Glossary of Mathematical Terms

Glossary of Mathematical Terms with a few examples and illustrations

By Roger Bickley

LASPHHOND The mnemonic LATSPHHOND helps you to remember the names and sides of the first 10 regular polygons:

1

L

Line

2

A

Angle

3

T

Triangle

4

S

Square

5

P

Pentagon

6

H

Hexagon

7

H

Heptagon

8

O

Octagon

9

N

Nonagon

10

D

Decagon

Acknowledgement: We are grateful to the energies and imagination of the contributors to the website http://morguefile.com for permission to use images on that site in this publication

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2-D shapes Shapes in two dimensions – i.e. which can be drawn on paper. Examples include triangles, squares, pentagons etc

3- D shapes Objects in 3 dimensions – i.e. which have height, length and breadth, for example cubes, cuboids, prisms

12-hour clock Most domestic clocks have a clock face which shows the numbers 1 to 12 around the edge. Times are said (or written) using the term a.m. (antemeridian – i.e. before 12 o‟clock mid-day) or p.m. (post meridian – i.e. after 12 o‟clock mid-day) to indicate whether the time is morning or afternoon – e.g. 7:30 am is half-past seven in the morning and 9:20 pm is twenty past nine in the evening

24-hour clock This clock (usually) has two sets of numbers around the dial – 1 – to 12 around the outside and 13 to 24 around the inside – giving two numbers for every hour – e.g. 1 o‟clock is also 13 o‟clock, 6 o‟clock is also 18 o‟clock and so on – except we don‟t say „o‟clock‟ but simply „hours‟ and the time is written differently – so 6 o‟clock in the morning is 0600 hours on the 24 hour clock and 6 o‟clock in the evening is 1800 hours. The simple rule is that if the time is before 12 noon the hours stay as they are – e.g. 0830 and if they are after noon we add twelve to the number – e.g. 8:30 in the evening is 2030 hours

14 minutes past nine in the evening

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Acute angle

Less than 900

An angle bigger than 00 and less than 900

Adjacent “Next to” – in angle terms this means angles next to each other, as in the illustration: Angles a and b are adjacent b a

Algebra The branch of mathematics which uses letters to represent unknown quantities – for example we might say three apples and four bananas cost 30 pence, and this could be written as: 3a + 4b = 30

Alternate angles Angles which are the same size and are created by drawing a straight line across a pair of parallel lines

c The angles c are equal

c am Stands for ante-meridian and means times between midnight 00.00 and Noon 12.00 (see also p.m.). Times are written (for example) 2.35am which means „twenty-five minutes to three in the morning‟

Area A measure of the „space‟ within a shape – the area is sometimes given by a formula (e.g. the area of a square is l x l – where l is the length of the side) and sometimes you need to work out the area by working out the areas of small parts of the shapes and adding the separate areas together.

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Area of a rectangle Area of rectangle = length x breadth of A = w x l where l is the length of one side of the rectangle and w is the length of the other side

w

Area of rectangles = wxl

l Area of a parallelogram

Area of parallelogram = wxh

h

w

Area of a triangle Area of triangle = ½ x base x perpendicular height = 1/2 x b x h

h b Arc

A part of the circumference of a circle

Arc

Circumference

Arrowhead A quadrilateral (four-sided shape) in the shape of an arrow:

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Average (see also Mean) A quick measure of the general „size‟ of a set of data. Calculated by adding up all the separate piece of data and then dividing by the number of pieces of data.

For example the average of 2, 3, 7, 9, 14 is 2 + 3+ 7 + 9+ 14 divided by 5 = 7

Axes of symmetry

A line drawn on a shape or graph so that the part of the shape on one side of the line is a mirror image of the shape on the other side of the line Axis of symmetry

Bar chart A type of picture used to illustrate data. It is created by first

A Vertical Bar Chart

A horizontal bar chart

Bearing

The direction of one point from another – e.g. we might say that B is 900 in relation to A (which in fact would mean that B was due East of A

A

900

B

Binary system The system of arithmetic which uses only the numbers 0 and 1 to represent any number (as against the 0,1,2,3,4,5,6,7,8,9 we use in the decimal system)

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BODMAS A „made up word‟ standing for the order in which arithmetic operations are to be carried out. The letters stand for: B– Brackets (these are to be worked out first) O – Order D – Division M – Multiplication A – Addition S – Subtraction

Calculator An electronic machine used for carrying out calculations. Simple calculators can ‟do‟ normal addition, subtraction, multiplication and division, together with percentages and possible square roots. More complex calculators (often called Scientific calculators, can do more complex mathematical tasks (like drawing graphs on the screen) and often can be programmed

For some examinations you will be allowed to use a calculator – for others you won‟t

Calendar A chart which shows the days of the week and months of the year – in particular the 31 days in January, March, May, July, August, October, December; the 30 days in April, June. September and November and the peculiarity of February which has 28 in it each year, except a Leap Year when it has 29 days

Cancelling fractions The process of making fractions smaller and more manageable by dividing the top number (the numerator) by the same number as the denominator – e.g. the fraction 8/12 can be simplified by cancelling down – divide top and bottom by 4 and we have 2/3, the simplified fraction Example: 6/12 can be simplified by dividing top and bottom by 6 to give 1/2 – the fractions 6/12 and 1/2 are called Equivalent Fractions

Capacity, units of Units used to measure volume – e.g. cubic centimetres (c.c), cubic feet etc

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Celsius

A unit of temperature measure – 00c is freezing point of water 1000c is the boiling point of water

Centilitre A measurement within the metric system equal to 1/100 of a litre

Centimetre A measurement of length within the metric system = 1/100 of a metre

Centre of rotation The point around which an object is to be rotated. In many/most cases the centre of rotation will be the centre of the object – but it doesn‟t need to be so:

A

The triangle has been rotated 900 clockwise about the Centre of Rotation A

Certainty The mathematical probability of 1 – (if the probability of event happening is 0 then the event is impossible - b) – e.g. it is certain that the sun will rise tomorrow morning (probability 1 - a) and it is impossible that there will be a 30 February (probability 0)

Chance The likelihood of something happening – e.g. the chance of getting a head when tossing a coin is ½

Chord A line drawn across the inside of a circle, touching the circle twice and which doesn‟t go through the centre.

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Circle Strictly a circle is formed by the path (locus) of a point moving at the same distance from another point. This is achieved, usually, by means of a compass – where the pencil stays the same distance from the point, as the compass is rotated.

Circumference The circumference of a circle is the distance around it The circumference of a circle is calculated as follows;

Centre

Circumference – 2 x Π x r Where r is the radius and Π is often given as 3.14

Class interval The upper and lower limit of a band of data – e.g. you might have class intervals of 10 which could be 0 – 9, 10 – 19, 20 – 29 and so on. You may very well use banding when collecting data – e.g. of the heights so pupils.

