Summary IGCSE Further Pure Math

%
indice


1



INDEX qua
func


2

Iden
&
ineq
>>>> Summary
3

1 Logarithm Functions and indices Graph
&
func

2 The Quadratic Function 4


3 Identities and inequalities :
4 Graphs and Functions :
5

in

5 Series °m
i




6 The Binomial Series :
6


f-
7
O


Scalar and Vector quantities r




7

8 Rectangular Cartesian Coordinates Co
Or
-




9 Calculus 8

Cal


10 Trigonometry %

9


Trig


10

,
, SHAPES :
" LN serie
E. Log Laws
1) In ✗
pogey
=



arithmetic series :
a ( d) + ( at 2d )
1099×9=1099×+10999
-1 a +




.ua/s
CYLINDER volume =
Tlrzh 2) the / =L It term znd↑term zrdtterm
-1 ogee ↳
=




10991¥ ) 1099×-109 aY
r
= g

Curve surface Ztrh o
nth (n 1) d
•

area
3) 1h1
-




a +
=
s =
0 term >
-




h •
+
toga ( X )
"
=
Klogax
¥
n
g) em
± , s
Tota, ,wfa , , , ,rn+z , , × , ,a+,n
.




sum
g.
=
area =
o u , =
,
109b$
I
s
toga ✗ =


logba 5) Inxn =
nlnx
CONE Volume =
b- Tlr2h
toga (E) = -




logax sn= nz / a -1L )
\ curve surface Trl 109 ab =
1

area
logba
=
e
Binomial
n
Expanding nun
0




s.ir#-Ttasrfaearea:Trl-Tr Discriminant A2 -

B' =/ A- B) ( ATB )
•

£
0
- ( y+ × )n=y+n×+n(
n -




2 ,
t )


b.
2-
49C > 0 2 solution A2t2ABtB2=( A- + B) ( ATB ) :( A -11372 U
SPHERE Volume =
4-3 Ttr
}
b2 -
Hac = 0 1 solution A2 ZAB -1132 :( A- B) ( A- B)
_ =
( A- B)
2
VECTOR
"
b " " < ° "" °"
?
" "




( Xy )
}
-133=11--13111-2-1 AB -1132 )
-


N
A ×; +
yj
r
.

Total surface area = 4 # rz
>



¥
AB -1132 )
}
°
Alpha & A -1-133=(1-+13) / A2 -




9×2 + b. ✗ + c. 0 ✗

B4 ( A2 -1132 ) ( A2
"
B2 )
2-110×+9=0 1×2+92
A
-




AB→
= -
✗
_




us
-




CUBOID volume lwh
a
/ →
:
( A2 -1132 ) / A -11311A -



B) +

g-
Total surface
✗ ,
→ ✗ × , -1×2=-1-1 -



p ≤ unit vector : a

7N area
✗ z
→
B X , Xz =
G- / of Rate of
change
,
a

wtwh+ Length
: DX
,
dr dl

d+µb
,




Pb
✗ ✗ a +
POLYNOMIAL dt dt dt =


PYRAMID
volume =
É( base area )h m f- ( a ) :O (x -

a) is a factor volume : dv SECTOR
dt

É
sin r
Total surface area f( %-) :O then ( ax b) is a factor Arc length
:

ro
-




i. DA =
e
o Area :
+ ☐ + A -1A -1A s dt
w u divided
by ( ax
-

b) → remainder f- ( ka ) cosin
M ᵈT
Differentiation
Temperature :
dt Area :
Érzg Area :{
dd-=a(
" ☐ ""
)(f( ✗ 7)
y=a( f- ( x ) ) f. ( X )
-




n -
I > n

axh
☐
> a ( n ) × ""

G-
' '


/
☐
ax
y U V > Vu + UV
axndx
= - =
= + c
'
n , ,

D)
'
☐
dy d2Y o d' Vu Uu " "
Distance s
Y
-

☐
Caxtb )
y
> '

y
,
/ ( a×+b)nd×
= = ,

DX
=
+ c
v2 •
ay d ✗
2
s + a n -11
nzx D
•
-
efl× ) D) f. ( ) et " ' £ I I
,
y x
=


/
=
o
°
In
Integration axtbdx axtb + c
distance
=

E
É
a
"

z -11
y
-

_
sin f( × )
☐
>
% =
f- (
'

× )cosf( × )
=
'
ea×+b + c
<
I

, SHAPES :
CYLINDER Volume = Tlr - h

r


curve surface 211Th
•

area
-

=



h


Total surface 211Th ZTIRZ
-




area = t




CONE Volume =
b- Tirah
l curve surface area = Irl
e
n



oar
\ Total surface area :
Trl + Tlrz



SPHERE volume =
4-3 tr
'




\
r
.
.
Total surface area = 4 Tlr
2




CUBOID volume : 1Wh


Total surface
Tn area


w
= 21W -12Wh + 21h
,



PYRAMID
Volume =
15 ( base area )h


n
Total surface area =


7 l

+ A + At A + D
w