Glossary of Terms
Below is a finite list of mathematical terms which are commonly used. It is easy to confuse different concepts and words in maths, so this may be of help. Keep posted as we are constantly updating this list.
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Accumulate |
Interest is said to accumulate when it builds up
over time into a relatively large amount of money. |
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Acute angle |
An angle which is smaller than 90o (a right angle) |
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Alternate angles |
Alternate angles are on the opposite side and at
opposite ends of a line (the transversal) that cuts a pair of parallel
lines |
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Angle of depression |
An angle measured below the horizontal |
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Angle of elevation |
An angle measured above the horizontal. |
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Anticlockwise |
Turning in the opposite direction to the hands moving round a clock
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Bar Chart or Bar Graph |
A bar chart is a way of showing information by the lengths of a set of bars. The bars are drawn vertically or horizontally.
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Bisect |
The prefix bi means two e.g. bicycle – two wheels. If you bisect something you cut it into two identical parts. The bisector can be a point, a line or a plane that cuts something into two identical parts.
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Breadth
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This is another word used to mean width |
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Circumference of a circle |
We find the length of the circumference of a circle
using the formula:
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Clockwise |
Turning round in the same direction as the hands of a clock
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Common denominator |
A number which can be divided exactly by all
denominators of a given set of fractions |
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Complement of a set |
The complement of a set, A, in a particular domain
is the set of all objects which are not in A, but are in the domain. It
is written as A’. |
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Congruent triangles |
Two triangles are congruent if they are identical
in every way except for their position, one can be turned into the other
simply by moving it around and/or flipping it over. |
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Cylinder |
Usually a solid, whose ends are two parallel
circles of equal size and which are joined together by a curved surface.
Tins of food are good examples of cylinders.
In fact, the ends of cylinders do not have to be circles; they
can be any shape that has no corners, as long as they are parallel and
both the same shape. |
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A line joining two points on the circumference of a
circle,
which passes through the centre of the circle, dividing the circle in
half. |
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Discount |
A discount is an amount that is subtracted from a
price, usually in order to sell something faster. It may be a particular
amount of money, like €5 off, or it may be a fraction or a percentage:
50% off; 1/3 off, etc |
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Element |
A member of a set.
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Equiangular |
A shape, which is equiangular, has all of its
angles the same size. e.g. a rectangle
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Equilateral triangle |
A triangle with all its sides the same length. Each
of the angles in an equilateral triangle is 60° |
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Equivalent sets |
When two or more sets have the same number of
elements they are said to be equivalent. |
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Exchange Rate |
The number of units of one currency which you can
buy for one unit of another currency. It is the ratio of how much the
two different currencies are worth. |
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Exterior angle
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Exterior means being on the outside (the opposite
of interior, being on the inside). The exterior angles of a polygon are
the angles formed by extending the polygon's sides; the angle between
one side, and the extension of the next side. |
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Factor |
Something which will divide a number exactly. For
instance, the factors of 20 are 1, 2, 5, 10 and 20. The factors of 23
are 1 and 23. |
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Foot |
An Imperial measure of length. It is equivalent to
12 inches, and 3 feet are equivalent to 1 yard. The plural of foot is
feet. 1 foot (1' or 1ft) is about 30.48cm. |
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Fraction |
A way of writing numbers, especially numbers that
are not whole numbers, as the ratio of one number to another. The two
numbers used are usually whole numbers, but they do not have to be;
sometimes they can be fractions or even decimals. |
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Geometry
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That part of mathematics which involves the study
of points, lines, shapes and solids.
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Hectagon |
A polygon with 100 edges. |
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Hectare |
A metric unit of area, equal to 10000 square metres,
or the area of a square of side 100m. |
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Highest Common Factor |
The largest number which will divide exactly into
two or more other numbers. E.g. the hcf of 18, 21 and 24 is 3, the hcf
of 12, 24, and 30 is 6.
