Core Maths C1 Revision Notes - Mr Barton Maths

1 Algebra
Indices
Rules of indices
a m × a n = a m+n
a m ÷ a n = a m–n a 0 = 1
(a m ) n = a mn
a –n =
1
n
a
a
1
n
m n
=
n
a
n
( )
n m
a = a = a
m
Examples:
(i) 5 –3 × 5 4 = 5 –3 + 4 = 5 1 = 5.
7 –4 × 7 –2 = 7 –4 + –2 = 7 –4 – 2 = 7 –6 =
(ii) 3 5 ÷ 3 –2 = 3 5 – –2 = 3 5 + 2 = 3 7 .
9 –4 ÷ 9 6 = 9 –4 – 6 = 9 –10 1
=
9 10
1
7 6 .
11 –3 ÷ 11 –5 = 11 –3 – –5 = 11 –3 + 5 = 11 2 = 121
(iii) (6 –3 ) 4 = 6 –3 × 4 = 6 –12 1
=
6 . 12
(iv)
2 1
2
64 3
64 3 2
= ⎛ ⎝ ⎜ ⎞⎟ ⎠
= ( 4)
= 16
− 2 1
(v) 125 3
= since minus means turn upside down
2
125 3
1
3
= , since 3 on bottom of fraction is cube root, 125 = 5
2
5
1
=
25
Example: (16 a ) ÷ (8 b ) = (2 4 ) a ÷ (2 3 ) b = 2 4a ÷ 2 3b = 2 4a – 3b .
Example: Find x if 9 2x = 27 x + 1 .
Solution: First notice that 9 = 3 2 and 27 = 3 3 and so
9 2x = 27 x + 1 ⇒ (3 2 ) 2x = (3 3 ) x + 1
⇒ 3 4x = 3 3x + 3
⇒ 4x = 3x + 3 ⇒ x = 3.
C1 14/04/2013 SDB
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