Collecting terms In algebra the process of simplifying calculations by collecting terms of the same type – e.g. 3a + 5a – 2a = 6a

Compass An instrument used for measuring direction. Most compasses identify North, South, East, West, South-East, South-West.

North-East, North-West

Compasses A instrument used for drawing circles, or parts of a circle.

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Complementary Angle

Two angles are complementary if they add up to 900 In both cases a and b are complementary angles

b

a

b

a

Concave When a shape is „bowed‟ inwards rather than outwards (as in convex) - think of the idea of a „cave‟ and that it goes into the rock.

The impression when you remove the stone from an avocado is concave

Cone A three dimensional object which has a round base which tapers upward to a point (or vertex)

Pine Cone

Traffic Cone

Ice Cream Cone

Congruence Meaning the same as in every detail – so two shapes are only congruent if each side on one shape has a similar sized side on the other and each angle on one shape has an equivalent sized angle on the other.

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Consecutive One after another – e.g. the next three consecutive numbers after 5, 6, 7, 8 are 9, 10, 11

Conjecture An „educated guess‟ – i.e. a prediction based on evidence. So, you might say pattern which you have found in a series of numbers suggests that the next number will be such and such, and the nth number will be such and such. It is then up to you to prove your conjecture!

Constant A constant is a number, usually a real number, whose value is fixed – i.e. doesn‟t vary. For example the number 5 in the equation

3x2 + 9x – 5 is a constant, whereas x is a variable (it can change)

Construction A drawing which is made using (usually) only ruler and compass.

Constructions are often of, for example, triangles or hexagons etc

Continuous data Data which can have all possible values in a given range – e.g. you might have tree height of 1m, 2m, 3m, 4m and so on – but trees can have any value between 1 and 2m and 2 and 3m etc

Convert To change from one form to another – e.g. change from one currency to another (£ to $) or from one form of measure to another e.g. miles to kilometres

Conversion graph A graph used to convert one quantity into another – e.g. converting money from one currency to another, or metric to imperial measures.

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Convex A shape which „bows‟ outward – as opposed to inward (concave)

A example of using the idea of convexity in a mirror

Co-ordinates The system of locating where a point is – using pairs of numbers (x,y) where the first number is taken to be horizontal (along the x-axis) and the second number to be vertical (along the y-axis)

Correlation The relationship between two or more sets of data.

Correlation, negative

Number pof motorists caught speeding

A situation where the relationship between two sets of data is downward

In this scatter diagram we might come to the conclusion that the more cameras there are the less likely motorists are likely to be caught speeding

Number of speed cameras

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Correlation, positive A situation where there is a close upward relationship between two sets of data – e.g. the amount of homework done by students and their performance in examinations – e.g. the more homework they do, the better their performance in exams.

Corresponding angles Angle which have the same relationship to one another, usually created using parallel lines.

b The angles b are equal

b

Cosine Rule A rule (or formula) to work out an angle or a side when you are given certain information – e.g. two of the sides and the included angle

b2 = a2 + c2 + 2ac Cos B

Counting numbers The „normal‟ numbers we use to count objects – 1,2,3,4,5,6 …..

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Cross-section A „slice‟ through a solid object, showing what the object is like „from the inside‟.

A „slice through a hollow shape

Cube A three-dimensional object with all faces being squares

Cuboid A three dimensional „box‟ with opposite sides equal and all angles equal to 900

Cumulative Frequency A rolling sum – where you add up each of the preceding frequencies to get the next one. The example below shows how it is done Frequency: 4 6 3 2 6 4

Cumulative Frequency: 4 10 13 15 21 25

(4 (4 (4 (4 (4

+ + + + +

6) 6+ 6+ 6+ 6+

3) 3 + 2) 3 + 2 + 6) 3 + 2 + 6 + 4)

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Currency The general name given to the means by which goods and services are bought and sold – in the UK the currency is the £ and in the United States the dollar.

Data, continuous Data (numbers) which „flow‟ together without there being a break – e.g. heights of children, temperatures etc

Data, discrete Data which is separate from other data – e.g. the number of people who like a particular flavour of crisps, people with particular colour eyes etc

Data collection sheet

Data collection sheet to collect information about people‟s attitudes to recycling

Decimal fraction A decimal fraction is simply a decimal which can be converted into a fraction For example 0.2 is 1/5 and 0.3333333333333 is 1/3

Decimal system A system of arithmetic which uses the ten digits 0,1,2,3,4,5,6,7,8,9 to express and carry out calculations – dec meaning TEN

Decrease Make smaller or lessen. The result of a decrease is always a quantity which is smaller than the one you started with.

Degree A measure of rotation – there being 360 degrees to go around completely!

Denominator The number on the bottom of a fraction - in the fraction 3/4 the 4 is the denominator

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Diagonal A line drawn from one vertex (point) of a shape to another vertex.

Diameter Any line drawn from one side of a circle to the other, and going through the centre

All lines are diameters

Directed numbers Number which have a sign associated with them – the sign will be either positive + or negative -

Discount The amount of money which is deducted from the price of an article, usually in order to stimulate sales. The discount is often stated as a percentage – e.g.

10% off the original price.

Discrete Data Data which goes up in steps (usually whole numbers) – like the number of children in a family. See also continuous data

Division The technique for finding how many times one number will „fit‟ into another.

Division is a method of repeated subtraction – you can simply subtract one number from the other and count how many times you can do it

Edge The place where two edges meet – usually a line, often sharp

EDGES

Enlargement The size of an object which is larger than the original. The making of the object larger is usually done according to a rule. NOTE: If you are told to enlarge an object by a number less than 1 (e.g. ½ then the result (the object) will be smaller than the original.

Enlargement, centre of The point from which an enlargement is carried out

Centre of enlargement

.

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Equally Likely Events which are equally likely are also described as „Evens‟ or 50-50

Equation A way of stating the relationship between two or more quantities. All equations have an = sign in them and this means that what is on one side of the = is of the same value as that which is on the other side of the = sign For example v = rt + ½ rt2

Equilateral triangle A triangle which has all sides and all angles equal (all the angles are equal to 600 – there are 1800 is all triangles and this triangles has three angles equal) b

All angles equal to 600 All sides equal

b

b

Equivalence Equivalence means that two or more expressions, shapes etc can, for all practical purposes, be treated as being exactly the same. The most common examples are equations – where the left-hand side is to be treated exactly the same as the right-hand side; and congruent shapes – which are the same in every way.

Estimation The technique for approximating the answer to a calculation. NOTE that does not mean guessing the answer but involves rounding up parts of the „information‟ to make the calculation simpler and give an idea of the general „size‟ of th answer expected of the full calculation.

Even number A number which is divisible by 2 and leaves no remainder.

The first five even numbers are 0, 2, 4, 6, 8 and any other number ending in one of the these numbers is also even.

