Maths Terms for 11-13 Yr Olds
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James says: "This is glossary of terms for UK KS3 Maths,[ages 11-13] taken Works quite well with a 'random glossary entry' html block on a main course page since the definitions are in a small font size.
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ALGEBRA |
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Cartesian Co-ordinatesA 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. | |
Co-ordinateA position in 2D or 3D space, represented by numbers, letters or both. See 'Cartesian co-ordinates'. | |
ConsecutiveFollowing 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. | |
Cube1. 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'. | |
CubicAdjective 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. | |
Cubic CurveA 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. | |
DifferenceThe amount by which one number or value is greater than another, obtained by subtracting the smaller from the larger. | |
ExpressionA 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 =. | |
GradientA 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. | |
GraphA diagram showing a relationship between variables. Adjective: graphical. A graph showing information that isn't continuous is often called a 'chart' instead. | |
IdentityAn 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. | |
InequalityStatements 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. | |
InterceptThe 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. | |
LinearIn 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. | |
NotationAny convention for recording mathematical ideas in writing and symbols. Example: Money is recorded using decimal notation e.g. £2.50. | |
OriginA 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). | |
PatternA systematic arrangement of numbers, shapes, values or other objects according to a rule. | |
PlotThe 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. | |
ProofA chain of reasoning that establishes the truth of a proposition. | |
Proportion1. 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. | |
QuadrantOne of the four regions into which a plane is divided by the x and y axes in the Cartesian co-ordinate system. | |
Relation, RelationshipA 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'. | |
Tangent1. A line that touches a curve at one point only. 2. A trigonometric function (more on these at GCSE level). | |
TheoremA 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. | |
UniformNot 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. | |
VectorA 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. | |
GEOMETRY AND MEASURES |
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1D. 2D, 3DOne-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 | |
Acute AngleAn angle between zero and ninety degrees. | |
Alternate AnglesWhere two straight lines are cut by a third, as in the diagrams, the angles d and f (also c and e) are alternate. Where the two straight lines are parallel, alternate angles are equal. | |
AngleWhere 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. | |
ArcA portion of a curve. Often used for a portion of a circle. | |
AreaA measure of surface. Area is usually measured in square units e.g. square metres. | |
AxisA fixed, reference line along which or from which distances or angles are measured, and shapes are translated. For axis of symmetry, see 'reflection symmetry'. | |
BearingThe 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. | |
BisectIn geometry, to divide into two equal parts. | |
BisectorA 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. | |
CapacityVolume, 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 litre is equivalent to 1000 cubic centimetres (cm3) | |
Cartesian Co-ordinatesA 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. | |
Centi-Prefix meaning one-hundredth (of) | |
CentilitreSymbol: cl. A unit of volume equivalent to one-hundredth of a litre. | |
CentimetreSymbol: cm. A unit of linear measure, one hundredth of a metre. | |
CentreThe middle point. | |
ChordA straight line segment joining two points on a circle or other curve. | |
CircleA 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. | |
CircumferenceThe 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 ?r, or ?d units. For a sphere the circumference is the length of a 'great circle' on the sphere - this is like the equator on our planet. | |
ClockwiseIn 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. | |
Co-ordinateA position in 2D or 3D space, represented by numbers, letters or both. See 'Cartesian co-ordinates'. | |
Complementary NumbersTwo angles with the sum of 90 degrees . | |
Compound MeasuresMeasures with two or more dimensions. Examples: speed calculated as distance ÷ time; density calculated as mass ÷ volume; car efficiency measured as litres per 100 kilometres; and rate of inflation measured as percentage increase in prices. | |
ConcaveAdjective 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 . | |
ConcentricUsed to describe circles that have the same centre, e.g. in some castles two turrets are built around each other for double the protection; their cross sections will form concentric circles. | |
ConeA 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. | |
ConsecutiveFollowing 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. | |
ConvexAdjective 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 | |
CornerIn elementary geometry, a point where two or more lines or line segments meet. Also called a vertex, or vertices (plural). Example: a rectangle has 4 vertices; a cube has 8. | |
