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 radius (plural: radii) the distance from the centre of a circle (or sphere) to its outside edge (circumference)

Related links: Circles and cylinders — Area of a circle Circles and cylinders — Volume of a cylinder Congruent and similar shapes — Scale factor Exploring geometry — Constructing lines and angles

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Term Definition random choice a choice made without a reason

Related links: Chance — Listing possible outcomes

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Term Definition range the difference between the highest score and the lowest score The range indicates how spread out the scores are.

Related links: Representing data — Grouping data Equations and inequalities — Inequalities Analysing data — The mode, the median and range Analysing data — Analysing dot plots Analysing data — Analysing stem-and-leaf plots Analysing data — Analysing tables

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Term Definition rate the number of units of one quantity for each single unit of another quantity Example The rate (speed) of 60 km per hour means travelling 60 units of distance (km) for a single unit of time (1 hour).

Related links: Ratios and rates — Rates

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Term Definition ratio a way of comparing quantities of the same kind that are measured in the same units The two parts are separated by a colon (:). Example If cordial needs four cups of water for each cup of cordial concentrate, the ratio of water to concentrate is 4:1.

Related links: Ratios and rates — Using ratios

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Term Definition rational numbers numbers that can be expressed in a fraction form ie as an integer divided by an integer (see also irrational numbers) Examples , , , , ,

Related links: Decimals — Decimals of a quantity Percentages — Common conversions

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Term Definition ray a straight line that extends infinitely from one point, called its end point Example The ray in the diagram has an end point A.

Related links: Angles — Points, lines and intervals Angles — How to measure an angle Angles — Types of angles Angles — Angle theorems

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Term Definition reciprocal numbers two numbers that multiply together to give 1 A reciprocal is an inverse under multiplication. Example and are reciprocal numbers: × = 1

Related links: Fractions — Dividing by harder fractions

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Term Definition rectangle a quadrilateral with both pairs of opposite sides equal and parallel, and with all angles right angles

Related links: Algebra — Substitution Length, perimeter and area — Perimeter Length, perimeter and area — Areas of rectangles and squares 2D shapes — Plane shapes 2D shapes — Classifying quadrilaterals 2D shapes — Angle sum of a quadrilateral Pythagoras' theorem — Pythagoras, perimeter and area Representing data — Divided bar graphs Congruent and similar shapes — Scale factor Exploring geometry — Exploring parallelograms and rectangles Exploring geometry — Exploring rhombuses and squares

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Term Definition rectangular prism a prism with a rectangular cross-section

Related links: Measuring solids — Volume of rectangular prisms Measuring solids — Volume of any prism Measuring solids — Surface area Measuring solids — Capacity 2D shapes — Plane shapes 3D shapes — Drawing solids

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Term Definition recurring decimal a decimal in which a single digit, or a group of digits, is endlessly repeated Notation A dot is placed above a single digit that repeats. When the repeating pattern contains two or more digits, dots are placed above the first and last digits in the pattern. Examples = 0.041666666 ... (written as ) = 0.272727272 ... (written as ) = 0.142857142857 ... (written as )

Related links: Decimals — Changing fractions to decimals Decimals — Recurring decimals Percentages — Common conversions

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Term Definition reduce make smaller or simpler (see also decrease; cancelling down) Examples When a price of $100 is reduced by 20% the new price of $80 is smaller than $100. When the fraction is reduced to its lowest terms it keeps the same value but is written in the simpler form of .

Related links: Decimals — Changing decimals to fractions

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Term Definition reduce (scale) make smaller 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 reflection an image seen in a mirror; the result of flipping a geometrical figure across a line An object can also be reflected in a point or a plane.

Related links: 2D shapes — Line of symmetry 2D shapes — Reflection Congruent and similar shapes — Congruent shapes

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Term Definition reflex angle an angle that measures between 180° and 360°

Related links: Angles — How to measure an angle Angles — Types of angles

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Term Definition regular polygon a polygon with all sides equal and all angles equal Examples equilateral triangle, square

Related links: 2D shapes — Plane shapes

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Term Definition remainder leftover quantity after one number has been divided by another (see also division) Example 4 divides into 10 twice with a remainder of 2.

Related links: Whole numbers — Dividing whole numbers Whole numbers — Long division methods Number theory — Factors and multiples Decimals — Dividing decimals by whole numbers Time — Calculating hours, minutes and seconds Manipulating algebra — Factorising

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Term Definition repeating decimal see recurring decimal

Related links: Decimals — Recurring decimals Percentages — Common conversions

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Term Definition revolution an angle of exactly 360° (full circle; full turn)

Related links: 2D shapes — Angle sum of a quadrilateral Angles — Types of angles Angles — Angle theorems

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Term Definition rhombus a quadrilateral with both pairs of opposite sides parallel and all sides equal

Related links: Fractions — What is a fraction? 2D shapes — Classifying quadrilaterals Exploring geometry — Exploring rhombuses and squares Exploring geometry — Constructing lines and angles

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Term Definition right-angled triangle a triangle in which one of the angles is a right angle(also known as a right triangle)

Related links: Algebra — Substitution Length, perimeter and area — Areas of parallelograms Measuring solids — Volume of any prism 2D shapes — Classifying triangles 2D shapes — Angle sum of a triangle Pythagoras' theorem — Length of the hypotenuse Pythagoras' theorem — Length of any side Pythagoras' theorem — Pythagoras, perimeter and area

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Term Definition right angle an angle of exactly 90°

Related links: 2D shapes — Classifying triangles 2D shapes — Classifying quadrilaterals 2D shapes — Rotation Angles — Points, lines and intervals Angles — Types of angles Angles — Angle theorems Pythagoras' theorem — Length of any side Exploring geometry — Exploring parallelograms and rectangles Exploring geometry — Exploring rhombuses and squares Exploring geometry — Constructing lines and angles Exploring geometry — Bisecting angles and intervals

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Term Definition right triangle a triangle in which one of the angles is a right angle (also known as a right-angled triangle)

Related links: 2D shapes — Classifying triangles

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Term Definition Roman numerals system of numbering used in ancient Rome based on groups of 5 and 10 Examples TV programs and films may write their production/copyright dates in Roman numerals, as in MCMXCVIII; older style clock faces use Roman numerals from 1 to 12 (I, II, III, IV, ... XII). The illustration shows Roman numerals on the magnified reverse side of a US one-dollar bill.

Related links: Whole numbers — Roman and Greek numerals

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Term Definition rotation a turn around a centre point or axis Example The diagram shows a picture of an apple rotated about a point.

Related links: Time — Time measurements 2D shapes — Rotational symmetry 2D shapes — Rotation Congruent and similar shapes — Congruent shapes

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Term Definition rotational symmetry applies if a plane figure fits onto itself exactly when rotated through any angle less than 360°

Related links: 2D shapes — Rotational symmetry

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Term Definition round off approximate a number to a specified number of places or digits Examples Rounding 153 off to the nearest hundred, gives 200 (round up). Rounding 153 off to the nearest ten, gives 150 (round down).

Related links: Whole numbers — Estimation and rounding off Number theory — Square roots Decimals — Subtracting decimals Decimals — Rounding decimals Decimals — Money Time — Time on a calculator Pythagoras' theorem — Length of any side Pythagoras' theorem — Pythagoras, perimeter and area Applying percentages — Finding the whole amount Circles and cylinders — Pi and the circumference

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Term Definition row list or pattern shown horizontally (across)