Multiplication & Roots

21²

441 12²=144 21²=441

45-45-90 triangles

45-45-90 The base and height are equal each leg = x hypotenuse = x√2

9x8

72

Is 1 a prime number?

No

3.102 x 10² in normal form

shift the decimal 2 places to the right (because 10²) 3.102 → 310.2

Surface area of cylinder

2x the surface area of the circle, then the rectangle in the middle. SA = 2πr² + (circumference of circle x h)

π

3.14 this is actually the ratio of the circumference to the diameter. ie: every circle's circumference is 3.14x its diameter

30-60-90 triangles

30-60-90 30° leg = x 60° leg = x√3 90° leg = 2x

3x 3x 3x equals

3³x³ which is the same thing as 3x³

√50²

50

2⁹

512

23²

529

6x9

54

9x6

54

7x8

56

5⁶ ÷ 5⁴

5² subtract the exponents

8x9

72

2³

8

3⁴

81

9x9

81

12x7

84

division algorithm

A divided by B A = BQ + R Q = quotient R = remainder

√225

15

2⁴

16

8x2

16

√256

16

13²

169

√289

17

√324

18

14²

196

isosceles

2 sides of equal length

√5

2.25

√441

21 12²=144 21²=441

√484

22

15²

225

√529

23

√576

24

3⁵

243

√625

25

16²

256

2⁸

256

3x9

27

3³

27

4x7

28

7x4

28

canonical forms - even

2n

canonical forms - odds

2n + 1

probability

# of possibilities that meet my conditions ÷ # of possibilities

Sum of interior angles of a polygon

(#sides - 2) * 180°

if your average free throw percentage is 75%, what is the likelihood of getting 10 free throws in a row?

(.75)¹⁰

2(3ⁿ+3ⁿ+3ⁿ)=162

(3ⁿ+3ⁿ+3ⁿ) = 3(3ⁿ) = 3ⁿ⁺¹ 2(3ⁿ⁺¹)=2¹3⁴

6³ x 6⁶

(6x6x6)(6x6x6x6x6x6) = 6⁹ so you add the exponents

(a³)⁴

(axaxa)(axaxa)(axaxa)(axaxa) total of 12 a's = a ¹² so here you multiply the exponents

area of trapezoid

(b₁+b₂)h ÷ 2

10-³

.001 here the 3 represents number of PLACES behind the decimal, NOT zeroes

if n is a positive integer and the product of all the integers from 1 to n is divisible by 990, what is the least possible value of n?

1 to n = n! every prime factor of 990 must be a factor of n! so... prime factor 990.. pick the greatest number

10³

1,000 1 with 3 zeroes

√2

1.4 Valentine's day

√3

1.7 St. Patricks Day

area of triangle

1/2 b x h

2-⁴

1/2⁴ = 1/16

x-¹

1/x

2¹⁰

1024

12x9

108

9x12

108

11x11

121

5³

125

2⁷

128

√169

13

11x12

132

12x11

132

probability - number of possibilities

you are rolling two die - how many possibilities of combinations are there? 6 x 6 = 36

rate problems - formula

D/W = R × T

Divisibility rules: 8

If the last 3 digits are divisible by 8

probability of a OR b

P(a) + P(b) - P(a&b)

permutations vs. combinations contd

a combination is when order DOESN'T matter. For example, you have 5 shirts, but only space for 3 shirts in your suitcase. To solve: 5 × 4 × 3 ÷ 3 × 2 × 1

permutations vs. combinations

a permutations is when order DOES matter. For example, when you have 3 seats available and 5 people. To solve: 5 × 4 × 3

difference of squares

a² - b² = (a + b)(a - b)

a² x aⁿ

a²+ⁿ we learned in the card above that we add exponents with equal bases.

area of parallelogram

b x h

rate problems - combined rates

combined rates is just the sum of the rates

.0000516 in scientific notation

count digits up to the first non-zero: 5 5.16 x 10-⁵

7,012,000,000,000 in scientific notation

count the digits after the first non-zero (in this instance the number of digits after the 7): 12 7.012 x 10¹²

number line: |a+b|

distance between a and -b on the # line ex: |x+1| ≤ 4 -1 would be the center, with 4 on either side so.. -5 to 3

number line: |a-b|

distance between a and b on the # line ex: |x-1| ≤ 4 +1 would be the center, with 4 on either side so.. -3 to 5

average speed is NOT the average of the speeds

it is total distance ÷ total time

for a prime to divide a factorial

it must be in the factorial

triangle inequality theorem

length of a side must be < sum of lengths of other 2 sides

multiples/factors

more multiples, fewer factors.

likelihood of a coin landing on heads and an even rolling a 6-sided die

multiply each likelihood = 1/2 x 3/6 = 1/2 x 1/2 = 1/4

probability of getting heads, tails, heads, in this exact order P (H,T,H)

multiply probability of each 1/2 x 1/2 x 1/2 = 1/8

algebraic expression for: the sum of {1,2,3,4....n)

n(n+1)/2 Ex: The sum of {1,2,3,4} 4(4+1)/2 4(5)/2 20/2 = 10

algebraic expression for: the sum of {12,14,16,18....n} where there are 250 terms

n₁+n₂₅₀ ÷ 2 × 250

must be =

process of elimination

1.75 x 10-³ in normal form

shift the decimal 3 places to the left 1.75 →.00175

Volume of a cylinder

surface area of the circle, times the height V = πr²h

dividend

the number being divided ie: 8 divided by 2 dividend = 8

divisor

the number you are dividing the main number by "x divided by DIVISOR" ie: 8 divided by 2 divisor = 2

rate problems - if work isn't given

then W = 1

circumference =

πd where d = diameter

√196

14

12²

144

9x2

18

√361

19

17²

289

2⁵

32

4x8

32

8x4

32

18²

324

7³

343

3x12

36

4x9

36

9x4

36

19²

361

√2⁴

4

6x7

42

4x12

48

6x8

48

8x6

48

22²

484

7²

49

8x7

56

24²

576

12x5

60

25²

625

5⁴

625

7x9

63

9x7

63

2⁶

64

12x6

72

6x12

72

7x12

84

3²

9

12x8

96

8x12

96

Always chose which answers to check

B & D

Divisibility rules: 9

If the sum of the digits is divisible by 9

Is 2 a prime number?

Yes, the only even prime

Divisibility rules: 6

divisible by 2 and 3

0 is even or odd

even

even * even

even

even * odd

even

even + even

even

odd + odd

even

Divisibility rules: 7

if the diff between 2x the ones digit & the remaining digits is a multiple of 7 ex: 672 → 67-2(2) = 63 = a multiple of 7 (chop the ones digit)

Divisibility rules: 11

if the diff between the sum of the digits in odd places & even places (left to right) is a multiple of 11 ex: 2,849→ (9+8) - (4+2) = 11-11 = 0 → counts as divisible by 11

Divisibility rules: 4

if the last 2 digits are divisible by 4

Divisibility rules: 3

if the sum of the digits is divisible by 3

even + odd

odd

odd * odd

odd

Powers of 2 patterns (2ⁿ)

units digit of answer: 2,4,8,6,2,4,8,6

√x²

|x|