DSST Math for Liberal Arts key terms

A number that can be written as a fraction of two integers, with a nonzero denominator. Its decimal form either terminates or repeats forever in a fixed pattern.

A real number that cannot be expressed as a fraction of two integers. Its decimal expansion never terminates and never settles into a repeating block, as with pi or the square root of two.

A horizontal line where every point corresponds to exactly one real number, with zero at the center, negatives to the left, and positives to the right. It visually orders numbers by size.

The distance of a number from zero on the number line, always zero or positive. Written with vertical bars, so the absolute value of negative seven is seven.

The agreed sequence for evaluating expressions: grouping symbols first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. It guarantees one correct value for an expression.

A collection of distinct objects, called elements, considered as a single whole. Sets may be listed in braces or described by a rule, and order plus repetition do not matter.

A set whose every element also belongs to another set. For example, the vowels form a subset of the English alphabet, since each vowel is a letter.

The set containing every element that appears in at least one of the combined sets. Duplicates are dropped, so combining sets that share elements does not repeat them.

The set of elements shared by two or more sets, meaning elements present in all of them at once. If the sets share nothing, the intersection is the empty set.

All elements of the universal set that are not in the given set. It depends on which universal set is declared, so the same set can have different complements.

A statement of the form if P then Q, where P is the hypothesis and Q is the conclusion. It is false only when the hypothesis is true but the conclusion is false.

The statement formed by swapping the hypothesis and conclusion of a conditional. The converse of a true statement is not automatically true, so it must be checked separately.

The statement formed by swapping and negating both parts of a conditional: if not Q then not P. It always has the same truth value as the original conditional.

A ratio expressing the same quantity in two different units, such as 1 kilometer over 1000 meters. Multiplying by it changes units without changing the actual amount.

A word or symbol attached to a base unit to show a power of ten, such as kilo for a thousand or milli for one thousandth. Prefixes let one base unit cover a huge range of sizes.

A method of converting and checking measurements by tracking units through multiplication and cancellation. If the leftover units are wrong, the setup of the calculation is wrong.

The total distance around the outside of a flat figure, found by adding the lengths of all its sides. It is measured in linear units such as centimeters.

The amount of flat surface a two-dimensional figure covers, measured in square units. Common formulas include length times width for rectangles and pi times radius squared for circles.

The amount of three-dimensional space a solid occupies, measured in cubic units. For a rectangular box it equals length times width times height.

A measure of how steeply a line rises or falls, computed as the change in vertical value divided by the change in horizontal value between two points. A horizontal line has slope zero.

The point where a graph crosses the vertical axis, occurring where the input value is zero. In a real-world model it often represents a starting amount or fixed cost.

A function whose graph is a straight line and whose output changes by a constant amount for each equal step in the input. It can be written in the form y equals mx plus b.

A rule that assigns exactly one output value to each allowed input value. Repeated inputs are fine, but a single input cannot produce two different outputs.

The domain is the full set of input values a function accepts; the range is the full set of output values it produces. Both may be restricted by context, such as time not being negative.

Two or more linear equations considered together, solved by finding values that satisfy all of them at once. Graphically the solution is the point where the lines meet.

A technique for solving systems by rearranging one equation to express a variable, then replacing that variable in the other equation. It reduces the system to a single equation in one unknown.

A technique for solving systems by adding or subtracting equations, sometimes after multiplying one, so that a variable cancels. The result is one equation with one variable.

A statement comparing two linear expressions with less than, greater than, or their or-equal forms. Its solution is a range of values, graphed as a half-plane or a segment of a number line.

The overlapping area on a graph where all constraints of an inequality system are satisfied simultaneously. In linear programming, the best value of the objective occurs at a corner of this region.

A small raised number showing how many times a base is multiplied by itself, so three to the fourth means three used as a factor four times. Negative and fractional exponents follow special rules.

The exponent to which a base must be raised to produce a given number. A logarithm answers the question of what power gives a certain result, and it undoes exponentiation.

A way of writing very large or very small numbers as a number between one and ten multiplied by a power of ten. It makes the scale of a measurement easy to read and compare.

Interest calculated on both the original principal and on interest already earned, so the balance grows by a fixed percentage each period. The growth follows an exponential pattern over time.

If one choice can be made in m ways and a second in n ways, the two together can be made in m times n ways. It extends to any number of independent stages.

An arrangement of items in which the order matters, such as finishing order in a race. The count of arrangements of n items taken r at a time divides factorials to remove the unused items.

A selection of items in which order does not matter, such as choosing members of a committee. Its count is smaller than the matching permutation because rearrangements are not counted separately.

A number from zero to one describing how likely an event is, where zero means impossible and one means certain. For equally likely outcomes it is favorable outcomes divided by total outcomes.

The probability that an event does not happen equals one minus the probability that it does. It is often the fastest route when counting the opposite outcome is simpler.

Two events where the occurrence of one does not change the probability of the other. For such events, the probability that both happen is the product of their separate probabilities.

Three measures of center: the mean is the arithmetic average, the median is the middle value of ordered data, and the mode is the most frequent value. Each summarizes a data set differently.

A measure of how spread out data values are around their mean, roughly the typical distance from the average. A small value means values cluster tightly; a large one means they scatter widely.