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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

Events A or B happens or A and B happens:

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