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Maths glossary
Maths glossary
Subject(s):
Maths
Age group(s):
12–14, 15–16
Topic:
Maths revision
Licence information | This resource is free to use for educational purposes. ©British Council 2015
Source | This resource has been developed by EAL Nexus.
Numbers
Digits
0,1,2,3,4,5,6,7,8,9
Negative numbers
-4 -3 -2
-1
0
Positive numbers
1
2
3
4
Multiplication and division of negative numbers
+ x + = + - x + = - + ÷ + = +
- ÷ + = + x - = - - x - = + + ÷ - = - ÷ - = +
Even numbers can be divided exactly by 2
Large odd numbers end in 1,3,5,7,9
Even numbers– 2,4,6,8,10,…,100, etc.
Odd numbers– 1,3,5,7,9,11,…,101, etc.
Place value
Thousands Hundreds Tens Units
(5,218 – five thousand two hundred and eighteen)
5
4
2
8
A prime number can be divided exactly only by 1 or itself.
2,3,5,7,11,13, etc.
1 is not a prime number
Factors are numbers you can multiply together to get another number
The factors of 6 are 1,2,3 and 6
1x6=6 and 2×3=6
A prime factor is a factor which is a prime number.
2x3=6
2 and 3 are prime factors
A multiple is the result of multiplying a number by another number
12 is a multiple of 3, 3x4=12
©British Council 2015
A square number is a number multiplied by itself
5²= 5x5
5²= five squared
A square root √ of a number is a number which
multiplied by itself gives you the original number
√25 = 5 (5x5=25) and √25 = -5 (-5x-5=25)
Cube numbers
𝟑
5³= 5x5x5 = 125
√𝟏𝟐𝟓 = 𝟓
Indices=powers
 When multiplying indices, add them
p3×p7 = p3+7 = p10
 When dividing indices, subtract
them
s5÷s3 = s5-3 = s2
 (d3)5 = d3x5 = d15
 Any number to the power of 0 is 1
a0 = 1
Addition +
add, plus, and, total of, increase by, sum of, altogether, more, extra
Subtraction - subtract, minus, take away, less, decrease by, reduce by, difference between
Multiplication
x
Division ÷
Equals =
More than >,
less than <
BIDMAS
multiply by, times, groups of, lots of, the product of
5a = 5xa
divided by, share equally, each, part of, portion
equals, is, is the same as, makes, has the same value as
> more than, is greater than, is bigger than
< is less than, is smaller than, is not as big as
≥ greater than or equal to
≤ smaller than or equal to
brackets, indices, division, multiplication, addition, subtraction
7 + (6 × 52 + 3) = 7 + ((6 × 25) + 3) = 7 + (150 + 3) = 7 + 153 = 200
©British Council 2015
Perimeter
Perimeter is the distance around a 2D shape.
Perimeter of a rectangle = length + width + length+ width
a=6cm
Area
b=3cm
Perimeter = a+b+a+b
Area means how much space a flat (2D) shape takes up. We measure area in square units,
e.g. cm2
Area of a rectangle = length x width
b
Area = a x b
a
Area of a parallelogram = base x height
Area = b x h
Area of a triangle = base x height
2
A = b x h
2
Area of a trapezium = (a+b) x h
a
h
b
©British Council 2015
Volume
Volume means how much space a solid 3D shape takes up. We measure volume in cubic
units, e.g. cm3
Volume of a cube or cuboid = length x width x height
c
a
Volume = a x b x c
b
Volume of a cone = 1/3 x π x radius² x height
Volume = 1/3πr²h
Volume of a sphere = 4/3 x π x r³
Volume = 4/3πr3
©British Council 2015
Lines
Angles
straight line
horizontal line
curved line
vertical line
perpendicular lines
parallel lines
diagonal line
Any two lines meet at an angle. Angles are measured in degrees (º). There are different
kinds of angles.
