Summary AQA Level 2 Further Maths Notes with Examples

Further maths

,1
. Number




1 1 Basic-fractions decimals ratio
proportions BIDMA
.
, ,
percentages , , ,




1 2 of
.
The
product rule
counting
-n ! =
nx(n -

1) x (n 2) ...
-
1

↳ for 0 and
only positive integers
EXAMPLE:

4
digit number -
first is
prime ,
number is even


1st Ind 3rd Ht


4 10 10 S
X X X
=

prime
:
2 3 3 7
, , ,



even : 0 2 4 6 8
, , , ,




1
.
3 Surds
↳
addition/subtraction
↳
need to have same base

EXAMPLE :
EXAMPLE : EXAMPLE :
To + V32 - -

Vz Eis-Tz +- 3S
t
↓ ↓ ↓
-x4x5
↓ +
jaxz VExJz 59 / x 59x /3 Jes 3(π6 (3)x


3(45)
= 35 = 452 = 753 : 353 = 3 53 = 2
= 1253

34 + 46 =
>z 75 -
35 =
45 35 -
253 + 1253 =
1553


denominators
rationalising
↳



multiply top by
↳ surd
and bottom

-
difference of two
complex squares
:




EXAMPLE :




25X(5
+ 1)
(5 + 1)
=
65 + 6 + 26 + 25
s + 5 5 - - 1



-
=
2 5 + 4




.
2 ALGEBRA




2 .
1 Basic rules




2 .
I Function

↳ notation :
f(x) :
...




EXAMPLE :

f(x) =
x3 -
2


f(s) =
(s)3 - 2

=
12) -
IT

=
98

, .
2 3 Domain and
Range
↳ Domain : set of
inpur
values it can take (values
EXAMPLE :

f(x) =
3x + 1 -
1


f(x) = x2 domain is infinite


f(x) = O


Range of
ly values)
↳
set
ourpur
:
values

4) domain
dependent on




usually an
inequality
EXAMPLE :




for
f(x) =
3x + 1 -

22x7


range
:




f( 2) - =
3) 2) -
+ 1

S
=
-




f() =
3() + 1
= 22


-
> =
j(x) < 22




2 4 functions
composite
.




↳
Ourpur of first function becomes of second function
input
EXAMPLE :


f(x) =
x2g(x) =
3x + 1

find the of such than
fg(x) gf(x)
=
values


fg(x) = (3x +
1)2g +(x)
=
3 +1




(3x + 1)2 = 3x + 1

qx + 6x + 1 = 3x2 + 1


6x2 + 6x =
O


6x(x + 1)
=
0


x
=
0 or K = -1




2 .

S inverse functions
- notation :
f"(x)
EXAMPLE :




f(x) =
3x -
1


Let =
3x-1 ! must be written
y
+ 1 = 3x
y
11 x
=
make the
subject


f(x) and

11
=

interchange y




Expanding
6
simplifying
-
2 and brackets