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 cancelling down reducing a fraction to its lowest terms Example Cancelling down gives . (Divide top and bottom by 3.)

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Term Definition capacity how much liquid a container can hold

Related links: Fractions — This as a fraction of that Measuring solids — Capacity Measuring solids — Mass Circles and cylinders — Volume of a cylinder

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Term Definition capital an amount of money that is borrowed or invested (see also principal) Example Someone starting up a new business may invest their capital (a large sum) into it.

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Term Definition cardinal numbers the set of whole numbers starting at zero

Related links: Number theory — Simple number patterns

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Term Definition categorical data data that fits in a category or group Examples Eye colour Gender Type of car

Related links: Representing data — Organising data into tables Representing data — Graphs and spreadsheets Analysing data — Analysing tables

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Term Definition cell a place in a spreadsheet where you can enter data, formulas or labels It is the intersection of a column and a row.

Related links: Manipulating algebra — Formulas in spreadsheets

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Term Definition cell address a letter and number showing a location in a spreadsheet (also called cell reference) B2 is the cell in column B row 2.

Related links: Manipulating algebra — Formulas in spreadsheets

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Term Definition cell reference a letter and number showing a location in a spreadsheet (also called cell address) B2 is the cell in column B row 2.

Related links: Manipulating algebra — Formulas in spreadsheets

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Term Definition census a survey involving the entire population

Related links: Analysing data — The mean

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Term Definition centimetre (cm) unit of metric measurement for length (100 cm = 1 m)

Related links: Number theory — Square roots Fractions — This as a fraction of that Decimals — Rounding decimals Algebra — Substitution Length, perimeter and area — Units of length Length, perimeter and area — Units of length Length, perimeter and area — Measuring length Length, perimeter and area — Perimeter Length, perimeter and area — Areas of rectangles and squares Length, perimeter and area — Areas of triangles Length, perimeter and area — Areas of parallelograms Length, perimeter and area — Converting area units and estimating Measuring solids — Volume Measuring solids — Volume of rectangular prisms Measuring solids — Volume of any prism Measuring solids — Surface area Measuring solids — Capacity Measuring solids — Mass Pythagoras' theorem — Length of the hypotenuse Pythagoras' theorem — Pythagoras, perimeter and area Representing data — Line, conversion and step graphs Representing data — Grouping data Representing data — Stem-and-leaf plots Equations and inequalities — Equations and formulas Circles and cylinders — Pi and the circumference Circles and cylinders — Area of a circle Circles and cylinders — Volume of a cylinder Analysing data — The mean Congruent and similar shapes — Congruent shapes Congruent and similar shapes — Scale factor Congruent and similar shapes — Scale drawings Ratios and rates — Using ratios Exploring geometry — Exploring trapeziums and kites Exploring geometry — Exploring parallelograms and rectangles Exploring geometry — Exploring rhombuses and squares

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Term Definition central tendency to be in or near the middle

Related links: Analysing data — The mean Analysing data — Analysing dot plots Analysing data — Analysing stem-and-leaf plots Analysing data — Analysing tables

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Term Definition centre of rotation fixed point about which a figure rotates

Related links: 2D shapes — Rotational symmetry 2D shapes — Rotation

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Term Definition chord a line interval joining two points on the circumference of a circle

Related links: Circles and cylinders — Pi and the circumference

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Term Definition circle a plane shape that is perfectly round Each point on the circle is the same distance from the centre.

Related links: Fractions — Dividing by simple fractions 2D shapes — Plane shapes 2D shapes — Line of symmetry 2D shapes — Rotation 3D shapes — Classifying solids Representing data — Sector graphs Representing data — Line, conversion and step graphs Equations and inequalities — Inequalities Manipulating algebra — Factorising Circles and cylinders — Pi and the circumference Circles and cylinders — Area of a circle Circles and cylinders — Volume of a cylinder Congruent and similar shapes — Congruent shapes Congruent and similar shapes — Which shapes are similar? Congruent and similar shapes — Scale factor Exploring geometry — Bisecting angles and intervals

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Term Definition circle centre the point in the middle of a circle All points on the circumference are exactly the same distance from the centre.