©British Council 2015
a right angle equals
90º
an acute angle is less
than 90º
an obtuse angle is
more
than
90º.
a reflex angle is
more than
180º
a straight angle
lies on a straight
line and equals 180º
a full angle (= a circle)
equals 360º
alternate (Z-shape)
angles are opposite to
each other
and equal
α=β
corresponding
(F-shape) angles
are equal
α=β
a and b are
vertically opposite
angles and they are
equal
x and y are co-interior
angles, they add up to
180º
Angles in a
quadrilateral
(4-sided
shape)
add up
to 360°
a
b
©British Council 2015
2D shapes
Polygons
a square has four
equal sides and four
right angles
a rectangle has four
right angles and opposite
sides are equal
a parallelogram has
a quadrilateral is
parallel opposite sides any shape with
and equal opposite
four straight sides
angles
a trapezium has one
pair of parallel sides
a kite has two pairs of
equal sides
a pentagon has five
sides and five angles
a rhombus has 4
straight equal
sides. The
opposite sides are
parallel and the
opposite
angles
are
equal
A polygon is any flat shape with three or more straight sides. When all the sides and
angles of a polygon are equal, it is called a regular polygon.
©British Council 2015
triangle quadrilateral pentagon hexagon
Number 3
of
sides
Circles
4
5
6
heptagon
octagon nonagon decagon
7
8
9
10
a circumference is the distance around the circle
a radius is any line from the centre of the circle to the
circumference
a diameter is a straight line from one side of the circumference to
the other side through the centre of the circle
an arc is a part of the circumference
a chord is a line across the inside of a circle
a tangent is a line which touches the circumference at only one point
a sector is the section between two radiuses
a segment is a sector cut off by a chord
a semi-circle is a half circle
concentric circles are circles which have the same centre
Area = π x radius²
Circumference = π x diameter
Area of a sector = π r2 ( central angle ° )
360°
A=πr²
C=πD
©British Council 2015
Triangles
3D shapes
Isosceles - Two
sides are the same
length. The two
angles at
the base
are
equal
Equilateral - All three
angles are equal. All
three sides are the
same length
A cube has 6
square faces all
the same size. It
also has 8 vertices
and 12
edges
A cuboid has 6
rectangular faces, 8
vertices and 12 edges
A cone has a circle
as its base, a
curved face
and a point
on the top
Right-angled - One of
Scalene – All sides
the angles measures
and angles are
90º. The longest side is different
called
hypotenuse
The angles of a triangle
always add up to 180º.
a+b+c=180°
A prism is a solid
shape with matching
ends. It has the same
cross-section all
across its
length
A square-based pyramid
has 1 square face and 4
triangular faces, 5
vertices and 9 edges
A sphere has only
one
curved face, no
vertices
or edges
A cylinder has circular
faces at each
end and a
curved face
A net is what a 3D
shape would look
like if it were
opened out flat
©British Council 2015
Symmetry
A line of symmetry is the line which divides the shape into two equal parts. Different
shapes can have 0, 1, 2, 3, etc. lines of symmetry
0 lines
1 line
4 lines
Rotational symmetry is when a shape can be rotated without changing its form
Transformations
Order 1 (none)
Order 2
Order 3
Order 4
Rotation means
turning
around a centre
Reflection is when Translation means Enlargement
a shape is flipped moving/sliding the means to make
over a line
shape without
bigger
changing it
Order 5
Congruent –
same size,
same shape
©British Council 2015
Data
Data is a collection of facts, like values or measurements
Quantitative
 Discrete - can be counted
 Continuous - can be measured
Qualitative – can be described
The mean is the average of a set of numbers. To calculate it: add up all the numbers and
divide by how many numbers there are
2, 2, 4, 6, 7, 10, 11
2+2+4+6+7+10+11 = 42
42÷7 = 6
the mean is 6
The median is the middle number in a set of numbers
2, 2, 4, 6, 7, 10, 11
the median is 6
The range is the difference between the lowest and highest values
2, 2, 4, 6, 7, 10, 11
11-2 = 9
the range is 9
Graphs
The mode is the number which appears most often in a set of numbers
2, 2, 4, 6, 7, 10, 11
the mode is 2
A tally/frequency table A bar chart compares
A pictogram uses
things between different
pictures to show
groups
data
Always put the
numbers in order:
smallest to largest!
