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 edge the line interval where two faces of a solid meet

Related links: Measuring solids — Capacity 2D shapes — Plane shapes 3D shapes — Faces, edges and vertices 3D shapes — Classifying solids 3D shapes — Nets of solids 3D shapes — Drawing solids 3D shapes — Views of solids

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Term Definition eg abbreviation for "for example" Example + is the symbol for addition, eg 4 + 7 = 11

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Term Definition element a member of a set; a single item in a group

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

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Term Definition elimination a problem-solving method where wrong answers are crossed off

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Term Definition ellipse oval-shaped closed curve

Related links: 2D shapes — Plane shapes

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Term Definition empty set null set; set containing no elements and represented by empty braces { } or by the symbol

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

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Term Definition end point point at which an interval or ray or curve stops

Related links: Angles — Points, lines and intervals Exploring geometry — Bisecting angles and intervals

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Term Definition enlarge make bigger in size without changing the original shape All angles and proportions remain unchanged.

Related links: Congruent and similar shapes — Scale factor Congruent and similar shapes — Drawing similar figures

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Term Definition equal sets sets with identical elements

Related links: Set theory — Introducing sets

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Term Definition equal addends method of subtraction where equal amounts are added to both numbers in the subtraction

Related links: Whole numbers — Subtracting whole numbers

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Term Definition equation a mathematical statement that contains an equal sign The left side has the same value as the right side. Examples 3 + 4 = 7 0.3 × 10 = 2 + 1 2x − 7 = 13

Related links: Algebra — Substitution Pythagoras' theorem — Length of any side Equations and inequalities — Working backwards Equations and inequalities — Keeping the balance Equations and inequalities — Guess, check and improve Equations and inequalities — A formal approach Equations and inequalities — Equations to solve problems Equations and inequalities — Equations and formulas Equations and inequalities — Inequalities Manipulating algebra — Reading algebra Circles and cylinders — Area of a circle The number plane — Graphs from equations The number plane — Equations from lines The number plane — Comparing lines and equations The number plane — Intersecting lines

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Term Definition equilateral triangle a triangle in which all three sides are the same length All three angles will also be the same size (60°)

Related links: Fractions — What is a fraction? 2D shapes — Plane shapes 2D shapes — Classifying triangles 2D shapes — Rotational symmetry 3D shapes — Nets of solids Pythagoras' theorem — What is Pythagoras' theorem? Exploring geometry — Constructing lines and angles

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Term Definition equivalent equal in value

Related links: Fractions — Equivalent fractions Fractions — Comparing and ordering fractions Percentages — Percentage/fraction/decimal connection Percentages — Common conversions Algebra — Equivalent expressions Representing data — Line, conversion and step graphs Ratios and rates — Using ratios

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Term Definition equivalent sets sets with the same number of elements but not necessarily identical elements

Related links: Set theory — Introducing sets

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Term Definition equivalent fractions fractions that can be reduced to the same basic fraction; fractions that have the same value but different denominators Example Here are five equivalent fractions for the basic fraction :

Related links: Fractions — Equivalent fractions Fractions — Comparing and ordering fractions Percentages — Changing fractions to percentages

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Term Definition equivalent ratios ratios that represent the same proportions Examples 1 : 2 and 5 : 10

Related links: Ratios and rates — Using ratios

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Term Definition estimate an informed guess To estimate means to approximate an answer quickly without calculating exactly. Example The estimate for the answer to 3.9 × 6.2 would be 24 (ie 4 × 6). A better estimate would be 4 × 6.2 = 24.8

Related links: Whole numbers — Estimation and rounding off Number theory — Square roots Number theory — Square roots Number theory — Cube roots Fractions — Multiplying mixed numerals Decimals — Adding decimals Decimals — Subtracting decimals Decimals — Multiplying decimals Decimals — Dividing decimals by whole numbers Decimals — Money Length, perimeter and area — Converting area units and estimating Measuring solids — Capacity Angles — Types of angles Representing data — Divided bar graphs Representing data — Line, conversion and step graphs Applying percentages — Percentage of a quantity Circles and cylinders — Area of a circle Congruent and similar shapes — Scale drawings

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Term Definition Euler's formula F + V = E + 2 (also written as V − E + F = 2   or   F + V − E = 2) where F is number of faces of a polyhedron, V is the number of vertices and E is the number of edges Example A cube has: 6 faces 8 vertices 12 edges F + V − E = 6 + 8 − 12 = 2

Related links: 3D shapes — Faces, edges and vertices

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Term Definition evaluate find (calculate) the numerical value of Example "Evaluate 5 + 4 − 2" means to calculate that 5 + 4 − 2 = 7.

Related links: Integers — Adding and subtracting integers Integers — Dividing integers Algebra — Substitution

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Term Definition even number a whole number that can be divided or is divisible by 2 (with no remainder) Example Any whole number ending in the digits 0, 2, 4, 6, 8. The first ten even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

Related links: Number theory — Simple number patterns Number theory — Factors and multiples Number theory — Divisibility tests Chance — Probability Equations and inequalities — Equations to solve problems Analysing data — The mode, the median and range Analysing data — Analysing dot plots Analysing data — Analysing tables

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Term Definition expand remove grouping symbols Example 3(2k − 1) = 6k − 3

Related links: Algebra — Removing grouping symbols Equations and inequalities — A formal approach Manipulating algebra — Reading algebra Manipulating algebra — Factorising

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Term Definition expanded form an expression with no grouping symbols (see also factored form) Example 2x + 6 is the expanded form of 2(x + 3)

Related links: Algebra — Equivalent expressions Manipulating algebra — Factorising

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Term Definition expanded notation a way of writing numerals to show the place value of each digit (as the sum of powers of ten or as the sum of its units, tens, hundreds, and so on) Example The expanded notation for 3254 is: 3 × 1000 + 2 × 100 + 5 × 10 + 4 × 1 OR 3 × 103 + 2 × 102 + 5 × 10 + 4

Related links: Whole numbers — Place value and expanded notation Whole numbers — Index notation Decimals — What is the point?

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Term Definition exponent another name for power or index Example 43 = 4 × 4 × 4 means 4 to the power of 3. The small raised 3 is called the exponent, and shows that there are three factors of 4.

Related links: Whole numbers — Index notation Algebra — What is algebra?

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Term Definition exponential notation abbreviated way of representing repeated multiplication of the same number (see also index notation) Example 54 is exponential notation for 5 × 5 × 5 × 5

Related links: Whole numbers — Index notation Algebra — What is algebra?

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Term Definition expression a group of mathematical terms Examples 7 + 8 − 14 x + y 34 × 6 − 8 ÷ 2

Related links: Decimals — Decimals of a quantity Algebra — What is algebra? Algebra — Algebra pictures Algebra — Words into algebra Algebra — Removing grouping symbols Algebra — Substitution Algebra — Adding and subtracting terms Algebra — Equivalent expressions Equations and inequalities — Inequalities Manipulating algebra — Formulas in spreadsheets Manipulating algebra — Factorising Manipulating algebra — Algebraic fractions

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Term Definition exterior angle the angle formed between the extended side of a polygon and the adjacent side "Exterior" means these angles are outside the shape.