Related links: Representing data — Sector graphs Circles and cylinders — Pi and the circumference Circles and cylinders — Area of a circle Circles and cylinders — Volume of a cylinder

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Term Definition circumference the curved boundary of a circle or of the great circle of a sphere

Related links: Circles and cylinders — Pi and the circumference Circles and cylinders — Area of a circle

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Term Definition classify to divide items into groups according to their characteristics

Related links: Angles — Types of angles 3D shapes — Classifying solids

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Term Definition clockwise the direction in which the hands of a clock turn

Related links: 2D shapes — Rotation Angles — How to measure an angle

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Term Definition closed figure a plane figure that joins up with itself leaving no gaps in its perimeter (eg a  circle or an ellipse)

Related links: 2D shapes — Plane shapes

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Term Definition cluster to gather around or gather together

Related links: Representing data — Scatter diagrams Representing data — Dot plots Analysing data — Analysing tables

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Term Definition co-interior angles a pair of angles lying between two lines on the same side of a transversal (a line that cuts the two lines) In the diagram, the angles marked d and e on one side of the transversal form a pair of co-interior angles, as do the angles marked c and f on the other side of the transversal. Because the lines in the diagram are parallel these pairs of co-interior angles are supplementary.

Related links: Angles — Angles in parallel lines Exploring geometry — Exploring trapeziums and kites

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Term Definition collinear points points that lie on the same straight line

Related links: Angles — Points, lines and intervals

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Term Definition column a list or pattern shown vertically (up/down)

Related links: Whole numbers — Place value and expanded notation Whole numbers — Index notation Whole numbers — Adding whole numbers Whole numbers — Subtracting whole numbers Whole numbers — Multiplying whole numbers Whole numbers — Long division methods Decimals — What is the point? Decimals — Adding decimals Decimals — Subtracting decimals Length, perimeter and area — Areas of rectangles and squares Representing data — Organising data into tables Representing data — Histograms and polygons Representing data — Grouping data Representing data — Dot plots Representing data — Stem-and-leaf plots Manipulating algebra — Formulas in spreadsheets Analysing data — Analysing dot plots Analysing data — Analysing tables

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Term Definition column graph a graph with individual columns, where the height of each column represents a value; a visual representation to compare data

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Term Definition commission earnings of a salesperson based on a percentage of the value of goods sold Example Real estate agents receive a percentage of the selling price of the properties they sell.

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Term Definition common shared Examples Fractions with the same bottom part are said to have a common denominator. Since 3 and 6 are both factors of 6 and 12, then 12 and 6 are said to have common factors of 3 and 6. Adjacent angles share a common vertex and a common arm Sets that intersect have common elements.

Related links: Angles — Types of angles Angles — Types of angles Decimals — Changing decimals to fractions Decimals — Changing fractions to decimals Exploring geometry — Exploring trapeziums and kites Fractions — Equivalent fractions Length, perimeter and area — Units of length Manipulating algebra — Algebraic fractions Manipulating algebra — Factorising Number theory — HCF and LCM for large numbers Number theory — Highest common factor (HCF) Number theory — Lowest common multiple (LCM) Percentages — Common conversions Ratios and rates — What is a ratio? Set theory — Set relationships and Venn diagrams

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Term Definition commutative law when adding and multiplying, the order in which two numbers are combined does not matter Examples 14 × 20 = 20 × 14 9 + 7 = 7 + 9

Related links: Whole numbers — Multiplying whole numbers

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Term Definition compasses abbreviated and commonly used term for the geometrical instrument pair of compasses

Related links: Congruent and similar shapes — Congruent shapes Exploring geometry — Constructing lines and angles Exploring geometry — Bisecting angles and intervals

