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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© 2007 HOTmaths Pty Ltd

Term Definition 24-hour clock a clock showing the time of day in a range of 24 hours without using am or pm The hours in one day are counted from midnight to midnight rather than from 0 to 12 twice. The 24-hour clock always expresses time in four figures from 0000 to 2359.        Examples 1300 hours (or 13:00) indicates 1 pm 0415 hours (or 04:15) means 4:15 am

Related links: Time — Time of day Time — Timetables and charts

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Term Definition 2D (two-dimensional) having two dimensions, like a surface, but no depth; requiring two coordinates to specify a point A shadow is two-dimensional

Related links: Algebra — Patterns on the number grid Length, perimeter and area — Perimeter Length, perimeter and area — Areas of rectangles and squares 2D shapes — Classifying triangles 2D shapes — Angle sum of a triangle 2D shapes — Exterior angles of triangles 2D shapes — Classifying quadrilaterals 2D shapes — Angle sum of a quadrilateral 2D shapes — Line of symmetry 2D shapes — Rotational symmetry 2D shapes — Translation 2D shapes — Reflection 2D shapes — Rotation 3D shapes — Faces, edges and vertices Representing data — Histograms and polygons Congruent and similar shapes — Congruent shapes

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Term Definition 3D (three-dimensional) having three dimensions, like a solid; requiring three coordinates to specify a point

Related links: Measuring solids — Volume 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 table of values a set of ordered pairs (arranged in table format) that may be used to plot the points to draw a graph Example This table shows the values for four points on the line y = x + 2  x  −1  0   1   2   y   1   2   3   4

Related links: Algebra — Picture patterns and pronumerals Algebra — Number patterns and pronumerals Algebra — Patterns on the number grid The number plane — Graphs from equations The number plane — Equations from lines

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Term Definition tangent a line which touches a circle at one point It does not cut or pass through the circle.

Related links: Circles and cylinders — Pi and the circumference

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Term Definition temperature measured amount of heat recorded as degrees Fahrenheit, degrees Celsius or Kelvin

Related links: Integers — What are directed numbers? Representing data — Scatter diagrams Representing data — Organising data into tables The number plane — Plotting positive integers The number plane — Extending the number plane

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Term Definition terminating decimal a decimal that contains a finite number of digits When a terminating decimal is written as a fraction, its denominator is only divisible by 2 or 5. Examples 0.625, 14.13057

Related links: Decimals — Changing fractions to decimals Decimals — Recurring decimals

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Term Definition tessellate to make a pattern of repeating shapes (see tessellation)

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Term Definition tessellation any repeating pattern of interlocking shapes, sometimes also known as tilings

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Term Definition tetrahedron a solid with four triangular faces; a triangular pyramid A regular tetrahedron (one of the five Platonic solids) has four congruent equilateral triangles as faces.

Related links: 3D shapes — Classifying solids

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Term Definition theorem a mathematical statement that can be proved logically Example The theorem "The sum of the three angles of a triangle equals 180°" can be deduced from the properties of angles in parallel lines. In the diagram, the alternate angles in the parallel lines are equal. Therefore the sum of the three angles of the triangle equals the straight angle (180°).

Related links: Number theory — Square roots Algebra — Substitution Angles — Angle theorems Pythagoras' theorem — What is Pythagoras' theorem? Pythagoras' theorem — Length of the hypotenuse Pythagoras' theorem — Length of any side Pythagoras' theorem — Pythagoras, perimeter and area

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Term Definition time period of existence that is measured in seconds, minutes, hours, days, weeks, months, years, and so on (or this process considered as a whole)

Related links: Whole numbers — Ancient number systems Whole numbers — Index notation Time — Time measurements Time — Time of day Time — Calculating hours, minutes and seconds Time — Time on a calculator Time — Timetables and charts Time — Time zones Representing data — Scatter diagrams The number plane — Plotting positive integers Ratios and rates — Rates

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Term Definition tonne (t) unit of measurement for weight or mass equal to 1000 kg

Related links: Measuring solids — Mass

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Term Definition total sum

Related links: Decimals — Multiplying decimals Algebra — Algebra pictures Algebra — Words into algebra Measuring solids — Surface area Measuring solids — Capacity Time — Calculating hours, minutes and seconds Chance — Listing possible outcomes Manipulating algebra — Reading algebra

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Term Definition trading exchanging one ten for ten ones, one hundred for ten tens, one thousand for ten hundreds, and so on, when carrying out additions and subtractions

Related links: Whole numbers — Subtracting whole numbers

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Term Definition transformation the process of changing a shape's position, size or shape by flipping, spinning, sliding, enlarging, reducing and/or distorting it If the object and the image are congruent the transformation is called a congruence transformation. The only congruence transformations are reflection, rotation and translation.

Related links: 2D shapes — Translation 2D shapes — Reflection 2D shapes — Rotation Congruent and similar shapes — Congruent shapes

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Term Definition translation movement of an object a certain distance in a given direction Example The triangle in the diagram has been translated a few units to the right of its original position.

Related links: 2D shapes — Translation Congruent and similar shapes — Congruent shapes

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Term Definition transversal a line that cuts two or more lines Transversal cutting two lines Transversal cutting two parallel lines

Related links: Angles — Angles in parallel lines

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Term Definition trapezium a quadrilateral with at least one pair of parallel sides

Related links: Fractions — What is a fraction? 2D shapes — Plane shapes 2D shapes — Classifying quadrilaterals Pythagoras' theorem — Pythagoras, perimeter and area Equations and inequalities — Equations and formulas Exploring geometry — Exploring trapeziums and kites Exploring geometry — Exploring rhombuses and squares

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Term Definition travel graph a special form of line graph that describes a traveller's position at different times

Related links: Representing data — Travel graphs

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Term Definition tree diagram a diagram used to show all the possibilities when several different options are available A tree diagram can show all the possible outcomes when a coin is tossed several times. A factor tree can show factorisations of a whole number. Example The tree diagram shows the possible outcomes for the three spinners below.

Related links: Number theory — Factor trees Number theory — HCF and LCM for large numbers Number theory — Square roots

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Term Definition trend a general shape or direction created by data

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

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Term Definition triangle plane figure with three straight sides and three angles

Related links: Length, perimeter and area — Areas of triangles 2D shapes — Plane shapes 2D shapes — Classifying triangles 2D shapes — Angle sum of a triangle 2D shapes — Exterior angles of triangles Chance — Probability Pythagoras' theorem — What is Pythagoras' theorem? Pythagoras' theorem — Length of the hypotenuse Pythagoras' theorem — Length of any side Pythagoras' theorem — Pythagoras, perimeter and area Congruent and similar shapes — Which shapes are similar? Congruent and similar shapes — Scale factor Congruent and similar shapes — Drawing similar figures Congruent and similar shapes — Scale drawings Ratios and rates — What is a ratio? Ratios and rates — Using ratios Ratios and rates — Rates Exploring geometry — Constructing lines and angles

© 2007 HOTmaths Pty Ltd

Term Definition triangular number a whole number that can be represented by dots in the shape of a triangle Example The first ten triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45, 55. The first six triangular numbers

Related links: Number theory — Further patterns in numbers

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

Related links: Measuring solids — Volume of any prism Measuring solids — Surface area 3D shapes — Faces, edges and vertices 3D shapes — Classifying solids 3D shapes — Nets of solids

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Term Definition triangular pyramid a pyramid with a triangular base

Related links: 3D shapes — Classifying solids

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Term Definition triple multiply by three