HOTmaths dictionary

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

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Term

Definition

acute-angled triangle

a triangle in which all three angles are acute angles

Related links:
2D shapes — Classifying triangles

Term

Definition

acute angle

an angle measuring between 0° and 90°

Related links:
2D shapes — Classifying triangles
2D shapes — Angle sum of a triangle
Angles — Types of angles

Term	Definition
addition	sum, or total

Related links:
Whole numbers — Adding whole numbers
Whole numbers — Order of operations
Fractions — Adding and subtracting fractions
Fractions — Adding and subtracting mixed numerals
Decimals — Adding decimals
Integers — Adding and subtracting integers
Integers — Two signs together
Integers — Mixing the operations
Algebra — Adding and subtracting terms
Length, perimeter and area — Measuring length
Length, perimeter and area — Perimeter
2D shapes — Angle sum of a triangle
2D shapes — Angle sum of a quadrilateral
Equations and inequalities — Working backwards
Manipulating algebra — Formulas in spreadsheets

Term

Definition

adjacent

next to (see also adjacent angles)

Related links:
2D shapes — Classifying quadrilaterals
Angles — Types of angles
Exploring geometry — Exploring trapeziums and kites
Exploring geometry — Exploring parallelograms and rectangles
Exploring geometry — Exploring rhombuses and squares

Term

Definition

adjacent angles

angles that are next to one another

Adjacent angles share a common arm and vertex.

Adjacent angles

Non-adjacent angles

Related links:
2D shapes — Classifying triangles
Angles — Types of angles
Exploring geometry — Exploring trapeziums and kites
Exploring geometry — Exploring parallelograms and rectangles
Exploring geometry — Exploring rhombuses and squares

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Term	Definition
algebra	branch of mathematics that substitutes letters or symbols (known as pronumerals) for numbers

Related links:
Number theory — Further patterns in numbers
Number theory — Factors and multiples
Number theory — Highest common factor (HCF)
Algebra — What is algebra?
Algebra — Algebra pictures
Algebra — Words into algebra
Algebra — Substitution
Algebra — Picture patterns and pronumerals
Algebra — Recognising patterns
Algebra — Number patterns and pronumerals
Algebra — Patterns on the number grid
Algebra — Adding and subtracting terms
Algebra — Multiplying and dividing terms
Algebra — Equivalent expressions
Length, perimeter and area — Areas of rectangles and squares
Pythagoras' theorem — What is Pythagoras' theorem?
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
Manipulating algebra — Formulas in spreadsheets
Manipulating algebra — Removing grouping symbols
Manipulating algebra — Factorising
Manipulating algebra — Algebraic fractions
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

Term

Definition

algebraic equation

a mathematical sentence including an equal sign and at least one pronumeral

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

Term

Definition

algebraic expression

mathematical expression containing both numbers and pronumerals

Related links:
Algebra — What is algebra?
Algebra — Algebra pictures
Algebra — Words into algebra
Algebra — Substitution
Algebra — Adding and subtracting terms
Algebra — Equivalent expressions
Equations and inequalities — Inequalities
Manipulating algebra — Reading algebra
Manipulating algebra — Removing grouping symbols
Manipulating algebra — Factorising

Term

Definition

algebraic fraction

a fraction containing pronumerals as well as numbers

Related links:
Manipulating algebra — Algebraic fractions

Term

Definition

alternate angles

two angles that lie between two lines on either side of a transversal that cuts the lines

The angles marked

(alpha) form a pair of equal alternate angles; so do the angles marked

(beta).
This is because alternate angles are equal when the lines cut by the transversal are parallel.

