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
sample (statistics)	part of a population from which you collect information This information is used to draw conclusions about the entire population.

Related links:
Chance — The language of chance
Chance — Listing possible outcomes
Chance — Probability
Analysing data — The mean

Term	Definition
sample space	the list of all the possible outcomes of an event

Related links:
Chance — The language of chance
Chance — Listing possible outcomes

Term	Definition
scale (drawing)	a ratio which compares a drawing or a model to the real object Image : Real life Examples 3 : 1 (drawing is 3 times larger than the real object) 1 : 3 (the real object is 3 time larger than the drawing)

Related links:
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

Term	Definition
scale (graph)	a system of ordered marks at fixed intervals referred to as a standard in measurement Examples A protractor that has scale in degrees A ruler that has scale in centimetres or inches

Related links:
Percentages — One whole is 100%
Angles — How to measure an angle
Representing data — Divided bar graphs
Representing data — Line, conversion and step graphs
Representing data — Travel graphs
Representing data — Histograms and polygons
The number plane — Graphs from equations
The number plane — Comparing lines and equations

Term	Definition
scale factor	the number you multiply each side by to enlarge or reduce a shape

Related links:
Congruent and similar shapes — Scale factor
Congruent and similar shapes — Drawing similar figures

Term

Definition

scalene triangle

a triangle in which all three sides are different lengths and all three angles are different sizes

Related links:
2D shapes — Plane shapes
2D shapes — Classifying triangles

Term

Definition

secant

a straight line which cuts a circle twice

Related links:
Circles and cylinders — Pi and the circumference

Term	Definition
section	a part of the whole; to divide into parts

Related links:
Length, perimeter and area — Areas of rectangles and squares
3D shapes — Classifying solids
3D shapes — Drawing solids
Representing data — Divided bar graphs
The number plane — Extending the number plane

Term

Definition

sector

part of a circle bounded by two radii and an arc (see also quadrant)

Related links:
Representing data — Sector graphs
Circles and cylinders — Pi and the circumference

Term

Definition

sector graph

a graph where the size of each sector of the circle represents a particular amount − also called a pie graph

Related links:
Representing data — Sector graphs

Term

Definition

segment

part of a circle bounded by a chord and an arc (see also semicircle)

Related links:
Circles and cylinders — Pi and the circumference

Term	Definition
selling price	how much retailers charge for goods

Related links:
Applying percentages — Profit and loss

Term

Definition

semicircle

half a circle

Related links:
2D shapes — Plane shapes
Circles and cylinders — Pi and the circumference
Circles and cylinders — Area of a circle

Term

Definition

set

a collection of objects or numbers

A capital letter is used to denote a set and its members (elements) are written inside braces { }.

Examples
The set of dwarves in Snow White:
D = {Doc, Happy, Grumpy, Bashful, Sneezy, Dopey, Sleepy}
D has 7 elements and is a finite set.

The set of positive even numbers:
E = {2, 4, 6, 8, 10, 12, ...}
The three dots show there are more members of the set. E has infinitely many members.

Related links:
Number theory — Simple number patterns
Algebra — What is algebra?
Pythagoras' theorem — What is Pythagoras' theorem?
Representing data — Scatter diagrams
Representing data — Line, conversion and step graphs
Representing data — Dot plots
The number plane — Plotting positive integers
Analysing data — The mean
Analysing data — The mode, the median and range

Term

Definition

similar figures

figures of the same shape but not the same size

The angles of similar figures are the same size, but their side lengths are unequal, although in the same proportion.

Similar triangles

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

Term	Definition
simple event	chance events that have equally likely outcomes

Related links:
Chance — The language of chance

Term	Definition
simple interest	percentage rate per year paid on a loan Generally charged on money borrowed for a short period of time (interest stays the same for each term). Formula SI = principal × rate × time where: principal is the amount borrowed rate is the percentage charged per year time is the number of years of the loan

Term	Definition
simplify	find the simplest possible expression for Example Simplify . (The simplest form of is ).

