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Formulas Flashcards

1
Q

sinA

A

opposite/hypotenuse

or

cos(90°-A)

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2
Q

cosA

A

adjacent/hypotenuse

or

sin(90°-A)

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3
Q

tanA

A

opposite/adjacent

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4
Q

cscA

A

hypotenuse/opposite

or

1/sinA

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5
Q

secA

A

hypotenuse/adjacent

or

1/cosA

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6
Q

cotA

A

adjacent/opposite

or

1/tanA

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7
Q

sin(-A)

A

-sinA

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8
Q

cos(-A)

A

cos(A)

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9
Q

sin2A

A

2sinAcosA

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10
Q

cos2A

A

cos2A-sin2A

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11
Q

pythagorean identities

A

sin2A + cos2A = 1

and

tan2A + 1 = sec2A

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12
Q

1-cos2A=

A

sin2A

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13
Q

sec2A-1=

A

tan2A

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14
Q

Area of a circle

Circumference

ArcLength

Asector

A

A = πr2

C = 2πr = π

ArcLength = (-) / 360 (2πr)

Asector = (-) / 360 (πr2)

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15
Q

Area of a sphere

Volume

A

A = 4 πr2

V = (4/3)πr3

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16
Q

Area of a cylinder

Volume

A

A = 2πrh

V = πr2h

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17
Q

Area of an Ellipse

A

πab

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18
Q

Area of a triangle

A

(1/2)b•h

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19
Q

Area of a rhombus

A

b•h

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20
Q

distance

A

= velocity • time

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21
Q

time

A

= distance/ velocity

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22
Q

average velocity

A

= [total distance traveled]/ [total time elasped]

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23
Q

combination formula

A

the number of ways that r things can be chosen from n things when order does not matter:

C (n,r) = [n!/(n-r)!•r!]

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24
Q

Permutation formula

A

the number of ways that r things can be chosen from n things when order does matter:

P (n,r) = [n!/(n-r)!]

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25
Q

binomial probability distribution

A

the probability that there will be exactly r outcomes out of n trials when the probability of success in each trial is uniformly p:

C (n,r)•pr(1-p)n-r

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26
Q

probability dealing with identical

A

the number of ways that n things can be ordered when a of them are identical, b of them are identical, c of them are identical, etc. (as in the letters in the word TENNESSEE):

n!/(a!•b!•c!•…)

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27
Q

mean of n scores

A

µ = Σxi/n

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28
Q

variance

A

σ2 = Σ(xi - µ)2/n

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29
Q

standard deviation

A

σ =

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30
Q

Empirical Rule

A
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31
Q

Logbx = n

A

bn = x

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32
Q

log(A•B) =

A

log (A) + log (B)

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33
Q

log(A/B)=

A

log (A) - log (B)

34
Q

log(An)=

A

n•log(A)

35
Q

Ellipse

A

x2/a2 + y2/b2 = 1

where a = the semi major axis (the “long radius”)

and b = the semi minor axis (the “short radius”)

c2 = a2 - b2

where c is the distance from the center of the ellipse to either focus.

36
Q

The total time

Ttotal

A

The total time Ttotal it takes to complete a task when a task is simultaneously being worked on by more than one agent. If, when working alone, the time it takes one agent to coplete the task is t1, the time it takes another agent is t2, etc., then the total time Ttotal is given by the following formula:

1/t1 + 1/t2 + 1/t3 + etc. = 1/Ttotal

37
Q

Simple interest

A

always based on the amoun of the original principal. it thus remains constant for each interest paid (usually measured by the year).

38
Q

Compound interest

A

means that new interest is based on an amount equal to the principal plus the total accumulated interest. the amount of interest earned therefore increases each interest period (usually measure by the year).

