Math formulas, equations, and
symbols
Chapter 1 -
Different types of numbers:
1. Natural numbers – Any whole number from 1 to
infinity. 0 is not included
2. Odd numbers – A whole number that cannot be
divided by 2
3. Even numbers – A whole number that can be divided
exactly by 2
4. Integers – Any of the negative and positive whole
numbers, including 0
5. Prime numbers – A whole number greater than 1 that
has only 2 factors: the number itself and 1
6. Fractions – A number representing parts of a whole
number, can be written as a common (vulgar) fraction
in the form of a/b or a decimal using the decimal point
7. Multiples – A multiple of a number is found when you
multiply that number by a positive integer
8. LCM – The lowest common multiple of two or more
numbers is the smallest number that is a multiple of all
the given numbers
9. HCF – The highest common factor of two or more
numbers is the highest number that is a factor of all the
given numbers
10.
Factors – They are numbers that divide exactly
into another number with no remainder
11.
Prime numbers – They have exactly two factors: 1
and the number itself
12.
Composite numbers – They have more than two
factors

The number 1 has only one factor so it is not
prime nor composite
13.
Prime factors – They are the factors of a number
that are also prime
14.
Squares – They are formed when a number
multiplies by itself
15.
Square roots – Square roots of a number is the
number that was multiplied by itself to get the square
number.
16.
Cubes – A number is cubed when multiplied by
itself and then multiplied by itself again.
17.
Cube roots – The cube root of a number is the
number that was multiplied by itself to get the cube
number.
18.
Directed numbers – They are numbers with both
size and direction
Divisibility tests
A number is exactly divisible by:
2 – if it ends with 0, 2, 4, 6 or 8
3 – if the sum of its digits is a multiple of 3
4 – if the last two digits can be divided by 4
5 – if it ends with 0 or 5
6 – if it is divisible by both 2 and 3
8 – if the last three digits are divisible by 8
9 – if the sum of the digits is a multiple of 9
10 – if the number ends in 0
BODMAS/BIDMAS Rule:
Brackets
Of / Indices
Division
Multiplication
Addition
Subtraction
Chapter 2 –
Lines and Angles:
1. Point – A point is usually where two lines meet, and on
paper it is mostly represented by a dot (.) or a cross (x)
2. Line – A line is a straight figure that extends to infinity
in both directions
3. Parallel – A pair of lines that are the same distance
apart all along their length in parallel. The symbol for
this is ||
4. Angle – When two lines meet at a point it is called an
angle The meeting point is called the vertex of the
angle and the two lines are called the arms of the angle
5. Perpendicular – When two lines meet at right angles,
they are perpendicular to each other
6. Acute angle – An acute angle is > 0° but <90°
7. Right angle – A right angle is an angle of exactly 90°
8. Obtuse angle – An obtuse angle is > 90° but < 180°
9. Straight angle – A straight angle is an angle of 180°. A
line is a straight angle
10.
Reflex angle – A reflex angle is an angle that is >
180° but < 360°
11.
Revolution – A revolution is a complete turn; an
angle of exactly 360°
Angle relationships
1. Complementary angles – Angles in a right angle add up
to 90°. The sum of those two angles are
complementary angles
2. Supplementary angles – Angles in a straight line add up
180°. The sum of those two angles are supplementary
3. Angles round a point – Angles at a point make a
complete revolution. The sum of the angles at a point is
360°
4. Vertically opposite angles – When two lines intersect,
two pairs of vertically opposite angles are formed.
Vertically opposite angles are equal in size
Angles and parallel lines
1. Corresponding angles (F) – When two parallel lines are
cut by a transversal four pairs of corresponding angles
are formed. Corresponding angles are equal
2. Alternate angles (Z) – When two parallel lines are cut
by a transversal two pairs of alternate angles are
formed. Alternate angles are equal
3. Co-interior angles (C) – When two parallel lines are cut
by a transversal two pairs of co-interior angles are
formed. Co-interior angles are supplementary
Triangles
1. Scalene triangle – Scalene triangles have no sides of
equal length and no angles that are of equal sizes
2. Isosceles triangle – Isosceles triangle have two sides of
equal length. The angles at the bases of the equal sides
are equal in size
3. Equilateral triangle – Equilateral triangles have three
equal sides and three equal angles (each being 60°)
4. a) Acute-angled triangles have three angles, each < 90°
b) Right-angles triangles have one angle = 90°
c) Obtuse-angled triangles have one angle > 90°
Triangle formulas
1. The sum of interior angles of a triangle:
(n-2)180
2. Each interior angle of a triangle:
(n-2)180
n
3. The sum of exterior angles of a triangle:
360
4. Each exterior angle of a triangle:
360
n
Quadrilaterals
1. Parallelogram – Opposite sides parallel and equal
Opposite angles are equal
Diagonals bisect each other
2. Rectangle – Opposite sides parallel and equal
All angles = 90°
Diagonals are equal
Diagonals bisect each other
3. Square – All sides equal
All angles = 90°
Diagonals equal
Diagonals bisect each other at 90°
Diagonals bisect angles
4. Rhombus – All sides equal in length
Opposite sides parallel
Opposite angles equal
Diagonals bisect each other at 90°
Diagonals bisect angles
5. Trapezium – One pair of sides parallel
6. Kite – Two pairs of adjacent sides equal
One pair of opposite angles is equal
Diagonals intersect at 90°
Diagonals bisect angles
Circles
Chapter 4 –
Types of data:
1. Categorical data – It is non-numerical data. It names or
describes something without reference to number or
size. It is also known as qualitative data
2. Numerical data – Number form data. It can be an
amount, a measurement, a time, or a score. It is also
known as quantitative data. It can divide into 2 groups:
a) Discrete data – This is data that can only take certain
values. When you count things, your collecting
discrete data
b) Continuous data – This is data that could take any
value between two given values. When your
measuring something, your collecting continuous
data.
Methods of collecting data:
1. Primary data – Data from primary sources is known as
primary data. You can collect primary data by doing
surveys or interviews, by asking people to complete
questionnaires, by doing experiments or by counting
and measuring.
2. Secondary data – Data from secondary sources is
known as secondary data. This involves using existing
data to find the information you need. For example, if
you use data from an internet site to answer a
question, to you this is a secondary source.
Organising data:
1. Tally tables – Tallies are marks that are used to keep a
record of items you count. A tally table is used to keep
a record when you are counting things
2. Frequency tables – A frequency table shows the totals
of the tally marks. Some frequency tables include the
tallies
A grouped frequency table contains results in class
intervals
3. Stem-and-leaf diagrams – It is a special type of table
that allows you to organise and display grouped data
using the actual data values.
A back to back steam-and-leaf diagram is used to show
two sets of data
4. Two-way tables – They show the frequency of certain
results for two or more sets of data.
Different charts to display data:
1. Pictograms – They are charts that use small symbols to
represent quantities. The meaning of the symbol and
the amount it represents (a key) must be provided for
the graph to make sense.
2. Bar charts – They are normally used to display discrete
data. The chart shows information as a series of bars
plotted against a scale on the axis. The bars can be
horizontal or vertical.
3. Compound bar charts – They display two or more sets
of data on the same set of axes to make it easy to
compare the data.
4. Pie charts – It is a circular chart which uses slices or
sectors of the circle to show data.
5. Line graphs – Values are plotted against ‘number lines’
on the vertical and horizontal axes, which should be
clearly marked and labelled.