Event An occurrence of a particular activity. If you are studying the numbers which appear on a die when throwing it – every throw of the die is an event

Exhaustive Events The total of all the possible outcomes of an experiment – i.e. every possible result is covered. For example, if you throw a normal 6-sided die you MUST get 1, 2, 3, 4, 5 or 6

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Expanding Multiplying out an expression and, usually, collecting all the like terms together:

Example: Expand 3x(2x – 3) + 5x(x + 7) We get 6x2 – 9x +5x2 + 35x = 11x2 + 26x

Experimental Probability In order to work out the probability (likelihood) of an event (or events) happening you need to make the event happen a large number of times and then divide the number of successes by the number of events – e.g. you would find the probability of throwing a head by tossing the coin a large number of times (perhaps thousands) and dividing the number of heads by the number of tosses of the coin

You may need to throw the die a lot more times, in order to get very close to the theoretical probability

Expression A collection of unknowns and, possibly, numbers which means something. For example to hire a car might mean putting a deposit down of £10 and renting at £25 per day.

We can write the cost for any rental as 10 + 25d – where d stands for the number of days‟ rental If we put another unknown and an equal sign in we get an equation – e.g. c = 10 + 25d where c is the cost E

Exterior angles a

A

b

d

A a

`

B

e

c C

B b

D

The sum of the exterior angles of any polygon add up to 3600

c C

In the triangle, if you walk along the line AB and turn through the angle b, you walk along line BC, then you turn through angle c and travel along line CA – back to where you started! The angles created (a, b and c) are the exterior angles.

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Faces The „sides‟ of a three-dimensional object – e.g. a cuboid has six faces.

Factor(s) The numbers which will divide into another number – e.g. the factors of 12 are 1, 2, 3, 4, 6, 12 – because all these numbers will divide into 12 without leaving a remainder.

NOTE: All numbers have the factors 1 and themselves

Fair/unfair (as in dice) A description usually applied to an object (or objects) which will be used in probability calculations. An object is fair if all possible outcomes (i.e. results) are equally likely – e.g. in a fair die the probability of getting a 1, 2, ,3 ,4 ,5 or 6 are all equally likely

The number of dots on opposite sides of a die (the singular of dice) add up to 7

Fibonacci numbers Named after a 14 century mathematician the numbers come from adding each pair of numbers to get the next one. E.g. if the first two numbers are 0 and 1 the third number is 0 = 1 = 1, the second number is 1 + 1 = 2, the fourth number is 1 + 2 = 3 the next 2 + 3 = 5, the next 3 + 5 = 8 and so on. The first twelve Fibonacci numbers are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89

Foot A unit of length measurement in the Imperial system. 3 feet make a yard and there are 12 inches in a foot.

Formula A way of expressing a relationship between quantities using letters and numbers. – e.g. we might say that the area of a rectangle is A = L x B where A is the Area, L is the length and B is the Breadth

Four Operations The four operations on numbers are Addition, Subtraction, Multiplication and Division

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Fractal A fractal is a geometric shape which is created by repeated, well defined, operations on a starting shape, with the same rule being applied to successive results. For example, the Sierpinski Triangle starts as a filled in triangle and then triangles are subtracted from it as in the successive illustrations below:

Fraction A way of describing parts of a whole. A fractions has two parts – the top part (called the Numerator) and the bottom part (called the Denominator). The bottom part tells how many parts the whole has been split into, and the top part tell how many part we are to take.

The circle on the left has been cut into three pieces and 2 of them coloured in – giving us 2/3 coloured in The circle on the right has been cut into 12 pieces with 8 slides coloured in – giving us 8/12 coloured in And these two fractions are clearly the same

Frequency The number of times something happens. In mathematics it might be the number of times the Ace of spades is drawn when a pack of cards is cut, of the number of times a 6 appears when a dice is thrown.

Frequency polygon A shape drawn on a bar chart where the point of the shapes are the mid points of the bars.

The frequency polygon

Function A formula or procedure which carries out a set series of operations – e.g. ou might say “take a number, double it and add 5”

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Gallon A unit of liquid measurement within the Imperial system. There are 8 pints in a gallon and a gallon is approximately equal to ?? litres

Generate Produce – e.g. an equation such as y=2x+3 will generate a series of numbers as you substitute for values of x

Gramme A unit of weight measurement within the metric system. A gramme is approximately equal to 0.035 of an ounce.

Greater than > A sign used to indicate which of two items in the larger – e.g. we would write 5 > 3 meaning 5 is greater than 3, or 2 > -4 meaning 2 is greater than –4, or even x – 4 > 6 meaning that x-4 is greater than 6

Grouping data Collecting data together within given ranges – e.g. you might group age data in bands of, say, -=5, 1-6. 7– 12 years etc

HCF (Highest Common Factor) The Highest Common Factor (HCF) of a series of numbers is the largest number which will divide into all of them, without leaving a remainder Example the HCF of 18 and 24 is 6

Heptagon A seven-sided shape (or polygon)

Hexagon A six-sided shape (or polygon)

Histogram A histogram is a graphical display of frequencies. All the bars are next to each other – with no spaces. A histogram is different form a bar chart in that it is the AREA of the bars which illustrates the measure – rather than the height.

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Hyperbola The curve created by cutting a cone through its base with a plane.

Alternatively, the curve created when drawing the graph of Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

The hyperbola used in the design of a cooling tower

Image The new shape created after „operating‟ on an original (called the object) e.g. we might reflect a triangle in a mirror line – the original is called the object and the new triangle is called the image

Imperial measure The „old style‟ system of measuring distance, weight etc. The principle units are ounces, pounds, stones (weight); inches, feet, yards, miles (distance).

Impossibility If the mathematical probability of an event happening is 0 (zero) this means that it is impossible for the event to happen.. If the probability of the event happening is 1, then it is certain that the event will happen.

0 Impossible

1

50/50

Certain

Inch An Imperial Measure of distance. There are 12 inches in a foot and 36 inches in a yard.

Income tax Money paid to the government from earnings. Everybody has a certain amount of money on which they don‟t have to pay tax. A percentage of the remainder of their income is deducted and paid to the government (although some people work out their own tax, or get an accountant to work it out for them).