Corresponding AnglesWhere two straight-line segments are intersected by a third, as in the diagrams, the angles a and e are corresponding. Similarly b and f, c and g and d and h are corresponding. Where parallel lines are cut by a straight line, corresponding angles are equal. | |
Cross-sectionIn 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. | |
Cube1. 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'. | |
CubicAdjective 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. | |
Cubic CentimetreSymbol: cm3. A unit of volume. The three-dimensional space equivalent to a cube with edge length 1cm. | |
Cubic CurveA 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. | |
Cubic MetreSymbol: m3. A unit of volume; a three-dimensional space equivalent to a cube of edge length 1m. | |
CuboidA 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. | |
CylinderA 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. | |
DataInformation 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. | |
DatabaseA means of storing sets of data, for example in an Excel spreadsheet. | |
DecimalRelating 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. | |
Decimal FractionTenths, 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. . | |
DegreeIn the measurement of angles, a unit of turn, usually clockwise. One whole turn is equal to 360 degrees, written 360o. | |
DiameterThe length of any of the chords of a circle or sphere that pass through it's centre. Compare with 'chord'. | |
DifferenceThe amount by which one number or value is greater than another, obtained by subtracting the smaller from the larger. | |
Division1. 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. | |
DodecahedronA polyhedron with twelve faces. The faces of a regular dodecahedron are regular pentagons. A dodecahedron has 20 vertices and 30 edges. | |
Elevation1. 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. | |
EnlargementA 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. | |
EquilateralAn adjective describing a polygon with sides of equal length. | |
ExpressionA 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 =. | |
FaceIn geometry, one of the flat surfaces of a solid shape. Example: a cube has six faces. | |
FootSymbol: 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. | |
GallonSymbol: 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. | |
GeometryThe aspect of mathematics concerned with the properties of space and figures or shapes in space. | |
GradientA 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. | |
GramSymbol: g. The unit of mass equal to one thousandth of a kilogram. | |
HeptagonA polygon with seven sides or edges. | |
HexagonA polygon with six sides or edges. Adjective: hexagonal, having the form of a hexagon. | |
HorizontalParallel to the horizon. Also in the direction of the x axis in a Cartesian co-ordinate system. | |
IcosahedronA polyhedron with 20 faces. In a regular icosahedron all faces are equilateral triangles. | |
Imperial UnitsA 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. | |
InchSymbol: in. An imperial unit of length. 12 inches = 1 foot. 36 inches = 1 yard. 1 inch in metric units is approximately 2.54 cm. | |
InterceptThe 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. | |
Interior AngleAt a vertex of a polygon, the angle that lies within the polygon. | |
IntersectTo 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. | |
Inverse OperationsOperations 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. | |
Isoceles TriangleA 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. | |
KilogramSymbol: kg. The base unit of mass in SI units ('Système International d'Unités' in French, also known as metric). 1kg. = 1000g. | |
KilometreSymbol: km. A unit of length in SI units ('Système International d'Unités' in French, also known as metric). 1km. = 1000m. | |
KiteIn geometry, a quadrilateral shape with two pairs of equal, adjacent sides whose diagonals consequently intersect at right angles. | |
LineA 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. | |
LinearIn 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. | |
LitreSymbol: l. A metric unit used for measuring volume or capacity. A litre is equivalent to 1000 cubic centimetres . | |
LocusThe 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. | |
MassA 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. | |
MensurationIn the context of geometric figures this noun just means the process of measuring or calculating angles, lengths, areas and volumes. | |
MetreSymbol: m. The base unit of length in SI ('Système International d.Unités' in French, also known as metric). | |
Metric UnitsUnits 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. | |
MileAn imperial measure of length. 1 mile = 1760 yards. Five miles is approximately 8 kilometres. | |
Milli-Prefix meaning 'one-thousandth'. | |
MillilitreSymbol: ml. One thousandth of a litre. | |
MillimetreSymbol: mm. One thousandth of a metre. | |
MinuteUnit 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. | |
Net1. 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. | |
NotationAny convention for recording mathematical ideas in writing and symbols. Example: Money is recorded using decimal notation e.g. £2.50. | |
OblongSometimes used to describe a non-square rectangle. | |
Obtuse AngleAn angle greater than 90 degrees but less than 180 degrees. | |
OctagonA polygon with eight sides. Adjective: octagonal, having the form of an octagon. | |
OctahedronA polyhedron (3D polygon) with eight faces. A regular octahedron has faces that are equilateral triangles. | |
OriginA 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). | |
