AP PRE-CALC

Types of Functions

Linear, quadratic, polynomial, rational, exponential, logarithmic.

Graph Transformations

Alterations of the graph including shifts, stretches, compressions, and reflections based on function types.

Unit Circle

A circle in the coordinate plane with a radius of 1, used to define sine, cosine, and tangent.

Sine Function

The ratio of the opposite side to the hypotenuse in a right triangle.

Cosine Function

The ratio of the adjacent side to the hypotenuse in a right triangle.

Tangent Function

The ratio of the opposite side to the adjacent side in a right triangle.

Trigonometric Identities

Equations involving trigonometric functions that are true for all values of the involved variables.

Complex Numbers

Numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit.

Polar Form

Representation of a complex number in terms of its magnitude and angle using the form r(cos θ + i sin θ).

De Moivre's Theorem

A formula used to raise complex numbers to powers and extract roots.

Arithmetic Sequence

A sequence of numbers in which the difference between consecutive terms is constant.

Geometric Sequence

A sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number.

Summation Notation

A concise way of writing the sum of a series of terms, typically represented with the Greek letter sigma (Σ).

Limits

A fundamental concept in calculus that describes the behavior of a function as its argument approaches a particular point.

Continuity

A property of a function if it is continuous at a point, meaning the function is defined at that point and the limit approaches the function value.

Graphing Calculator

A device that can plot graphs, solve equations, and perform other mathematical computations.

Study Schedule

A planned timetable that outlines studying goals and specifies when to cover particular topics.