Download LINEAR Foundation Maths GCSE Key Facts

Maths GCSE LINEAR – Things to Remember
Multiples of a number are the numbers in its multiplication
table
e.g. multiples of 7 are 7, 14, 21, 28, 35 ........
Factors of a number are the numbers that divide into it without
any remainder
e.g. factors of 12 are 1 and 12, 2 and 6, 3 and 4
A prime number has only two factors, one and the number
itself
e.g. the first few prime numbers are 2, 3, 5, 7, 11, 13 ........
A square number is the result you get when multiplying a
number by itself
e.g. 3 squared (or 32) = 3 x 3 = 9
so 9 is a square number (9 is the square of 3)
The first few square numbers are 1, 4, 9, 16, 25 ....
A square root is the opposite or inverse of a square number
e.g. the square root of 9 is 3 (√9 = 3)
the square root of 25 is 5, etc.....
A cube number is the result you get when multiplying a
number by itself and then by itself again
e.g. 2 cubed (or 23) = 2 x 2 x 2 = 8
so 8 is a cube number (8 is the cube of 2)
The first few cube numbers are 1, 8, 27, 64, 125 ....
A cube root is the opposite or inverse of a cube number
e.g. the cube root of 8 is 2 (3√8 = 2)
the cube root of 27 is 3, etc.....
Mean
Median
Mode
Range
- add up and divide
by how many there are
- middle number
WHEN IN ORDER
- the MOST common
number in the list
- take the lowest from
the highest
When finding MEAN FROM A TABLE, remember to MULTIPLY the data
by the frequency (then sum of data ÷ total frequency)
Fractions, Decimals and Percentages:
F → D → P
÷
x 100
e.g.
2 = 2 ÷ 5 = 0.4, and 0.4 x 100 = 40%
5
5 of 24 = 24 ÷ 8 x 5 = 3 x 5 = 15
8
 30% of 60 = 3 lots of 10% of 60 = 3 x 6 = 18
 8 as a percentage of 20 = 8_ = _40 = 40%
20
100
BIDMAS – the order in which calculations
are done
Brackets
Indices (or powers)
Division
Multiplication
Addition
Subtraction
e.g. 4 + 6 x 5 = 4 + 30 = 34
Expanding and Factorising
To expand a bracket, multiply all the terms inside the bracket
x(x – 4) = x2 – 4x
e.g. 3(x + 7) = 3x + 21
Factorising is the opposite of expanding
x2 + 8x = x(x + 8)
e.g. 6x – 15 = 3(2x – 5)
To expand a double bracket, use the FOIL method
e.g. (x +3)(x + 7) = x2 + 7x + 3x + 21
= x2 + 10x + 21
Laws of Indices
ax x a y = a x + y
e.g. 35 x 37 = 312
ax ÷ a y = a x – y
e.g. x8 ÷ x3 = x5
nth term of a sequence
the sequence 8, 11, 14, 17…….
has a common difference of 3, so the nth term must include
3n
but the sequence for 3n is 3, 6, 9, 12…..
So the sequence 8, 11, 14, 17……. must be 3n + 5
Areas
Area of a Triangle = (base x height) ÷ 2
Area of a Circle = π x radius x radius
or
A = π r²
Circumference of a Circle = π x diameter (or C = πD)
Pythagoras’ Theorem
c2 = a 2 + b 2
(c is the hypotenuse,
the longest side)
a2 = c2 – b2
b2 = c2 – a2
(a and b are the shorter sides)
Angles
Angles on a straight line add to 1800
Angles in a triangle add to 1800
Angles at a point add to 3600
Angles in a quadrilateral add to 3600
Angles on parallel lines:
Bearings – remember: North is 00
Measure angle clockwise
TERRy
Translate – describe how far across (right or left) and how far up or down
Enlarge – describe scale factor and centre of enlargement
Rotate – describe angle and direction of rotation and centre of rotation
Reflect – describe the equation of the mirror line
Y
Remember that the information below is always provided on the
formula sheet at the start of your exam paper
When you first open your exam paper, you should write down all
the key formulae and information that you have revised for the
exam before you start answering questions
Do this now as a practice……………….