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Term Definition compensation a mental method of calculation Step 1 Round a number to make the problem easier. Step 2 Add or subtract a small amount from the answer to compensate for the change. Example 1 681 − 492 = 681 − 500 + 8 = 181 + 8 = 189 Example 2 5034 + 195 = 5034 + 200 − 5 = 5234 − 5 = 5229

Related links: Whole numbers — Adding whole numbers Whole numbers — Subtracting whole numbers Decimals — Subtracting decimals

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Term Definition complement the angle added to an acute angle to make a right angle (see also complementary angles) Example The complement of 30° is 60° since 30° + 60° = 90°

Related links: Angles — Types of angles

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Term Definition complement (sets) a set containing the elements that are NOT in a given set The complement of a set is denoted using a wavy line above the set"s name: is the complement of A. Example If the universal set = {all counting numbers} and E = {even counting numbers} then = {odd counting numbers}

Related links: Set theory — Applying Venn diagrams

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Term Definition complementary angles two angles whose sum is 90° Example 55° and 35° are complementary angles (55° + 35° = 90°)

Related links: Angles — Types of angles

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Term Definition complementary events opposite events Event + its complement = all possible events Probability (event) + probability (complement) = 1 Example Throwing a 5 on a die or throwing a number that is NOT 5.

Related links: Chance — Probability

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Term Definition composite figure a shape without a special name that is made up of two or more shapes Example This composite figure is made up of a rectangle and two semicircles.

Related links: Length, perimeter and area — Areas of rectangles and squares Length, perimeter and area — Areas of triangles Pythagoras' theorem — Pythagoras, perimeter and area

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Term Definition composite number a number that has at least three factors ie factors other than itself and 1 (see also factor) Example The first 10 composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18.

Related links: Number theory — Prime and composite numbers Number theory — Factor trees

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Term Definition concurrent lines lines that pass through the same point

Related links: Angles — Points, lines and intervals

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Term Definition cone a solid that has a circular base and a slanting curved surface that tapers to a point called the apex Right cone Oblique cone

Related links: 3D shapes — Faces, edges and vertices 3D shapes — Classifying solids 3D shapes — Views of solids

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Term Definition congruent figures figures that are exactly the same size and shape

Related links: 2D shapes — Reflection 3D shapes — Faces, edges and vertices 3D shapes — Classifying solids 3D shapes — Nets of solids Congruent and similar shapes — Congruent shapes Congruent and similar shapes — Which shapes are similar?

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Term Definition consecutive numbers numbers that follow each other (in ascending or descending order) Examples Consecutive numbers between 19 and 27 are: 20, 21, 22, 23, 24, 25, 26. Consecutive even numbers from 40 to 52 are: 40, 42, 44, 46, 48, 50, 52.

Related links: Number theory — Simple number patterns Algebra — Words into algebra Algebra — Words into algebra Algebra — Recognising patterns Equations and inequalities — Equations to solve problems Equations and inequalities — Equations to solve problems

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Term Definition constant value that stays the same

Related links: The number plane — Comparing lines and equations

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Term Definition continuous data data that can be measured, with smooth progress from one measurement to the next Examples Your height over a period of time Air temperature Velocity of a car Time

Related links: Representing data — Line, conversion and step graphs Representing data — Travel graphs Representing data — Organising data into tables Representing data — Grouping data Representing data — Graphs and spreadsheets

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Term Definition conversion graph a special type of line graph that allows you to convert from one measurement to another Fahrenheit/Celsius conversion graph

Related links: Representing data — Line, conversion and step graphs

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Term Definition convex polygon a polygon where every diagonal lies inside this figure Examples rhombus, triangle, regular polygons Convex polygon Non-convex polygon

Related links: 2D shapes — Plane shapes

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Term Definition convex polyhedron a polyhedron where all line segments joining any two vertices lie within the solid or on the surface of the solid Convex polyhedron Non-convex polyhedron

Related links: 3D shapes — Classifying solids 3D shapes — Drawing solids

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Term Definition Coordinated Universal Time the modern name for Greenwich Mean Time, also called Universal Time Coordinated (UTC).

