WEST-E Middle Level Mathematics (NES 203) key terms

A number that can be written as a fraction where both numerator and denominator are integers and the denominator is not zero. Its decimal form either terminates or repeats.

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

Any point on the number line, including all rational and irrational values. Every real number can be compared, ordered, and used in arithmetic operations.

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

A straight line with points labeled by numbers at even spacing, used to visualize order, distance, and operations. It extends infinitely in both directions from zero.

A whole number that may be positive, negative, or zero, with no fractional part. The integers are closed under addition, subtraction, and multiplication but not division.

A whole number greater than one whose only positive divisors are one and itself. Two, three, five, and seven are primes; one is not prime.

A whole number greater than one that has at least one positive divisor besides one and itself. Every composite number can be written as a product of primes.

The expression of a whole number as a product of prime factors, unique up to order. For example, thirty-six equals two squared times three squared.

The largest whole number that divides evenly into each number in a given set. It is found by multiplying the shared prime factors of the numbers.

The smallest positive number that is a multiple of each number in a given set. It is useful when adding fractions with unlike denominators.

A number written as a quotient of two quantities, showing a part relative to a whole. The denominator names the size of the parts and the numerator counts them.

Different fractions that name the same value, produced by multiplying or dividing numerator and denominator by the same nonzero number. One half equals two fourths.

A ratio that compares a quantity to one hundred, so twenty-five percent means twenty-five out of every hundred. Percents convert to decimals by dividing by one hundred.

A comparison of two quantities by division, often written with a colon or as a fraction. It may compare a part to a part or a part to the whole.

An equation stating that two ratios are equal. Solving a proportion often uses cross multiplication to find an unknown quantity.

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 order of magnitude easy to compare.

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.

A small raised number that tells how many times a base is used as a factor. In three to the fourth power, four is the exponent and three is the base.

A letter or symbol that stands for an unknown or changing quantity in an expression or equation. It allows general statements to be written compactly.

A mathematical phrase combining numbers, variables, and operation symbols without an equals sign. It can be simplified or evaluated but not solved.

A statement that two expressions are equal, often containing a variable to be found. Solutions are values that make the statement true.

An equation whose graph is a straight line and in which every variable appears to the first power. It has the standard form a x plus b equals c in one variable.

A measure of the steepness of a line, computed as the change in vertical distance divided by the change in horizontal distance between two points. It equals rise over run.

The point where a graph crosses the vertical axis, occurring where the input value is zero. In a linear function it represents the starting value.

A rule that assigns exactly one output to each allowed input. Passing the vertical line test confirms that a graph represents a function.

The domain is the set of all allowable inputs of a function, and the range is the set of all resulting outputs. Together they describe a function completely.

A function whose highest power of the variable is two, graphed as a parabola. Its standard form is a x squared plus b x plus c with a not zero.

The U-shaped curve that is the graph of a quadratic function. It opens upward when the leading coefficient is positive and downward when it is negative.

The highest or lowest point of a parabola, where the curve changes direction. It lies on the axis of symmetry of the graph.

A list of numbers in which each term after the first is found by adding a fixed constant, called the common difference. Linear growth produces such sequences.

A list of numbers in which each term after the first is found by multiplying the previous term by a fixed nonzero constant called the common ratio. It models exponential growth or decay.

A function in which the variable appears in the exponent, producing rapid growth or decay by a constant factor. Its graph curves increasingly steeply or flattens toward a horizontal asymptote.

The total distance around the outside of a closed plane figure, found by adding the lengths of its sides. It is measured in linear units.

The amount of surface enclosed by a plane figure, measured in square units. Formulas differ by shape, such as base times height for a rectangle.

The amount of space occupied by a three-dimensional solid, measured in cubic units. It is computed by multiplying the area of a base by a height or related factor.

The distance around a circle, equal to pi times the diameter or two pi times the radius. It is the circle's analog of perimeter.

The relationship stating that in a right triangle the square of the hypotenuse equals the sum of the squares of the two legs. It is used to find unknown side lengths.

Figures with the same shape but possibly different sizes, having equal corresponding angles and proportional corresponding side lengths. Their scale factor relates all lengths.

Figures that have exactly the same size and shape, so corresponding sides and angles match. One can be mapped onto the other by rigid motions.

A change in a figure's position, orientation, or size on the coordinate plane, such as a translation, rotation, reflection, or dilation. Rigid motions preserve size and shape.

A measure of central tendency found by adding all values and dividing by the number of values. It is affected strongly by extreme data points.

The middle value of a data set ordered from least to greatest, or the average of the two middle values when the count is even. It resists distortion by outliers.

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

A data value far removed from the rest of the set, often due to error or a rare event. It can pull the mean noticeably toward itself.

A simple measure of spread found by subtracting the smallest value in a data set from the largest. It depends on only two data points.

A measure of how spread out data values are around the mean, roughly the typical distance from the mean. A larger value indicates greater variability.

A number from zero to one expressing how likely an event is, often computed as favorable outcomes divided by total equally likely outcomes. Zero means impossible and one means certain.

The set of all possible outcomes of a probability experiment. Listing it completely allows probabilities to be assigned systematically.

Two events whose outcomes do not affect each other, so the probability of both equals the product of their individual probabilities. Coin flips are a classic example.

An arrangement of items in which order matters. The number of permutations of n distinct items taken all at once is n factorial.

A selection of items from a group in which order does not matter. The count is found by dividing the corresponding permutation count by the factorial of the number chosen.

The product of all positive whole numbers from one up to a given number, written with an exclamation mark. By convention the factorial of zero equals one.