Increase Make bigger/larger

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Index Notation When writing powers of numbers (i.e. the number of times a number has to be multiplied by itself) we write: 2 x 2 x 2 x 2 x 2 = 25 This way of writing powers is called Index Notation and the small number (in this case the 5) is called the INDEX. The number being raised is called the BASE. When two or more numbers WITH THE SAME BASE are multiplied together we ADD the INDICES Example: 37 x 35 = 35+7 = 312 When we divide two numbers WITH THE SAME BASE we subtract the indices Example 58 divided by 53 = 58-3 = 55

Inequalities An inequality shows a relationship between two quantities – the relationship might show that they are equal, or that one is larger than the other. The symbols used are > (greater than) < (less than) >= (greater than or equal to) <= (less than or equal to) -5 < 4 equal to 2)

3> 2

2x >= 4 (this means that x is greater than or

Input/Output Terms often used in the context of computers – you enter data into the system (or formula), it is processed (a calculation is carried out) and you get output – otherwise known as the answer

Integer Any whole number – -34, 4, 6, 12345 etc

Interior angles The angles on the „inside‟ of a closed shape

d e

c

a

b

The sum of the interior angles of any polygon is equal to (2n-4) right angles where n is the number of sides of the polygon

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Intersection, point of The point where two or more lines cross

Intersecting lines Two lines which cross. Opposite angles are always equal where two straight line cross

Inverse The „opposite‟ - e.g. if I add 3 to a number the inverse operation would be to subtract 3 (and I would get back to where I started from)

Interval

Here the interval is 5 the difference between each pair of numbers

Usually, the gap between values. For example when creating graph of a function you would choose the gap (interval) between values against which to plot the graph:

Irrational numbers

The intervals here are 2 – the difference between two each pair of values

Irrational numbers are numbers which cannot be written as fractions or as exact decimals, such as pi and 2 . In decimal form these numbers go on forever and the same pattern of digits are not repeated.

Isometric

A type of drawing which shows objects in three dimensions

Isometric paper Paper on which dots or lines are printed in „diamond‟ formation. The paper is particularly useful for drawing 3-dimensional objects

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Isosceles triangle A triangle which has two sides equal and two angles equal

Base angles equal Two sides equal a

a

Key A guide to what symbols on a diagram or graph mean – e.g. you might use stick-men on a scatter diagram, so you need to say (in the key) what each stick-man stands for

Kilo The prefix to a word which means 1000 – e.g. kilogram – 1000 grams; kilometre – 1000 metres

Kilogram A measure of weight equivalent to 1000 grams

Kite A quadrilateral with two pairs of adjacent sides equal.

LCM (Lowest Common Multiple) The smallest number into which two or more number will divide, without leaving a remainder. For example, the LCM of 12 and 18 is 36 because 36 is smallest number into which BOTH 12 and 18 will divide.

Leap Year A year which occurs every four years and which has 366 days in it, as against the 365 days in a „normal‟ year. Leap years all have year numbers where the last two digits are divisible by 4 – e.g. 1896, 1900, 1904, 1956, 2000 were all Leap Years.

Length A one-dimensional measure, usually along a line – e.g. 6cm

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Less than < A symbol used to show that of two quantities – one is larger than the other.

The larger quantity is always on the right of the symbol

LHS (Left Hand Side) Usually refers to the left-hand side of an equation – and often said in a sentence like “whatever you do to the left-hand side of an equation, you must do exactly the same to the right-hand side”

Like Terms Parts of an equation or expression which are essentially the same – e.g. in the expression 5a2 + 3ab – 2a2 + 6c2 + 7ab – the 5a2 and –2a2 are like terms and the 3ab and 7ab are also like terms

Likely/unlikely An unmathematical way of describing the probability of an event happening

Line of best fit On a scatter graph, a straight (or sometimes curved) line which goes „through‟ the dots and creates the best path through the dots.

Line of symmetry

A line (often dotted) which divides a shape so that one side of the line is a mirror image of the other side.

Line graph, straight The graph of equations of the form y=mx+c is a straight line.

3 2 1 -2

-1

1

2

It usually needs three points to draw an accurate straight-line graph

-1 -2

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Linear equation An equation of the form y=mx+c where m is the coefficient of x and c is the constant. Examples include y=3x-6; y = 7-5x. The reason it is called a linear equation is because the graph of the equation is a straight line.

Here we have the graph of the linear equation y = 2x + 3

Litre The main metric measure of liquid volume – with all other measures being derived form the basic word – millilitre, centilitre etc

Loci The locus (plural loci) is a path which a point or line travels when you make a rule. For example the locus of a point which stays the same distance from a fixed point – is a circle

b

.

.

b

.

b

. b

.

.

The path travelled by a point which stays a constant distance from a fixed point

b

.

b

Long division The process of dividing one number by another number, without using a calculator.

Lowest terms We use the expression „lowest terms‟ often when we are working with fractions – and want the numbers as small as possible, by cancelling down (finding numbers which will divide into top and bottom. The “lowest terms” is reached when there is no number which will divide into top and bottom.

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Magic Square

A magic square is one in which all the numbers in any line (vertical, horizontal, diagonal – add up to the same number

8

3

4

1

5

9

6

7

2

In this magic square each row, column and diagonal adds up to 15

Map/Map Scales A scale „picture‟ of a real place (or places) - with actual distances on the ground being shown as smaller scaled images on paper. Most maps show the scale of the „paper picture‟ to the „real objects‟ - with, for example. 1:50000 means that 1cm on the „paper picture‟ corresponds to 50000 cm on the „ground.

Maps come in a wide variety of scales – the smaller the number on the right the greater the small detail shown on the map – for example a map with a scale of 1:50000 will have 50000 inches represented by just one inch on the map

Mean The technical term for Average – calculated by adding up all the numbers and then dividing by the number of numbers.

Take the numbers: 3

12

5

7

9

11

2

Adding them together gives us 49 There are 7 numbers, so the mean is 49/7 = 7

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Median A type of Average (see also Average and Mean) although not a particularly useful one! It is calculated by putting all the numbers in order (it doesn‟t matter whether the order is ascending or descending) and then finding the middle number – this is the median. If the number of numbers is even, find the two „middle numbers‟ add them together and divide by 2 to get the median Example: Data is 27 12 5 17 35 then, in order, this is: 5 12 17 27 35 and the Median is the middle number – 17

Metre The basic metric measure of distance (and where the word metric comes from!). All other distances come form this basic root – millimetre, kilometre etc

Metric system The system of measurement which uses grammes, metres etc.

Mile A measurement of distance within the Imperial system. There are 1,760 yards in a mile and a mile is approximately equal to 1.6 kilometres

Milligram A units of measurement within the metric system. There are 1000 milligrams in a gramme.

Millimetre A unit of measurement within the metric system. There are 1000 millimetres in a metre.

Millilitre 1000th of a litre – I.e. 1000 millilitres = 1 litre

Minimum Value The smallest value which an equation, expression or graph can achieve. In graphical terms it is usually where the curve is at its lowest.

Here we can see that the minimum value is -10

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Mirror line An imaginary line drawn through a shape which divide the shape so that the image on one side of the line is a mirror image of the shape on the other side of the line.

