FAST Math Grade 8 key terms

A real number that cannot be written as a ratio of two integers. Its decimal form goes on forever without repeating, such as the square root of 2 or pi.

A number that can be written as a fraction with integer numerator and denominator, where the denominator is not zero. Its decimal form either ends or repeats a pattern.

Any number on the number line, whether rational or irrational. Every point on the line matches exactly one real number.

A decimal that stops after a finite number of digits, such as 0.375. Every terminating decimal equals a fraction with a denominator that is a power of ten.

A decimal in which one or more digits repeat without end, often shown with a bar over the repeating block. Any repeating decimal can be rewritten as a fraction.

A value that, when multiplied by itself, gives the original number. The square root of 49 is 7 because 7 times 7 equals 49.

A number produced by squaring an integer, such as 1, 4, 9, 16, 25, or 36. Its square root is a whole number.

A value that, when used three times as a factor, gives the original number. The cube root of 27 is 3 because 3 times 3 times 3 equals 27.

A number produced by cubing an integer, such as 8, 27, 64, or 125. Its cube root is a whole number.

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 4.2 times 10 to the sixth.

A small raised number showing how many times the base is used as a factor. In 5 to the third, the exponent 3 means multiply three factors of 5.

The number that is repeatedly multiplied in an expression with an exponent. In 2 to the fifth, the base is 2 and it is used as a factor five times.

The result of raising a base to an exponent, or the whole expression such as 3 to the fourth. It equals the product of repeated factors.

A rule stating that when multiplying powers with the same base, you add the exponents. For example, 3 squared times 3 to the fifth equals 3 to the seventh.

A rule stating that when dividing powers with the same base, you subtract the exponents. For example, 7 to the sixth divided by 7 squared equals 7 to the fourth.

An exponent that tells you to take the reciprocal of the base raised to the matching positive power. For example, 2 to the negative third equals one eighth.

A rule stating that any nonzero base raised to the power zero equals 1. For example, 9 to the zero power equals 1.

The measure of steepness of a line, found as the change in y divided by the change in x between two points. It describes the constant rate of change.

The equation form y equals m x plus b, where m is the slope and b is the y-intercept. It makes graphing a line quick from its equation.

The point where a graph crosses the y-axis, written as zero comma b. In a real context it often represents a starting value.

The point where a graph crosses the x-axis, where the y-value is zero. It often represents when a quantity reaches zero.

An equation whose graph is a straight line and whose variables appear only to the first power. Its solutions form a set of points with a constant rate of change.

Two or more linear equations considered together, whose solution is the point or points satisfying all of them at once. Graphically it is where the lines intersect.

A way to solve a system by rewriting one equation for a single variable, then replacing that variable in the other equation with the resulting expression.

A way to solve a system by adding or subtracting the equations, sometimes after multiplying one, so that one variable cancels and the other can be found.

A statement comparing two expressions using less than, greater than, less than or equal to, or greater than or equal to. Its solutions form a range of values.

All values of the variable that make an equation or inequality true. For an inequality it is usually a range shown on a number line.

A picture of a solution set on a horizontal line, using open circles for strict inequalities and closed circles for ones that include the endpoint.

A rule that assigns exactly one output to each input. Each x-value in the domain pairs with only one y-value.

The set of all input values for which a function is defined. In a real situation it may be limited to whole numbers or positive amounts.

The set of all output values a function actually produces. It depends on both the rule and the allowed inputs.

How much one quantity changes for each unit change in another. For a linear function it is constant and equals the slope.

A function whose graph is a straight line and whose rate of change is constant. It can be written in the form y equals m x plus b.

A function whose graph is not a straight line, so its rate of change is not constant. Examples include curves from squaring or from exponential growth.

A movement or change of a figure on the coordinate plane, such as a translation, reflection, rotation, or dilation. Each type changes position or size in a set way.

A slide of a figure a set distance in a set direction without turning or resizing it. The image stays congruent to the original.

A flip of a figure over a line, producing a mirror image. Distances and angle measures are preserved, so the image is congruent.

A resizing of a figure by a scale factor from a center point. The image is similar to the original, with angles unchanged and side lengths multiplied.

The ratio comparing a length in an image to the matching length in the original figure. It tells how much a dilation enlarges or shrinks a shape.

Figures with exactly the same shape and size, so matching sides and angles are equal. Translations, reflections, and rotations produce congruent images.

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

A rule for right triangles stating that the sum of the squares of the two legs equals the square of the hypotenuse, written a squared plus b squared equals c squared.

The longest side of a right triangle, located opposite the right angle. Its length is found from the legs using the Pythagorean theorem.

One of the two sides of a right triangle that form the right angle. The legs are the shorter sides used in the Pythagorean theorem.

The amount of space a three-dimensional solid occupies, measured in cubic units. Formulas differ by shape, such as cylinder, cone, and sphere.

A graph of paired data points plotted on two axes, used to look for a relationship between two variables. Patterns can suggest positive, negative, or no association.

Data collected on two variables for each individual or item, such as height and shoe size. It is usually displayed in a scatter plot or two-way table.

A straight line drawn through a scatter plot that comes closest to the overall pattern of points. It can be used to estimate values and describe trend.

The general pattern between two variables in bivariate data. It can be positive, negative, or none, and can be strong or weak.

A table that organizes data by two categorical variables, showing counts in each category combination along with row and column totals.

A count divided by a total, giving a proportion or percent. In a two-way table it can be based on a row, a column, or the grand total.

A number from 0 to 1 describing how likely an event is, often found as favorable outcomes divided by total outcomes. It can come from equally likely results or from data.

An event made of two or more simpler events, such as rolling a 3 and then a 5. Its probability is found by combining the probabilities of the parts.

The set of all possible outcomes of an experiment. Listing it helps count favorable outcomes when computing a probability.

A method for finding the distance between two points on the coordinate plane by treating the horizontal and vertical gaps as legs of a right triangle.

A relationship in which one quantity is a constant multiple of another, graphed as a line through the origin. The equation has the form y equals k x.

A rate expressed for exactly one unit of the second quantity, such as miles per one hour. It is often the constant of proportionality in a proportional relationship.