AK STAR Math Grade 9 key terms

A real number that cannot be written as a fraction of two integers. Its decimal form never ends and never repeats, such as pi or the square root of two.

Any number that can be written as a ratio of two integers with a nonzero denominator. Its decimal form either ends or repeats a pattern forever.

A way of writing very large or very small numbers as a value between 1 and 10 multiplied by a power of ten, such as 3.2 × 10^5.

A value that produces a given number when multiplied by itself. For example, 9 is a square root of 81 because 9 × 9 = 81.

Rules for combining powers with the same base, such as adding exponents when multiplying and subtracting them when dividing, plus rules for zero and negative exponents.

A comparison of two quantities measured in different units where the second quantity is one, such as miles per hour or dollars per item.

A mathematical phrase built from numbers, variables, and operations without an equals sign. For example, 4x + 7 can be evaluated or rewritten in simpler form.

A statement that two mathematical expressions have equal value, written with an equals sign. Solving an equation means finding the values that make the statement true.

The number that multiplies a variable in an algebraic term. In 7y the coefficient is 7, and in −x it is −1.

An equation whose graph is a straight line and whose variables appear only to the first power. A common form is y = mx + b.

A measure of how steep a line is, found by dividing the vertical change by the horizontal change between two points on the line.

The point where a graph crosses the vertical axis. On the line y = mx + b, the number b gives the vertical position of that crossing.

Two or more equations that share the same variables. A solution gives values that make every equation in the group true at the same time.

A statement comparing two expressions that may not be equal, using symbols such as <, >, ≤, or ≥. Its solution is a range of values rather than one number.

Rewriting an expression as a product of simpler expressions. For example, x² + 5x + 6 factors as (x + 2)(x + 3).

An equation where the highest power of the variable is two, usually written ax² + bx + c = 0 with a not equal to zero. Its graph is a parabola.

A rule that pairs each input value with exactly one output value. Different inputs may share an output, but a single input never has two outputs.

The complete set of input values for which a function is defined. For a situation about time, for instance, the domain may include only nonnegative numbers.

The set of all output values a function actually produces for its domain, seen as the collection of y-values on the graph.

A way of naming a function's output with the function name and the input, such as f(3), meaning the output when the input is 3.

How much one quantity changes compared with another, calculated as the change in output divided by the change in input over an interval.

A function with the variable in the exponent, such as f(x) = 2^x or a growth model like 500(1.05)^t. Its values change by a constant factor.

The U-shaped curve that forms 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 gives the maximum or minimum value of the quadratic function.

A point where a graph crosses the horizontal axis, found by setting y equal to zero. For a function, these points are also called zeros.

In a right triangle, the square of the longest side equals the sum of the squares of the two shorter sides, written a² + b² = c².

Describing figures with exactly the same size and shape. Their matching sides and angles are equal, and rigid motions can move one onto the other.

Describing figures with the same shape but possibly different sizes. Matching angles are equal and matching side lengths share a constant ratio.

A transformation that enlarges or shrinks a figure by a scale factor from a fixed center point. Angles stay the same while side lengths change proportionally.

The amount of space a solid figure occupies, measured in cubic units. For a cylinder, it equals the area of the circular base times the height.

A line that crosses two or more other lines. Crossing parallel lines creates special angle pairs such as corresponding angles and alternate interior angles.

A rule based on the Pythagorean theorem that gives the distance between two points as the square root of the sum of squared coordinate differences.

The sum of all data values divided by how many values there are, also called the average. Very large or small values can pull it strongly.

The middle value when a data set is ordered, or the average of the two middle values when the count is even. It is not much affected by outliers.

The difference between the third quartile and the first quartile of a data set, describing the spread of the middle half of the values.

A graph showing paired data as points on a coordinate plane, used to look for a relationship or trend between two quantities.

A table that shows counts for two categorical variables, with rows for one category and columns for the other, plus row and column totals.

A number from 0 to 1 that describes how likely an event is. When all outcomes are equally likely, it equals favorable outcomes divided by total outcomes.

A group chosen from a population so that every member has an equal chance of being selected, helping results represent the whole population fairly.