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Histogram |
A histogram is a graph of grouped (binned) (at
least interval scale, continous) data in which the number of values in
each bin is represented by the area of a rectangular box. The boxes of a
histogram are drawn immediately next to each other, visualising that
every value is possible |
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Horizontal |
A line is horizontal if it is at right angles to
vertical |
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Hypotenuse |
The name given to the longest side of
a right angled triangle. It is always the side of a triangle which is
opposite the right angle |
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Improper Fraction |
A fraction whose numerator is greater than its
denominator. |
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Infinite |
Having no end. |
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Integer |
A whole number, positive or negative. We use the
symbol Z for the set {...,-3, -2, -1, 0, 1, 2, 3, ...} |
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Interest |
A certain amount of money; a proportion of how much
you have invested, which is paid to you by a bank every month or every
year. This compensates for the fact that inflation makes the value of
your money go down from year to year. If you borrow money from a bank,
you have to pay interest instead of receiving it. |
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Interior Angle |
Interior means inside, the opposite of being
outside (exterior). An interior angle is an angle inside the figure. A
quadrilateral has four interior angles, a triangle has three. Another
word for interior is internal, the opposite of external (outside). |
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Intersection |
The intersection of two things is the place where
they meet or overlap, ie the place where they intersect. Two lines
intersect in a point; two planes can intersect in a line; the
intesection of two sets is another set, etc. |
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Inverse |
The inverse of a number is 1 divided by the number.
The inverse of a function or a transformation is the function or
transformation which 'undoes' it. The inverse of an element of a set, or
a number, with respect to a particular operation, is what you have to
combine the element with in order to get that operation's identity
element. eg: The inverse of 5 is 1/5 The inverse of addition is
subtraction The inverse of a clockwise rotation is an anticlockwise
rotation. The additive inverse of 5 is -5, because 5 + (-5) is 0, which
is the additive identity. The inverse of the inverse always gets you
back to where you started. |
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Isosceles Triangle |
A triangle which has two equal sides. The third side is called the base. |
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Kilo |
Prefix meaning a thousand. The symbol k is used,
for instance one km is a thousand metres. |
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Kilogram |
A unit of mass, equal to a thousand grams. The
abbreviation is kg. One kilogram is about 2.2lb. |
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Kilometre |
A unit of measurement which is equal to 1000 metres |
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lb |
An abbreviation for 'pounds,' the imperial unit of
mass |
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Line |
An element of geometry that has only one dimension, its length. It has no breadth or width and is often thought of as a set of points that are so very closely set down there are no gaps between them. A line segment is usually part of a straight line between two given points on it. There are many different types of line segment. They can be diagonal, horizontal, vertical, oblique, parallel, perpendicular. When a line segment is not straight it is often called an arc. A line of symmetry is a line segment which can be used to divide a shape into two equal and matching parts, with one half folding over and fitting exactly on top of the other half. A line graph is a graph whose plotted points are joined by lines
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Line of symmetry |
The line which cuts a symmetrical figure into two identical mirror parts |
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Litre |
A metric unit of measurement. It is used when
measuring capacity and volume. The symbol for a litre is l . 1 litre
(1l) is equivalent to 1000 millilitres. 1 litre (1l) is also equivalent
to 1000 cubic centimetres. 1 litre is a bit less than 2 pints. |
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Loss |
How much money is lost by buying something and then
selling it at a lower price; for instance if a shopkeeper buys a pound
of apples for €1 and sells them for 70c, a loss of 30c has been made |
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Lowest common denominator |
The smallest number into which the denominators of two or more fractions will divide exactly. |
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Lowest common multiple |
The smallest number which is a multiple of each one
of a given set of numbers. For instance, for the set {2, 3, 4}, 24 is a
common multiple, but 12 is the lowest common multiple.
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Mean or Arithmetic Mean |
The mean or arithmetic mean is one measure of the
centre of a set of data. The mean is calculated by adding up all the
values and dividing the total by the total number of values. For
example, when the values 7, 4, 6, 5, 7, 7, 6 are added the sum is 42.
