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

pair of compasses

mathematical instrument used for marking equal units of length, commonly known as compasses

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

Term	Definition
palindrome	a number, word, phrase or sentence that is the same whether read from left to right or from right to left Examples 613316, 747, 9876789, radar, noon, Madam I'm Adam, race car

Related links:
Number theory — Simple number patterns

Term

Definition

parallel lines

lines that run in the same direction, or lines in the same plane that are the same distance apart and do not ever intersect

Related links:
Angles — Points, lines and intervals
Angles — Angles in parallel lines
The number plane — Comparing lines and equations
Exploring geometry — Exploring parallelograms and rectangles
Exploring geometry — Constructing lines and angles

Term

Definition

parallelogram

a quadrilateral with both pairs of opposite sides parallel

Related links:
Length, perimeter and area — Areas of parallelograms
2D shapes — Classifying quadrilaterals
2D shapes — Angle sum of a quadrilateral
2D shapes — Line of symmetry
Congruent and similar shapes — Drawing similar figures
Exploring geometry — Exploring parallelograms and rectangles
Exploring geometry — Exploring rhombuses and squares

Term	Definition
parentheses	grouping symbol ( )

Related links:
Whole numbers — Grouping symbols
Whole numbers — Order of operations
Integers — Two signs together
Algebra — Substitution
Manipulating algebra — Removing grouping symbols
Manipulating algebra — Factorising
The number plane — Plotting positive integers

Term	Definition
Pascal's triangle	triangular number pattern in which the top row is '1', the second row is '1 space 1' and thereafter each number is the sum of the two nearest numbers above First six rows of Pascal's triangle

Related links:
Number theory — Further patterns in numbers

Term

Definition

pattern

a set of shapes or numbers that are repeated in a predictable way, and may usually be described by a rule (see also number pattern)

Related links:
Number theory — Simple number patterns
Number theory — Further patterns in numbers
Decimals — Recurring decimals
Algebra — Picture patterns and pronumerals
Algebra — Recognising patterns
Algebra — Number patterns and pronumerals
Algebra — Patterns on the number grid
Pythagoras' theorem — What is Pythagoras' theorem?
Representing data — Scatter diagrams
Manipulating algebra — Reading algebra
The number plane — Graphs from equations
The number plane — Equations from lines
Congruent and similar shapes — Congruent shapes

Term

Definition

pentagon

a five-sided polygon

A regular pentagon has all its sides and angles equal.

Examples


Regular pentagon		Irregular pentagon

Related links:
Number theory — Further patterns in numbers
Measuring solids — Volume of any prism
2D shapes — Plane shapes

Term

Definition

pentagonal numbers

number pattern that is generated by starting with a vertex, or dot, then adding successive layers of pentagons from that vertex

Example

The first pentagonal number is represented by the dot (ie P₁ = 1).

The second number is found by the number of dots enclosed by the pentagon (ie P₂ = 5).

The third number is found by the number of dots enclosed by the next pentagon (ie P₃ = 12).

The fourth number is found by the number of dots enclosed by the next successive pentagon (ie P₄ = 22).

Related links:
Number theory — Further patterns in numbers
Measuring solids — Volume of any prism

Term	Definition
percent	per hundred; out of a hundred (represented by symbol %) Example If a tennis player is said to get 73% of first serves in, it means that out of every hundred first serves, 73 are successful. That is, 73% =

Related links:
Percentages — What is a percentage?
Percentages — One whole is 100%
Percentages — Writing percentages as fractions
Percentages — Changing fractions to percentages
Percentages — Changing percentages to decimals
Percentages — Changing decimals to percentages
Percentages — Percentage/fraction/decimal connection
Percentages — Common conversions
Chance — Probability
Applying percentages — One amount as a percentage of another
Applying percentages — Increasing and decreasing using percentages
Applying percentages — Profit and loss
Applying percentages — Finding the whole amount
Ratios and rates — Rates

