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Page 1

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Par
ti
al
Fract
ions
(x-3)(2x-1)

3x+5
An
algebr
aic
fr
act
ion
such
as
can
be
broken
down
int
o si
mpl
er
par
ts
A B
cal
led
par
ti
al
fr
act
i
o ns
so
that
i
t
is
in
the
for
m (x-3) + (2x-1)…

Page 2

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must be divided first
to
obt
ain
a number
and
a pr
oper
f
ract
ion
bef
ore
it
can
be
exp r
ess ed as
p a r
ti
al
fr
act
ions

Coor
dinat
e Geomet
ry
A
pa r
ame t
ri
c equation
of a
curve…

Page 3

Preview of page 3
Bi
nomi
nal
Expansi
on
The
previ
ous ver
sion
of
the
binomial
t
heorem onl
y wor
ks
when
n i
s a
posi
ti
ve
i
nteger
.
If
n
is
any f
ract
ion,
t
he bi
nomial
theor
em becomes:
2 3
n(n-1)x
(1 + x)n…

Page 4

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I
mpl
ici
t
D i
ff
erent
iat
ion
N orma l
ly,
w he n
dif
ferent
iat
ing,
it
i
s deal
ing
w i
th
`expl
ici
t
funct
ions'
of
x,
where
a
valu e
of y
is
d efi
ned only
in
terms of…

Page 5

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x
Di
ff
erent
iat
inga

Thi
s f
unct
ion
descr
ibes
growth
and decay,
and
it
s der
ivat
ive
giv
e s
a
measur
e of

t
he r
ate
of
change
of
thi
s gr
ow t
h/decay.

Si
ncey = ax
,
taki
ng
logs…

Page 6

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The
key
to
d oi
ng t
he se
probl
ems i
s t
o i
denti
fy
thr
ee comp onent
s and
w r
it
e t
hem
down
ma t
hema ti
call
y:
Wh at
you
a r
e gi
ven
Wh at
i
s r…

Page 7

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f (ax + b)dx = 1
a f (ax + b) + C



Usi
ng
the
rever
se
of
the
chai
n r
ule,
t
he
fol
lowi
ng
gener
ali
sat
ions
can
be
found:

n
(ax+b)
(ax + b)n dx = 1
a n+1 +C



eax+b dx =…

Page 8

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I
f
necessar
y,
use
u=f(
x)
to
change
the
val
ues f
or
the
li
mit
s of
i
ntegr
ati
on
Put
your
x'
s
back
in
agai
n at
t
he end
and
fi
nish
up.


Exampl
e
3
Suppose
we
wis
h
to
fi
nd
(9…

Page 9

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dv
Car
e must
be
taken
over
t
he
choi
ce
of
uand
dx .
The
aim
is
to
ensur
e t
hat
i
t
is
si
mpl
er
to
int
egr
ate
thanv du
dx .
So
choose
u t
o be
easy
to
dif
fer
ent
iat
e…

Page 10

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Di
ff
erent
ial
Equat
ions
I
n gener
al
a di
ff
erent
ial
equat
io n
ma y ha ve x an d
y t
erms
on bot
h si
des,
but
i
f
the
dy
equat
ion
is
of
a
cert
ain
form
f (x)g(y) dx =…

Comments

L.B

great revision source!

Sukhdeep

Did you know there is a thing called a scanner? im just saying this annoying to read off 


Harry Anderson

@Sukhdeep instead of being so rude , you could have said Thanks for giving me your revision notes, would it be possible if next time you upload a copy using a scanner. ... And  if its so hard to read make your own notes!

Housre

Thank you! Great notes :) Perfect for going through to make sure I know everything :)

Alex233

This is amazing! Do you have the same resource for any of the other maths modules? :)

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