MTEL 65 key terms

A number that can be written as a fraction of two integers with a nonzero denominator; its decimal form terminates or repeats.

A real number that cannot be written as a fraction of two integers; its decimal expansion neither terminates nor repeats. Familiar examples include pi and the square root of two.

A whole number in the set of positive counting numbers, their negatives, and zero; integers have no fractional or decimal part.

The distance of a number from zero on the number line, always nonnegative. It is written with vertical bars, such as |−5| = 5.

A way to write very large or very small numbers as a product of a number between 1 and 10 and a power of ten, such as 3.2 × 10^4.

The expression of a whole number greater than one as a product of prime numbers, usually written with exponents when factors repeat.

The smallest positive integer that is a multiple of each of two or more given integers, often used to find a common denominator.

The largest positive integer that divides each of two or more given integers without a remainder, also called the greatest common factor.

A standard sequence for simplifying expressions: evaluate grouping symbols first, then exponents, then multiplication and division from left to right, and finally addition and subtraction.

A rate expressed as a quantity per one unit of another quantity, such as miles per hour or cost per item, found by dividing the quantities.

The amount of increase or decrease divided by the original amount, then multiplied by 100 to express the change as a percent.

The number that gives zero when added to a given number; for any number a, its additive inverse is −a, also called its opposite.

The number that gives one when multiplied by a given nonzero number; for a fraction a/b, the multiplicative inverse is b/a.

A symbol, usually a letter, that represents an unknown value or a quantity that can change within a mathematical expression, equation, or function.

A mathematical phrase that combines numbers, variables, and operation symbols but does not contain an equality or inequality symbol, such as 3x + 5.

A statement that two mathematical expressions are equal, often solved to find values of unknown variables. It always contains an equals sign.

A statement that compares two expressions using symbols such as <, >, ≤, or ≥, showing that one side may be less than or greater than the other.

A relation that assigns exactly one output value to each input value from its domain; often written as f(x). A function may be represented by a table, graph, or rule.

The set of all input values for which a function is defined and produces a real output. It may be restricted by division by zero or even roots.

The set of all output values that a function actually produces as its input varies over the domain. It is not always the same as the codomain.

A function whose graph is a straight line and whose rule can be written in the form y = mx + b, where m and b are constants.

A measure of steepness for a line, calculated as the change in y divided by the change in x between two points.

A function that can be written as f(x) = ax² + bx + c, where a is nonzero; its graph is a parabola.

A set of two or more equations that share variables, solved together by finding values that satisfy every equation at once.

An expression made from variables and constants using only addition, subtraction, multiplication, and nonnegative whole-number exponents. Division by a variable is not allowed.

A figure formed by two rays sharing a common endpoint, called the vertex; angles are often measured in degrees or radians.

Figures that have exactly the same shape and size, so corresponding sides and angles are equal; one can be mapped onto the other by rigid motions.

Figures that have the same shape but not necessarily the same size; corresponding angles are equal and corresponding side lengths are proportional.

For a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs, written a² + b² = c².

The amount of two-dimensional space inside a closed figure, measured in square units such as square centimeters. Area formulas differ by shape.

The amount of three-dimensional space occupied by a solid, measured in cubic units such as cubic inches. It can be found by multiplying base area by height for prisms.

The total area of all exposed faces or surfaces of a three-dimensional figure, measured in square units. It is often found by summing the areas of each face.

A change in a figure's position, size, or orientation, such as a translation, rotation, reflection, or dilation. Transformations can preserve or change congruence and similarity.

The arithmetic average, found by adding all values in a data set and dividing the sum by the number of values.

The middle value in an ordered data set; if there is an even number of values, it is the mean of the two middle values.

The value or values that appear most often in a data set; a data set may have no mode or more than one mode.

A measure of how spread out values are from their mean, equal to the square root of the variance. A larger value indicates greater variability.

A number from 0 to 1 that expresses the chance an event occurs, often found by dividing favorable outcomes by total equally likely outcomes.

Two events whose outcomes do not affect each other; the probability that both occur equals the product of their individual probabilities.

The set of all possible outcomes of a probability experiment, such as heads and tails for one coin toss. It provides the denominator for classical probability.