Download Multiples of a number are the numbers in its multiplication table

Foundation Maths GCSE Unit 2 –
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 16 is 4 (√16 = 4),
the square root of 49 is 7, 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.....
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
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
20
100
= 40%
Ratio
To split £160 in the ratio 3 : 5, you need to split it into 3 + 5 = 8
parts……..
£160 ÷ 8 = £20
And then find what 3 parts and 5 parts are………
3 x £20 = £60
5 x £20 = £100
Estimation
When rounding numbers to ESTIMATE the answer to a calculation,
always round each number to 1 significant figure before doing any
calculating
Expanding and Factorising
To expand a bracket, multiply all the terms inside the bracket
e.g. 3(x + 7) = 3x + 21
x(x – 4) = x2 – 4x
Factorising is the opposite of expanding
e.g. 6x – 15 = 3(2x – 5)
x2 + 8x = x(x + 8)
nth term of a sequence
the sequence 3, 11, 19, 27…….
has a common difference of 8, so the nth term must include 8n
but the sequence for 8n is 8, 16, 24, 32…..
So the sequence 3, 11, 19, 27……. must be 8n – 5
Laws of Indices
x
y
x+y
x
y
x–y
a xa =a
a ÷a =a
5
7
12
8
3
5
e.g. 3 x 3 = 3
e.g. x ÷ x = x
Now try these questions to test your knowledge………..
1.
2
3
8
12
27
36
39
54
from the above list of numbers, write down:
- two factors of 24
- three multiples of 6
- two prime numbers
- a square number
- a cube number
- one number that is three times one of the other numbers
2. Express 72 as a product of prime factors
3. Place brackets in 3 + 8 x 4 – 5 = 39 to make the calculation correct
4. The cost of a DVD is increasing by 15%. If the previous price of the DVD was
£8, what will be the new price after the increase?
5. Find
3
of 24
8
6. Claire and Tom share £210 between themselves in the ratio 3 : 4.
How much money do they each receive?
7. Expand and simplify 4(3a – 5b) – 2(5a – 6b)
8. Factorise 9x2 - 15x
9. Solve 3x – 7 = 17
10. Find an expression for the nth term of the sequence 8, 11, 14, 17, 20…..