OunceSymbol: oz. An imperial unit of mass. In the imperial system, 16 ounces = 1 pound. 1 ounce is just over 28 grams. | |
ParallelIn geometry, two lines that are always equidistant (the same distance apart). Parallel lines, curves and planes never meet. | |
ParallelogramA quadrilateral whose opposite sides are parallel and consequently equal in length. | |
PatternA systematic arrangement of numbers, shapes, values or other objects according to a rule. | |
PentagonA polygon with five sides and five interior angles. Adjective: pentagonal, having the form of a pentagon. | |
PerpendicularNoun: a line or plane that is at right angles (90 degrees) to another line or plane. Adjective: having this property. | |
PiThe 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. | |
PintAn 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). | |
PlanIn geometry, a two-dimensional diagram of a three-dimensional object, usually the view from directly above. | |
PlaneA flat surface. A line segment joining any two points in the surface will also lie in the surface. | |
PlotThe 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. | |
PointAn element, in geometry, that has position but no magnitude, for example a corner (vertex). | |
PolygonA 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. | |
Pound (mass)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. | |
PrismA 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. | |
ProjectionA 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. | |
ProofA chain of reasoning that establishes the truth of a proposition. | |
Proportion1. 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. | |
ProtractorAn instrument for measuring angles. | |
PyramidA 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. | |
Pythagoras' TheoremIn 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. | |
QuadrantOne of the four regions into which a plane is divided by the x and y axes in the Cartesian co-ordinate system. | |
QuadrilateralA polygon with four sides. | |
RadiusIn 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. | |
RectangleA 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. | |
RectilinearBounded 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. | |
ReflectionIn 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. | |
Reflection SymmetryA 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. | |
Reflex AngleAn angle that is greater than 180 degrees but less than 360 degrees. | |
Regular1. 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. | |
Relation, RelationshipA 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'. | |
ResultantA vector that is equivalent to the vector sum of two or more vectors. | |
RhombusA parallelogram with all sides equal. | |
Right AngleOne 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'. | |
RotationIn 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. | |
Rotation SymmetryA 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 2D shape with rotation symmetry has rotation symmetry of order n when n is the largest positive integer for which a rotation of 360/n degrees produces an identical-looking shape in the same position. | |
ScalarScalar 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). | |
Scale FactorFor two similar geometric figures, the ratio of corresponding edge lengths. | |
Scalene TriangleA triangle with no two sides equal and consequently no two angles equal. | |
Section (Plane Section)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. | |
SectorThe 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. | |
Segment1. 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. | |
SetA well-defined collection of objects or numbers (themselves then called called members or elements). | |
Set SquareA drawing instrument for constructing parallel lines, perpendicular lines and certain angles. | |
Similar figuresA 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. | |
SphereA 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. | |
Square (Shape)In geometry, a 2D quadrilateral with four equal sides and four internal angles that are all right angles. | |
SurfaceA set of points defining a space in two or three dimensions. | |
SymmetryA 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. | |
Tangent1. A line that touches a curve at one point only. 2. A trigonometric function (more on these at GCSE level). | |
TetrahedronA solid with four triangular faces. A regular tetrahedron has faces that are equilateral triangles. Plural: tetrahedra. | |
TranslationIn 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). | |
TrapeziumA quadrilateral with exactly one pair of sides parallel. | |
TriangleA polygon with three sides. Adjective: triangular, having the form of a triangle. | |
UniformNot 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. | |
VectorA 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. | |
WeightThe 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. | |
YardSymbol: 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. | |
NUMBER |
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AdditionThe 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. | |
Analogue ClockA 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. | |
ApproximateA 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. | |
Arithmetic SequenceA 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. | |
ArrayAn ordered collection of counters, numbers etc. in rows and columns. | |
BracketsSymbols 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. | |
Cartesian Co-ordinatesA 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. | |
Co-ordinateA position in 2D or 3D space, represented by numbers, letters or both. See 'Cartesian co-ordinates'. | |