The mean is calculated by dividing 42 by the number of values (7),
giving a mean of 6. The arithmetic mean is sensitive to outlier values |
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Median of data |
The median is one measure of the central tendency
of a set of data. The median is the value halfway through data arranged
in order of size. When the values 7, 4, 6, 5, 7, 7, 6 are ordered, 4, 5,
6, 6, 7, 7, 7 we can see the median or middle score is 6. If there is an
even number of values, the median is half way between the middle pair of
values. When the values 4, 8, 5, 7, 7, 6 are ordered as 4, 5, 6, 7, 7, 8
the middle pair is 6 and 7, so the median is 6.5 or 6 ½. |
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Metre |
A standard metric unit used when measuring length;
the symbol for it is m. A hundred centimetres, or a thousandth of a
kilometre. One metre is about 4 inches more than 1 yard. |
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Mile |
An Imperial unit of length, equal to 1760 yards or
5280 feet, ie 1609.344 metres. |
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Millilitre |
A unit of capacity equal to a thousandth of a litre,
or a tenth of a centilitre. The abbreviation is ml. 1millilitre has the
same volume as 1 cubic centimetre. |
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Millimetre |
One thousandth of a metre. The symbol for
millimetre is mm. |
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Mode |
The mode is one measure of the centre of a set of
data. It is the value or number that occurs most often. It is possible
for a set of values to have more than one mode. The mode is the only
measure of central tendency for nominal data. For example, if the eye
colours of a group of friends are green, green, gray, gray, gray, blue,
blue, brown, brown, brown, brown, then the mode is brown because it is
the most common colour in the set. |
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mph |
Short for miles per hour, an imperial unit of speed
still widely used |
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Natural number or counting number |
A positive whole number. The natural numbers are: 1, 2, 3, 4, 5,....
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Negative |
A negative number is a number whose value is less
than nought. It is written with a minus sign in front of it. E.g. -5 is
the number 'negative five'; -3.25 is the number 'negative three point
two five' |
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Null or empty set |
A set which has no elements - nothing belongs to
it. It is shown as { } or by the symbol Ø. |
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Obtuse angle |
An angle which measures between 90o and 180o |
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Operation |
The act of combining elements of a set.
Multiplying, dividing, adding and subtracting are specific operations
used on the set of numbers. Two numbers can be combined using one of
these operations to produce a third number. Using the numbers 8 and 2:
multiplying them produces 16; dividing them produces 4(or a quarter);
adding them produces 10; while subtracting them produces 6 (or -6,
negative six). The order of doing operations on numbers is very
important. |
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Optimum |
The best, quickest or most efficient example of
something. |
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Parallelogram |
A special quadrilateral; a four sided figure whose
opposite sides are parallel. It has the property that the diagonals
bisect each other. |
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Percentage |
A quantity like 25 percent or 33% is called a
percentage. It is a way of expression a fraction as a number of parts
out of 100; for instance 25 per cent means 25/100. |
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Perimeter |
The distance all the way round the boundary - the edge of something Has your school got a perimeter fence - a boundary? The perimeter of a circle is called the circumference
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Perpendicular |
Perpendicular means 'at right angles'. A
perpendicular is a line that meets another line at right angles. The
horizontal is perpendicular to the vertical and vice versa. |
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Pictogram |
A graph which uses pictures or symbols to show
information about how often something occurs. |
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Pie chart |
A way of showing information using different sized
sectors of a circle, in such a way that it looks like the slices of a
pie. They allow easy comparisons to be made about the information that
is shown, particularly in relation to the whole. |
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Positive |
A positive number is a number which is greater than
zero. 13, 0.22, 7456.98, 23/5, 4¾, 1/5 are all numbers which can be
found to the right of zero on a number line. |
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Price |
How much money someone would be willing to exchange
for a particular object. |
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Prime Number |
A prime number is a number with exactly two
factors, which are one, and itself. 2 has the factors 1 and 2; |
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Probability |
Probability measures how likely an event or outcome
is. It is usually shown as a success fraction - the number of ways an
event could happen compared to the total number of events that could
happen - and is written:
Probability (of special event) = (Number of times that special event
occurs)
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Profit |
The amount of money which someone makes by buying a
particular object and then selling it. For instance if six apples are
bought for 50c and sold for €1.20, the profit that has been made is
70c. |
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Proper fraction |
A fraction where the top number is smaller than the
number below the line. That is, the numerator is smaller than the
denominator. e.g. 2/5; 3/4; 1/3; 4/7; 18/19 |
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Protractor |
A flat circular or semi- circular instrument for
measuring and drawing angles. |
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Pythagoras' theorem |
A statement attributed to Pythagoras - a Greek
mathematician who lived a long time ago. (585 - 500 BC). The theorem he
worked out concerns the sides of a right angled triangle; he proved
that: |
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Radius |
The radius of a circle is the distance from the
centre of the circle to its edge. The radius of a regular polygon is the
distance from the centre of the polygon to any one of its vertices. The
plural of radius is radii |
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Random |
A term used in probability, relating to things that
happen by chance. It means that there is no special pattern to the items
or numbers that are selected or chosen, that is, they happen in a
haphazard way. |
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Ratio |
A comparison made between two or more quantities.
