Maths Terms for 11-13 Yr Olds

One-dimensional, two-dimensional, three-dimensional. One-dimensional: able to be identified by one co-ordinate, for example points on a line.

Two-dimensional: requiring two co-ordinates for identification, for example points in a plane. Also used to describe flat geometric shapes.

Three-dimensional: requiring three co-ordinates for identification, for example points in space. Also used to describe solid geometric shapes

An angle between zero and ninety degrees.

The operation to combine two numbers or quantities to form a further number or quantity, the sum or total. Addition is the inverse operation to subtraction.

The part of mathematics that deals with generalised arithmetic. Letters are used to denote variables and unknown numbers and to state general properties. Example: a(x + y) = ax + ay shows a relationship that is true for any numbers a, x and y. Adjective: algebraic. See also equation, formula, identity and expression.

Where two straight lines are cut by a third, as in the diagrams, the angles d and f (also c and e) are alternate.

A clock usually with 12 equal divisions labelled 1 to 12 to represent hours. Each twelfth is subdivided into five equal parts providing sixty minor divisions to represent minutes. The clock has two hands that rotate about the centre. The minute hand completes one revolution in one hour whilst the hour hand completes one revolution in 12 hours.

Where two line segments meet at a point, this term describes the measure of rotation (normally clockwise) from one of the line segments to the other. In this way, a right angle measures 90 degrees, an acute angle is between 0 and 90 degrees, an obtuse angle is between 90 and 180 degrees and a reflex angle is greater than 180 degrees.

A number or result that is not exact. In a practical situation an approximation is sufficiently close to the actual number for it to be useful. Verb: approximate. Adverb: approximately. When two values are approximately equal, the first symbol below is used instead of the normal = sign. If all that's known is the order of magnitude, the second symbol below is used.

For example, there are approximately 365 days in a year (there are 365.25 to be exact, making each fourth year a leap year with 366 days), and the mass of the Sun in kg is known to be roughly 2 with 24 zeroes after it.

A portion of a curve. Often used for a portion of a circle.

A measure of surface. Area is usually measured in square units e.g. square metres.

A sequence of numbers in which terms are generated by adding or subtracting a constant amount to the preceding term. Examples: 3, 11, 19, 27, 35, . where 8 is added; 4, -1, -6, -11, . where 5 is subtracted.

An ordered collection of counters, numbers etc. in rows and columns.

See 'mean’. Compare with 'mode' and 'median'.

A fixed, reference line along which or from which distances or angles are measured, and shapes are translated. For axis of symmetry, see 'reflection symmetry'.

A format for representing statistical information. Bars, of equal width, represent frequencies and the lengths of the bars are proportional to the frequencies. Sometimes called bar graph.

Similar to a bar chart, the width of bars is reduced so that they appear as lines. The lengths of the bar lines are proportional to the frequencies. Sometimes called bar line graph.

The direction of a line specified by the angle it makes with a North-South line. The angle is measured in degrees from North in a clockwise direction. Bearings are usually given in a three figure format.

In geometry, to divide into two equal parts.

A point, line or plane that divides (a line, an angle or a solid shape) into two equal parts. A perpendicular bisector is a line at right angles to a line segment that divides it into two equal parts.

A diagram to represent a set of ranked numerical data. A box represents the interquartile range. Lines from the points representing the maximum and minimum values to the box are sometimes referred to as whiskers. The median is marked on the box by a line.

Symbols used to show items that should be treated as together or as having priority. In arithmetic and algebra, operations within brackets are given priority. Example: 2 x (3 + 4) = 2 x 7 = 14 whereas 2 x 3 + 4 = 6 + 4 = 10.

One way to simplify a fraction. The numerator and denominator are divided by a common factor. Also to ’reduce’ a fraction. Example: to simplify 6/16 the fraction is 'cancelled down' when the numerator and denominator are divided by 5 to give 1/3.

Volume, i.e. a measure of three-dimensional space, applied to liquids, materials that can be poured or the space within containers. Units include cubic centimetres and litres - a

A system used to define the position of a point in two-dimensional and three-dimensional space. Two axes at right angles to each other are used to define the position of a point in a plane. The convention is to label the horizontal axis as the x-axis and the vertical axis as the y-axis. In this case, the origin is the intersection of the axes. The ordered pair of numbers (x, y) that defines the position of a point is the coordinate pair. Each of the numbers is a co-ordinate. The numbers are also known as Cartesian co-ordinates, after the French mathematician, René Descartes.

Data arising from measurements taken on a categorical (unordered discrete) variable. Examples: pupils\' favourite colours; states of matter- solids, liquids, gases, gels etc; nutrient groups in foods - carbohydrates, proteins, fats etc; settlement types - hamlet, village, town, city etc; and types of land use - offices, industry, shops, open space, residential etc.

Prefix meaning one-hundredth (of)

Symbol: cl. A unit of volume equivalent to one-hundredth of a litre.

Symbol: cm. A unit of linear measure, one hundredth of a metre.

