AEPA Mathematics (NT304) key terms

A number that can be written as a fraction with integer numerator and nonzero integer denominator. Its decimal form either terminates or repeats forever in a fixed block of digits.

A real number that cannot be written as a ratio of two integers. Its decimal expansion never terminates and never settles into a repeating pattern, as with the square root of 2.

The property that between any two distinct real numbers there is always a rational number, and also an irrational number. This means rationals cannot be listed in order without gaps.

The distance of a number from zero on the number line, always nonnegative. Written with vertical bars, it equals the number itself when positive and its opposite when negative.

A way of writing very large or very small numbers as a product of a number between 1 and 10 and a power of ten. Useful for comparing magnitudes and for computation.

Solving problems by recognizing that two quantities change at a constant ratio. Includes setting up and solving proportions, unit rates, and scaling in recipes, maps, and similar figures.

A rate expressed per one unit of the second quantity, such as miles per one hour or cost per one item. Found by dividing one quantity by the other.

Rules for adding, subtracting, multiplying, and dividing positive and negative whole numbers, including that the product of two numbers with the same sign is positive and with opposite signs is negative.

The largest positive integer that divides two or more given integers with no remainder. Used to simplify fractions and to factor algebraic expressions.

Writing a whole number greater than one as a product of prime numbers only. By the fundamental theorem of arithmetic, this product is unique apart from order.

The smallest positive integer that is a multiple of two or more given integers. Used to find common denominators and to solve problems involving repeating events.

A rule that assigns to each input in its domain exactly one output. Multiple inputs may share an output, but one input can never produce two different outputs.

The domain is the set of all allowable inputs of a function; the range is the set of all outputs it actually produces. Both may be restricted by context or by the rule itself.

A function whose graph is a straight line, with constant rate of change. It can be written in slope-intercept form y = mx + b, where m is the slope.

The steepness of a line, computed as the change in the vertical coordinate divided by the change in the horizontal coordinate between two points. Horizontal lines have slope zero.

How much one quantity changes relative to another over a given interval. For a linear function it is constant and equals the slope; for other functions it may vary.

The change in a function's output divided by the change in input over an interval. It equals the slope of the secant line joining the two endpoints of that interval.

A function of the form f(x) = ax squared + bx + c with a not zero. Its graph is a parabola opening upward when a is positive and downward when a is negative.

The highest or lowest point on the graph of a quadratic function. It marks the maximum or minimum output and lies on the axis of symmetry.

A function of the form f(x) = a times b to the x power, where the base b is positive and not 1. It models constant percent growth or decay.

The multiplier applied to a quantity each period in an exponential model. A growth factor greater than 1 indicates increase; between 0 and 1 it indicates decay.

A list of numbers in which each term after the first is found by adding a fixed constant, the common difference. Its graph as a function of term number is linear.

A list of numbers in which each term after the first is found by multiplying by a fixed nonzero constant, the common ratio. It corresponds to an exponential function of term number.

A function that reverses another function, sending each output back to its original input. It exists only when the original function is one-to-one on its domain.

The input values for which the function's output equals zero. On a graph these are the horizontal intercepts, and they correspond to factors of the expression.

Shifting, stretching, compressing, or reflecting a parent graph by changing its equation. Adding outside the function moves the graph vertically; adding inside moves it horizontally.

Figures with the same shape but not necessarily the same size, having equal corresponding angles and proportional corresponding side lengths. Scale factors relate their lengths, areas, and volumes.

The ratio comparing a length in an image or model to the corresponding length in the original. Areas scale by its square and volumes by its cube.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. Its converse tests whether a triangle is right.

The distance between two points in the coordinate plane, found by applying the Pythagorean theorem to the horizontal and vertical separations of the points.

The amount of three-dimensional space a solid occupies, measured in cubic units. Formulas depend on the shape, such as prism, cylinder, pyramid, cone, or sphere.

The total area of all faces or curved surfaces of a three-dimensional figure, measured in square units. Nets help visualize and compute it for polyhedra.

A transformation that enlarges or reduces a figure by a scale factor about a fixed center point. It preserves angle measures and produces a similar figure.

Summary values describing a typical data point, mainly mean, median, and mode. The mean is affected by outliers, while the median is resistant to them.

Values describing how dispersed data are, including range, interquartile range, variance, and standard deviation. Larger values indicate data points farther from the center.

A measure of typical distance of data values from the mean, equal to the square root of the variance. Small values mean data cluster near the mean.

A symmetric bell-shaped distribution described by its mean and standard deviation. Roughly 68 percent of values fall within one standard deviation of the mean and 95 percent within two.

A data value that lies far from the rest of the data. It often signals an error or a special case and can strongly affect the mean and range.

The probability that an event occurs given that another event has already occurred, written as P(A given B). It equals the probability of both events divided by the probability of the given event.

Two events whose outcomes do not influence each other, so the probability of both equals the product of their individual probabilities. Knowing one occurred does not change the other's probability.

The long-run average outcome of a random experiment, computed by multiplying each outcome by its probability and summing the products. It need not be an achievable outcome.