CoefficientOften 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. | |
Common FractionA 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. | |
ConsecutiveFollowing 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. | |
Constant (noun)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. | |
Cube1. 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'. | |
Cube NumberA number that can be expressed as the product of three equal integers. Example: 27 = 3 x 3 x 3. 27 is therefore a cube number. So are 1, 8, 56, etc... | |
Cube Root
A value or quantity whose cube is equal to a given quantity. Example: the cube root of 8 is 2 since 2 x 2 x 2 = 8. | |
CubicAdjective 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. | |
Cubic CurveA 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. | |
DataInformation 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. | |
DatabaseA means of storing sets of data, for example in an Excel spreadsheet. | |
DecimalRelating 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. | |
Decimal FractionTenths, 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. . | |
DenominatorIn 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. | |
DifferenceThe amount by which one number or value is greater than another, obtained by subtracting the smaller from the larger. | |
DigitOne 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. | |
Digital ClockA clock that displays the time as hours and minutes passed, usually since midnight. Example: four thirty in the afternoon is displayed as 16:30. | |
DivisibilityThe 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. | |
Division1. 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. | |
EqualSymbol: =. 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. | |
EvaluateFind the value of a numerical or an algebraic expression. | |
ExponentAlso known as 'index' or 'power'. A number, positioned above and to the right of another, indicating repeated multiplication. Exponents may be fractional or negative. Examples: 81/3 = 2, which is the same as the cube root of 8. | |
ExpressionA 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 =. | |
FactorWhen 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). | |
FractionThe 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. | |
Frequency TableA table for a set of observations showing how frequently each event or quantity occurs. | |
GradientA 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. | |
Highest Common Factor (HCF)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. | |
Improper FractionAn 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. | |
IntegerAny of the positive or negative whole numbers and zero. Examples: -2, -1, 0, +1, +2. As opposed to decimal numbers. | |
InterceptThe 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. | |
Inverse OperationsOperations 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. | |
Irrational NumberA 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. . . | |
LinearIn 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. | |
Lowest Common Multiple (LCM)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. | |
MinusThe name for the symbol -, which represents the operation of subtraction. | |
Mixed FractionA 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. | |
MultipleFor 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). | |
MultiplicationThe 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. | |
Negative NumberA 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. | |
Net1. 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. | |
NotationAny convention for recording mathematical ideas in writing and symbols. Example: Money is recorded using decimal notation e.g. £2.50. | |
NumeralA 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. | |
Odd NumberAn integer that cannot be divided neatly into two integers. Examples: 1, 3, 5, 7, etc. | |
OriginA 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). | |
PatternA systematic arrangement of numbers, shapes, values or other objects according to a rule. | |
PercentageA 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%. | |
PiThe 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. | |
Place ValueThe 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. | |
PlotThe 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. | |
Positive NumberAny 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. | |
Prime FactorThe 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'. | |
Prime FactorisationThe process of expressing a number as the product of factors that are prime numbers. Example: 24 = 2 x 2 × 2 × 3 or 23 × 3 | |
ProductThe result of multiplying one number by another. Example: The product of 2 and 3 is 6 since 2 x 3 = 6. | |
ProofA chain of reasoning that establishes the truth of a proposition. | |
Proper FractionA proper fraction has a numerator that is less than its denominator. Example: 2/5 is a proper fraction whereas 9/4 is improper. | |
Proportion1. 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. | |
QuadrantOne of the four regions into which a plane is divided by the x and y axes in the Cartesian co-ordinate system. | |
QuantitativeRelating 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). | |
QuotientAnother word for the result of a division. Example: 5 is the quotient of 100/20. The number being divided, in this case 100, is sometimes known as the dividend. | |
RatioA 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. | |
Rational NumberA 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 | |
Real NumberA number that is rational or irrational. Real numbers are those generally used in mathematics, science and everyday contexts. | |
