HOTmaths dictionary

This illustrated dictionary offers free access to over several hundred mathematical symbols, terms and definitions from the early secondary syllabus.

Select any letter to see examples of mathematical terms with clear explanations and helpful diagrams.

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Term Definition icosahedron a solid with twenty faces A regular icosahedron (one of the five Platonic solids) has twenty congruent equilateral triangles as faces.

Related links: 3D shapes — Classifying solids 3D shapes — Nets of solids

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Term Definition ie abbreviation for "that is" Example Increase 4 by 3, ie find 4 + 3.

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Term Definition improper fraction a fraction where the numerator is greater than the denominator Examples

Related links: Fractions — Mixed numerals and improper fractions Fractions — Adding and subtracting fractions Fractions — Multiplying mixed numerals Fractions — Dividing by simple fractions Fractions — Dividing by harder fractions Percentages — Percentage/fraction/decimal connection

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Term Definition increase make bigger; to add on (see also addition, commission) Example Increase 7 by 5 means add 5 on to 7 (ie 7 + 5).

Related links: Whole numbers — Estimation and rounding off Decimals — Decimals of a quantity Decimals — Dividing by a decimal Representing data — Scatter diagrams Applying percentages — Increasing and decreasing using percentages

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Term Definition index (plural indices) exponent or power Example 23 means 2 to the power of 3, where 3 is the index

Related links: Whole numbers — Index notation Number theory — Factor trees Decimals — Multiplying and dividing by powers of 10 Integers — Mixing the operations Algebra — What is algebra? Algebra — Multiplying and dividing terms

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Term Definition index notation simple method of writing numbers that are multiplied by themselves (see also exponential notation) Example 36 is index notation for 3 × 3 × 3 × 3 × 3 × 3.

Related links: Whole numbers — Place value and expanded notation Whole numbers — Index notation Number theory — Factor trees Algebra — What is algebra?

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Term Definition indices (pronounced in-d-sees) plural of index

Related links: Whole numbers — Index notation Whole numbers — Order of operations Integers — Mixing the operations

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Term Definition inequality a mathematical statement that compares the size of two or more expressions or numbers The inequality sign always points towards the smaller value. 6 > 5 means six is greater than five y < 3 means the value of y is less than 3

Related links: Integers — What are directed numbers? Equations and inequalities — Inequalities

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Term Definition infinite endless; goes on forever without coming to a finish; not finite

Related links: Decimals — Recurring decimals 2D shapes — Line of symmetry Angles — Points, lines and intervals

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Term Definition infinity not a number nor a place but a term used to show that something is getting larger and larger, or further and further away, without any ending

Related links: Number theory — Simple number patterns Angles — Points, lines and intervals

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Term Definition integers the set of positive and negative whole numbers including zero Integers extend from zero in both directions (see also directed numbers)

Related links: Number theory — Simple number patterns Integers — What are directed numbers? Integers — Adding and subtracting integers Integers — Two signs together Integers — Multiplying integers Integers — Dividing integers Integers — Mixing the operations The number plane — Extending the number plane

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Term Definition interest amount earned by lending or investing a sum of money (see also simple interest)

Related links: Percentages — What is a percentage? Ratios and rates — Rates

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Term Definition interior angle any of the angles formed between adjacent sides of a polygon "Interior" means that these angles are inside the shape.

Related links: 2D shapes — Exterior angles of triangles Angles — Angles in parallel lines Exploring geometry — Exploring trapeziums and kites

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Term Definition intersect meet at a point; cross one another (see also transversal) Example In the diagram, the lines AB and XY intersect at the point P.

Related links: Angles — Angle theorems Angles — Angles in parallel lines 3D shapes — Faces, edges and vertices Manipulating algebra — Formulas in spreadsheets The number plane — Extending the number plane The number plane — Intersecting lines Exploring geometry — Bisecting angles and intervals

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Term Definition intersection (set) the elements that are common to two or more sets shown by the symbol Example If A = {1, 2, 3} and B = {2, 3, 4} then A  B = {2, 3}

Related links: Set theory — Applying Venn diagrams Set theory — Set relationships and Venn diagrams

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Term Definition interval (class) describes the boundaries of a group of data

Related links: Representing data — Grouping data Representing data — Stem-and-leaf plots

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Term Definition interval (geometry) a section of a straight line Example The interval in the diagram has end points A and B.

Related links: Decimals — Rounding decimals Length, perimeter and area — Measuring length Angles — Points, lines and intervals Representing data — Line, conversion and step graphs Circles and cylinders — Pi and the circumference Congruent and similar shapes — Congruent shapes Exploring geometry — Bisecting angles and intervals

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Term Definition inverse operations arithmetic operations that undo one another (also called opposite operations) Examples Adding and subtracting Multiplying and dividing Squaring and taking the square root

Related links: Equations and inequalities — Working backwards Equations and inequalities — A formal approach

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Term Definition irrational number a number that cannot be written as a fraction where p and q are integers When written as a decimal, the decimal places of an irrational number continue forever without ever forming a repeating pattern. Examples pi (), phi (),

Related links: Number theory — Square roots Circles and cylinders — Pi and the circumference

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Term Definition irregular polygon a polygon that does not have all sides equal and all angles equal Examples scalene triangle, trapezium, kite

Related links: 2D shapes — Plane shapes

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Term Definition isosceles triangle a triangle in which at least two sides are equal in length and at least two angles are equal in size