# Achieving QTS

# Glossary

**abscissa **the first number in a pair of Cartesian co-ordinates. The abscissa always represents the distance along the x-axis.

**angle **a measurement of turn.

**approximation **an inexact result adequate and appropriate for a given purpose.

**arc **a curved line that forms part of the circumference of a circle.

**associative law **numbers can be regrouped to simplify a question while making no difference to the answer. It is true for addition and multiplication:

(a + b) + c = a + (b + c) (a × b) × c = a × (b × c)

**average **the general term used for using one number to represent a set of data.

**bar graph **a graph that uses bars to represent data.

**bar-line graph **a graph that uses lines to represent data.

**block graph **a graph used to display discrete data where one block can represent one or many item(s) of data.

**BODMAS **the order of precedence given to the operations when working out complex expressions. It stands for:

B – brackets

O – of

D – division

M – multiplication

A – addition

S – subtraction

Could also be BIDMAS where the ‘I’ represents indices.

**box and whisker plot **a graphical representation that allows for comparison of two sets of data.

**capacity **how much liquid volume a container can hold when full.

**Cartesian co-ordinates **a pair of numbers that locate a point on a plane with reference to two axes (can also refer to three axes in order to locate a point in three dimensions).

**chord **a straight line connecting any two points on a curve. When a chord passes through the centre of a circle it is called the diameter.

**column value **the value of a digit defined by its position in a number.

**commutative law**: the order in which the operation is performed makes no difference to the answer. It is true for addition and multiplication:

a + b = b + a a × b = b × a

**congruence **shapes are said to be congruent if they are the same shape and size.

**conjecture **a hypothesis, something that has been surmised or deduced.

**conservation **understanding that the quantity of matter remains unchanged regardless of its arrangement.

**continuous data **data that is measured. Every item of data can be placed along a continuum, for example, lengths of leaves.

**counter-example **disproving an assertion by finding an exception.

**cumulative frequency **a table displaying the running total of a set of data.

**cumulative frequency curve **a graph of the running total of a set of data.

**data **a set of facts, numbers or information.

**decimal **a fractional number expressed using places to the right of the decimal point.

**deduction **a conclusion based on a set of true statements.

**denominator **the bottom number in a fraction, representing the number of fractional parts the unit has been divided into.

**discrete data **data that can be counted. Every item of data can be placed in a category, for example, colours of cars.

**distributive law **one operation is ‘distributed out’ over another operation. It is true for multiplication over addition and multiplication over subtraction:

a × (b + c) = (a × b) + (a × c) a × (b – c) = (a × b) - (a × c)

It is also true that division is ‘right distributive’ over addition and subtraction (i.e. the division needs to be on the right side of the brackets):

(a + b) ÷ c = (a ÷ c) + (b ÷ c) (a - b) ÷ c = (a ÷ c) - (b ÷ c)

**dividend **within the operation of division, the number that is divided by another number.

**divisor **within the operation of division, the number that divides another number.

**edge **the line where two faces join (i.e. the intersection of two plane faces of a solid).

**enlargement **each measurement is multiplied by a scale factor in order to enlarge or reduce an image.

**equation **a statement that two expressions are equal.

**estimation **the rough answer (a judgement of an approximate value or amount).

**exhaustion **a proof that is arrived at by considering all possibilities.

**experimental probability **the number between 0 and 1 that is found by dividing the number of outcomes by the total number of trials.

**expression **a general term used to describe mathematical terms.

**face **the flat surface of a solid shape (i.e. parts of planes).

**factor **a number that divides another number exactly, for example 8 is a factor of 32, but 5 is not.

**fraction **a fraction is expressed as the quotient of two numbers, the dividend is the numerator, the divisor the denominator.

**frequency diagram **a table displaying continuous data grouped into classes.

**frequency histogram **a graph displaying continuous data grouped into classes.

**function **a rule that changes or maps one number on to another.

**gradient **the slope of a graph.

**imperial measure **introduced in the Magna Carta in 1215, for example, pints, gallons, miles, etc.

**independent events **events when the outcome of one event does not affect the outcome of another event, for example, flipping two coins.

**index form (or index notation) **a concise way of writing repeated multiplication of a number by itself, for example, 10 × 10 × 10 × 10 = 10^{4}.

**inequality **a statement that one quantity is greater or less than another.

**integer **a whole number (not a fractional number), for example, 2, 57 and 389. Examples of non-integers are 1.2 and 0.5.

**interquartile range **the interval between the upper quartile and the lower quartile in a set of data.

**irrational numbers **the set of numbers that cannot be expressed in fractional form.

**inverse **in mathematics inverse means ‘opposite’. Thus, addition is the inverse of subtraction.

**line graph **a graph used to display continuous data, where curves or line segments join points of measured data.

**linear equation **takes the form ay + bx + c = 0. A linear equation can always be represented as a straight line graph.