Term

Definition

percentage

a convenient way of writing fractions with denominators of 100

Related links:
Decimals — Decimals of a quantity
Percentages — One whole is 100%
Percentages — Writing percentages as fractions
Percentages — Changing fractions to percentages
Percentages — Changing percentages to decimals
Percentages — Changing decimals to percentages
Percentages — Percentage/fraction/decimal connection
Percentages — Common conversions
Applying percentages — Percentage of a quantity
Applying percentages — Increasing and decreasing using percentages
Applying percentages — Profit and loss
Applying percentages — Finding the whole amount
Applying percentages — Finding the whole amount
Ratios and rates — Rates

Term	Definition
percentage decrease	to decrease a quantity by a given percentage

Related links:
Applying percentages — Increasing and decreasing using percentages

Term	Definition
percentage increase	to increase a quantity by a given percentage

Related links:
Applying percentages — Increasing and decreasing using percentages

Term	Definition
perimeter	the total distance (length) around the outside of a figure, calculated by adding together the lengths of all sides Example The perimeter of a triangle with side lengths of 6 cm, 7 cm and 8 cm is 21cm, since 6 + 7 + 8 = 21.

Related links:
Length, perimeter and area — Perimeter
Length, perimeter and area — Areas of rectangles and squares
Pythagoras' theorem — Pythagoras, perimeter and area
Circles and cylinders — Pi and the circumference
Exploring geometry — Exploring parallelograms and rectangles
Exploring geometry — Exploring rhombuses and squares

Term

Definition

perpendicular

at right angles to another line (see diagram) or surface

Related links:
Algebra — Substitution
Length, perimeter and area — Areas of triangles
Length, perimeter and area — Areas of parallelograms
Angles — Points, lines and intervals
3D shapes — Faces, edges and vertices
Pythagoras' theorem — Pythagoras, perimeter and area
Equations and inequalities — Equations and formulas
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

perpendicular bisector

a line that cuts an interval in half, and is at right angles to that interval

Related links:
Exploring geometry — Bisecting angles and intervals

Term

Definition

perspective

the drawing of a scene or solid object, giving an impression of having three dimensions

Related links:
3D shapes — Drawing solids

Term	Definition
phi	Greek letter (pronounced fie) used to denote the golden ratio

Related links:
Ratios and rates — Using ratios

Term	Definition
pi	Greek letter pi, , used to represent the ratio of the circumference of a circle to its diameter Writing pi as a decimal cannot be written as a terminating decimal or as a repeating decimal. It represents an irrational number. = 3.14159...

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

Term	Definition
pictogram	a graph where pictures are used to represent the data − also called a picture graph

Term	Definition
picture graph	a graph where pictures are used to represent data − also called a pictogram

Term

Definition

pie graph

(also called a sector graph) a graph where the size of each section of the circle represents a particular amount

Related links:
Representing data — Sector graphs

Term	Definition
place value	the value of a digit in a number as determined by its position Example The place value of 3 in 76 307 is 300.

Related links:
Whole numbers — Ancient number systems
Whole numbers — Roman and Greek numerals
Whole numbers — Place value and expanded notation
Whole numbers — Index notation
Decimals — What is the point?
Decimals — Changing decimals to fractions
Decimals — Adding decimals
Decimals — Multiplying and dividing by powers of 10

Term	Definition
plan	drawing showing the layout of rooms in a building as viewed from above

Related links:
The number plane — Maps and plans
Congruent and similar shapes — Scale drawings

Term	Definition
plane	a flat surface that extends endlessly in all directions (see also number plane)

Related links:
Algebra — Patterns on the number grid
2D shapes — Plane shapes
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

plane figure

a two-dimensional shape; a figure that lies on a flat surface

Examples
triangle, square, pentagon, circle, quadrilateral

Related links:
2D shapes — Plane shapes
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
Circles and cylinders — Area of a circle
Exploring geometry — Exploring trapeziums and kites
Exploring geometry — Exploring parallelograms and rectangles
Exploring geometry — Exploring rhombuses and squares

Term

Definition

Platonic solid

regular convex polyhedron with identical (congruent) regular polygons as faces

There are exactly five Platonic solids: the tetrahedron, hexahedron (cube), octahedron, dodecahedron and icosahedron.