ReciprocalThe 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). | |
Recurring DecimalA 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. | |
Relation, RelationshipA 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'. | |
RemainderIn the context of division requiring a whole number answer (quotient), the amount remaining after the operation. Example: 29 divided by 7 = 4 remainder 1. | |
ScalarScalar 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). | |
SequenceA 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. | |
Sign
With numbers, a positive + or negative - sign indicates whether it is higher or lower than zero. It can also indicate direction in the sense of a vector, e.g. a ball thrown directly upwards could be said to have a negative velocity on its way back to the ground, to make it clear that it is moving in the opposite direction to which it started moving in. | |
Significant FiguresThe 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 | |
Simple FractionA fraction where the numerator and denominator are both integers. Also known as a common or vulgar fraction. | |
Square NumberA number that can be expressed as the product of two equal numbers. Example 36 = 6 x 6 and so 36 is a square number. | |
SurdAn expression including one or more square roots (or cube roots, fourth roots, etc.) | |
UniformNot 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. | |
VectorA 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. | |
ZeroAlso 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. | |
STATISTICS |
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AverageSee 'mean’. Compare with 'mode' and 'median'. | |
Bar ChartA 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. | |
Bar Line ChartSimilar 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. | |
Box PlotA 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. | |
Categorical DataData 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. | |
ConsecutiveFollowing 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. | |
Continuous DataData 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. Compare with discrete data. | |
CorrelationA 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. | |
Cumulative Frequency DiagramA 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. | |
DataInformation 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. | |
DatabaseA means of storing sets of data, for example in an Excel spreadsheet. | |
DecimalRelating 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. | |
Decimal FractionTenths, 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. . | |
DifferenceThe amount by which one number or value is greater than another, obtained by subtracting the smaller from the larger. | |
Discrete DataData 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. | |
Frequency TableA table for a set of observations showing how frequently each event or quantity occurs. | |
HistogramA 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. | |
Line of Best FitA line drawn on a scatter graph to represent the best estimate of an underlying linear relationship between the variables. | |
LinearIn 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. | |
Mean (also Arithmetic Mean)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. | |
MedianThe '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. | |
ModeThe 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). | |
Net1. 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. | |
NotationAny convention for recording mathematical ideas in writing and symbols. Example: Money is recorded using decimal notation e.g. £2.50. | |
OriginA 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). | |
PatternA systematic arrangement of numbers, shapes, values or other objects according to a rule. | |
PercentageA 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%. | |
PictogramA 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. | |
Pie ChartAlso 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. | |
PlotThe 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. | |
ProbabilityThe 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. | |
ProofA chain of reasoning that establishes the truth of a proposition. | |
PropertyAny 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. | |
Proportion1. 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. | |
QuadrantOne of the four regions into which a plane is divided by the x and y axes in the Cartesian co-ordinate system. | |
QualitativeRelating 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). | |
QuantitativeRelating 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). | |
QuartileWhere 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. | |
Random SampleIn statistics, a selection from a population where each sample of this size has an equal chance of being selected. | |
RangeA measure of spread in statistics. The difference between the greatest value and the least value in a set of numerical data. | |
Raw DataData as they are collected, unprocessed. | |
Relation, RelationshipA 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'. | |
SampleA 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. | |
Scatter GraphA 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. | |
Stem and Leaf DiagramA 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. | |
Stratified SampleWhere 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. | |
TallyTo make marks to represent objects counted, and record these marks in a table (tally chart). | |
Tree DiagramA 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. | |
UniformNot 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. | |