Related links:
Whole numbers — Grouping symbols
Number theory — Highest common factor (HCF)
Fractions — Equivalent fractions
Fractions — Multiplying mixed numerals
Decimals — Changing decimals to fractions
Percentages — Writing percentages as fractions
Integers — Two signs together
Integers — Mixing the operations
Algebra — Adding and subtracting terms
Algebra — Adding and subtracting terms
Algebra — Multiplying and dividing terms
Algebra — Multiplying and dividing terms
Manipulating algebra — Algebraic fractions
Ratios and rates — What is a ratio?

Term	Definition
skew edges	edges that lie on different planes and never intersect, and are not parallel

Related links:
3D shapes — Faces, edges and vertices

Term

Definition

solid

a three-dimensional figure

Examples
cube, cylinder, prism, pyramid, sphere

Related links:
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
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
solution	the value/s that give a true statement when substituted for the unknown in an equation Example For the equation a + 5 = 8, the solution is a = 3.

Related links:
Equations and inequalities — Guess, check and improve
Equations and inequalities — A formal approach
Equations and inequalities — Equations to solve problems
Equations and inequalities — Inequalities

Term	Definition
solve	find the value for the unknown quantity Examples Solve 3 + k = 8, means find the value of k that makes this equation true. Therefore k = 5 is the solution.

Related links:
Algebra — Substitution
Algebra — Recognising patterns
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 — Inequalities

Term

Definition

speed

a measure of how fast an object is moving; that is, the distance it travels in a certain period of time

Example
A car's speed is usually measured in kilometres per hour (km/hr). The rate of speed can also be expressed in metres per second (m/s).

Related links:
Integers — Multiplying integers
Ratios and rates — Rates

Term

Definition

sphere

a solid in the shape of a round ball

Every point on the surface of a sphere is the same distance (radius) from the centre point.

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

Term	Definition
spreadsheet	a table comprised of rows and columns for entering data and headings Computer spreadsheet programs allow you enter formulas that will manipulate data electronically and update results immediately when data is changed.

Related links:
Representing data — Graphs and spreadsheets
Manipulating algebra — Formulas in spreadsheets
Analysing data — Analysing tables

Term	Definition
square (operation)	to multiply a number by itself Example 8² = 8 × 8 = 64

Related links:
Number theory — Further patterns in numbers
Pythagoras' theorem — Length of the hypotenuse
Pythagoras' theorem — Length of any side
Pythagoras' theorem — Pythagoras, perimeter and area
Manipulating algebra — Reading algebra

Term

Definition

square (plane shape)

a quadrilateral with all sides equal in length and with all angles right angles and with opposite sides parallel

Related links:
Length, perimeter and area — Areas of rectangles and squares
2D shapes — Plane shapes
2D shapes — Classifying quadrilaterals
Circles and cylinders — Area of a circle
Congruent and similar shapes — Which shapes are similar?
Exploring geometry — Exploring rhombuses and squares

Term	Definition
square number	result of multiplying a number by itself (squaring) Examples These first ten square numbers are found by squaring the first ten whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 (ie 1², 2², 3², 4², 5², 6², 7², 8², 9², 10²).

Related links:
Whole numbers — Index notation
Number theory — Further patterns in numbers
Number theory — Square roots
Algebra — Recognising patterns

Term

Definition

square prism

a prism that has a square cross-section

Related links:
Measuring solids — Volume of rectangular prisms

Term

Definition

square pyramid

a pyramid with a square base

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

Term	Definition
square root	name for symbol that indicates you should "take the square root of" (ie the opposite operation of squaring) means "What number do you multiply by itself to give y?" Example = 5 since 25 = 5²

Related links:
Number theory — Square roots
Number theory — Cube roots
Pythagoras' theorem — Length of the hypotenuse

Term	Definition
squared	multiplied by itself; raised to the power of 2 (see also square number) Example Five squared is: 5² = 5 × 5

Related links:
Whole numbers — Index notation
Number theory — Square roots
Decimals — Changing decimals to fractions
Algebra — What is algebra?
Algebra — Words into algebra
Length, perimeter and area — Areas of rectangles and squares

Term

Definition

stem-and-leaf plot

groups the actual scores and lists them in order horizontally

The data themselves create something similar to horizontal columns like a sideways histogram or dot plot.