The middle point.

A straight line segment joining two points on a circle or other curve.

A set of points in a plane at a fixed distance (the radius) from a fixed point (the centre) also in the plane; alternatively the path traced by a single point travelling in a plane at a fixed distance (the radius) from a fixed point (the centre) in the same plane. One half of a circle cut off by a diameter is a semi-circle.

The length of a circle (its perimeter). If the radius of a circle is r units, and the diameter d units, then the circumference is 2

In the direction in which the hands of clock travel, and the direction bearings and angles are usually measured. Anti-clockwise or counter-clockwise are terms used for the opposite direction.

Often used for the numerical coefficient. More generally, a factor of an algebraic term. Example: in the term 4xy, 4 is the numerical coefficient of xy but x is also the coefficient of 4y and y is the coefficient of 4x.

A fraction where the numerator and denominator are both integers. Also known as a simple or vulgar fraction. Contrast with a compound or complex fraction where the numerator or denominator or both contain fractions. See also decimal fraction.

Two angles with the sum of 90 degrees

Measures with two or more dimensions. Examples: speed calculated as distance

Adjective to describe a line or surface curving inwards (like the shape of a cave). A concave polygon has at least one re-entrant angle i.e. one interior angle greater than 180 degrees

A 3D shape consisting of a circular base, a vertex (point) in a different plane, and line segments joining all the points on the circle circumference to the vertex.

Adjective describing two or more geometric figures that are the same in every way except their position in space. Example: Two figures, where one is a reflection of the other, are congruent since one can be transposed onto the other without changing any angle or edge length.

Noun: congruence.

Following in order. Consecutive numbers are adjacent in a count. Examples: 5, 6, 7 are consecutive numbers. 25,30,35 are consecutive multiples of 5. In a polygon, consecutive sides share a common vertex and consecutive angles share a common side.

A number or quantity that does not vary. Example: in the equation y = 3x + 6, the 3 and 6 are constants, whereas x and y are variables.

Data arising from measurements taken on a continuous variable (examples: lengths of caterpillars; weight of crisp packets) that can take on an infinite or effectively infinite set of values. 

Adjective to describe a line or surface that describes outwards, like the shape of a circle. .

A convex polygon has all its interior angles less than or equal to 180 degrees

In elementary geometry, a point where two or more lines or line segments meet.

A measure of the strength of the association between two variables. High correlation implies a close relationship and low correlation a less close one. If an increase in one variable results in an increase in the other, then the correlation is positive. Example: there should be a positive correlation between your understanding of maths and your enjoyment of it. If an increase in one variable results in a decrease in the other, then the correlation is negative. The term zero correlation does not necessarily imply no relationship, but merely no linear relationship.

Where two straight-line segments are intersected by a third, as in the diagrams, the angles

In geometry, a section in which the plane that cuts a figure is at right angles to an axis of the figure. Example: In a cube, a square is revealed when a plane cuts at right angles through a face.

1. In geometry, a three-dimensional figure with six identical, square faces. Adjoining edges and faces are at right angles.

2. In number and algebra, the result of multiplying the same value by itself, then by itself again.

Example: 2 x 2 x 2 is written a 2³.

This is said as '2 cubed', or '2 to the power of three'.

Adjective to describe a mathematical expression of degree three, i.e. with a power equal to 3. 

A cubic polynomial is one of the type ax³ + bx² + cx +d, where the highest power is equal to 3. The coefficients b,c, and d could equal zero which would just leave the cubic term.

Symbol: cm³.

A curve described by an algebraic equation containing at least one cubic term, i.e. a term raised to the power of three, and no terms with higher powers than three.

Symbol: m³.

A three-dimensional figure with six rectangular faces. Different to a cube in that the lengths of the sides are not necessarily the same; a 3D rectangle.

A graph for displaying cumulative frequency. At a given point on the horizontal axis the sum of the frequencies of all the values up to that point is represented by a point. These graphs always curve upwards because the vertical co-ordinates will be proportional to the sum of frequencies, which can't decrease.

A three-dimensional object whose uniform cross-section is a circle. A right cylinder can be defined as having circular bases with a curved surface joining them, this surface formed by line segments joining corresponding points on the circles. The centre of one base lies over the centre of the second.

Information of a quantitative nature consisting of counts or measurements. Initially data are nearly always counts or things like percentages derived from counts. When they refer to measurements that are separate and can be counted, the data are discrete. When they refer to quantities such as length or capacity that are measured, the data are continuous. Singular: datum.

A means of storing sets of data, for example in an Excel spreadsheet.

Relating to the base ten. Most commonly used synonymously with decimal fraction where the number of tenths, hundredth, thousandths etc. are represented as digits following a decimal point. The decimal point is placed at the right of the units column. Each column after the decimal point is a decimal place. Example: The decimal fraction 0.275 is said to have three decimal places. The system of recording with a decimal point is decimal notation. Where a number is rounded to a required number of decimal places, to 2 decimal places for example, this may be recorded as 2 d.p.