The mirror line

Mixed number A number which has a whole part and a fraction part For example: 5½ is mixed 5 is the whole part and ½ the fraction

Mode A measure of the „shape‟ of a set of data. The Mode of a set of data is the most frequently occurring number Take the set of data: 2

5

7

12

3

2

6

8

2

17

The MODE of this set of data is 2

Multiplication A shorter way than repeated addition. E.g. we could add 5 + 5 + 5 + 5 + 5 + 5 + 5 but since there are 7 5‟s we say 7 x 5 = 35 – I.e. we multiply 5 by 7

Multiples The numbers which are multiples of a given number – e.g. 4, 8, 12, 16, 20, 24 and so on are all multiples of 4. You will alos know these series of numbers as your multiplication tables!

Mutually Exclusive Events Two or more events are mutually exclusive if the both CANNOT occur – e.g. if you toss a coin you cannot get BOTH a Head and a tail. However, if you threw a die you could get a number which was even AND larger that 3 – e.g.

4, so these two events (evenness and larger than 3) are NOT mutually exclusive.

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Nth term Suppose we have a sequence of numbers as follows: 1

3

5

7

9

11

13 …….

It is straightforward to see that the next one will be 15, the next 17, the next 19 and so on But we need to be able to have a general expression for any term in the sequence, and this expression is called the nth term So in the example above we have an equation which says that Nth term is 2n-1 And when we substitute for n=1, n=2, n=3 etc we get the series

Negative number All numbers less than zero (0). If you add the positive digit part of a negative number to the negative number you always get 0 – e.g. if we take –45 and add the digit part (45) we get –45+45 = 0

Nets The flattened two-dimensional shapes which when folded make 3 dimensional solids

The net of a cuboid

Nonagon A nine-sided polygon A regular nonagon has internal angles which total 7 x 1800 = 12600 Which gives us the internal angle as 1260/9 = 1400

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Number line A line used to help work with positive and negative numbers. The line has the positive numbers to the right, the negative numbers to the left and the number zero (0) in the middle

Number sequence A series of numbers which is linked by a rule – e.g. 3, 7, 11, 15 ….. Has the rule „add 4‟

Numerator The number on top of a fraction

Object The shape of „thing‟ which are going to operate on – e.g. we might have the drawing of a square and we are going to move it (translate it) to another position – the original square is called the object, and the square in its new position is called the image.

Oblong Another (and non-mathematical) name for a rectangle

Object/image If, you enlarge an shape (say a triangle) then this is called the object. The result of the enlargement is called the image.

object

image

Obtuse angle

A angle which is greater than 900 and less than 1800

Octagon

d

d is an obtuse angle

An eight sided polygon.

An octagon with all sides and angles equal is called a REGULAR OCTAGON

Odd number Any whole number which cannot be divided by 2 without leaving a remainder – e.g. 1,3,5,7,9,11,13,15,17…...

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Opposite angles Angles which are opposite one another in a shape or diagram – in cases where the opposite angles are as a result of two line crossing, the angles are equal.

a

The angles a are equal

a

Order 1 The order of an equation or expression is the largest power present in the equation/expression For example The expression 3x6 – 5x3 + 2x2 – 8x + 9 is of power 6 because this is largest power of x

Order 2 To order a series of numbers means to put them in a sequence where each one is larger (or smaller) than the one before – called Ascending and Descending For example the following numbers are in Ascending order: 3.1, 3.15, 4.01, 4.1, 5.23, 5.27

Order of rotational symmetry The number of times a shape will „fit‟ onto itself when it is rotated through 3600

Origin The point where the X and Y axes cross (in, for example a graph). The point is usually (0,0)

Y

.(0,0)

X

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Outcome (usually) The result of carrying out a series of experiments – often associated with trying to work out the probability of an event happening.

Parabola The curve created when the graph of a quadratic equation is plotted, or the shape created when you slice a cone through its slope and down to the base:

A parabola-shaped bridge at Abersoch in Wales

Parallel lines Line which do not meet (or which are the same distance apart forever!) and are usually shown as parallel with one or more „ticks‟ on them:

Parallelogram A quadrilateral which has opposite sides equal and parallel (NOTE: the opposite angles are also equal)

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Parallelogram, area of (See Area of parallelogram)

Pascal’s triangle The sequence of numbers (often drawn as a triangle) which show the coefficients of the variable in the expansion on (1+x)n

Pentagon A five-sided figure (or polygon).

Percentage The number of 1/100ths (as expressed as a fraction) - e.g. 25% means 25/100 = 1/4

Percentage change The amount (measured as a percentage) by which an amount (e.g. the price of an article) goes up or down – e.g. if an item cost £100 and was re-priced as £120 there would have been a 20% change (upwards!)

Percentage profit The amount of profit (measured as a percentage) made by someone selling goods or services – e.g. is a television is bought for £200 and sold for £250 they there has been a 50/200 x 100 = 25% profit

Perimeter

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The distance around the outside of an object – e.g. around a square it is the sum of the lengths of the sides – as is the perimeter of a rectangle

5.5

5.5

5

Perimeter = 5 + 5 + 5.5 + 5.5 + 6 = 27

5 6

Perpendicular

Or vertical as it is often called. A line which is at 900 to the horizontal

Pictogram A chart which uses small pictures to show how data.

Pie chart A pictorial representation of data in the form of a circle with „slices‟ cut out of it to show the proportions.

BBC CH4 BBC2 ITV

Place Value Every digit in both whole numbers and decimals has its own individual value – called its place value. The value of a digit is a power of 10 Example the value of the integer 7 in the number 6783 is 700 and the value of the integer 7 in the number 34.076 is 7/100

Plan The view looking down on a three-dimensional object

Plane (mathematical) A plane can be thought of as a 2-dimensional sheet (say of paper). Often such a plane will be used to cut a 3-dimensional object, as in the case of the cone below:

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Plane of Symmetry A „slice‟ through a 3-dimensional object so that the two „halves‟ are identical

pm Meaning post-meridian pm indicates times between 12 noon and midnight

Points of the compass The main four points are North, South, East, West and these are, clockwise from North South – 1800; East – 900; West – 2700

Polyhedron The general term given to geometric shapes (examples of polyhedra are pentagon, hexagon, octagon etc)

Polygon, irregular Any polygons which doesn‟t have all its sides and angles equal.

Irregular Polygons

Polygon, regular

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A polygon )many-sided shape) which has all sides equal and all angle equal

Examples of regular polygons

Polygon The general name given for any closed shape – e.g. square, rectangle, pentagon, hexagon etc are all examples of polygons

Polynomial Function Poly means „many‟ so a polynomial function means any function which is made up of variables and constants and the operations of addition, subtraction and multiplication and whole number powers For example 5x2 – 3x + 9 is a polynomial, but 3x2 – 4/x + x2/3 isn‟t because the constant 4 is divided by the variable x and the power (or exponent) of x is 3/2 – not a whole number

Population The complete set of people or things which we sample. For example the population could be all the pupils in a class, the coloured balls in a bag, all the people who live in Liverpool

Positive number All numbers greater than 0. Every positive number has an „opposite‟ such that when you add the positive number to its opposite you get 0 (zero). This „opposite‟ is called the negative of the number.

