Important formulas for class 9th B
Answers
1. Polynomial Expresssions Formulas
Monomial
3
,
2
x
,
2
3
y
e
t
c
.
Binomial
(
2
x
+
3
y
)
,
(
3
x
−
2
y
)
e
t
c
.
Trinomial
x
2
+
4
x
+
5
e
t
c
.
Linear Polynomial
x
+
2
,
3
x
+
5
e
t
c
.
Quadratic Polynomial
a
x
2
+
b
x
+
c
e
t
c
.
Cubic Polynomial
x
3
+
4
x
2
+
5
e
t
c
.
Biquadratic Polynomial
x
4
+
5
x
3
+
2
x
2
+
3
2. Coordinate Geometry Formulas
Equation of a line
a
x
+
b
y
+
c
=
0
Equation of a circle
x
2
+
y
2
=
r
2
Here ‘
r
’ is the radius of the circle
Equation of a parabola
y
2
=
4
a
x
Equation of an ellipse
x
2
a
2
+
y
2
b
2
=
1
Equation of hyperbola
x
2
a
2
−
y
2
b
2
=
1
Distance formula
D
=
⎷
[
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
]
Angle between two lines
θ
=
tan
−
1
(
m
2
−
m
1
1
+
m
1
m
2
)
3. Circles Formulas
Area of circle
π
r
2
Diameter of circle
2
r
Circumference of circle
2
π
r
Sector angle of circle
θ
=
(
180
×
l
)
(
π
r
)
Area of the sector
(
θ
2
)
×
r
2
Area of the circular ring
=
π
×
(
R
2
−
r
2
)
θ
=
Angle between two radii
R
=
Radius of outer circle
r
=
Radius of inner circle
4. Surface Area and Volume Formulas
Cuboid
Volume of Cuboid (LSA)
l
×
b
×
h
Lateral Surface Area of Cuboid (LSA)
2
h
(
l
+
b
)
Total Surface Area of Cuboid (TSA)
2
(
l
b
+
b
h
+
h
l
)
Cube
Volume of Cube
x
3
Lateral Surface Area of Cube (LSA)
4
x
2
Total Surface Area of Cube (TSA)
6
x
2
Sphere
Volume of Sphere
4
3
×
π
r
3
Lateral Surface Area of Sphere (LSA)
4
π
r
2
Total Surface Area of Sphere (TSA)
4
π
r
2
Right Circular Cylinder
Volume of Right Circular Cylinder
π
r
2
h
Lateral Surface Area of Right Circular Cylinder (LSA)
2
×
(
π
r
h
)
Total Surface Area of Right Circular Cylinder (TSA)
2
π
r
×
(
r
+
h
)
Right Pyramid
Volume of Right Pyramid
1
3
×
[
Area of
the Base
]
×
h
Lateral Surface Area of Right Pyramid (LSA)
1
2
×
p
×
L
Total Surface Area of Right Pyramid (TSA)
LSA
+
[
Area of
the Base
]
Right Circular Cone
Volume of Right Circular Cone
1
3
×
(
π
r
2
h
)
Lateral Surface Area of Right Circular Cone (LSA)
π
r
l
Total Surface Area of Right Circular Cone (TSA)
π
r
×
(
r
+
L
)
Hemisphere
Volume of Hemisphere
2
3
×
(
π
r
3
)
Lateral Surface Area of Hemisphere (LSA)
2
π
r
2
Total Surface Area of Hemisphere (TSA)
3
π
r
2
Prism
Volume of Prism
B
×
h
Lateral Surface Area of Prism (LSA)
p
×
h
Total Surface Area of Prism (TSA)
π
×
r
×
(
r
+
L
)
l
=
Length,
h
=
Height,
b
=
Breadth
r
=
Radius of Sphere
L
=
Slant Height
5. Statistics Formulas
Mean
¯¯¯
x
∑
x
n
x
=
Sum of the Values
n
=
Number of Values
Standard Deviation,
σ
σ
=
⎷
∑
n
i
=
1
(
x
i
−
¯¯¯
x
)
2
N
−
1
x
i
=
Terms Given in the Data
,
¯¯¯
x
=
Mean
,
N
=
Total Number of Terms
Range
R
R
=
[
Largest
value
]
−
[
Smallest
value
]
Variance,
σ
σ
2
=
∑
x
i
−
¯¯¯
x
N
x
=
Item given in the data
,
¯¯¯
x
=
Mean of the data
,
N
=
Total number of terms
6. Heron's Formula
Perimeter
Right-angle triangle
P
=
b
+
h
+
d
Height
=
h
,
Base
=
b
,
Hypotenuse
=
d
,
Isosceles right-angle triangle
p
=
2
a
+
a
√
2
a
=
Equal Sides
Triangle with different sides
a
,
b
,
c
P
=
a
+
b
+
c
Square with side
a
P
=
4
a
Rectangle
P
=
2
L
+
2
B
Length
=
L
,
Breadth
=
B
Parallelogram with
two sides
a
and
b
P
=
2
a
+
2
b
Rhombus with diagonals
d
1
and
d
2
P
=
2
√
d
2
1
+
d
2
2
Area
Right-angle triangle
A
=
1
2
×
b
×
h
Isosceles right-angle triangle
A
=
1
2
×
a
2
Triangle with different sides
a
,
b
,
c
A
=
2
√
s
(
s
−
a
)
(
s
−
b
)
(
s
−
c
)
Here,
s
=
a
+
b
+
c
2
Square with side
a
A
=
a
2
Rectangle
A
=
L
×
B
Parallelogram with two sides
a
and
b
A
=
Base
×
Height
Rhombus with diagonals
d
1
and
d
2
A
=
1
2
d
1
d
2
7. Probability Formulas
Probability
=
No. of Favourable Outcomes
Total No. of Outcomes