Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
32 Cards in this Set
- Front
- Back
|
Factor
x²-y² |
(x + y)(x - y)
|
|
|
Factor
x²+y² |
No real factorization
Using complex numbers, with i = sqrt(-1) (x+yi)(x-yi) |
|
|
Factor
x³+y³ |
(x+y)(x²-xy+y²)
|
|
|
Factor
x³-y³ |
(x-y)(x²+xy+y²)
|
|
|
Factor
x²+2xy+y² |
(x+y)²
|
|
|
Pythagorean Theorem
|
For a right triangle with legs of length a and b, and hypotenuse of length c
a²+b²=c² |
|
|
Perfect Squares [0,50]
|
0²=0
1²=1 2²=4 3²=9 4²=16 5²=25 6²=36 7²=49 |
|
|
Perfect Squares [50,250]
|
8²=64
9²=81 10²=100 11²=121 12²=144 13²=169 14²=196 15²=225 |
|
|
Powers of 2 [1,500]
|
2^0 = 1
2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 |
|
|
Perfect Cubes [1,1000]
|
1³=1
2³=8 3³=27 4³=64 5³=125 6³=216 7³=343 8³=512 9³=729 |
|
|
Factorials [1,360000]
|
0! = 1
1! = 1 2! = 2 3! = 6 4! = 24 5! = 120 6! = 720 7! = 5040 8! = 40320 |
|
|
Factor
x^4 - y^4 |
(x-y)(x+y)(x²+y²)
|
|
|
Factor
x^5 - y^5 |
(x - y)(x^4 + x³y + x²y² + xy³ + y^4)
|
|
|
Factor
x^5 + y^5 |
(x + y)(x^4 - x³y + x²y² - xy³ + y^4)
|
|
|
Factor
x^6 - y^6 |
(x-y)(x+y)(x²+xy+y²)(x²-xy+y²)
|
|
|
Factor
x^6 + y^6 |
(x² + y²) (x^4 - x²y² + y^4)
|
|
|
ax² + bx + c = 0
i) Discriminant ii) Quadratic Formula |
i) D=b²-4ac
ii) x = [ -b ± sqrt(D)] / 2a D < 0 -> complex roots |
|
|
ax²+bx+c=0
Properties of the Discriminant D = b² - 4ac |
i) D>0 and a perfect square
-> 2 rational roots ii) D>0 and not a perfect square -> 2 irrational roots iii) D=0 -> 1 root, multiplicty 2 iv) D<0 -> 2 complex conj. roots |
|
|
Primative Pythagorean Triples
with perimeter < 100, |
a b c p
3 4 5 12 5 12 13 30 8 15 17 40 7 24 25 56 20 21 29 70 12 35 37 84 9 40 41 90 |
|
|
Heron's Formula
for the area A of an arbitrary triangle with side lengths a, b, c, and semiperimeter s |
A² = s(s-a)(s-b)(s-c)
-or- A = sqrt[s(s-a)(s-b)(s-c)] |
|
|
Primes [2,197]
|
2 29 67 107 157
3 31 71 109 163 5 37 73 113 167 7 41 79 127 173 11 43 83 131 179 13 47 89 137 181 17 53 97 139 191 19 59 101 149 193 23 61 103 151 197 |
|
|
Digits of pi
|
3.14159 26535 89793 23846
26433 83279 50288 4197 ... irrational and transcendental unknown whether normal |
|
|
Digits of e
|
2.71828 18284 59045 23536
02874 71352 66249 7757... Known to be both irrational and transcendental; e is maximally transcendental, with irrationanality measure, mu(e)=2. it is unknown whether e is normal |
|
|
The Golden Ratio phi
|
1.61803 39887 49894 84820
45868 34365 63811 7720... irrational and algebraic phi = ½ [ 1 + sqrt(5) ] |
|
|
The Euler-Mascheroni constant gamma
|
0.57721 56649 01532 86060
65120 90082 40243 1042... unknown if irrational |
|
|
Catalan's Constant K
|
K = 0.915965594177...
unknown whether irrational |
|
|
Apéry's constant zeta(3)
|
zeta(3) = 1.2020569...
known to be irrational not known to be transcendental or normal |
|
|
Pascal's Triangle
|
1
1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 |
|
|
Perfect Number
|
a # equal to the sum of its factors
6 28 496 8128 33550336 8589869056 137438691328 2305843008139952128 |
|
|
The Hardy-Ramanujan Number
|
The smallest "taxicab number",
a number that has two representations as the sum of two cubes. 1729 = 1³+12³ = 9³+10³ |
|
|
Platonic Solids
|
Solid f v e
Tetrahedron 4 4 6 Cube 6 8 12 Octahedron 8 6 12 Dodecahedron 12 20 30 Icosahedron 20 12 30 Note f+v-e=2 |
|
|
The Kepler-Poinsot Solids
|
great dodecahedron
great icosahedron great stellated dodecahedron small stellated dodecahedron |
