Mathematics Formula Sheet Page 2
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10Pure Mathematics
Mensuration
π
2
Surface area of sphere =
4 r
π
×
Area of curved surface of cone =
r
slant
height
Arithmetic Series
= a + (n − 1)d
u
n
n [2a + (n − 1)d]
1
1
S
=
n(a + l) =
n
2
2
Geometric Series
n−1
u
= ar
n
−
n
a
1 (
r
)
S
=
n
−
1
r
a
S
=
for | r | < 1
∞
−
1
r
Summations
n
∑
2
=
1
+
+
r
n
(
n
1
)(
2
n
) 1
6
=
r
1
n
∑
3
2
2
=
1
( +
r
n
n
) 1
4
=
r
1
Binomial Series
+
⎛
⎞
⎛
⎞
⎛
⎞
n
n
n
1
⎜ ⎜
⎟ ⎟
+
⎜ ⎜
⎟ ⎟
=
⎜ ⎜
⎟ ⎟
+
+
r
r
1
r
1
⎝
⎠
⎝
⎠
⎝
⎠
⎛
⎞
⎛
⎞
⎛
⎞
n
n
n
−
−
−
n
n
n
1
n
2
2
n
r
r
n
⎜ ⎜
⎟ ⎟
⎜ ⎜
⎟ ⎟
⎜ ⎜
⎟ ⎟
+
=
+
+
+
+
+
+
∈
N N
(
a
b
)
a
a
b
a
b
a
b
b
(
n
)
K
K
1
2
r
⎝
⎠
⎝
⎠
⎝
⎠
⎛
⎞
n
n
!
n
⎜ ⎜
⎟ ⎟
=
=
where
C
r
−
r
r
( !
n
r
)!
⎝
⎠
−
−
−
+
n
(
n
) 1
n
(
n
) 1
(
n
r
) 1
K
n
2
r
+
=
+
+
+
+
+
<
∈
1 (
x
)
1
nx
x
x
(
x
, 1
n
R R
)
K
K
1
2 .
1
2 .
r
K
Logarithms and exponentials
x
ln
a
x
=
e
a
Complex Numbers
n
n
θ
θ
θ
θ
+
=
+
{
r
(cos
i
sin
)}
r
(cos
n
i
sin
n
)
θ
i
θ
θ
=
+
e
cos
i
sin
π
2
k
i
n
=
=
=
−
The roots of
z
1
are given by
z
e
, for
k
0
, 1 ,
, 2
,
n
1
n
K
2
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