Related links:
3D shapes — Classifying solids
3D shapes — Nets of solids

Term

Definition

abbreviation for post meridiem, which means after midday ie the time from midday until midnight (afternoon and evening)

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

Term

Definition

point

represents a position, usually marked by a small round dot and named with a capital letter

Related links:
Integers — What are directed numbers?
Algebra — Patterns on the number grid
2D shapes — Rotational symmetry
2D shapes — Translation
2D shapes — Reflection
2D shapes — Rotation
Angles — Points, lines and intervals
Angles — How to name an angle
Representing data — Line, conversion and step graphs
Representing data — Travel graphs
Representing data — Histograms and polygons
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
Congruent and similar shapes — Scale factor
Exploring geometry — Constructing lines and angles

Term

Definition

point symmetry

applies to a plane figure that will be exactly the same when rotated through 180° (eg the letters S and N, a square)

Related links:
2D shapes — Rotational symmetry

Term

Definition

polygon (2D)

a two-dimensional shape where three or more straight line segments are joined together to form a closed figure (see also plane figure)

A hexagon

Examples
triangle, square, pentagon, quadrilateral, rectangle

Related links:
Length, perimeter and area — Areas of rectangles and squares
Length, perimeter and area — Areas of triangles
2D shapes — Plane shapes
2D shapes — Classifying triangles
3D shapes — Classifying solids
Congruent and similar shapes — Congruent shapes
Exploring geometry — Exploring parallelograms and rectangles
Exploring geometry — Exploring rhombuses and squares

Term	Definition
polygon (data)	refers to a line graph obtained by joining the midpoints of the tops of the columns in a histogram

Related links:
Representing data — Histograms and polygons
Representing data — Grouping data

Term	Definition
polygonal numbers	figurate numbers that are generated by regular polygons such as triangles, squares and pentagons

Related links:
Number theory — Further patterns in numbers

Term

Definition

polyhedron

(plural polyhedrons or polyhedra) a three-dimensional figure made by joining polygons at their edges

Examples
pyramid, rectangular prism, cube, Platonic solids

Related links:
Measuring solids — Volume of rectangular prisms
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
3D shapes — Drawing solids
3D shapes — Views of solids

Term	Definition
population (statistics)	the entire group of people, animals or other things that you want to find out about

Related links:
Analysing data — The mean

Term	Definition
positive number	a number greater than zero; a number to the right of zero on the number line (eg +4, +71, +12, +0.5, +213) Note that numbers without a sign are assumed to be positive.

Related links:
Integers — What are directed numbers?
Integers — Adding and subtracting integers
Integers — Two signs together
Integers — Multiplying integers
Integers — Dividing integers
Integers — Mixing the operations
Pythagoras' theorem — What is Pythagoras' theorem?
The number plane — Plotting positive integers
The number plane — Extending the number plane

Term	Definition
power	another name for index or exponent; a number multiplied by itself one or more times Example m⁴ = m × m × m × m means m to the power of 4. This small raised 4 shows how many ms are multiplied together.

Related links:
Whole numbers — Index notation
Whole numbers — Multiplying whole numbers
Decimals — Multiplying and dividing by powers of 10
Percentages — Changing decimals to percentages
Integers — Mixing the operations
Algebra — What is algebra?
Algebra — Recognising patterns
Length, perimeter and area — Areas of rectangles and squares
Manipulating algebra — Formulas in spreadsheets

Term	Definition
power set	the set containing all the subsets of any given set Example The power set of the set {3, 5, 8} is: { { }, {3}, {5}, {8}, {3, 5}, {3, 8}, {5, 8}, {3, 5, 8} }

Related links:
Set theory — Set relationships and Venn diagrams

Term	Definition
preferred multiples	in long division, the largest multiple of the divisor that can be easily subtracted

Related links:
Whole numbers — Long division methods

Term	Definition
prime number	an integer greater than 1 that only has two factors, itself and 1 Example The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

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

Term	Definition
principal	an amount of money invested in a financial institution, or lent to a person or organisation (see also capital)

Term

Definition

prism

a solid where each cross-section in a particular direction is exactly the same

All faces of a prism must be polygons. Prisms have no curved surfaces so cylinders are not prisms.


