Mathematics Concepts Overview

These flashcards cover key vocabulary terms and concepts related to basic arithmetic, algebra, geometry, trigonometry, statistics, and logarithms.

Percent

A ratio expressed as a fraction of 100.

Percent Change

Calculated as (new value - original value) / original value x 100.

New Value after Percent Change

Expressed as original value x (1 ± percent change).

Average (Mean)

Sum of all values divided by the number of values.

Weighted Average

Sum of (value x weight) divided by the sum of weights.

Distance Formula

Rate x Time = Distance.

Linear Equation

An equation that models a straight line, typically in the form y = mx + b.

Slope Formula

Calculated as (y2 - y1) / (x2 - x1).

Point-Slope Form

Equation of a line given by y - y1 = m(x - x1).

Midpoint Formula

Calculated as ((x1 + x2)/2, (y1 + y2)/2).

Exponential Growth/Decay Formula

y = a(b^x).

Quadratic Formula

Used to find the roots of a quadratic equation: x = [-b ± √(b² - 4ac)] / 2a.

Pythagorean Theorem

A fundamental relation in Euclidean geometry among the three sides of a right triangle: a² + b² = c².

Trigonometric Ratios - Sine, Cosine, Tangent

Sine = opposite/hypotenuse, Cosine = adjacent/hypotenuse, Tangent = opposite/adjacent.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values.

Logarithm Definition

The inverse of exponentiation, expressed as log_b(x) = y if and only if b^y = x.