For example the „opposite‟ of 3.25 is –3.25 because when you add them together you get 0

Power The number of times a number is to be multiplied by itself – shown as a small superscript number – e.g. 53 means multiply the number 5 by itself 3 time – 5 x 5 x 5 = 125

Prime numbers Numbers which cannot be divided by ant other numbers apart form themselves and 1 – the prime numbers up to 100 are are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Prime Factor Decomposition The prime factors are 2, 3, 5, 7, 11, 13, 17 and so on.

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Any number can be written as a series of prime factors multiplied by each other (some factors may be repeated) Example: 24 = 2 x 2 x 2 x 3 and 100 = 2 x 2 x 5 x 5

Priority of operations The order in which mathematical operations are to be carried out – often remembered by the acronym BODMAS – Brackets, Over, Division, Multiplication, Addition, Subtraction

Prisms A three-dimensional object which has the same cross-section throughout its length

A triangular prism

Prism, volume of The volume of a prism = area of cross section x length

Probability The likelihood (or chance) of an event happening is called the probability of the event happening.

For example a pack of cards has 52 cards – A 2 3 4 5 6 7 8 9 10 J Q K And 4 suits = Hearts, Clubs, Diamonds, Spades So, for example, there are 4 Aces, 4 twos, 4 threes etc Therefore the probability of getting an ace is 4/52 = 1/13 (when cancelled down)

Proper/improper fraction A proper fraction is one where the numerator (the top number) is smaller than the denominator (the bottom number). – so 5/12 is a proper fraction whereas 21/5 is an improper fraction 3/7 is a proper fraction 12/7 is an improper fraction

Probability scale A measure of probability – usually a line with 0 at one end (impossible) and 1 at the other end (certain) along which every event must lie

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Probability of an event The likelihood of an event happening defined as number of „successes Possible number of outcomes

Proportion

Two quantities are in proportion if they increase (or decrease) at a similar rate (or ratio as it is called). For example 3 pints of blue and 1 pint of white paint will make enough paint to paint two walls of a square room. In order to paint all four walls we need to double the amount of blue and the amount of white paint – 6pints of blue and 2 pints of white paint.

Protractor An instrument, often semi-circular for measuring and drawing angles

Pyramid A three dimensional object which has a flat base of three or four sides and an apex to which flat, triangular. Sides rise form the base. A p[pyramid with a triangular base is also called a tetrahedron.

The entrance to the Louvre museum in Paris is a square-based pyramid

Pythagoras’ Theorem The theorem which states that “The square on n the hypotenuse of a rightangled triangle is equal to the sum of the squares on the other two sides”

b

h

As an equation Pythagoras‟

Theorem states: h2 = a2 + b2

a

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Quadrant A quarter of a whole – e.g. the section which has only the positive/positive co-ordinates, the quadrant which has the positive/negative co-ordinates etc

Quadrilateral Any four-sided figure – examples are square, rectangle, rhombus, parallelogram, trapezium, kite.

Examples of quadrilaterals Qualitative A feature of a person or object which cannot be (easily) measured – e.g. beautiful, elegant, red.

Quantitative A feature of a person or object which can be measured – height, weight etc

Quartile

There are three quartiles which divide sorted data into four equal parts The first quartile (lower quartile) cuts off the bottom 25% of the data The second quartile is the Median and cuts the data in two The third quartile (upper quartile) cuts of the bottom 75% or highest 25% of the data

Questionnaire A form used to record information (often from questions asked!).

Quotient The result of dividing one umber by another – e.g. if we divide 12 by 3 we get the answer 4 – which is the quotient

Radius The distance between the centre of a circle and the circumference

Radius)

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Random An event which happen without any planning or outside influence – often used to indicate a trial where there outcome is unknown (e.g. throwing a die)

Random Sample When a survey is being conducted it is, usually, impossible to survey the entire population you are interested in – so you take a representative and random sample. This means sampling things or people who have been chosen randomly, without any pattern to their choice.

Range The range of set of numbers is the difference between the largest and smallest number. NOTE that this is not a particularly useful measure – since extreme numbers at the beginning and end of a set of numbers can give a false picture.

Ratio A means of sharing things – e.g. sweets might be shared in the ration of 3:2 – this means that there are 5 shares (3+2) and one person will get 3 shares and the other person 2 shares

Rational numbers A rational number is a number which can be written as a fraction where numerator and denominator are integers (where the top and bottom of the fraction are whole numbers). For example 1/2, 4, 1.75 (=7/4).

Raw Data Data which has simply been collected (for instance ion questionnaires) and not yet been collated or analysed.

Rectangle, area of The area of a rectangle is length x breadth W

Rectangle

Area = W x B

B

A quadrilateral (four-sided shape) which has opposite sides equal and all angles equal to 900 The external angles of a rectangle are each equal to 900 – making their total 3600

Reciprocal The reciprocal of a number is that number turned upside down – e.g. the reciprocal of 2/3 is 3/2 and the reciprocal of 7 is 1/7

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Recurring Decimal A recurring decimal is one which has a number, or set of numbers, repeating after the decimal point â&#x20AC;&#x201C; e.g. 1/9 = 0.111111111and 1/7 = 0.142857142857142857

Rectangular Prism A prism with a cross section of a rectangle Volume of prism = (2a + 3) x a x 3a 3a Surface area of prism = 2 ((2a + 3) x a)) + 2(a x 3a) + 2((2a + 3) x 3a))

a 2a + 3

Reflection The image of a shape as seen in a mirror (or an imaginary, drawn mirror

Reflex angle

An angle which is greater than 1800 and less than 3600

f

Regular (as in polygon) All the sides and angles are the same

A square

A regular octagon

A regular hexagon

An equilateral triangle

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Resultant of Two Vectors The resultant of two vectors is diagonal of a parallelogram drawn using the two vectors as adjacent sides

F1 and F2 are the vectors and Fnet is the resultant

Rhombus A four-sided figure (quadrilateral) with all sides equal and opposite angles equal (NOTE: all the angles in a rhombus are NOT equal)

RHS (Right Hand Side) Usually refers to the right-hand side of an equation â&#x20AC;&#x201C; and remembering that what you do to the RHS you must do the same to the LHS

Right-angles triangles

A triangle which has one angle of 900. The side opposite the right-angle is called the hypotenuse hypotenuse

Root A number which, when multiplied by itself a given number of times will equal a given number Example the square root of 16 is 4 because 4 x 4 = 16 The third root of 8 is 2 because 2 x 2 x 2 = 8 The square root of a number is written as (for example)

16 = 4

Rotation

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The „turning‟ of a shape, often by a given number of degrees – e.g. a shape might be rotated by 900, or 1800 etc

Rotational symmetry The number of times a shape will „fit‟ onto itself when it is rotated

Rotation symmetry, order of The number of times a shape will „fit‟ onto itself as it is rotated.

a e

b

d

This (regular) pentagon has order of rotational symmetry 5 – you can turn it through 720 each time and it will occupy the same space

c This parallelogram has order of rotational symmetry 2 – you can turn it through 1800 and it occupies its original position

Rounding „Tidying up‟ a number to a pre-determined level of accuracy – e.g. we might round 199 to 200, or 4.003 to 4

Rule A set of steps which have been laid down and which have to be followed in a particular sequence – e.g. “take a number, double it, add 3 and divide by 2”.