Related links: Time — Time zones

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Term Definition coordinates numbers or letters used to give a location or position; an ordered pair written in the form (x, y) that states the location of a point on a number plane, map or plan Example The coordinates of the point (2, 1) mean that the point is located 2 units to the right along the x-axis and 1 unit up the y-axis.

Related links: Algebra — Patterns on the number grid The number plane — Plotting positive integers The number plane — Extending the number plane The number plane — Maps and plans 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 corresponding angles (in lines) pairs of angles in the positions shown below that are formed by two lines being cut by a third (a transversal) If the two lines are parallel, then corresponding angles are equal. In the illustration, the purple coloured letters show a pair of corresponding angles, as do the other pairs of similarly coloured letters. Since the two lines are marked as parallel, the pairs of corresponding angles are equal.

Related links: Angles — Angles in parallel lines

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Term Definition corresponding angles (in shapes) angles in matching positions in two or more shapes Example C corresponds to F because they both are opposite the longest side oftheir respective triangle.

Related links: Congruent and similar shapes — Congruent shapes Congruent and similar shapes — Which shapes are similar? Congruent and similar shapes — Scale factor

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Term Definition corresponding sides sides in two or more shapes that are in the same position in the shapes Examples Longest sides Sides that form the same angle

Related links: Congruent and similar shapes — Congruent shapes Congruent and similar shapes — Which shapes are similar? Congruent and similar shapes — Scale factor

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Term Definition cost price how much retailers pay for goods

Related links: Applying percentages — Profit and loss

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Term Definition counting numbers the set of whole numbers starting at 1: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ... }

Related links: Number theory — Simple number patterns Number theory — Factors and multiples Number theory — Prime and composite numbers

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Term Definition cross-section the cut surface (plane figure) formed when you slice a solid parallel to one of its surfaces Example The green square is the cross-section of the cube.

Related links: Measuring solids — Volume of rectangular prisms Measuring solids — Volume of any prism 3D shapes — Classifying solids Circles and cylinders — Volume of a cylinder

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Term Definition cube (3D) a solid with six congruent square faces; a prism with all cross-sections square

Related links: Measuring solids — Volume Measuring solids — Volume of rectangular prisms Measuring solids — Volume of any prism Measuring solids — Surface area 3D shapes — Faces, edges and vertices 3D shapes — Nets of solids 3D shapes — Drawing solids 3D shapes — Views of solids Equations and inequalities — Keeping the balance

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Term Definition cube (index) the third power of a number

Related links: Whole numbers — Index notation Number theory — Cube roots Decimals — Changing decimals to fractions

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Term Definition cube root (of a number) whatever number must be multiplied by itself and then by that product (cubed) in order to get the original number Example = 2 since 8 = 23 The cube root of 8 is 2 because 2 must be multiplied by 2 (itself) to get 4, then 4 must be multiplied by 2 to get 8.

Related links: Number theory — Cube roots

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Term Definition cubed raised to the power of 3; three of the same number being multiplied together Example "Four cubed" means 43 = 4 × 4 × 4 = 64

Related links: Whole numbers — Index notation Number theory — Cube roots

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Term Definition cubic unit unit of measurement for volume Some common cubic units of measurement are: cubic metres (m3) cubic centimetres (cm3 or cc). Example The diagram shows a cubic centimetre with all sides of length one cm.

Related links: Number theory — Cube roots Measuring solids — Volume Measuring solids — Volume of rectangular prisms Measuring solids — Volume of any prism Measuring solids — Capacity Circles and cylinders — Volume of a cylinder

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Term Definition cylinder a solid with two parallel, congruent circular faces connected by a curved surface Right cylinder Oblique cylinder