ALGEBRA

Let P(x₁, y₁) and Q(x₂, y₂).

Distance between P and Q is .

Pythagorean theorem: If ΔABC is a right triangle with sides a and b, and hypotenuse c (the side opposite the right angle) then a² + b² = c².

Quadratic formula: If ax² + bx + c = 0, a ≠ 0, then x = .

Factoring rules: x² − y² = (x − y)(x + y)
x³ − y³ = (x − y)(x² + xy + y²)
x³ + y³ = (x + y)(x² − xy + y²)

Factorial: n! = n(n − 1)(n − 2)···3·2·1; 0! = 1; n! = n(n − 1)!

Binomial expansion: (a + b)² = a² + 2ab + b²
(a + b)³ = a³ + 3a²b + 3ab² + b³
(a + b)ⁿ =

GEOMETRY

(A represents area, P represents perimeter, C represents circumference, V represents volume, S represents total surface area)

TRIGONOMETRY

Trigonometric functions Let θ be an angle in standard position with A = (a, b) the point of intersection of θ and the unit circle. Then the trigonometric functions are defined by:

PROBABILITY

The probability of an event E occurring on any trial of an experiment (e.g. flip of a coin or roll of a die) is equal to the proportion of times the event actually occurs in n independent trials of the experiment as n → ∞.

If a trial of an experiment has a discrete set of outcomes (e.g. being dealt a particular one of 52 cards, or the sum of two rolled dice) then the “value” of the outcome is said to be a discrete random variable X.

If a trial of an experiment has a continuum of outcomes (e.g. the height or weight of a randomly chosen person) then the “value” of the outcome is said to be a continuous random variable X.

A probability density function (PDF) of a continuous random variable X is a nonnegative function such that the probability of X lying in the interval [a, b] = f(x)dx.

The cumulative distribution function (CDF) of a random variable X is the function F defined by F(x) = P(X ≤ x), i.e. the probability X is less than or equal to x. If X describes a data set, then F(x) equals the fraction of data in the interval (−∞, x].

For a continuous random variable X with PDF f(x), the mean of X is given by xf(x)dx provided that the improper integral is convergent.

For a continuous random variable X with PDF f(x) and mean μ, the variance of X is given by σ² = (x − μ)² f(x)dx provided the improper integral converges. The standard deviation of X is given by σ, the square root of the variance.

The Gauss error function (or simply error function) is a function defined as erf (x) = for all x ≥ 0.

Standard Normal Distribution Values (z-scores). See Table 7.3 on page 566.

LIMIT FORMULAS

Euler number: e =

Continuously compounded interest: A = = Pe^rt where A is the future value and P is the initial investment

Trigonometric:

DIFFERENTIATION FORMULAS

PROCEDURAL RULES

Constant multiple	(cf)′ = cf′ for a constant c
Sum rule	(f + g)′ = f′ + g′
Difference rule	(f − g)′ = f′ − g′
Linearity rule	(af + bg)′ = af′ + bg′ for constants a and b
Product rule	(fg)′ = fg′ + f′g
Quotient rule
Chain rule

BASIC FORMULAS

DIFFERENTIAL EQUATION FORMULAS

INTEGRATION FORMULAS

PROCEDURAL RULES

BASIC FORMULAS