Often a rule is given in short-hand by a formula

Scale drawing A smaller drawing of an actual (and much bigger) object – e.g. the plans of your house!

Scale factor The amount by which a shape has been increased or decreased in size. If the number is greater than 1 this means that the shape has been made larger; if the number is less than 1 the shape is made smaller. If the number is equal to 1 the shape remains the same.

Scalene triangle A triangle which has all sides all angles of different sizes.

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Scatter diagrams A diagram showing two sets of different data – e.g. the amount of homework done by pupils and their success in examinations, which allows a comparison between the two sets of data Number of weeds

Graph showing the number of weeds in the garden and the number of children in the family

Number of children

Segment

A portion of a circle bounded by two points on the circumference

.

Sequence A series of numbers which are „related‟ to one another by a rule – e.g. the numbers 2 4 8 16 32 are related by the rule “multiply by 2”

Simplest form Simplest form is the name given to a (usually) fraction which cannot be cancelled down any further For example 8/12 can be cancelled down to 2/3 (by dividing top and bottom by 4) – but it can‟t be cancelled any further, so is in simplest form

Simplifying Making an expression, fraction etc as simple as possible – b collecting together terms, or cancelling down (in the case of fractions)

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e.g. 3x + 5y – 2y + 7x – y + 8x can be simplified to 18x + 2y and 18/24 can be simplified to 3/2 by dividing top and bottom by 6

Simultaneous Equations Two linear equations which have a common solution. For example the equations 5x + 2y = 16 and 3x – y = 3 have the solution x = 2 and y = 3

Sine Rule A collection of expressions which allow you to work out the angles of a triangle, using the sines of the angles and the lengths of sides

a = b = c sinA sinB SinC

Solution The value(s) which, when substituted in an equation, makes the equation true – e.g. the solution to 2x + 3 = 9 is x = 3 because when we replace the x with the value 3 the equation is tru

Sphere A three-dimensional object which has a cross-section always of a circle

Standard Form A way of writing very large or very small numbers using index notation (powers of 10) – e.g. 56000000 can be written 5.6 x 107 and 0.0000000056 can be written 5.6 x 10-9 IMPORTANT NOTE – the number used (in this case 5.6 must itself be between 1 and 10

Stem and Leaf Diagrams A way of grouping data into classes – particularly useful since the original data can still be seen

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Example: the original data is shown below 154, 143, 148, 139, 143, 147, 153, 162, 136, 147, 144, 143, 139, 142, 143, 156, 151, 164, 157, 149, 146 NOTE: the data is first of all organised into classes of equal width – in this case 5 (136 – 139 etc). Then the diagram is simplified to look as follows

Subject, change of Making a particular unknown (x, y etc) the subject of an equation means putting it (the unknown) on its own on the left-hand side of the equation, with everything else on the other side. Then the unknown will be the subject of the equation.

Example suppose we have y = 3x + 7. In this case y is the subject. Suppose we want to change it so that x is the subject. We will get x = (y – 7)/3 – and here x is the subject.

Symmetrical See Line of symmetry

Significant figure The digits to the right of any 0 (zero) in a number - e.g. 123 has 3 significant figures; 0.0034 has two significant figures

Solids A three-dimensional object. The most common ones are: Tetrahedron, Square-based pyramid; Cone; Cylinder; Cube; Cuboid, Hexagonal prism……………..

Solving (equations) Finding the value of variable(s) in an equation which make the equation true (solve it) - e.g. for the equation 3x + 2 = 8 if we put x = 2 in it we get x 2 + 2 = 8 and so the solution to the equation is x = 2

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Square

A quadrilateral having all sides equal and all angles equal (to 900)

Square numbers The sequence of numbers obtained by multiplying the whole numbers by themselves. The first 6 square numbers are 1 x 1 = 1; 2 x 2 = 4; 3 x 3 = 9; 4 x 4 = 16; 5 x 5 = 25 NOTE: Square numbers get their name from the fact that they are the areas of squares which have whole number (integer) length sides

4cm

The area of this square is 4 x 4 = 16cm2

4cm

Square root Given any number the square root is the number which, when multiplied by itself will equal the given number â&#x20AC;&#x201C; e.g. given the number 64 the square root is 8 because 8 x 8 = 64 If we know that the area of this square is 49cm2 then we can work out the length of the sides (which are all the same) by working out the square root of the area = 7cm

Statistics A branch of mathematics which is concerned with presenting and analysing data with a view to understanding or presenting it better. E.g. a set of data can be described by using measures such as Mean, Mode, Median and data can be illustrated using bar and pie charts

Straight line

There are 1800 in a straight line. You can solve problems using this piece of information â&#x20AC;&#x201C; in the diagram below, if we know that one angle is 1450 we can work out the other to be 350 by subtracting the 1450 from 1800

49

1450

350

Substitution The process of replacing letters in an equation or expression with numbers, often to find out an answer.

If we have an expression such as 5x + 3y and we substitute x = 3 and y = 4 we get: 5 x 3 + 3 x 4 = 27

Subscript A number of letter which appear to the right of another number of letter, but smaller and a little lower. We write chemical formulae using subscripts – e.g.

H2SO4 – the 2 and 4 are subscripts

Superscript A letter or number which appear to the right of another letter or number but smaller and higher. Superscripts are used to denote powers – e.g. 52 means 5 x5

Symmetry, line of An artificial line which has a perfect mirror image of an object (or part of an object) on each side of the line

b

a

a

b

NOTE that the image on the right is an exact copy of the image on the left – but „back to front‟.

NOTE: also that each point on one image has a corresponding point on the other image – exactly the same distance from the line of symmetry

Tally marks Ticks you write down to help you when you are counting – e.g. if you were to count the number of different coloured cars passing you,. You would have a list of the possible colours and put a tick against a colour every time a car

50

passed. It is usual to put down four ticks and then cross them through with the fifth tick, to form „five-barred gates‟ - it helps to count the ticks.

Tally-table The table on which you record the data collected on a questionnaire or other data collection form.

