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Summary AQA Level 2 Further Maths Notes with Examples

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Module
Level 2 Further Maths

Institution
GCSE

Unlock success in AQA Level 2 Further Maths with my comprehensive notes! My meticulously crafted resource covers every specification point, providing clear explanations and numerous examples to enhance understanding. Perfect for students seeking mastery and exam success, these notes are your essent...

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Uploaded on April 1, 2024
Number of pages 19
Written in 2022/2023
Type Summary

further maths
gcse
level 2
aqa
specification specific
specification
examples
maths
detailed
tips
notes
summary

Institution GCSE
Education GCSE
Module Level 2 Further Maths
School year 200

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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

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