**lower quartile **the value one quarter of the way along a set of ordered data.

**mass **the amount of matter contained in an object.

**mean **the sum of the values in a set of data divided by the total number of items in that set.

**median **the middle value of a set of ordered data.

**minuend **the quantity from which another quantity is to be subtracted.

**mode **the value that occurs most often in a set of data.

**mutually exclusive events **events which, having happened, exclude any other outcome from occurring in that same event, for example, throwing a 3 on a die excludes a 1, 2, 4, 5 or 6 being thrown at the same time.

**net **a flat shape that can be folded to form a solid.

**numerator **the top number in a fraction representing the number of fractional parts.

**ordering **putting a collection of items in order from smallest to biggest/biggest to smallest according to weight, length, thickness, etc.

**ordinate **the second number in a pair of Cartesian co-ordinates. The ordinate always represents the distance along the y-axis.

**parallel **lines travelling in the same direction but which will never meet.

**percentage **fractions with a denominator of 100. They can also be represented as decimals, for example 1/4 = 25/100 = 0.25 = 25%

**perpendicular **two lines are said to be perpendicular if they meet at right angles.

**pi (π) **an irrational number found when the circumference of a circle is divided by the diameter. It is approximately equal to 3.141592…

**pictogram **a form to display discrete data where one picture/symbol can represent one or many item(s) of data.

**pie chart **a circle graph cut into sectors.

**place value **place value is used by number systems that allow the same digit to carry different values based on its position.

**Platonic solids **the five regular polyhedra, comprising the regular tetrahedron, the cube, the regular octahedron, the regular dodecahedron and the regular icosahedron.

**polygon **a plane shape with straight sides and many angles.

**polyhedron (pl. polyhedra) **a solid formed from many flat faces.

**prism **a solid shape with a uniform cross section.

**probability **used to measure the likelihood of certain events occurring in the future.

**probability scale **a scale from 0 to 1 that is used to measure the likelihood of an event occurring, with 0 being impossible and 1 being certain.

**proportion **compares part of a quantity with the whole, for example, a ratio of 1:3 results in proportions of 1 out of 4 and 3 out of 4.

**pyramid **a solid that has a polygon base and all other faces triangular.

**quantity value **the value you assign to a digit when you have established its column value.

**quotient **the result when one number is divided by another number.

**range **the interval between the greatest and least values in a set of data.

**ratio **a comparison between two quantities.

**rational numbers **the set of all numbers that can be written as fractions.

**real numbers **the set of rational numbers and irrational numbers combined.

**recurring decimal **a fraction in which a figure or a group of figures reoccur indefinitely, for example, 3.33333 or 2.14514145, etc.

**reduction **combining different parts of an equation to make it simpler.

**reflection **when a shape is reflected, a mirror image is created. The shape and size remain unchanged and the two images are congruent.

**reflective symmetry **also sometimes called line symmetry. A shape is said to have reflective symmetry if it can be folded so that one half fits exactly on top of the other half.

**restoration **simplifying an equation by performing the same operation on each side.

**rotation **rotation involves a turn around a fixed point. The shape and size remain unchanged, the two images are congruent.

**rotational symmetry **a shape is said to have rotational symmetry if it looks the same in different positions when rotated about its centre.

**scattergraph **a graph representing two types of data plotted as co-ordinates.

**sector **a wedge from a circle (like a slice of pie).

**sigma **means ‘the sum of’. The symbol for sigma is Σ. **similarity **shapes are said to be similar if all the angles are the same size and the shapes are the same but of different size, i.e. one is an enlargement of the other.

**simultaneous linear equations **two linear equations which have a common solution.

**square number **the number we get by multiplying an integer by itself.

**standard form **sometimes called standard index form as it uses powers of 10, i.e. 10 expressed in index form. It is a shorthand way of writing very small and very large numbers that would require a huge number of digits if written in full.

**statistics **statistics help us to bring order to data and to draw information from it.

**subtrahend **the number or term to be subtracted.

**Système International (S.I.) **determines the units of measurement used in the metric system, for example, millimetres, kilograms, litres, etc.

**terms **algebraic quantities that are separated from each other in expressions by operations.

**theoretical probability **the number between 0 and 1 that is found by dividing the number of actual outcomes by the total number of possible outcomes.

**transitivity **a mathematical relationship used to compare two objects or events, for example, if A is shorter than B, and B is shorter than C, then A must be shorter than C.

**translation **this takes place when a shape is moved from one place to another just by sliding it (without rotating, reflecting or enlarging).

**upper quartile **the value three-quarters of the way along a set of ordered data.

**vertex **the point of intersection of edges.

**volume **the amount of three-dimensional space an object occupies.

**vulgar fraction **a fraction expressed by numerator and denominator, not decimally; used in ordinary calculations (the original meaning of the word ‘vulgar’ was ‘as used by ordinary people’).

**weight **the force exerted on a body due to gravity.

**y-intercept **the point at which a graph crosses the y-axis.