Study your flashcards anywhere!
Download the official Cram app for free >
 Shuffle
Toggle OnToggle Off
 Alphabetize
Toggle OnToggle Off
 Front First
Toggle OnToggle Off
 Both Sides
Toggle OnToggle Off
 Read
Toggle OnToggle Off
How to study your flashcards.
Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key
Up/Down arrow keys: Flip the card between the front and back.down keyup key
H key: Show hint (3rd side).h key
A key: Read text to speech.a key
32 Cards in this Set
 Front
 Back
Factor
x²y² 
(x + y)(x  y)


Factor
x²+y² 
No real factorization
Using complex numbers, with i = sqrt(1) (x+yi)(xyi) 

Factor
x³+y³ 
(x+y)(x²xy+y²)


Factor
x³y³ 
(xy)(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 
(xy)(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 
(xy)(x+y)(x²+xy+y²)(x²xy+y²)


Factor
x^6 + y^6 
(x² + y²) (x^4  x²y² + y^4)


ax² + bx + c = 0
i) Discriminant ii) Quadratic Formula 
i) D=b²4ac
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(sa)(sb)(sc)
or A = sqrt[s(sa)(sb)(sc)] 

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 EulerMascheroni 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 HardyRamanujan 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+ve=2 

The KeplerPoinsot Solids

great dodecahedron
great icosahedron great stellated dodecahedron small stellated dodecahedron 