These facts are considered essential for students competing on math teams in middle school and high school. Making flash cards of these facts is an excellent way to drill them. Our team learns 1/3 of these facts each month for a three month period. Drill sheets for each month are also included.
Squares: 1 - 30
Cubes: 1 -12
Powers of 2: From 21 to 212.
21
22
23
24
25
26
27
28
29
210
211
212
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=
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2
4
8
16
32
64
128
256
512
1024
2048
4096
Prime numbers from 2 to 109:
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97
101
103
107
109
Pythagorean Theorem: a2 + b2 = c2
Pythagorean Triples:
The 45o - 45o - 90o right triangle, or right isosceles triangle: If the leg is s, then the hypotenuse is s times the square root of 2.
The 30o - 60o - 90o right triangle: This is half of an equilateral triangle. The short leg, the one opposite the 30o angle, is s, the hypotenuse is 2s, and the long leg, which is opposite the 60o angle, is s times the square root of 3.
Fraction, decimal, percent equivalencies:
Turning a repeating decimal into a simple fraction.
Take the number that repeats and divide it by however many 9's as there are digits in the original number. E.g. for the repeating decimal .5757... the answer would be 57 / 99 which simplifies down to 19 / 33.
Turning a fractional percent into a simple fraction. E.g.20 5/6%
20 5/6% = 125/6 % = 125/600 = (25 x 5) / (25 x 24) = 5/24
A Useful Formula:
To find 1 + 2 + 3 + 4 + 5 + ... + n, just take n, multiply it by its higher consecutive number, and divide by 2.
Example: find 1+2+3+4+5+...+25.
25 (25 + 1) / 2 = 325
Number of diagonals in an s-sided polygon: s(s-3)/2
(where s is the number of sides of the polygon.)
A polygon having 35 sides has 35*(35-3)/2 = 560 diagonals.
Diagonal of a cube: s times square root of 3
(where s is the edge of the cube).
Area and Volume:
Area of a square, given the side: A = s 2
Area of a square, given diagonal: A = d 2/2
Area of a rhombus, given diagonals: A = (d1 d2)/2
Area of triangle: A = (bh) / 2
Area of circle: A = π r 2
Area of trapezoid: A = 1/2 h (b1 + b2)
Volume of cylinder and prism: V = B h
Volume of cone and pyramid: V = 1/3 (B h)
Volume of a sphere: V = 4/3 π r 3
Surface area of a sphere: A = 4 π r 2
The equation of a line is y = mx + b
0! = 1