A prism		NOT a prism

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 — Faces, edges and vertices
3D shapes — Classifying solids
3D shapes — Nets of solids
3D shapes — Drawing solids
3D shapes — Views of solids
Circles and cylinders — Volume of a cylinder

Term	Definition
probability	a measure of the likelihood that an event will occur Probablility is measured on a scale between 0 and 1.

Related links:
Chance — The language of chance
Chance — Probability

Term	Definition
product	result of multiplication Example The product of 8 and 7 is 56, since 8 × 7 = 56.

Related links:
Whole numbers — Multiplying whole numbers
Number theory — Factors and multiples
Number theory — Factor trees
Number theory — HCF and LCM for large numbers
Number theory — Square roots
Fractions — Multiplying fractions
Fractions — Multiplying mixed numerals
Decimals — Multiplying and dividing by powers of 10
Decimals — Multiplying decimals
Integers — Multiplying integers
Algebra — Words into algebra
Algebra — Multiplying and dividing terms
Length, perimeter and area — Areas of parallelograms
Equations and inequalities — Equations to solve problems
Manipulating algebra — Reading algebra
Manipulating algebra — Factorising

Term	Definition
profit	the amount of money made by selling for more than the cost Profit = selling price − cost price

Related links:
Applying percentages — Profit and loss
Applying percentages — Finding the whole amount

Term	Definition
pronumeral	a letter of an alphabet, or a symbol, used to represent a number (see also variable and unknown)

Related links:
Algebra — What is algebra?
Algebra — Algebra pictures
Algebra — Words into algebra
Algebra — Substitution
Algebra — Picture patterns and pronumerals
Algebra — Number patterns and pronumerals
Algebra — Patterns on the number grid
Algebra — Adding and subtracting terms
Algebra — Multiplying and dividing terms
Algebra — Equivalent expressions
Measuring solids — Volume of any prism
Angles — Angle theorems
Equations and inequalities — Working backwards
Equations and inequalities — Keeping the balance
Equations and inequalities — Guess, check and improve
Equations and inequalities — Equations to solve problems
Equations and inequalities — Equations and formulas
Equations and inequalities — Inequalities
Manipulating algebra — Formulas in spreadsheets
Manipulating algebra — Factorising
Manipulating algebra — Algebraic fractions
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
proper fraction	a fraction where the numerator is less than the denominator Examples , , ,

Related links:
Fractions — What is a fraction?
Fractions — Comparing and ordering fractions
Fractions — Dividing by simple fractions
Fractions — Dividing by harder fractions

Term

Definition

protractor

a semicircular or circular tool for measuring or drawing angles

Related links:
2D shapes — Angle sum of a triangle
2D shapes — Exterior angles of triangles
2D shapes — Angle sum of a quadrilateral
Angles — How to measure an angle
Angles — Types of angles
Representing data — Sector graphs
Congruent and similar shapes — Drawing similar figures
Exploring geometry — Constructing lines and angles

Term

Definition

pyramid

a solid where the base is a polygon and the other faces are formed by triangles with a common vertex (the apex)

A pyramid is classified according to the shape of its base.


A triangular pyramid		A square pyramid

Related links:
3D shapes — Faces, edges and vertices
3D shapes — Classifying solids
3D shapes — Nets of solids
3D shapes — Drawing solids
3D shapes — Views of solids
Equations and inequalities — Equations and formulas

Term

Definition

Pythagoras

Greek mathematician and philosopher (circa 570−490 BC)

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

Term	Definition
Pythagoras' theorem	states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides

Term	Definition
Pythagorean triad	a set of three positive numbers where the largest number squared equals the sum of the squares of the other two numbers Examples {3, 4, 5} {5, 12, 13} {8, 15, 17}

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