The symbol frequently used to show items in ratio to each other is :
A ratio is often written as fraction. |
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Reflex angle |
A reflex angle is an angle that is so big that it
looks as if it has bent back on itself. It is an angle that is greater
than 180 degrees but less than 360 degrees. |
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Remainder |
What is left over when you try to share a whole
number out into a particular number of equal parts. |
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Right-angled triangle |
A triangle in which one of the angles is a right
angle. This is the kind of triangle for which the trigonometric
functions are defined. The side opposite the right angle is always the
triangle's longest side; it is called the hypotenuse. Pythagoras'
theorem tells us about the lengths in a right angled triangle. |
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Rotation |
Turning; changing of direction. A transformation
where a figure turns through a specific angle about a fixed point,
called the centre of rotation. The centre of rotation may be inside or
outside the figure which is being transformed. If the figure is turned
in an anti-clockwise direction, the rotation is considered positive,
while a negative rotation turns the figure clockwise. |
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Sale Price |
A price to which something is reduced in order to
sell it more quickly |
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Scalene triangle
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A triangle whose sides are all of different lengths and whose angles are all different in size |
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Sector |
A sector is an area bounded by part of a curve and
two radii. Often the curve is an arc of a circle, but it can be part of
another curve. |
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Segment |
Part of the circle enclosed by an arc of the
circumference and its chord |
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Semicircle |
Half of a circle. It is the area enclosed by a
diameter and an arc of the circle joining its two ends |
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Set |
A collection of items which may or may not be
related to each other. The members of a set are called elements. The
symbol for a set is a pair of curly brackets, with the elements of the
set between them: {A, B, C} |
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Square foot |
A unit of area, equal to the area of a square with
sides one foot long. One square foot is 144 square inches, or 929.0304
cm2. |
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Square root |
The square root of a given number is that number
which when multiplied by itself gives the original number. 'The square
root ' is written √ |
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Statistics |
The collecting, classify and interpreting of data,
facts and figures. The main concerns of statistics are: |
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Subset |
A set of elements which are part of a larger set. A
subset can be the whole or part of the larger set, or the empty set. The
set of pupils who play the recorder includes: {Anna, Claire, David,
Diane, Emma, John, Kate, Kip, Liam, Sally, Tom}, one subset is; {David,
John, Kip, Liam,Tom}, another is: {David, Diane}, another is: {}- the
empty set. |
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Sum of interior angles |
In a triangle, the interior angles add up to 180?.
In a quadrilateral, the interior angles add up to 360?. In a pentagon,
the interior angles add up to 540?. In a polygon with n edges, the
interior angles add up to (180n-360)?. |
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Symmetry |
A figure has symmetry if it remains the same after
a reflection or a rotation of less than a whole turn. |
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Transversal |
A line that cuts across two or more lines. Usually
it cuts across parallel lines, to produce special kinds of angles:
alternate or corresponding angles. |
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Triangle |
A three-sided polygon. The sum of the interior
angles of a triangle is always 180°. Triangles can be classified:
either by their angles, as acute, obtuse, right-angled or equiangular;
or by their sides, as scalene, isosceles or equilateral. |
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Union |
The union of two sets means to bring together the
two sets, so that all the elements of both the two sets and no other
elements are involved |
