1/a + 1/b = 1/t

a & b = number of hours takes people to complete task

t = time

interest = (principal) x (interest rate*) x (time**)

*expressed as a decimal

**expressed in years

(final balance) = (principal) x (1+ interest/c)^(time)(c)

c= number of times compounded annually

Number added = (new sum) - (original sum)

Number deleted = (original sum) - (new sum)

2! = 2 x1 =2

4! = 4 x 3 x 2 x 1 =24

NOTE: 0! = 1! = 1

NOTE: 6! = 6 x 5! = 6 x 5 x 4!

REMEMBER TO FACTOR/CANCEL

How many ways are there to arrange 7 items along a shelf? = 7!

OR if the number of ways to arrange a smaller group drawn from a larger group:

_nP_k = n!/(n-k)!

n= # in the larger group

k= # you're arranging

Five runners run in a race. The runners who come in first, second and third place will win gold, silver and bronze medals respectively. How many possible outcomes for gold, silver, and bronze medal winners are there?

Standard deviation is a measure of how spread out a set of numbers is (how much the numbers deviate from the mean). The greater the spread, the higher the standard deviation.

HOW TO MULTIPLY POWERS

x^a x x^b

HOW TO DIVIDE POWERS

x^a/x^b

HOW TO RAISE A POWER TO A POWER TO AN EXPONENT

(x^a)^b = 

(x^a)^b = x^ab

(3⁴)⁵ = 3²⁰

NEGATIVE POWERS

5^-3

A number raised to the exponent -x is the reciprocal of that number raised to the exponent x.

5^-3 = 1/5³ = 1/5x5x5 = 1/125

n^-1 = 1/n

n^-2 = 1/n²

FRACTIONAL POWERS

x^1/2 = 

x^1/2 = √x

Fractional exponents relate to square roots.

FRACTIONAL POWERS

(x^-2)^1/2 = 

(x^-2)^1/2 = x^(-2)(1/2) = x^(-1) = 1/x

Fractional exponents relate to roots.

CUBE ROOTS

³√-125

(-5) x (-5) x (-5) = -125

so

³√-125 = -5

CUBE ROOTS

³√1/8

1/2 x 1/2 x 1/2 = 1/8 

so

³√1/8 = 1/2

How to ADD, SUBTRACT, MULTIPLY, and DIVIDE ROOTS

√2 + 3√2 =

√2 - 3√2 = 

√2 + √3 = 

√2 + 3√2 = 4√2

√2 - 3√2 = -2√2

√2 + √3 = Cannot be combined

HOW TO SIMPLIFY A RADICAL

√48 = 

√180 = 

√48 = √16 x √3 = 4√3

√180 = √36 x √5 = 6√5

Sum of the interior angles in a polygon with n sides:

(n - 2) x 180

Degree measure of one angle in a regular polygon with n sides:

(n - 2) x 180

n

HOW TO FIND THE LENGTH OF AN ARC

(Arc = fraction of a circle's circumference)

arc = n/360 x 2Πr

n = angle

r= radius

AREA OF A SECTOR

(sector = a fraction of a circle's area)

Area of sector = n/360 x Πr²

n = angle

r= radius

Π(diameter)

Heptagon

Sides (across from angles)

90º = 2

30º = 1

60º = √3

Ratio 1: √3: 2

Other sides of a 30 - 60 - 90 triangle with side (across from angle) equal to

5.

Special 3, 4, 5 right triangle.

15.

Special 3, 4, 5  right triangle.

Mean

or

Arithmetic Mean

The number that evenly divides the terms in two groups.

If there are an even number of terms, the median will be halfway between the two terms closest to the middle.

1

n²

√ab

(√5)(√20) = √100

√a

√b

√a/b

9 to 21

9:21

9/21

Can be reduced to

3 to 7

3:7

3/7

(x/y)^a

y = mx + b

b = y-intercept

m = slope

Verticle Angles

Same measurements

3.14

or

22/7

If the number of ways to arrange a smaller group drawn from a larger group does NOT matter and you only need the number of combinations:

_nCk = n!/[(n-k)!k!]