A pie chart
compares parts of
a whole
©British Council 2015
Y axis
grid
(6,5)
y=3
coordinates (6, 5)
meaning x=6, y=5
X axis
axes
X=3
Table of values
Y = x+3 Substitute! Y = -2+3 = 1
X
-2
-1
0
1
2
y
1
2
3
4
5
Plot the points!
©British Council 2015
Fractions
Numerator
(top)
Denominator (bottom)
Proper fraction
(bottom larger
than top)
2½
Mixed number whole number and
proper fraction
Equivalent fractions mean
equal, the same
Addition and subtraction
x7
3 + 5
x4
4
7
=
21 + 20 = 41
28
28
28
Multiplication
x 1x3
½x¾=3/8
x
Improper fraction
(top larger than
bottom)
Division
3 ÷ 2
4 3
2x4
= 3 x 3 = 9
4 x 2 8
Swap top and bottom and multiply
Decimals
tens
units
hundredths
thousandths
tenths
2 5 3 6 3
Add/subtract decimals: Line up the decimals and add/
subtract
75.25–5.45 = 75.25
-3.21
78.46
Decimal point
Rounding to one decimal place
7.35
= 7.4
less than 5 (1,2,3,4) round down
5 or above (5,6,7,8,9) round up
©British Council 2015
Percentage
Percentage means ‘out of 100’
Fraction
Decimal
2
20
2÷20
0.1
0.1 x 100
Percentage
Diagram
10%
0f means x
15% of £50 is 15x50 = £7.50
100
Measurements Length
Weight
10mm = 1cm
100cm = 1m
1000m = 1km
Algebra
Time
1000mg = 1g
60s = 1 min
1000g = 1kg*
24h = 1 day
1000kg = 1tonne 60 mins = 1 hour
(ton)
7 days = 1 week
Simplifying: Collecting like terms
2x+5y+x-3y 2x+5y+x-3y = (2x+x)+(5y-3y) = 3x+2y
Expanding: Multiplying out brackets
x
5(2a-3) = 5x2a-5x3 = 10a-15
Fraction
Decimal Percentage
1/4
0.25
25%
1/2
0.50
50%
3/4
0.75
75%
4/4 = 1
1
100%
Comparison
more than / greater than
less than
heavier than
lighter than
higher than
lower than
longer than
shorter than
+
Multiplying out brackets is the opposite to
factorising
x
©British Council 2015
Equations
Bearings
Factorising (putting brackets in)
6a-9 = 6a(÷3)-9(÷3) = 3(2a-3)
4y + 6 = 18
4y + 6 - 6 = 18 – 6
Balance the equation by
4y = 12
doing the same thing to
4y ÷4 = 12 ÷4
both sides of the equation
y = 3
North
North
A bearing is an angle, measured clockwise from
the north direction. The bearings are always
given in three figures, 075°.
The bearing of the island from the ship is 075°;
75º
the bearing of the ship from the island is 240°.
240º
©British Council 2015
Probability
The probability of throwing a fair die/dice and getting a 6 is 1/6
= 1/6
The probability of throwing a number bigger than 7 is 0
A weighted die/dice is not fair
The probability of throwing/flipping/tossing a coin and getting heads is ½
=
1/2
©British Council 2015
If there are 4 red, 6 green and 2 blue beads/marbles/counters in a bag, the probability of
picking a blue bead is 2/12 = 1/6
2/12 = 1/6
Probability scale
0
0
0
impossible
25%
¼
0.25
unlikely
50%
½
0.5
even
75%
¾
0.75
likely
100%
1
1.0
certain
©British Council 2015
7
It is impossible to get a 7 throwing a six-sided dice.
It is unlikely to snow in June.
The chance of getting the same number of black and white squares on a chess board is even.
It is likely to grow a flower from a flower bulb.
It is certain that Christmas is on the 25th December.
©British Council 2015