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E Math
4048
A Math
4049
4048 Mathematics GCE O-Level
Mathematical Formulae
1. Compound Interest
Total amount
A
=
P
(
1
+
r
100
)
n
A = P\left(1 + \dfrac{r}{100}\right)^n
A
=
P
(
1
+
100
r
)
n
2. Mensuration
Curved surface area of a cone
A
=
π
r
l
A = \pi r l
A
=
π
r
l
Surface area of a sphere
A
=
4
π
r
2
A = 4\pi r^2
A
=
4
π
r
2
Volume of a cone
V
=
1
3
π
r
2
h
V = \dfrac{1}{3}\pi r^2 h
V
=
3
1
π
r
2
h
Volume of a sphere
V
=
4
3
π
r
3
V = \dfrac{4}{3}\pi r^3
V
=
3
4
π
r
3
Area of triangle ABC
A
=
1
2
a
b
sin
C
A = \dfrac{1}{2}ab\sin C
A
=
2
1
ab
sin
C
Arc length
s
=
r
θ
s = r\theta
s
=
r
θ
Area of sector
A
=
1
2
r
2
θ
A = \dfrac{1}{2}r^2\theta
A
=
2
1
r
2
θ
3. Trigonometry
Sine rule
a
sin
A
=
b
sin
B
=
c
sin
C
\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}
sin
A
a
=
sin
B
b
=
sin
C
c
Cosine rule
a
2
=
b
2
+
c
2
−
2
b
c
cos
A
a^2 = b^2 + c^2 - 2bc\cos A
a
2
=
b
2
+
c
2
−
2
b
c
cos
A
4. Statistics
Mean
x
ˉ
=
∑
f
x
∑
f
\bar{x} = \dfrac{\sum fx}{\sum f}
x
ˉ
=
∑
f
∑
f
x
Standard deviation
σ
=
∑
f
x
2
∑
f
−
(
∑
f
x
∑
f
)
2
\sigma = \sqrt{\dfrac{\sum fx^2}{\sum f} - \left(\dfrac{\sum fx}{\sum f}\right)^2}
σ
=
∑
f
∑
f
x
2
−
(
∑
f
∑
f
x
)
2
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