Glossary (Version 8.4)

In geometry, an image refers to the result of a transformation of a figure.

In mathematical modelling, the independent variable is a measurable or observable quantity that has a relation to (or a causal effect on) one or more other quantities, called the dependent variables.

For example, a scientific investigation considers the relationship between the amount of water supplied and the growth of a plant. It is assumed that there is a causal link between the two quantities. A choice is made to make the amount of water the independent variable, because it is the quantity whose effect is to be investigated, thus making the growth of the plant the dependent variable.

When graphing the results of such an investigation, the convention is to display the independent variable (the amount of water) on the horizontal axis and the dependent variable (the growth of the plant) on the vertical axis.

Two events are independent if knowing the outcome of one event tells us nothing about the outcome of the other event.

Index laws are rules for manipulating indices. They include

\(x^ax^b=x^{a+b};\text{   }\left(x^a\right)^b=x^{ab}\text{ }\)

\(x^ay^a=\left(xy\right)^a\)

and

\(x^0=1;\text{   }x^{-a}=\frac1{x^a};\text{  and  }x^{1/a}=\sqrt[a]x\)

When the product of \(a×a×a\) is written as \(a^3\), the number 3 is called the index, often also referred to as the ‘power’ or the ‘exponent’.

(plural) See index.

An inequality is a statement that one number or algebraic expression is less than (or greater than) another. There are five types of inequalities:

The relation a is less than b is written a<b

a is greater than b is written a>b

a is less than or equal to b is written a≤b

a is greater than or equal to b is written a≥b.

a is unequal to b is written a≠b.

Informal units are not part of a standardised system of units for measurement; for example, an informal unit for length could be paperclips of uniform length. An informal unit for area could be uniform paper squares of any size. Informal units are sometimes referred to as non-standard units.

The integers are the “whole numbers” including those with negative sign ⋯-3, -2, -1, 0, 1, 2, 3⋯. In Latin, the word integer means “whole.” The set of integers is usually denoted by Z. Integers are basic building blocks in mathematics.

The interquartile range (IQR) is a measure of the spread within a numerical data set. It is equal to the upper quartile (Q₃) minus the lower quartile (Q₁); that is, IQR = Q₃ – Q₁.

The IQR is the width of an interval that contains the middle 50% (approximately) of the data values. To be exactly 50%, the sample size must be a multiple of four.

An interval is a subset of the number line.

An irrational number is a real number that is not rational, that means, it cannot be represented as a fraction. Some commonly used irrational numbers are \(\pi,e\text{ and }\sqrt[{}]2\).

Decimal representations of irrational numbers are non-terminating. For example, the Euler Number e is an irrational real number whose decimal expansion begins

\(e=2.718281828⋯\).

An irregular shape is a shape where not all sides and angles are equal in length or magnitude. By contrast, a regular shape has sides and angles that are equal in length and magnitude; for example, a square is a regular shape, while a scalene triangle is irregular.