Formulas

Question 1

sinA

Answer 1

opposite/hypotenuse

or

cos(90°-A)

Question 2

cosA

Answer 2

adjacent/hypotenuse

or

sin(90°-A)

Question 3

tanA

Answer 3

opposite/adjacent

Question 4

cscA

Answer 4

hypotenuse/opposite

or

1/sinA

Question 5

secA

Answer 5

hypotenuse/adjacent

or

1/cosA

Question 6

cotA

Answer 6

adjacent/opposite

or

1/tanA

Question 7

sin(-A)

Answer 7

-sinA

Question 8

cos(-A)

Answer 8

cos(A)

Question 9

sin2A

Answer 9

2sinAcosA

Question 10

cos2A

Answer 10

cos²A-sin²A

Question 11

pythagorean identities

Answer 11

sin²A + cos²A = 1

and

tan²A + 1 = sec²A

Question 12

1-cos²A=

Answer 12

sin²A

Question 13

sec²A-1=

Answer 13

tan²A

Question 14

Area of a circle

Circumference

ArcLength

A_sector

Answer 14

A = πr²

C = 2πr = π

ArcLength = (-) / 360 (2πr)

A_sector = (-) / 360 (πr²)

Question 15

Area of a sphere

Volume

Answer 15

A = 4 πr²

V = (4/3)πr³

Question 16

Area of a cylinder

Volume

Answer 16

A = 2πrh

V = πr²h

Question 17

Area of an Ellipse

Answer 17

πab

Question 18

Area of a triangle

Answer 18

(1/2)b•h

Question 19

Area of a rhombus

Answer 19

b•h

Question 20

distance

Answer 20

= velocity • time

Question 21

time

Answer 21

= distance/ velocity

Question 22

average velocity

Answer 22

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

Question 23

combination formula

Answer 23

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!]

Question 24

Permutation formula

Answer 24

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

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

Question 25

binomial probability distribution

Answer 25

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)•p^r(1-p)^n-r

Question 26

probability dealing with identical

Answer 26

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!•...)

Question 27

mean of *n* scores

Answer 27

µ = Σx_i/n

Question 28

variance

Answer 28

σ² = Σ(x_i - µ)²/n

Question 29

standard deviation

Answer 29

σ =

Question 30

Empirical Rule

Question 31

Log_bx = n

Answer 31

bⁿ = x

Question 32

log(A•B) =

Answer 32

log (A) + log (B)

Question 33

log(A/B)=

Answer 33

log (A) - log (B)

Question 34

log(Aⁿ)=

Answer 34

n•log(A)

Question 35

Ellipse [![]()](https://s3.amazonaws.com/brainscape-prod/system/cm/030/967/531/q_image_thumb.png?1365729535)

Answer 35

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.

Question 36

The total time T_total

Answer 36

The total time T_total 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 T_total is given by the following formula: 1/t₁ + 1/t₂ + 1/t₃ + etc. = 1/T_total

Question 37

Simple interest

Answer 37

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

Question 38

Compound interest

Answer 38

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).

Question 39

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

Answer 39

[![]()](https://s3.amazonaws.com/brainscape-prod/system/cm/030/969/636/a_image_card.png?1365730165)

Question 40

Midpoint Formula

Answer 40

[![]()](https://s3.amazonaws.com/brainscape-prod/system/cm/030/969/964/a_image_thumb.png?1365730333)

Question 41

Area of an Equilateral triangle

Answer 41

[![]()](https://s3.amazonaws.com/brainscape-prod/system/cm/030/970/573/a_image_card.png?1365730469)

Question 42

Rules of exponents Xⁿ•X^m =

Answer 42

X^n+m

Question 43

Rules of exponents 1/Xⁿ

Answer 43

= X^-n

Question 44

Rules of exponents Xⁿ/X^m

Answer 44

X^n-m or 1/x^m-n

Question 45

Polygon Formulas

Answer 45

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)

Question 46

Percent increase and decrease

Answer 46

given 2 numbers X₁ and X₂, the percent increase or decrease is given by: D%= (x₂-x₁)/x₁ x 100 If x_{2 >} x₁, then D% is positive, representing an increase If x₂ \< x₁, then D% is negative, representing a decrease

Question 47

Percentage equations

Answer 47

% = IS/OF x 100 or % = Part/Whole x 100

Question 48

Conversions Temperature Kelvin (K)

Answer 48

K = °C + 273

Question 49

Conversions Temperature Ferenheit (°F)

Answer 49

°F = 9/5(°C) + 32

Question 50

Conversions Temperature Celsius (°C)

Answer 50

°C = 5/9 (°F - 32) or °C = K - 273

Question 51

1/2

Answer 51

50%

Question 52

1/3

Answer 52

33.3%

Question 53

1/4

Answer 53

25%

Question 54

1/5

Answer 54

20%

Question 55

1/8

Answer 55

12.5%

Question 56

1/10

Answer 56

10%

Question 57

1/20

Answer 57

5%

Question 58

1/25

Answer 58

4%

Question 59

1²= \_\_ 2²= \_\_ 3²=\_\_ 4²=\_\_ 5²= \_\_ 6²=\_\_ 7²= \_\_ 8²=\_\_ 9²=\_\_ 10²=\_\_ 1³=\_\_ 2³=\_\_ 3³=\_\_ 4³=\_\_ 5³=\_\_ 3⁴=\_\_

Answer 59

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\_

Question 60

Terra Giga Mega Kilo Centi Milli Micro Nano Pico Femto

Answer 60

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

Question 61

in. to cm

Answer 61

1in = 2.54 cm

Question 62

yd to ft.

Answer 62

1 yard = 3ft.

Question 63

mile to ft.

Answer 63

1 mile = 5280 ft.

Question 64

mile to km

Answer 64

1 mile = 1.6km

Question 65

kg to pounds

Answer 65

1 kg = 2.2 lbs

Question 66

pound to ounces

Answer 66

1 lb = 16 oz.

Question 67

galloon to quarts

Answer 67

1 gal. = 4 qts.

Question 68

quart to pints to ounces

Answer 68

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

Question 69

pint to cups

Answer 69

1 pt. = 2 cups

Question 70

Dilutions

Answer 70

M₁V₁=M₂V₂ or C₁V₁=C₂V₂ M=mol/L

Question 71

log(A) + log(B)

Answer 71

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

Question 72

log(A) - log(B)

Answer 72

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

Question 73

Rules of exponents (x^a)^b

Answer 73

(x^a)^b = x^ab

Question 74

Rules of exponents | (a^x)(b^x)

Answer 74

(a^x)(b^x) = (ab)^x

Question 75

Rules of exponents a^x/b^x

Answer 75

a^x/b^x = (a/b)^x

Question 76

Logarithms

Answer 76

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

Question 77

Area of rectangle

Answer 77

A = l x w

Question 78

Area of parallelogram

Answer 78

A = b x h

Question 79

Area of trapezoid

Answer 79

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

Question 80

Volume of cone and Area of cone

Answer 80

V = 1/3πr²h A = 1/2C x l

Question 81

Volume of pyramid

Answer 81

V = 1/3 A_base x h