Tenths, hundredths, thousandths etc. represented by digits following a decimal point. Example 0.125 is equivalent to 1/10 + 2/100 + 5/1000 or 125/1000 or 1/8

The decimal fraction representing 1/8 is a terminating decimal fraction since it has a finite number of decimal places. Other fractions such as 1/3 produce recurring decimal fractions.

These have a digit or group of digits that is repeated indefinitely.

In the measurement of angles, a unit of turn, usually clockwise.

One whole turn is equal to 360 degrees, written 360^o.

In the notation of common fractions, the number written below the line i.e. the divisor. Example: In the fraction 1/3, the denominator is 3.

The length of any of the chords of a circle or sphere that pass through it's centre. Compare with 'chord'.

The amount by which one number or value is greater than another, obtained by subtracting the smaller from the larger.

One of the symbols of a number system- most commonly the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Examples: the number 29 is a 2-digit number; there are three digits in 2.95. The position or place of a digit in a number conveys its value.

A clock that displays the time as hours and minutes passed, usually since midnight. Example: four thirty in the afternoon is displayed as 16:30.

Data resulting from measurements taken on a discrete variable, i.e. one that can't be divided up into infinitely small parts (examples: value of coins in pupils’ pockets; number of peas in a pod).

Discrete data may be grouped. Example: Having collected the shoe sizes of pupils in the school, the data might be grouped into ’number of pupils with shoe sizes 3, 5, 6, 8, 9, 11, etc.

The property of being divisible by a given number. Example: A test of divisibility by 9 checks if a number can be divided by 9 with no remainder.

1. An operation on numbers interpreted in a number of ways. Division can be sharing - the number to be divided is shared equally into the stated number of parts; or grouping - the number of groups of a given size is found. Division is the inverse operation to multiplication.

2. On a geometric scale, one part. Example: Each division on a ruler might represent a millimetre.

A polyhedron with twelve faces. The faces of a regular dodecahedron are regular pentagons. A dodecahedron has 20 vertices and 30 edges.

1. The vertical height of a point above a base (line or plane).

2. The angle of elevation from one point A to another point B is the angle between the line AB and the horizontal line through A.

A transformation of the plane in which lengths are multiplied whilst directions and angles are preserved. A centre and a positive scale factor are used to specify an enlargement. The scale factor is the ratio of the distance of any transformed point from the centre to its distance from the centre prior to the transformation. Any figure and its image under enlargement are 'similar' - having the same internal angles and ratios between the length of its sides.

Symbol: =. Read as 'is equal to' or 'equals'. Having the same value. Example: 7 -  2 = 4 + 1 since both expressions, 7 - 2 and 4 + 1 have the same value, 5.

The equals sign combines the two expressions together and makes an equation.

An adjective describing a polygon with sides of equal length.

Find the value of a numerical or an algebraic expression.

Also known as 'index' or 'power'. A number, positioned above and to the right of another, indicating repeated multiplication. 

A mathematical form expressed symbolically. Examples: 7 + 3; a² + b².

An expression is different from an equation in that it doesn't have an equals sign =. 

In geometry, one of the flat surfaces of a solid shape. Example: a cube has six faces.

When a number, or polynomial in algebra, can be expressed as the product of two numbers or polynomials, these are factors of the first. Expressing a number of polynomial as a product of its factors is known as factorising.

Example: 1, 2, 3, 4, 6 and 12 are all factors of 12.

Example: (x-1) and (x+4) are factors of (x² + 3x - 4).

Symbol: ft. An imperial measure of length. 1 foot = 12 inches. 3 feet = 1 yard. 1 foot is approximately 30 cm.

Imperial measurements are rarely used in modern times. 

An equation linking sets of physical variables, and allowing them to be evaluated, i.e. allowing their value to be found using other variables. Plural: formulae.

The result of dividing one integer by a second integer, which must be non-zero. The dividend (number being divided) is the on the numerator (top of the fraction) and the non-zero divisor is on the denominator (bottom of the fraction). Example: 1 divided by 3 is written as 1/3.

Symbol: gal. An imperial measure of volume or capacity, equal to the volume occupied by ten pounds of distilled water. In the imperial system, 1 gallon = 4 quarts = 8 pints. One gallon is just over 4.5 litres. Imperial units are rarely used in modern times.

The aspect of mathematics concerned with the properties of space and figures or shapes in space.

A measure of the slope of a line. On a coordinate plane, the gradient of the line through the points (x1, y1) and (x2, y2) is defined as (y2 - y1) / (x2 - x1).

The gradient may be positive, negative or zero depending on the values of the co-ordinates. In a straight line graph of the form y = mx+c, m represents the gradient.

Symbol: g. The unit of mass equal to one thousandth of a kilogram.

A diagram showing a relationship between variables. Adjective: graphical. A graph showing information that isn't continuous is often called a 'chart' instead.

A polygon with seven sides or edges.