Sweets

Above is a tally table showing the preferences of children for food at lunch time

Tangent A tangent at a point of a curve is a straight line which just touches the curve at one point

Term The name given to letters in (for example) equations – e.g. 3x, 4t, 2d are all terms

Term, nth See nth term

Terminating Decimal A decimal which „finishes, with a digit – rather than going on. For example 0.35, 0.206 and 0.22 are all terminating decimals, whereas 0.333333, 0.11111 are non-repeating decimals

Tessellation

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Another word for „tiling‟ - a method of „cutting up‟ as space using the same shape – e.g. you can tile a wall with squares, hexagons, parallelograms but not with pentagons, octagons etc Some examples are:

The idea of tiling is used extensively in textiles

As can be seen from the tessellation on the right – tiles don‟t have to be boring or of the conventional square, triangle etc – but they must cover the area without leaving spaces

Tetra Meaning 4 – as in „tetrahedron‟ - a four-sided solid

Tetrahedron A four-sided solid (similar to a pyramid)

Theorem A mathematical statement which has been proved – e.g. Pythagoras‟ Theorem.

Transformation The movement of an object so as to change its side, position or orientation

Translation The movement of an object in a straight (or series of straight) lines

Image

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Trapezium A quadrilateral which has one pair of opposite sides parallel

Trapezium, area of a

h

b Area = 1/2 x h(a + b)

Travel graph A travel graph shows the pattern of movement during a journey. The axes, typically, will be Time and Distance.

Tree Diagrams Tree diagrams can be a useful way of showing a series of outcomes and helping to work out probabilities.

For example, if we have a box with two red, two green and two white balls in it, and we choose two balls without looking, what is the probability of getting two balls of the same colour?

P(same color) = P(RR or GG or WW) We use the tree diagram to the left to help us identify the possible combinations of outcomes. Here we see that there are nine possible outcomes, listed to the right of the tree diagram

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Trial and improvement The technique of solving equations by substituting a ‟guess‟ into the equation and refining (improving) the guess so as to get nearer and nearer to the solution.

Triangle

A three-sided polygon whose internal angles add up to 1800. There are four types of triangle – Scalene, Isosceles, Equilateral, Right-angled (see also under the names of individual triangles)

Scalene

Isosceles

Equilateral

Right-angled

Triangular numbers A series of numbers which come from stacking (for example) objects in a triangular format:

.

1

. .

.

3

. . .

. . .

6

. . . .

. . .

. .

.

10

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The first stack has 1 object, the next stack has two rows and three objects, the next stack has 1 + 2 + 3 = 6. The first 6 triangular numbers are: 1; 1 + 2 = 3; 1 + 2 + 3 = 6; 1 + 2 + 3 + 4 = 10; 1+ 2 + 3 + 4 + 5 = 15; 1 + 2 + 3 + 4 + 5 + 6 = 21

Triangular Prism A prism which has a triangular cross-section (the one below is an Isosceles triangular prism): The volume of the triangular prism is: ½bxhxl Surface area of the prism is: A = bxh + 2 x l x s + l x b

Trigonometric Functions There are loads of trigonometric functions â&#x20AC;&#x201C; so we will just introduce a few of the early ones you will meet. All these functions are related to angles between two lines, usually in a right-angled triangle.

The initials functions are: Sin A = opposite hypotenuse

=a h

Cos A =

adjacent = b hypotenuse h

Tan A =

opposite adjacent

= a b

The extension to these functions is given in the table below (the angle measures are in radians)

Sine

sin

Cosine

cos

Tangent

tan (or tg)

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Cosecant

csc (or cosec)

Secant

sec

Cotangent

cot (or ctg or ctn)

Turn A movement in a circle (or part of a circle). Movement can be clockwise (in the direction in which the hands of a clock move) or anti-clockwise.

A complete turn is 3600; a half-turn is 1800 and a quarter turn is 900

Turn, full

A rotation of 3600

Turn, Half

A rotation of 1800 (in clockwise or anti-clockwise direction)

Turn, quarter

A rotation of 900 (in clockwise or anti-clockwise direction)

Unit The name given to a measurement â&#x20AC;&#x201C; e.g. cm, inches, metres, millimetres and so on.

Upper Quartile Test Scores

Frequency

Cumulative Frequency

76-80

3

3

81-85

7

10

86-90

6

16

91-95

4

20

56

The total frequency is 20.

The quartile information for this data is: Lower Quartile

0.25 · 20 = 5 The lower quartile falls in the interval 81 - 85.

Median Quartile 0.50 · 20 = 10 The median quartile falls in the interval 81 - 85.

Upper Quartile 0.75 · 20 = 15 The upper quartile falls in the interval 86 - 90.

Variable A part of an equation or expression which can take a variety of values For example in the expression 5x2 – 3x + 9 x is the variable and 9 is a constant

VAT Standing for Value-Added Tax, VAT is the tax the government demands on many goods and services. It is currently (2000) 17.5% To work out the VAT on an item you multiply by 0.175 (which is 17.5% To work out how much an item will be with VAT ADDED you multiply b 1.175 (which is the same as the orginal price of the item plus the VAT)

Vector A vector is a line which has length and direction Here we have a simple vector whose „tail‟ in on the origin (0,0) and whose „point‟ is on the point (4,3) – the length can be worked out using Pythagoras‟ Theorem as 5

Here we have two vectors A and B and the result of adding them together - C

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Venn Diagram A diagram which shows all the mathematical, or logical, relationships between groups of things. These groups are usually shown as circles and, often, the circles will overlap: For example if we show the relationship between „All wooden things‟ and “all tables” w can draw this as a two circle Venn diagram: Circle representing the group of wooden things

Circle representing the group of all tables

Intersection of the circles – representing ALL WOODEN TABLES

Vertex The point where two or more edges meet – NOTE that it is a point, not a line (which are edges) - e.g. a cube has 8 vertices.

Vertical (or upright)

A line which is at right angles (900) to a horizontal line V E R T I C A L

Horizontal

Vertices The points at which edges or faces meet – e,g, a triangle has 3 vertices and a cube has 8 vertices

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A pentagon has five vertices

A cube has 8 vertices

Volume The capacity of a three-dimensional object – e.g. the volume of a cuboid is length x width x height

The volume of this cuboid is 10 x 5 x 4 = 200

The volume of this cylinder is Πr2 x h

Whole number Any of the counting numbers, positive or negative – excluding fractions and decimals part of a number

X-axis The horizontal axis used to locate points on a graph – the first number in a pair of point (e.g. (2,3) is always the x-axis point

Y-axis The vertical axis used to locate points on a graph – the second number in a pair of point (e.g. (2,3) is always the y-axis point

Yard An Imperial unit of measure. There are 1760 yards in a mile, 36 inches in a yard and 3 feet in a yard. A metre is equal to approximately 39 inches

Prime, Squares, Cubes and Triangular Numbers

1

2

3

4

5

6

7

8

9

10 59

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Prime numbers

Triangular numbers

Square Numbers

Cube Numbers

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