to the other.

2 5 5 |

------ * ----- X = ---- 8 | X = 20

5 2 2 |

34

##
Find the Lowest Common Denominator:

3x 1 x

---- + ---- = ----

4 2 3

###
The LCD is 12, multiply the top by 12 to get:

36x 12 12x |

------- + ------- = -------- | 9x + 6 = 4x solve for x

4 2 3 |

35

##
Cross Multiplication:

a c

--- = ---

b d can be written

### a*d = b*c

36

##
Two Variables/Systems of Equations:

SUBSTITUTION METHOD

3x + y = 17 and 2x - 2y = 6

###
1). Solve for y in one equation

3x + y = 17 (subtract 3x)

y = 17 - 3x

2). Input the solution for y into the other problem:

2x - 2 (17 - 3x) = 6

2x + 6x - 34 = 6

8x = 40 divid by 8 | x = 5

37

##
Two Variables/Systems of Equations:

ELIMINATION METHOD

3x + y = 17 and 2x - 2y = 6

###
1). Line the equations up on-top of each other:

3x + y = 17

2x - 2y = 6

2). My the two "y"s cancel by multiplying by 2:

2(3x + y) = 2(17)

6x + 2y = 34

3). Line the problems up again and solve:

6x + 2y = 34

+ 2x - 2y = 6

8x = 40 | solve for x

38

## If two lines intersect what is the sum of the four resulting angles?

### 360

39

## Polygon

### Any figure with three or more sides

40

## The total degrees of a polygon:

### total degrees = 180 (n-2) where n = # of sides

41

## The Area of a Triangle

###
1

Area = -- b*h

2

42

##
Special Right Triangle:

45-45-90

###
Leg1 : Leg2 : Hypotenuse

x : x : x√2

43

##
Special Right Triangle:

30-60-90

###
Leg1 : Leg2 : Hypotenuse

x : x√3 : 2x

44

## Pythagorean Triples

###
3 - 4 - 5

5 - 12 - 13

8 - 15 - 17

7 - 24 - 25

45

## The Area of Circle

###
2

Area = π*r

46

## Circumference of a Circle

### Circumference = 2*π*r

47

## Arc Length

###
r

Arc Length = ------- 2*π*r

360

48

## Area of a Sector

###
r 2

Area of sector = ------- π*r

360

49

## If two inscribed angles hold the same chord...

### the two inscribed angles are equal

50

## A chord is...

### a line segments between two points on a circle

51

## An inscribed angle holding the diameter is...

### a right angle

52

## The Perimeter of a Square

### perimeter = 4s , where 2 = side

53

## The Area of a Square

###
2

area = s

54

## The Area of a Rectangle

### area = L*W

55

## The Perimeter of a Rectangle

### perimeter = 2L+2W

56

## The Area of a Trapezoid

###
base1 * base2

area = ------------------------ x height

2

57

## The Volume of a Cube

###
3

volume = s

58

## The Surface Area of a Cube

###
2

surface area = 6s

59

## The volume of a cube and the surface area of a cube are equal when s (the side length) =

### 6

60

## The Area of a Rectangular Solid

### volume = height*depth*width

61

## The Surface Area of a Rectangular Solid

### 2*H*W + 2*H*W + 2*H*W

62

## The Volume of a Cylinder

###
2

volume = r * π * H

63

## The Surface Area of a Cylinder

###
2

surface area = 2π*r + 2π*r*h

64

## The slope of any line can be found

###
by substracting the y values of a pair and dividing it by the difference in the x values:

(y2 - y1)

slope = m =--------------

(x2 - x1)

65

## To find the y intercept plug in

### 0 for x and solve for y

66

## The Distance Formula

###
___________________

√ 2 2

√(x2 - x1) + (y2 - y1)

67

## Distance

###
rate

distance = ----------

time

68

## Rate

###
distance

rate = --------------

time

69

## Time

###
rate

time = ------------

distance

70

## Average Speed

###
total distance traveled

average speed = --------------------------------

total time

71

##
Work Rate:

OUTPUT

### output = rate * time

72

##
Work Rate:

TOTAL WORK

###
1 1 1

--------------- = ----------------- + -----------------

TotalWork WorkRate1 WorkRate2

73

## Simple Interest

###
( RT )

Interest = P ( 1+ ----- )

( 100 )

where p is principal, rate, time

74

## Compound Interest

###
nt

( r )

Interest = P ( 1+ --------- )

( 100n )

where n = the number of time compounded per year.

75

## Mean

###
The average of all the numbers: total sum

-------------

n

76

## Median

### The middle most value, for even amount of numbers use the average of the two

77

## Mode

### The number that occurs most frequently

78

## Weighted Average

### (proportion)*(group A average) + (proportion)*(group B average) ... etc

79

## Range

### greatest value - least value

80

## Standard Deviation

###
_____________________

√ 2 2 2

√ (a-m) + (b-m) + (c-m)

SD =√------------------------------------- etc

√ n

81

## Probability that event A will happen:

###
number of outcomes where A occurs

P(A) = -------------------------------------------------------

total number of outcomes

82

## The chance that the event does not occur:

### P(event happens) + P(event does not happen) = 1

83

## Mutually Exclusive Events:

### Events that cannot happen together; P (A and B) = 0

84

## Events A and B (if they are independent events):

### P (A and B) = P(A) * P(B)

85