A polygon with six sides or edges. Adjective: hexagonal, having the form of a hexagon.

The common factor of two or more numbers which has the highest value. Example: 16 has factors 1, 2, 4, 8, 16. 24 has factors 1, 2, 3, 4, 6, 8, 12, 24.

56 has factors 1, 2, 4, 7, 8, 14, 28, 56. The common factors of 16, 24 and 56 are 1, 2, 4 and 8. Their highest common factor is 8.

A particular form of representation of grouped data. Segments along the x axis are proportional to the class interval. Rectangles are drawn with the line segments as bases. The area of the rectangle is proportional to the frequency in the class. Where the class intervals are not equal, the height of each rectangle is called the frequency density of the class.

Parallel to the horizon. Also in the direction of the x axis in a Cartesian co-ordinate system.

A polyhedron with 20 faces. In a regular icosahedron all faces are equilateral triangles.

An equation that holds for all values of the variables, as opposed to a normal equation which has only one or two fixed solutions. An equals sign with three horizontal lines rather than two is sometimes used when writing an identity. For example the identity below is true no matter what the values of a and b are.

A unit of measurement system historically used in the United Kingdom and other English speaking countries. Units include inch, foot, yard, mile, acre, ounce, pound, stone, ton, pint, quart and gallon. Now largely replaced by metric units.

An improper fraction has a numerator that is greater than its denominator. Example: 9/4 is improper and could be expressed as the mixed number 2 1/4.

Symbol: in. An imperial unit of length. 12 inches = 1 foot. 36 inches = 1 yard. 

Statements such as b > c are inequalities.

They differ from equations in that they don't have equals signs and don't have fixed solutions, only boundary solutions. For example in the above it is known that b must be at least greater than c, but how much greater is not known. Boundary solutions to inequalities can be indicated graphically using shading.

Any of the positive or negative whole numbers and zero. Examples: -2, -1, 0, +1, +2. As opposed to decimal numbers.

The value of the non-zero coordinate of the point where a line on a graph cuts an axis. The y intercept is given the symbol c in straight line graphs of the form y = mx + c.

At a vertex of a polygon, the angle that lies within the polygon.

To have an intersect is to have a common point or points. Examples: Two intersecting lines intersect at a point; two intersecting planes intersect in a line.

Operations that, when they are combined, leave the entity on which they operate unchanged. Examples: addition and subtraction are inverse operations e.g. 5 + 6 - 6 = 5. Multiplication and division are inverse operations e.g. 6 × 10 / 10 = 6.

Some operations, such as reflection in the x-axis, are self-inverse.

A number that is not an integer and cannot be expressed as a common fraction with a non-zero denominator. Real irrational numbers, when expressed as decimals, are infinite, nonrecurring decimals.

Examples: the square root of three. Pi is also an irrational number.

A triangle in which two sides have the same length and consequently two angles are equal. This definition includes an equilateral triangle as a special case.

Symbol: kg. The base unit of mass in SI units ('Système International d'Unités' in French, also known as metric). 1kg. = 1000g.

Symbol: km. A unit of length in SI units ('Système International d'Unités' in French, also known as metric). 1km. = 1000m.

A set of adjacent points that has length but no width. A curve. A straight line is completely determined by two of its points, say A and B. The part of the line between any two of its points is a line segment.

A line drawn on a scatter graph to represent the best estimate of an underlying linear relationship between the variables.

In algebra, an adjective describing an expression, equation or relationship of degree one. Example: 2x + 3y = 7 is a linear equation. This linear equation with its two variables, x and y, can be represented as a straight line graph. The relationship between x and y is linear.

Symbol: l. A metric unit used for measuring volume or capacity. A litre is equivalent to 1000 cubic centimetres

The set of all points that satisfy given conditions. Example: in 3-D the locus of all points that are a given distance from a fixed point is a sphere. Plural: loci.

The common multiple of two or more numbers which has the lowest value. Example: 3 has the multiples 3, 6, 9, 12, 15, 18, 21, 24, etc. 4 has the multiples 4, 8, 12, 16, 20, 24... and 6 has the multiples 6, 12, 18, 24, 30... 

The common multiples of 3, 4 and 6 include 12, 24 and 36. So the lowest common multiple of 3, 4 and 6 is 12.

A characteristic of a body, relating to the amount of matter within it. Mass differs from weight, the force with which a body is attracted towards the earth’s centre. Whereas, under certain conditions, a body can become weightless, mass is constant. In a constant gravitational field weight is proportional to mass.

A measure of the average of a set of data, calculated by adding up all terms and dividing by the number of terms in the set. For example the mean of 3, 5, and 13 is the numbers added together (21) divided by the amount of numbers (3) which works out as 7.

The mean takes account of all values and finds the overall average. Finding the mean is the most common way of measuring a data set's average, but can be problematic if one or two anomalous (wrong) values are taken and skew the result.