39
Q

distance formula

given 2 points P1 (X1,Y1) and P2 (X2, Y2)

40
Q

Midpoint Formula

41
Q

Area of an Equilateral triangle

42
Q

Rules of exponents

Xn•Xm =

43
Q

Rules of exponents

1/Xn

44
Q

Rules of exponents

Xn/Xm

A

Xn-m

or

1/xm-n

45
Q

Polygon Formulas

A

N= number of sides of a regular polygon.

S= length from center to a center.

Area = (1/2) N sin(360°/N)S2

Sum of the interior angles = (N-2) x 180°

The number of diagonals = (1/2) N(N-3)

46
Q

Percent increase and decrease

A

given 2 numbers X1 and X2, the percent increase or decrease is given by:

D%= (x2-x1)/x1 x 100

If x2 > x1, then D% is positive, representing an increase

If x2 < x1, then D% is negative, representing a decrease

47
Q

Percentage equations

A

% = IS/OF x 100

or

% = Part/Whole x 100

48
Q

Conversions

Temperature

Kelvin (K)

A

K = °C + 273

49
Q

Conversions

Temperature

Ferenheit (°F)

A

°F = 9/5(°C) + 32

50
Q

Conversions

Temperature

Celsius (°C)

A

°C = 5/9 (°F - 32)

or

°C = K - 273

51
Q

1/2

52
Q

1/3

53
Q

1/4

54
Q

1/5

55
Q

1/8

56
Q

1/10

57
Q

1/20

58
Q

1/25

59
Q

12= __ 22= __ 32=__

42=__ 52= __ 62=__

72= __ 82=__ 92=__

102=__ 13=__ 23=__

33=__ 43=__ 53=__

34=__

A

12=_2_ 22=_4_ 32=_9_

42=_16_ 52= _25_ 62=_36_

72= _49_ 82=_64_ 92=_81_

102=_100_ 13=_1_ 23=_8_

33=_27_ 43=_64_ 53=_125_

34=_81_

60
Q

Terra

Giga

Mega

Kilo

Centi

Milli

Micro

Nano

Pico

Femto

A

Terra= 1012

Giga= 109

Mega= 106

Kilo= 103

Centi= 10-2

Milli= 10-3

Micro= 10-6

Nano= 10-9

Pico= 10-12

Femto= 10-15

61
Q

in. to cm

A

1in = 2.54 cm

62
Q

yd to ft.

A

1 yard = 3ft.

63
Q

mile to ft.

A

1 mile = 5280 ft.

64
Q

mile to km

A

1 mile = 1.6km

65
Q

kg to pounds

A

1 kg = 2.2 lbs

66
Q

pound to ounces

A

1 lb = 16 oz.

67
Q

galloon to quarts

A

1 gal. = 4 qts.

68
Q

quart to pints to ounces

A

1 qt. = 2 pints = 32 fl. oz.

69
Q

pint to cups

A

1 pt. = 2 cups

70
Q

Dilutions

A

M1V1=M2V2

or

C1V1=C2V2

M=mol/L

71
Q

log(A) + log(B)

A

log(A) + log(B) = log(AB)

72
Q

log(A) - log(B)

A

log(A) - log(B) = log (A/B)

73
Q

Rules of exponents

(xa)b

A

(xa)b = xab

74
Q

Rules of exponents

(ax)(bx)

A

(ax)(bx) = (ab)x

75
Q

Rules of exponents

ax/bx

A

ax/bx = (a/b)x

76
Q

Logarithms

A

log(0.01) = log(10-2) = -2

log(0.1) = log(10-1) = -1

log(1) = log(100) = 0

log(10) = log(101) = 1

log(100) = log(102) = 2

77
Q

Area of rectangle

78
Q

Area of parallelogram

79
Q

Area of trapezoid

A

A = (baseavg)(height) = (base1 + base2/ 2)(height)

80
Q

Volume of cone

and

Area of cone

A

V = 1/3πr2h

A = 1/2C x l

81
Q

Volume of pyramid

A

V = 1/3 Abase x h

Quantative Reasoning (2 decks)

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