Grade 8 Mathematics key terms

A number that cannot be written as a fraction of two integers. Its decimal form never ends and never repeats, 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 stops or repeats a pattern.

The decimal form of a number, showing its digits after the decimal point. It may terminate, repeat a block of digits, or continue forever without a repeating pattern.

A decimal in which one or more digits repeat forever after some point, often marked with a bar over the repeating block. It always represents a rational number.

A number that, when multiplied by itself, gives the original number. For example, 9 has square root 3 because 3 times 3 equals 9.

The result of multiplying an integer by itself, such as 1, 4, 9, 16, or 25. Its square root is a whole number.

A number that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3.

Any whole number, including positive numbers, negative numbers, and zero, but no fractions or decimals. Examples are -7, 0, and 12.

The distance of a number from zero on the number line, always zero or positive. It is written with two vertical bars around the number.

A way of writing very large or very small numbers as a number between 1 and 10 multiplied by a power of 10, such as 4.2 times 10 to the sixth power.

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

An exponent that is a whole number, including zero and negative whole numbers. A negative exponent means take the reciprocal of the base raised to the opposite positive power.

The result of raising a base to an exponent, or the expression itself. For example, 2 to the fifth power equals 32.

In an expression with an exponent, the number or variable that is repeatedly multiplied. In 7 squared, the base is 7.

A number formed by multiplying ten by itself a whole number of times, such as 10, 100, or 1000. Negative powers of ten create decimals like 0.01.

An equation whose graph is a straight line, usually written with variables raised only to the first power. An example is 3x plus 5 equals 20.

A value or set of values that makes an equation or inequality true when substituted for the variable. Checking a solution means putting it back into the original statement.

An operation that undoes another operation, such as addition and subtraction, or multiplication and division. Solving equations often uses inverse operations to isolate a variable.

A letter or symbol that stands for an unknown or changing number in an expression or equation. For example, x in the expression 2x plus 7.

The number multiplied by a variable in a term. In the term 6y, the coefficient is 6, and in -x it is -1.

A mathematical phrase built from numbers, variables, and operations but with no equals sign. For example, 4x minus 9 is an expression, not an equation.

A single part of an expression separated by plus or minus signs. In 5x plus 3y minus 8, the terms are 5x, 3y, and -8.

Terms that have exactly the same variable factors and can be combined by adding or subtracting their coefficients. For example, 4x and -9x are like terms.

A rule that assigns exactly one output value to each input value. The set of allowed inputs is the domain, and the set of results is the range.

The value put into a function, often called x. Each input in the domain of a function produces exactly one output.

The result a function produces for a given input, often called y or f of x. It depends on which input value is used.

How much one quantity changes compared with another, often found as change in output divided by change in input. For a straight line it equals the slope.

The steepness of a line, measured as the vertical change divided by the horizontal change between two points. It describes the line's rate of change.

The point where a graph crosses the vertical axis, occurring when the input value is zero. In the form y equals mx plus b, it is the value b.

A way of writing a linear equation as y equals mx plus b, where m is the slope and b is the y-intercept. It makes graphing a line quick.

A relationship between two quantities where one is a constant multiple of the other, so their graph is a straight line through the origin. The equation has the form y equals kx.

The fixed number k that relates two proportional quantities in the equation y equals kx. It equals the ratio of y to x for every matching pair of values.

A rate in which the second quantity is one unit, such as 60 miles per 1 hour or 3 dollars per 1 pound. It is found by dividing the first quantity by the second.

A comparison of two quantities by division, often written with a colon or as a fraction. For example, the ratio of 6 to 8 simplifies to 3 to 4.

An equation stating that two ratios are equal, such as 3 over 4 equals 9 over 12. Cross multiplication is a common way to solve one.

A ratio that compares a number to 100, shown with the percent symbol. For example, 45 percent means 45 out of every 100, or 0.45.

The amount a quantity increases or decreases, divided by the original amount, then written as a percent. It compares the change to the starting value.

A line that crosses two or more other lines at different points. The angles it forms help determine whether the crossed lines are parallel.

Lines in the same plane that never meet, no matter how far they are extended. A transversal cutting them creates equal angle pairs such as alternate interior angles.

A pair of angles on opposite sides of a transversal and between the two lines it crosses. When the lines are parallel, these angles are equal in measure.

Angles in matching positions at each intersection where a transversal crosses two lines. When the lines are parallel, corresponding angles have equal measures.

A rule stating that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. It is written a squared plus b squared equals c squared.

The longest side of a right triangle, located opposite the right angle. In the Pythagorean theorem it is the side labeled c.

One of the two shorter sides of a right triangle that form the right angle. In the Pythagorean theorem, the legs are labeled a and b.

A triangle containing one angle that measures exactly 90 degrees. Its longest side is opposite that right angle and is called the hypotenuse.

The amount of space a three-dimensional figure occupies, measured in cubic units. For a cylinder it is the base area multiplied by the height.

A three-dimensional solid with two parallel circular bases joined by a curved surface. Its volume equals pi times the radius squared times the height.

A graph that displays paired data as points on a coordinate plane, used to look for a relationship between two quantities. Points may show a positive, negative, or no pattern.

The overall pattern linking two quantities in a scatter plot, described as positive or negative and as strong or weak. It describes how one variable tends to move as the other changes.

A straight line drawn through a scatter plot that comes closest to the points and summarizes their trend. It can be used to make predictions.

A data value that is far from the rest of the values in a set. In a scatter plot it appears distant from the general pattern of points.

The average of a data set, found by adding all values and dividing by how many there are. It is affected strongly by unusually large or small values.

The middle value of a data set when the values are arranged in order. If there is an even number of values, it is the mean of the two middle values.

The average distance between each data value and the mean of the set. It measures how spread out the data are.