The 'median' is the middle value in a data set when the set is arranged in order from smallest to largest. For example in 3, 4, 5, 6, 7, the median value is 5. For sets containing an even amount of numbers, the median is halfway between the central pair.

The median is another way of analysing a data set, and along with the mean and mode is another form of an 'average'. In some situations it would be more appropriate, such as when the highest and lowest values are expected to be large and inaccurate.

In the context of geometric figures this noun just means the process of measuring or calculating angles, lengths, areas and volumes.

Symbol: m. The base unit of length in SI ('Système International d.Unités' in French, also known as metric).

Units of measurement in the metric system. Metric units include the metre, centimetre, millimetre, kilometre, gram, kilogram, litre and millilitre. The metric system was developed in the 18th century in France. Most of the world now uses a modern form of metric units known as SI units (Système International d'Unités in French), especially in science and technology. Some exceptions exist, for example in the UK draught beer must be sold in pints, and speedometers must diplay miles per hour, which are imperial units.

An imperial measure of length. 1 mile = 1760 yards. Five miles is approximately 8 kilometres.

Prefix meaning 'one-thousandth'.

Symbol: ml. One thousandth of a litre.

Symbol: mm. One thousandth of a metre.

The name for the symbol -, which represents the operation of subtraction.

Unit of time. One-sixtieth of an hour. 1 minute = 60 seconds.

In the measurement of angles, 1/60 of a degree is also known as a minute.

A whole number and a fractional part expressed as a common fraction.

Example: 1 2/3 (one and two thirds) is a mixed fraction. Also known as a mixed number.

The most common value in a set of data. For example in 2, 3, 3, 3, 3, 2, the modal value would be 3. If no value is repeated, no mode exists.

In some situations the mode could be thought of as the most appropriate 'average' value for the data, e.g. in samples involving whole numbers or quantities (the mean, as opposed to mode, will usually give a decimal number).

For any integers a and b, a is a mulitple of b if a third integer exists such that a = b x c.

Example: 14 = 7 x 2, 49 = 7 x 7 and 70 = 7 x 10. So 14, 49 and 70 are all multiples of 7.

-21 is also a multiple of 7 since -21 = 7(-3).

The operation of combining two numbers to give a third number, the product. Example: 12 x 3 = 36 is a multiplication. Multiplication can be seen as the process of repeated addition.

Example: 3 x 5 = 3 + 3 + 3 + 3 + 3 = 15.

Multiplication is the inverse operation of division, and it follows that 7 ÷ 5 × 5 = 7.

A number less than zero. Example: -0.25. Where a point on a line is labelled 0 and equally spaced points to one side of it are labelled -1, -2, -3 etc, these, and the numbers represented by points between them, are negative numbers.

Negative numbers can also be used to represent direction, for example when describing the velocity (speed and direction) of a projectile. If a ball hits a wall and is said to move at 20 metres per second and then -2 metres per second, this just means that at some point it moves in the opposite direction it started moving (i.e. it bounces back off the wall at a speed of 2 metres per second.

1. In geometry, a plane figure in 2D composed of polygons which by folding and joining can form a 3D polyhedron.

2. Adjective meaning 'remaining after deductions'. Example: for businesses net profit is their profit after deducting all operating costs and expenses.

Any convention for recording mathematical ideas in writing and symbols. Example: Money is recorded using decimal notation e.g. £2.50.

A symbol used to denote a number. The Roman numerals I, V, X, L, C, D and M represent the numbers one, five, ten, fifty, one hundred, five hundred and one thousand. The Arabic numerals 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are used in the Hindu-Arabic system giving numbers in the form that is widely used today.

Sometimes used to describe a non-square rectangle.

An angle greater than 90 degrees but less than 180 degrees.

A polygon with eight sides. Adjective: octagonal, having the form of an octagon.

A polyhedron (3D polygon) with eight faces. A regular octahedron has faces that are equilateral triangles.

An integer that cannot be divided neatly into two integers. Examples: 1, 3, 5, 7, etc.

A fixed point from which measurements are taken. See also Cartesian co-ordinate system. On a graph the origin is normally given by the point at which the x axis meets the y axis, at the co-ordinate (0,0).

Symbol: oz. An imperial unit of mass. In the imperial system, 16 ounces = 1 pound. 1 ounce is just over 28 grams.

In geometry, two lines that are always equidistant (the same distance apart). Parallel lines, curves and planes never meet.

A quadrilateral whose opposite sides are parallel and consequently equal in length.

A systematic arrangement of numbers, shapes, values or other objects according to a rule.

A polygon with five sides and five interior angles. Adjective: pentagonal, having the form of a pentagon.

A fraction expressed as the number of parts per hundred and recorded using the notation %. Example: One half can be expressed as 50%; the whole can be expressed as 100%.

Noun: a line or plane that is at right angles (90 degrees) to another line or plane. Adjective: having this property.

The length of any circle divided by the length of its diameter is a constant called pi, which has the symbol below.

Pi is an irrational number. It has an infinite number of non-repeating decimal places. To 8 decimal places, pi is 3.14159265.

