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Maths glossary

Maths glossary

Subject(s): Maths

Age group(s): 12–14, 15–16

Topic: Maths revision

This project and its actions were made possible due to co-financing by the European Fund for the Integration of Third-Country Nationals

Nexus resource

©British Council 2015

Numbers Digits

0,1,2,3,4,5,6,7,8,9

Negative numbers Positive numbers

-4 -3 -2 -1 0 1 2 3 4

Multiplication and division of negative numbers

+ x + = + - x + = -

+ x - = - - x - = +

+ ÷ + = + - ÷ + = -

+ ÷ - = - - ÷ - = +

Even numbers– 2,4,6,8,10,…,100, etc.

Odd numbers– 1,3,5,7,9,11,…,101, etc.

Even numbers can be divided exactly by 2

Large odd numbers end in 1,3,5,7,9

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

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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

5³= 5x5x5 = 125 √

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

multiply by, times, groups of, lots of, the product of

5a = 5xa

Division ÷ divided by, share equally, each, part of, portion

Equals = equals, is, is the same as, makes, has the same value as

More than >,

less than <

> 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

BIDMAS

brackets, indices, division, multiplication, addition, subtraction

7 + (6 × 52 + 3) = 7 + ((6 × 25) + 3) = 7 + (150 + 3) = 7 + 153 = 200

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a

b

Perimeter Perimeter is the distance around a 2D shape.

Perimeter of a rectangle = length + width + length+ width

Perimeter = a+b+a+b

Area 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

Area of a triangle = base x height

2

A = b x h

2

Area of a parallelogram = base x height

Area = b x h

Area of a trapezium = (a+b) x h

b=3cm

Area = a x b

a=6cm

a

b

h

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a b

c

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

Volume = a x b x c

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

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Lines straight line

horizontal line

diagonal line

curved line

vertical line

perpendicular lines

parallel lines

Angles Any two lines meet at an angle. Angles are measured in degrees (º). There are different

kinds of angles.

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a b

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°

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2D shapes a square has four

equal sides and four

right angles

a rectangle has four

right angles and opposite

sides are equal

a parallelogram has

parallel opposite sides

and equal opposite

angles

a quadrilateral is

any shape with

four straight sides

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

Polygons 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.

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triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon

Number

of

sides

3

4

5

6 7

8

9 10

Circles 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 A=πr²

Circumference = π x diameter C=πD

Area of a sector = π r2 ( central angle ° )

360°

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Triangles 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

Right-angled - One of

the angles measures

90º. The longest side is

called

hypotenuse

Scalene – All sides

and angles are

different

The angles of a triangle

always add up to 180º.

a+b+c=180°

3D shapes A cube has 6

square faces all

the same size. It

also has 8 vertices

and 12

edges

A cone has a circle

as its base, a

curved face

and a point

on the top

A cuboid has 6

rectangular faces, 8

vertices and 12 edges

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 cylinder has circular

faces at each

end and a

curved face

A sphere has only

one

curved face, no

vertices

or edges

A net is what a 3D

shape would look

like if it were

opened out flat

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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

Order 1 (none)

Order 2

Order 3

Order 4

Order 5

Transformations

Rotation means

turning

around a centre

Reflection is when

a shape is flipped

over a line

Translation means

moving/sliding the

shape without

changing it

Enlargement

means to make

bigger

Congruent –

same size,

same shape

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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

Always put the

numbers in order:

smallest to largest!

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

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

Graphs A tally/frequency table

A bar chart compares

things between different

groups

A pictogram uses

pictures to show

data

A pie chart

compares parts of

a whole

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Table of values

Y = x+3 Substitute! Y = -2+3 = 1 Plot the points! X -2 -1 0 1 2

y 1 2 3 4 5

coordinates (6, 5)

meaning x=6, y=5

axes

(6,5)

grid Y axis

X axis

X=3

y=3

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Fractions

Addition and subtraction

x7 3 + 5 x4

4 7 =

21 + 20 = 41

28 28 28

Multiplication

x 1x3

½x¾=3/8

x 2x4

Division

3 ÷ 2 = 3 x 3 = 9

4 3 4 x 2 8 Swap top and bottom and multiply

Decimals

Decimal point

Add/subtract decimals: Line up the decimals and add/

subtract

75.25–5.45 = 75.25

-3.21

78.46

Rounding to one decimal place less than 5 (1,2,3,4) round down

7.35 = 7.4 5 or above (5,6,7,8,9) round up

2 5 3 6 3

units hundredths

thousandths tens tenths

Numerator (top)

Denominator (bottom)

Mixed number -

whole number and

proper fraction

2½

Improper fraction

(top larger than

bottom)

Proper fraction

(bottom larger

than top)

Equivalent fractions mean

equal, the same

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Percentage Percentage means ‘out of 100’ Fraction Decimal Percentage

2 2÷20 0.1 0.1 x 100 10%

20

Diagram Fraction Decimal Percentage

1/4 0.25 25%

1/2 0.50 50%

0f means x

15% of £50 is 15x50 = £7.50

100

3/4 0.75 75%

4/4 = 1 1 100%

Measurements Length

10mm = 1cm

100cm = 1m

1000m = 1km

Weight

1000mg = 1g

1000g = 1kg*

1000kg = 1tonne

(ton)

Time

60s = 1 min

24h = 1 day

60 mins = 1 hour

7 days = 1 week

Comparison

more than / greater than

less than

heavier than

lighter than

higher than

lower than

longer than

shorter than

Algebra

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

Multiplying out brackets is the opposite to

factorising

x

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Factorising (putting brackets in)

6a-9 = 6a(÷3)-9(÷3) = 3(2a-3)

Equations 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

Bearings 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°;

the bearing of the ship from the island is 240°. 75º

240º

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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

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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

Probability scale

0 25% 50% 75% 100%

0 ¼ ½ ¾ 1

0 0.25 0.5 0.75 1.0

impossible unlikely even likely certain

2/12 = 1/6

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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.