Related links:
Angles — Angles in parallel lines

Term

Definition

abbreviation for ante meridiem, which means "before midday" ie the time from midnight until midday (morning)

Related links:
Time — Time of day
Time — Time zones

Term

Definition

analog clock

a traditional type of clock that displays the time of day using an hour hand and a minute hand

Related links:
Time — Time of day

Term

Definition

angle

two rays starting from the same point; the measure of turn between two lines, measured in degrees; the difference in direction between two lines

Related links:
2D shapes — Plane shapes
2D shapes — Angle sum of a triangle
2D shapes — Angle sum of a quadrilateral
Angles — Points, lines and intervals
Angles — How to name an angle
Angles — How to measure an angle
Angles — Types of angles
Angles — Angle theorems
Angles — Angles in parallel lines
Pythagoras' theorem — What is Pythagoras' theorem?
Representing data — Sector graphs
Congruent and similar shapes — Congruent shapes
Congruent and similar shapes — Which shapes are similar?
Congruent and similar shapes — Scale factor
Congruent and similar shapes — Drawing similar figures
Ratios and rates — Using ratios
Exploring geometry — Exploring trapeziums and kites
Exploring geometry — Exploring parallelograms and rectangles
Exploring geometry — Exploring rhombuses and squares
Exploring geometry — Constructing lines and angles
Exploring geometry — Bisecting angles and intervals

Term

Definition

angle sum

the total measure of the angles in a plane figure

Examples

The angle sum of any triangle is 180°.
The angle sum of any quadrilateral is 360°.

Related links:
2D shapes — Angle sum of a triangle
2D shapes — Exterior angles of triangles
2D shapes — Angle sum of a quadrilateral
Angles — Angle theorems

Term

Definition

anticlockwise

opposite to the direction in which the hands of a clock turn

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

Term

Definition

apex

the highest point (or top) of a shape or object

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

Term	Definition
approximately equal	almost equal; represented by the symbol ≈ or Examples $99.98 ≈ $100 29.6 mm 3 cm

Related links:
Whole numbers — Estimation and rounding off
Whole numbers — Long division methods
Length, perimeter and area — Converting area units and estimating
Angles — Types of angles
Pythagoras' theorem — Length of the hypotenuse
Pythagoras' theorem — Length of any side
Applying percentages — Percentage of a quantity

Term	Definition
approximation	a value that is close to the real value (see also approximately equal)

Related links:
Number theory — Cube roots
Length, perimeter and area — Measuring length
Pythagoras' theorem — Length of the hypotenuse
Circles and cylinders — Pi and the circumference
Circles and cylinders — Area of a circle

Term

Definition

arc

part of the circumference of a circle between two points; part of a curve

Related links:
Circles and cylinders — Pi and the circumference
Exploring geometry — Constructing lines and angles
Exploring geometry — Bisecting angles and intervals

Term

Definition

area

the space inside a 2D shape; the amount of surface the 2D shape covers

Units of area are squares such as square millimetres square centimetres, square metres, square kilometres and hectares. The abbreviations for these units are mm², cm², m², km² and ha.

Area = 6 cm²

Related links:
Number theory — Square roots
Fractions — Multiplying fractions
Algebra — Substitution
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 — Surface area
2D shapes — Plane shapes
Pythagoras' theorem — What is Pythagoras' theorem?
Pythagoras' theorem — Length of the hypotenuse
Pythagoras' theorem — Pythagoras, perimeter and area
Equations and inequalities — Equations and formulas
Manipulating algebra — Formulas in spreadsheets
Manipulating algebra — Algebraic fractions
Circles and cylinders — Area of a circle
Circles and cylinders — Volume of a cylinder
Ratios and rates — Rates

Term

Definition

area of a circle

Area =

× radius² (where

≈ 3.142)

Area	≈ 3.142 × 5²
	= 78.55 cm²

Related links:
Circles and cylinders — Area of a circle
Circles and cylinders — Volume of a cylinder

Term

Definition

area of a parallelogram

Area = base × height (where the height is perpendicular to the base)