A format for representing statistical information using pictures. Suitable pictures, symbols or icons are used to represent objects. For large numbers one symbol may represent a number of objects and a part symbol then represents a rough proportion of the number.

Also known as pie graph. A form of presentation of statistical information - within a circle, sectors like the slices of a pie represent the quantities involved. The frequency or amount of each quantity is proportional to the angle at the centre of the circle.

An imperial measure of volume applied to liquids or capacity. In the imperial system, 8 pints is equal to 4 quarts, or 1 gallon. 1 pint is just over 0.5 litres in metric (568ml).

The value of a digit that relates to its position or place in a number. Example: in 1482 the digits represent 1 thousand, 4 hundreds, 8 tens and 2 units respectively; in 12.34 the digits represent 1 ten, 2 units, 3 tenths and 4 hundredths respectively.

In geometry, a two-dimensional diagram of a three-dimensional object, usually the view from directly above.

A flat surface. A line segment joining any two points in the surface will also lie in the surface.

The process of marking points. Points are usually defined by co-ordinates and plotted with reference to a given coordinate system. Noun - a collection of these points on a graph.

An element, in geometry, that has position but no magnitude, for example a corner (vertex).

A closed plane figure bounded by straight lines. The name derives from 'many angles'.

If all interior angles are less than 180 degrees the polygon is convex. If any interior angle is greater than 180 degrees, the polygon is concave.

If the sides are all of equal length and the angles are all of equal size, then the polygon is regular; otherwise it is irregular. Adjective: polygonal.

A 3D closed solid figure bounded by surfaces (faces) that are polygonal. Its faces meet in line segments called its edges. Its edges meet at points called vertices. For a polyhedron to be convex, it must lie completely to one side of a plane containing any face. If it is not convex it is concave. A regular polyhedron has identical regular polygons forming its faces and equal angles formed by its surfaces and edges. Example: a cube. Plural: polyhedra.

Any number greater than zero. Where a point on a line is labelled 0 and equally spaced points to one side of it are labelled +1, +2, +3 etc., these, and the numbers represented by decimal points between them, are positive numbers and are read ’positive one, positive two, positive three’ etc.

Symbol: lb. An imperial unit of mass. In the imperial system, 14 lb = 1 stone. 1 lb is approximately 455 grams. 1 kilogram is approximately 2.2 lb.

The factors of a number that are prime. Example: 2 and 3 are the prime factors of 12 (12 = 2 x 2 x 3). See also 'factor'.

The process of expressing a number as the product of factors that are prime numbers.

A whole number greater than 1 that has exactly two factors, itself and 1.

Examples: 2 (factors 2, 1), 3 (factors 3, 1). 51 for example is not prime (factors 51, 17, 3, 1). All prime numbers (except 2) are odd.

A 3D solid bounded by two congruent polygons that are parallel (the bases) and lateral faces formed by joining the corresponding vertices of the polygons. Prisms are named according to the base e.g. triangular prism, quadrangular prism, pentagonal prism etc. Example: If the lateral faces are rectangular and perpendicular to the bases, the prism is a right prism.

The likelihood of an event happening. Probability is often expressed on a scale from 0 to 1. Where an event cannot happen, its probability is 0 and where it is certain its probability is 1. It can also be expressed as a fraction or a percentage. The probability of scoring 1 with a fair dice is 1/6. The chance of rolling an even number is 3/6, or 50%. The denominator of the fraction expresses the total number of equally likely outcomes. The numerator expresses the number of outcomes that represent a 'successful' occurrence. Where events are mutually exclusive and exhaustive the total of their probabilities is 1.

The result of multiplying one number by another. Example: The product of 2 and 3 is 6 since 2 x 3 = 6.

A mapping of points on a three dimensional geometric figure onto a plane according to a rule. Example: A map of the world is a projection of some type such as Mercator's projection. Plans and elevations are vertical and horizontal mappings.

A chain of reasoning that establishes the truth of a proposition.

A proper fraction has a numerator that is less than its denominator.

Example: 2/5 is a proper fraction whereas 9/4 is improper.

Any attribute or characteristic. Examples: One property of a square is that all its sides are equal. A property of rational numbers is that they can be expressed as fractions.

1. A part to whole comparison. Example: Where £20 is shared between two people in the ratio 3:5, the first receives £7.50 which is 3/8 of the whole £20. This is his proportion of the whole.

2. If two variables x and y are related by an equation of the form y = kx, then y is directly proportional to x; it may also be said that y varies directly as x. When y is plotted against x this produces a straight line graph through the origin. If two variables x and y are related by an equation of the form y = then y is inversely proportional to x; it may be said that y varies inversely as x.

An instrument for measuring angles.

A solid with a polygon as the base and one other vertex, the apex, in another plane. Each vertex of the base is joined to the apex by an edge. Other faces are triangles that meet at the apex. Pyramids are named according to the base: a triangular pyramid (which is also called a tetrahedron, having four faces), a square pyramid, a pentagonal pyramid etc.

