Notable Pre-Calculus Formulae & Concepts

Simple Interest

PRT: Principle (Initial Amount) x (Interest) Rate x Time (number of years invested)

Compound Interest

Permutation Formula

nPr = n!/(n-1)! {Order is important}

Combination Formula

nCr = n!/r!(n-r)! {Order is NOT important}

Probability Formula

Favorable Outcomes/Total Possible Outcomes

Vertex of a Parabola

x= -b/2a

Complex Conjugates Theorem

if f is a polynomial function with real coefficients, and a+bi is an imaginary zero of f, then a-bi is also a zero of f

Logarithm of a Product Property

log(A x B) = log(A) + log(B)

Logarithm of a Quotient Property

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

Conic Section

One of four possible two-dimensional figures formed by intersecting a double right cone (one cone placed onto another at the points) with a plane, each of the four shapes is determined by the four possible orientations of the plane intersecting with the cones

Circle (Multi-dimensional representation)

Ellipse (Multi-dimensional representation)

Hyperbola (Multi-dimensional representation)

Standard Form of a Circle

(x-h)^2+(y-k)^2=r^2 (where h is the x-coordinate of the center, k is the y-coordinate of the center, and r is the radius)

Standard Form of an Ellipse

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

Derivation of Circle from Ellipse and Ellipse from Circle

Parabola

A set of points equidistant to a point (focus) and a line (directrix)

Parabola (Multi-dimensional representation)

Standard Form of a Parabola

y = ax^2 + bx + c

Vertex Form of a Parabola

Alternative Form of a Parabola

Focus

a fixed point from the parabola

Directrix

a fixed line from the parabola

Vertices of Ellipse

Endpoints of the Major Axis

Standard Form of a Hyperbola (Horizontal)

Co-Vertices of Ellipse

Endpoints of the Minor Axis

Standard Form of a Hyperbola (Vertical)

Foci (of Hyperbola, Function)

Points on an Ellipse in which distances between any point on the Ellipse made connecting the point to both of these points for any point along the Ellipse

Focal Distance

Distance between center of an ellipse and (each of) its foci