Formulas Flashcards
(116 cards)
1
Q
Pythagorean triples
A
3-4-5
5-12-13
7-24-25
8-15-17
2
Q
1²
A
1
3
Q
2²
A
4
4
Q
3²
A
9
5
Q
4²
A
16
6
Q
5²
A
25
7
Q
6²
A
36
8
Q
7²
A
49
9
Q
8²
A
64
10
Q
9²
A
81
11
Q
10²
A
100
12
Q
11²
A
121
13
Q
12²
A
144
14
Q
13²
A
169
15
Q
14²
A
196
16
Q
15²
A
225
17
Q
16²
A
256
18
Q
17²
A
289
19
Q
18²
A
324
20
Q
19²
A
361
21
Q
20²
A
400
22
Q
24²
A
576
23
Q
25²
A
625
24
Q
2¹
A
2
25
2²
4
26
2³
8
27
2⁴
16
28
2⁵
32
29
2⁶
64
30
2⁷
128
31
2⁸
256
32
2⁹
512
33
2¹⁰
1024
34
3¹
3
35
3²
9
36
3⁴
81
37
3³
27
38
3⁵
243
39
4¹
4
40
4²
16
41
4³
64
42
4⁴
256
43
5¹
5
44
5²
25
45
5³
125
46
5⁴
625
47
6¹
6
48
6²
36
49
6³
216
50
7¹
7
51
7²
49
52
7³
343
53
8¹
8
54
8²
64
55
8³
512
56
9¹
9
57
9²
81
58
9³
729
59
10¹
10
60
10²
100
61
10³
1000
62
1/4
0.25
63
1/3
0.33
64
1/5
0.20
65
1/6
0.16
66
1/8
0.125
67
1/2
0.50
68
2/3
0.66
69
2/5
0.40
70
5/6
0.83
71
3/8
0.375
72
3/4
0.75
73
3/5
0.60
74
5/8
0.625
75
4/5
0.80
76
7/8
0.875
77
a/b + c/d
ad+bc/bd
78
a/b x c/d
ac/bd
79
a/b / c/d
a/b x d/c
80
How to determine the largest fraction between two fractions?
Cross multiply up and see which has the largest number on top
ex. 4/9 or 5/12
48 // 45; since 48 is larger than 45, 4/9 is larger
81
Even + even
Even
82
Odd + odd
Even
83
Odd + even
Odd
84
Even x even
Even
85
Odd x even
Even
86
Odd x odd
Odd
87
Multiplying an odd number of negative numbers gives you a ______ number.
Negative
88
Multiplying an even number of negative numbers gives you a ______ number.
Positive
89
1st power repeating pattern of unit digits
2;3;4;7;8;9...
2¹=2, 3¹=3, 4¹=4, 7¹=7, 8¹=8, 9¹=9...
90
2nd power repeating pattern of unit digits
4;9;6;9;4;1...
2²=4, 3²=9, 4²=16, 7²=49, 8²=64, 9²=81
91
3rd power repeating pattern of unit digits
8;7;4;3;2;9
2³=8, 3³=27, 4³=64, 7³=343, 8³=512, 9³=729
92
4th power repeating pattern of unit digits
6;1;6;1
2⁴=16, 3⁴=81, 7⁴=2401, 8⁴=4096
93
5th power repeating pattern of unit digits
2;3;7;8
2⁵=32, 3⁵=243, 7⁵=16807, 8⁵=36268
94
2 - divisibility rules
The number is even
95
3 - divisibility rules
The sum of the digits is divisible by 3
96
4 - divisibility rules
The last two digits divide by 4
97
5 - divisibility rules
The number ends in 5 or 0
98
6 - divisibility rules
The number is even and divisible by 3
99
7 - divisibility rules
Just divide, it's easier :)
100
8 - divisibility rules
The last three digits are divisible by 8
101
9 - divisibility rules
The sum of the digits is divisible by 9
102
Prime Number Rules (3)
1 - 1 is NOT a prime number
2 - Is the smallest and only even prime number
3 - The square of any prime number has exactly three factors (1, itself, and the square of the prime number)
103
How many numbers are from X to Y?
Y - X +1
85-57=28+1=29
*This counts X and Y
104
How many numbers are between X and Y?
Y - X -1
85-57=28-1=27
*This does not count X and Y
105
Remainders: If a number "n" is divided by "d", with a quotient of "q" and a remainder of "r", then ______.
n=dq+r
*tip: if x is divided by 23 with a remainder of 17, the easiest number to use for x is 17.
106
Greatest common divisor/factor
The biggest number that goes into both of them.
To find GCF, express each number as a product of prime factors and then multiply each factor the greatest number of times it occurs in either number.
107
Least common multiple
The smallest number that both of the integers go into.
To find LCM, express each number as a product of prime factors and then multiply each factor by the greatest number of times it occurs in either number.
108
Number property theorems (2)
1-greatest common divisor
2-total number of divisors
1- If "x" is the greatest common divisor/factor of "A" and "B", and "y" is the least common multiple of "A" and "B", then AB=xy.
2-To find the total number of divisors/factors of a particular number, first express the number as a product of its primes. Add one to each exponent and then multiply the new exponents.
360=2³3²5
(3+1)(2+1)(1+1)= 4x3x2 =24
So, there are 24 factors of 360.
109
xᵃxᵇ=
xᵃ⁺ᵇ
110
xᵃ / xᵇ=
xᵃ⁻ᵇ
111
(xy)ᵃ=
xᵃyᵃ
112
(x/y)ᵃ=
xᵃ / yᵃ
113
(xᵃ )ᵇ=
xᵃᵇ
114
x⁻ᵃ=
1/xᵃ
115
x⁰=
1
116
ⁿ√x=
x^(1/n)