In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other sides i.e. the sides that bound the right angle.

One of the four regions into which a plane is divided by the x and y axes in the Cartesian co-ordinate system.

A polygon with four sides.

Relating to a quality or attribute. Used as an adjective to describe conclusions and explanations that use mostly words as opposed to numbers and equations (quantitative).

Relating to a quantity or number. Used as an adjective to describe conclusions and explanations that use mostly numbers and equations as opposed to words (qualitative).

Where quantitative data is ranked in ascending order, the three quartile values (first, second and third) divide the data into four equal parts.  The difference between the first and third quartiles, used as a measure of spread, is the interquartile range. The second quartile is also the median value.

In relation to a circle, the distance from the centre to any point on the circle. Similarly, in relation to a sphere, the distance from the centre to any point on the sphere.

In statistics, a selection from a population where each sample of this size has an equal chance of being selected.

A measure of spread in statistics. The difference between the greatest value and the least value in a set of numerical data.

A part to part comparison. The ratio of a to b is usually written a : b.

Example: In a recipe for pastry fat and flour are mixed in the ratio 1 : 2 which means that the fat used has half the mass of the flour. The mixture is 1/3 fat, and 2/3 flour.

A number that is an integer or that can be expressed as a fraction whose numerator and denominator are integers, and whose denominator is not zero. 

Rational numbers, when expressed as decimals, are recurring decimals or finite (terminating) decimals. Numbers that are not rational are irrational. Irrational numbers include square roots and pi, which have infinite, non-recurring decimal places

Data as they are collected, unprocessed.

A number that is rational or irrational. Real numbers are those generally used in mathematics, science and everyday contexts.

The multiplicative inverse of any non-zero number. Example: 1/3 is the reciprocal of 3. Any number multiplied by its reciprocal gives 1. Example 1/3 x 3 = 1. (Division by 0 is not defined and 0 has no reciprocal).

A parallelogram with an interior angle of 90 degrees.

Opposite sides are equal. If adjacent sides are also equal the rectangle is a square. If adjacent sides are not equal, the rectangle is an oblong. Adjective: rectangular.

Bounded by straight lines. A closed rectilinear shape is also a polygon. A rectilinear shape can be divided into rectangles and triangles for the purpose of calculating its area.

A decimal fraction with an infinitely repeating digit or group of digits. Example: The fraction 1/3 is the decimal 0.33333, referred to as nought point three recurring and may be written as 0.3 with a dot over the three. Where a block of numbers is repeated indefinitely, a dot is written over the first and last digit in the block.

In 2D, a transformation of the whole plane involving a mirror line or axis of symmetry in the plane, such that the line segment joining a point to its image is perpendicular to the axis and has its midpoint on the axis. A 2D reflection is specified by its mirror line.

A 2-D shape has reflection symmetry about a line if an identical-looking object in the same position is produced by reflection in that line. Example:

In the shape ABCDEF, the mirror line runs through B and E. The part shape BCDE is a reflection of BAFE. Point A reflects onto C and F onto D. The mirror line is the perpendicular bisector of AC and of FD.

1. Describing a polygon, having all sides equal and all internal angles equal.

2. Describing a tessellation, using only one kind of regular polygon. Examples: squares, equilateral triangles and regular hexagons all produce regular tessellations.

A common property or connection between two or more variables. Example: in a linear graph of the form y = 2x, there is a linear relationship between x and y. For every x, y is half the size. Compare with 'correlation'.

In the context of division requiring a whole number answer (quotient), the amount remaining after the operation. Example: 29 divided by 7 = 4 remainder 1.

A vector that is equivalent to the vector sum of two or more vectors.

A parallelogram with all sides equal.

One quarter of a complete turn. An angle of 90 degrees. An acute angle is less than one right angle. An obtuse angle is greater than one right angle but less than two. A reflex angle is greater than two right angles. Sometimes shortened to 'right' and used as an adjective, e.g. 'in a right cylinder the centre of one circular base lies directly over centre of the other'.

In 2D, a transformation of the whole plane which turns about a fixed point, the centre of rotation. A is specified by a centre and an (anticlockwise) angle.

A 2D shape has rotation symmetry about a point if an identical-looking shape in the same position is produced by a rotation through some angle greater than 0 degrees and less than 360 degrees.

A subset of a population. By carrying out a random survey of some school pupils for example, the pupils you survey would make up the sample, and all the pupils in that school would make up that population.

In statistics, samples are used to make inferences (estimated conclusions) about a larger population without having to survey the whole population.

Scalar quantities have magnitude (size) but no direction. Temperature, for example, is a scalar. This sets them apart from vectors, which have size and direction (for example gravitational attraction, which acts towards the centre of a mass (mostly the Earth) and varies in size depending how far you are from the Earth). 

A measuring device usually consisting of points on a line with equal intervals. Examples: a ruler is a type of scale, as is an axis on a graph.

