GCSE Maths

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Times Tables

You should learn these THOROUGHLY. The answers should spring into your mind without any delay.

1 x 2 = 2 1 x 3 = 3 1 x 4 = 4 1 x 5 = 5 1 x 6 = 6 1 x 7 = 7 1 x 8 = 8 1 x 9 = 9 1 x 10 = 10
2 x 2 = 4 2 x 3 = 6 2 x 4 = 8 2 x 5 = 10 2 x 6 = 12 2 x 7 = 14 2 x 8 = 16 2 x 9 = 18 2 x 10 = 20
3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 3 x 5 = 15 3 x 6 = 18 3 x 7 = 21 3 x 8 = 24 3 x 9 = 27 3 x 10 = 30
4 x 2 = 8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24 4 x 7 = 28 4 x 8 = 32 4 x 9 = 36 4 x 10 = 40
5 x 2 = 10 5 x 3 = 15 5 x 4 = 20 5 x 5 = 25 5 x 6 = 30 5 x 7 = 35 5 x 8 = 40 5 x 9 = 45 5 x 10 = 50
6 x 2 = 12 6 x 3 = 18 6 x 4 = 24 6 x 5 = 30 6 x 6 = 36 6 x 7 = 42 6 x 8 = 48 6 x 9 = 54 6 x 10 = 60
7 x 2 = 14 7 x 3 = 21 7 x 4 = 28 7 x 5 = 35 7 x 6 = 42 7 x 7 = 49 7 x 8 = 56 7 x 9 = 63 7 x 10 = 70
8 x 2 = 16 8 x 3 = 24 8 x 4 = 32 8 x 5 = 40 8 x 6 = 48 8 x 7 = 56 8 x 8 = 64 8 x 9 = 72 8 x 10 = 80
9 x 2 = 18 9 x 3 = 27 9 x 4 = 36 9 x 5 = 45 9 x 6 = 54 9 x 7 = 63 9 x 8 = 72 9 x 9 = 81 9 x 10 = 90
10 x 2 = 20 10 x 3 = 30 10 x 4 = 40 10 x 5 = 50 10 x 6 = 60 10 x 7 = 70 10 x 8 = 80 10 x 9 = 90 10 x 10 = 100

Multiplication

Multiply 69 by 4. This means: how many is 4 lots of 69?

  H T U
    6 9
X     4
  — — —
  2 7 6
  — — —
    3  

H stands for hundreds, T for tens and U for units.

  • We say "4 times 9 is 36" (from the times tables).
  • We write the units digit - the 6 - in the units column between the lines.
  • We write the tens digit - the 3 - in the tens column below the bottom line. (The 3 is carried.)
  • We then say 4 times 6 is 24 and add to this the carried 3 to make a total of 27.
  • We write the 7 in the tens column and the 2 in the hundreds column.

You should always make sure that your figures are lined up very carefully.

Multiply 214 by 8.

    2 1 4
X       8
  — — — —
  1 7 1 2
  — — — —
    1 3  
  • We say "8 times 4 is 32".
  • Write 2 down and carry 3.
  • 8 times 1 is 8 plus 3 makes 11.
  • Write down 1 and carry 1.
  • 8 times 2 is 16; adding the carried 1 makes 17, so write down 17.


Try working out: (a)
  8 3
X   5
  — —
  — —
(b) 672 x 8

Prime Numbers

Every number has itself and 1 as factors. If it has no other factors, it is said to be a prime number.

It is useful to memorise all of the prime numbers up to at least 19. The prime numbers up to 100 are:

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97

 

Indices (powers) and roots

You should memorise:

Square root 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Square 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256

You should also memorise:

Cube root 1 2 3 4 5 10
Cube 1 8 27 64 125 1000


Index Laws

Multiplication and division ap x aq = ap+q
  ap ÷ aq = ap-q
Brackets (ap)q = apxq
Zero index a0 = 1 (and remember a1 = a)
Reciprocal index 1/ap = a-p

Note: ap + aq does NOT equal ap+q. It can’t be simplified any more.


Problems to solve

Simplify:

Square root of a8
Square root of a2b4
80
(85)0
(x5)0
(x3y7)0
41
(x5)1
(55)1
(x3y7)
(6-4) ÷ (6-2)
(x-4) ÷ (x-2)
(9-374) ÷ (9-272)
(x-3y4) ÷ (x-2y2)