Need to Know Flashcards
1
Q
The Commutative Property
A
a+b=b+a ; ab=ba
2
Q
The Associative Property
A
(a+b) +c = a+(b+c) ; (ab)c = a(bc)
3
Q
The Distributive Property
A
a*(b+c) = ab+ac
4
Q
The Commutative and Associative Properties do not work with
A
Subtraction or Division
5
Q
Prime Numbers
A
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 and 59
6
Q
Factorization for 21
A
3 and 7 are prime factors
7
Q
Greatest Common Factor (GCF) of 56 and 70
A
The factorization of 56 is = 2227
The factorization of 70 is = 257
The two largest numbers in both is 27 = 14
8
Q
Least Common Factor (LCF) of 9 and 15
A
The factorization of 9 is = 33
The factorization of 15 is = 35
Multiply the shared primes (3*3) by the unshared primes (5) = 45
9
Q
The absolute value is…
A
The positive form of the number
10
Q
|x| and |-x| are equal to
A
x
11
Q
To find some part of a whole use
A
Part Percent
——– = ———–
Whole 100
12
Q
Percent Change
A
(Change * 100)
%change = ———————
Original
13
Q
Exponent Laws:
A B x * x equals
A
(A+B)
x
14
Q
Exponent Laws:
A X --------- B X equals
A
(A-B)
X
15
Q
Exponent Laws:
B
A
X equals
A
(A*B)
X
16
Q
1 raised to any power is
A
1
17
Q
0 raised to any nonzero power is
A
0
18
Q
Any number raised to the power of 0 is
A
1
19
Q
Fractions as Exponents:
1/2
x equals
A
__
√ x
20
Q
Fractions as Exponents:
2/3 x equals
A
_____
1 | 2
√ x
21
Q
Negative Exponents:
-1
x equals
A
x
22
Q
Negative Exponents:
-2
x equals
A
2
x
23
Q
A negative number raised to an even power is
A
positive
24
Q
A negative number raised to an odd power is
A
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)