Area	=	5 cm × 3 cm
	=	15 cm²

Related links:
Length, perimeter and area — Areas of parallelograms

Term

Definition

area of a rectangle

Area = length × breadth

Area	=	5 cm × 4 cm
	=	20 cm²

Related links:
Algebra — Substitution
Length, perimeter and area — Areas of rectangles and squares
Length, perimeter and area — Converting area units and estimating
Measuring solids — Volume of any prism
Measuring solids — Surface area
Pythagoras' theorem — Pythagoras, perimeter and area
Manipulating algebra — Formulas in spreadsheets

Term

Definition

area of a rhombus

Area =

× diagonal₁ × diagonal₂

Area	= × 4 cm × 7 cm
	= 14 cm²

Term

Definition

area of a square

Area = side²

Area	= 5 cm × 5 cm
	= 25 cm²

Related links:
Number theory — Square roots
Length, perimeter and area — Areas of rectangles and squares
Length, perimeter and area — Converting area units and estimating
Pythagoras' theorem — What is Pythagoras' theorem?
Pythagoras' theorem — Length of the hypotenuse

Term

Definition

area of a trapezium

Area = perpendicular height × average of the two parallel sides

Area	= 3 ×
	= 18 cm²

Related links:
Pythagoras' theorem — Pythagoras, perimeter and area
Equations and inequalities — Equations and formulas

Term

Definition

area of a triangle

Area =

× base × height

Area	= × 6 cm × 5 cm
	= 15 cm²

Related links:
Algebra — Substitution
Length, perimeter and area — Areas of triangles
Measuring solids — Volume of any prism
Measuring solids — Surface area
Pythagoras' theorem — Pythagoras, perimeter and area

Term

Definition

arm

line interval forming one side of an angle and having the vertex of the angle as an end point

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

Term

Definition

ascending order

from smallest to largest (as opposed to descending order)

Example
Place 6, −3, 4 in ascending order.

The answer is −3, 4, 6.

Related links:
Fractions — Comparing and ordering fractions
Decimals — Ordering decimals
Integers — What are directed numbers?

Term	Definition
associative law	states that the result of adding or multiplying three or more numbers does not depend on how pairs of them are grouped Examples (3 + 7) + 6 = 3 + (7 + 6) (3 × 7) × 6 = 3 × (7 × 6)

Term

Definition

asymmetrical

has no symmetry

Related links:
2D shapes — Line of symmetry

Term	Definition
average score	calculated by adding up all the scores and dividing by the total number of scores Example What is the average of 2, 5, and 11? Sum of scores: 2 + 5 + 11 = 18 Total number of scores: 3 So average is 18 ÷ 3 = 6

Related links:
Manipulating algebra — Formulas in spreadsheets
Analysing data — The mean
Analysing data — The mode, the median and range
Analysing data — Analysing stem-and-leaf plots
Analysing data — Analysing tables
Ratios and rates — Rates

Term

Definition

axes (number plane)

(pronounced ax-ees) vertical and horizontal lines that define the number plane quadrants

The horizontal line is called the x-axis and the vertical line is called the y-axis.

Related links:
Algebra — Patterns on the number grid
Representing data — Line, conversion and step graphs
Representing data — Travel graphs
Representing data — Histograms and polygons
Representing data — Grouping data
The number plane — Plotting positive integers
The number plane — Extending the number plane
The number plane — Graphs from equations
The number plane — Equations from lines
The number plane — Comparing lines and equations
The number plane — Intersecting lines

Term	Definition
axis (number plane)	a vertical or horizontal line that defines the number plane quadrants See axes (number plane).

Related links:
Algebra — Patterns on the number grid
Representing data — Line, conversion and step graphs
Representing data — Travel graphs
Representing data — Histograms and polygons
Representing data — Grouping data
Representing data — Dot plots
The number plane — Plotting positive integers
The number plane — Extending the number plane
The number plane — Graphs from equations
The number plane — Equations from lines
The number plane — Comparing lines and equations
The number plane — Intersecting lines

Term	Definition
axis (shape)	(plural axes, pronounced ax-ees) a reference line associated with a geometric figure or solid (see also axis of a cone, axis of a cylinder, axis of the Earth, axis of symmetry)