For two similar geometric figures, the ratio of corresponding edge lengths.

A triangle with no two sides equal and consequently no two angles equal.

A graph on which paired observations are plotted and which may indicate a relationship between the variables. Example: The heights of a number of people could be plotted against their arm span measurements. If height is roughly related to arm span, the points that are plotted will tend to lie along a line.

A plane geometrical configuration formed by cutting a solid figure with a plane. Example: A section of a cube could be a triangle, quadrilateral, pentagon or hexagon according to the direction of the plane cutting it.

The region within a circle bounded by two radii and one of the arcs they cut. Example:

The smaller of the two sectors is the minor sector and the larger one the major sector.

1. The part of a line between two points.

2. Within a circle, the region bound by an arc and the chord joining its two end points.

The smaller of the two regions, is the minor segment and the larger is the major segment.

A succession of terms formed according to a rule. There is a definite relation between one term and the next or between each term and its position in the sequence. Example: for the sequence 1, 4, 9, 16, 25 etc., each term is the square of number of the term's position in the sequence.

A well-defined collection of objects or numbers (themselves then called called members or elements).

A drawing instrument for constructing parallel lines, perpendicular lines and certain angles.

The run of digits in a number that is needed to specify the number to a required degree of accuracy. Additional zero digits may also be needed to indicate the number's magnitude. Examples: To the nearest thousand, the numbers 125 000, 2 376 000 and 22 000 have 3, 4 and 2 significant figures respectively; to 3 significant figures 98.765 is written 98.8

A geometric figure is similar to another if it is congruent to an enlargement of the other. Any two squares are similar, as are any two circles.

A fraction where the numerator and denominator are both integers. Also known as a common or vulgar fraction.

A closed surface, in three-dimensional space, consisting of all the points that are a given distance from a fixed point, the centre. A hemi-sphere is a half-sphere. Adjective: spherical.

In geometry, a 2D quadrilateral with four equal sides and four internal angles that are all right angles.

A number that can be expressed as the product of two equal numbers. Example 36 = 6 x 6 and so 36 is a square number.

A format for displaying grouped data. Class intervals form the stem and all observations are listed in order against them, forming the leaves. The numbers 29, 16, 18, 8, 4, 16, 27, 19, 13, 15 could be displayed as:

The 'class interval' is the tens digit of the numbers. The diagram resembles a histogram on its side.

Where a population has been divided into strata based on common characteristics, a random sample drawn from each of the strata. Example: for the purposes of a school survey the pupils might be divided into age groups. The size of the sample drawn at random from each age group might be proportional to the relative sizes of the different age group for greater precision.

An expression including one or more square roots (or cube roots, fourth roots, etc.)

A set of points defining a space in two or three dimensions.

A plane figure has symmetry if it is invariant under (unchanged after) a reflection or rotation i.e. if the effect of the reflection or rotation is to produce an identical-looking figure in the same position. See also reflection symmetry, rotation symmetry. Adjective: symmetrical.

To make marks to represent objects counted, and record these marks in a table (tally chart).

1. A line that touches a curve at one point only.

2. A trigonometric function (more on these at GCSE level).

A solid with four triangular faces. A regular tetrahedron has faces that are equilateral triangles. Plural: tetrahedra.

A mathematical statement derived from previously accepted premises and established by means of a proof. A 'theory' is slightly different - this is a testable model that can be used to make predictions, but isn't yet proven.

In geometry, a type of transformation in which every point of a shape moves the same distance in the same direction; a transformation that is  specified by a distance and direction (vector).

A quadrilateral with exactly one pair of sides parallel.

A branching, decision diagram in which probabilities may be assigned to each branch and used to determine the probability of any outcome of combined or compound events.

A polygon with three sides. Adjective: triangular, having the form of a triangle.

Not changing; remaining constant. Uniform acceleration, for example, would be to increase speed at a constant rate. Gravitational acceleration on Earth is uniform up to the point of terminal velocity- a falling body gains an extra 9.8 metres per second of speed every second.

A quantity that has magnitude and direction, for example displacement. Displacement (for example one metre North) combines a scalar quantity (distance displaced) with a direction to make a vector quantity.

The point at which two or more lines intersect. Every corner of a shape is a vertex. Plural: vertices.

The force exerted on an object possessing mass by the gravity of the earth, or any other gravitational body. In SI units this is measured in Newtons, as opposed to units of mass such as kilograms.

Symbol: yd. An imperial measure of length. In relation to other imperial units of length, 1 yard = 3 feet = 36 inches. 1760yd. = 1 mile. One yard is approximately 0.9 metres.

Also known as 'nought', 'nil' or 'nothing', zero (symbol 0) is the integer between one and minus one. In the place value system, it works as a place-holder. Example: 105. The zero represents that there are no 'tens' above the 100.

Any number raised to the power of zero is defined as equal to one. It is also defined that 1 divided by 0 is infinity, and anything multiplied by zero becomes zero.