EN VIII Mathematics key terms

A whole number that can be positive, negative, or zero, with no fractional or decimal part, such as -7, 0, or 12. Integers do not include fractions or decimals.

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

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

The distance of a number from zero on the number line, always zero or positive. Written with vertical bars, so the absolute value of -5 is 5.

A straight line on which every point matches a number, with zero at a chosen point and equal spacing marking units. It is used to compare and order numbers.

The number that, when added to a given number, gives zero. The opposite of 8 is -8, and the opposite of -3 is 3.

The number that, when multiplied by a given nonzero number, gives 1. The reciprocal of a fraction is that fraction turned upside down, so the reciprocal of 3/4 is 4/3.

A small raised number showing how many times a base is used as a factor. In 2 to the fifth power, the exponent 5 means multiply five copies of 2.

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

A way of writing very large or very small numbers as a number between 1 and 10 multiplied by a power of ten, such as 3.2 times 10 to the sixth power.

A relationship between two quantities in which their ratio stays constant, so doubling one doubles the other. Its graph is a straight line passing through the origin.

A rate in which the second quantity is one unit, found by dividing. If 12 pencils cost 3 dollars, the unit rate is 4 pencils per dollar or 0.25 dollars per pencil.

A letter or symbol that stands for an unknown or changing number in an expression or equation. In 3x plus 5, the letter x is the variable.

A mathematical phrase built from numbers, variables, and operations but with no equals sign. For example, 4x minus 7 is an expression that can be simplified or evaluated.

A statement that two mathematical expressions are equal, shown by an equals sign. Solving it means finding values of the variable that make the statement true.

A statement comparing two expressions that are not necessarily equal, using symbols such as less than, greater than, or not equal. Its solutions form a range of values.

A function whose graph is a straight line and whose rule can be written as y equals m times x plus b. It changes at a constant rate.

A measure of how steep a line is, found as the change in vertical value divided by the change in horizontal value between two points. It describes the line's rate of change.

The point where a graph crosses the vertical axis, occurring where the horizontal value is zero. In the rule y equals m x plus b, it is the value b.

Two or more equations that share the same variables and are solved together. A solution is a set of values that makes every equation in the system true at once.

A rule that assigns exactly one output value to each input value. Each input has a single result, though different inputs may share the same output.

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

The longest side of a right triangle, located opposite the right angle. Its length can be found using the Pythagorean Theorem when the other two sides are known.

A triangle containing exactly one angle of 90 degrees. The two sides forming that angle are called the legs, and the side opposite it is the hypotenuse.

Having exactly the same size and shape. Two figures are congruent if one can be moved onto the other by sliding, turning, or flipping without stretching.

Figures with the same shape but not necessarily the same size, whose corresponding angles are equal and whose corresponding side lengths share a constant ratio.

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

The ratio by which a figure is enlarged or reduced during a dilation or when comparing similar figures. A scale factor above 1 enlarges, and between 0 and 1 reduces.

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

The total area of all the faces or outer surfaces of a three-dimensional solid, measured in square units. It is found by adding the areas of every face.

The arithmetic 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 arranged in order. If there is an even number of values, it is the mean of the two middle values.

A data value that lies far away from most of the other values in a set. Outliers can pull the mean noticeably toward themselves.

A graph that plots points for paired data on a coordinate plane, used to see whether two quantities are related. The pattern of points may suggest a trend.

A number from 0 to 1 describing how likely an event is, where 0 means impossible and 1 means certain. It can be estimated from the ratio of favorable outcomes to total outcomes.

The set of all possible outcomes of a probability experiment. For a single roll of a standard die, the sample space is the numbers 1 through 6.

The likelihood of an event estimated from actual trials, found by dividing the number of times the event occurred by the total number of trials performed.