Related links:
Representing data — Stem-and-leaf plots
Analysing data — Analysing stem-and-leaf plots

Term	Definition
step graph	a special type of line graph that jumps in steps

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

Term

Definition

straight angle

an angle of exactly 180° (forms a straight line)

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

Term	Definition
subset	where all the elements of one set form part of another set The symbol means "is a subset of". Examples {1, 2, 3} is a subset of {counting numbers} {6, 8} {even numbers}

Related links:
Set theory — Applying Venn diagrams
Set theory — Set relationships and Venn diagrams

Term	Definition
substitute	replace one thing with another; in a formula, replace pronumerals with numerical values Example Given that a rectangle"s breadth is 4 cm and its length is 6 cm, you can find the area of the rectangle in cm² by substituting the numerical values (4 for b and 6 for l) in the formula A = l × b.

Related links:
Algebra — Substitution
Algebra — Picture patterns and pronumerals
Equations and inequalities — Working backwards
Equations and inequalities — Keeping the balance
Equations and inequalities — Guess, check and improve
Equations and inequalities — Equations and formulas

Term	Definition
subtraction	the opposite process to addition Example 17 − 9 = 8 is a subtraction. It is the opposite of the addition 9 + 8 = 17. 8 is the difference between 9 and 17.

Related links:
Whole numbers — Subtracting whole numbers
Fractions — Adding and subtracting fractions
Decimals — Subtracting decimals
Integers — Adding and subtracting integers
Algebra — Adding and subtracting terms

Term	Definition
successful event	when the result you want is achieved (also called favourable event) Example If you are trying to roll an even number on a die, the successful events are 2, 4 or 6.

Related links:
Chance — The language of chance

Term	Definition
sum	result of adding; total Example The sum of 15 and 13 is 28, since 15 + 13 = 28.

Related links:
Number theory — Divisibility tests
Decimals — Adding decimals
Algebra — Words into algebra
2D shapes — Angle sum of a triangle
2D shapes — Exterior angles of triangles
2D shapes — Exterior angles of triangles
Equations and inequalities — Equations to solve problems

Term	Definition
superimpose	lay one thing exactly over the top of another

Related links:
Congruent and similar shapes — Congruent shapes

Term	Definition
supplement	the amount needed to make 180° When the sum of two angles is 180°, each angle is the supplement of the other. Example The supplement of 60° is 120°.

Related links:
Angles — Types of angles
Angles — Angles in parallel lines

Term

Definition

supplementary angles

two angles that add together to make 180° (see also co-interior angles)

Related links:
Angles — Types of angles
Angles — Angles in parallel lines

Term	Definition
surface	the outside of a solid or any bounded part of the outside; a continuous two-dimensional set of points such as a plane Examples The surface of the Earth The six square, plane faces of a cube

Related links:
Length, perimeter and area — Areas of rectangles and squares
Length, perimeter and area — Areas of triangles
Measuring solids — Surface area
3D shapes — Classifying solids

Term

Definition

surface area

the number of square units needed to cover the outside of a solid

Example
The diagram shows three of the six faces of a cube with edge 3 cm and area 9 cm².

The total surface area is 6 × 9 cm² = 54 cm²

Related links:
Measuring solids — Surface area

Term	Definition
survey	a method of collecting information through an interview or a questionnaire

Related links:
Representing data — Divided bar graphs
Representing data — Histograms and polygons
Representing data — Dot plots
Representing data — Stem-and-leaf plots
Analysing data — The mean

Term

Definition

symmetry

can refer to line symmetry (see also line of symmetry) or point symmetry

A plane figure has line symmetry if one half of it can be folded over a line to fit exactly on the other half. It has point symmetry if one half of it can be rotated about a point to fit exactly on the other half.

Example
A square has symmetry because it can be folded into identical halves. Since a square can be folded four different ways into identical halves, it has four axes of symmetry as shown in the diagram.

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