Mathematics Formulas

Mathematics Formulas

Important mathematics formulas arranged class-wise from Class 1 to Class 12 (+2).

Class 1 Mathematics

Primary
Addition
a + b = Sum
Subtraction
a − b = Difference
Number Before
n − 1
Number After
n + 1
Counting
1, 2, 3, 4, …
Place Value
Number = place values added together

Class 2 Mathematics

Primary
Addition
a + b = Sum
Subtraction
a − b = Difference
Multiplication
a × b = Product
Division
Dividend ÷ Divisor = Quotient
Perimeter of Square
P = 4 × side
Time
1 hour = 60 minutes

Class 3 Mathematics

Primary
Multiplication
a × b = Product
Division
Dividend = Divisor × Quotient + Remainder
Perimeter of Rectangle
P = 2(l + w)
Perimeter of Square
P = 4a
Area of Rectangle
A = l × w
Area of Square
A = a²

Class 4 Mathematics

Primary
Average
Average = Sum of values ÷ Number of values
Perimeter of Rectangle
P = 2(l + w)
Area of Rectangle
A = l × w
Area of Square
A = a²
Fraction of a Number
Fraction × Number
Conversion
1 km = 1000 m

Class 5 Mathematics

Primary
Fraction Addition
a/b + c/b = (a + c)/b
Fraction Subtraction
a/b − c/b = (a − c)/b
Percentage
% = (Part ÷ Whole) × 100
Average
Average = Total ÷ Number of items
Area of Triangle
A = ½ × base × height
Volume of Cuboid
V = l × w × h

Class 6 Mathematics

Middle School
Ratio
a : b = a/b
Percentage
Percentage = (Part/Whole) × 100
Profit
Profit = SP − CP
Loss
Loss = CP − SP
Simple Interest
SI = (P × R × T)/100
Circle Circumference
C = 2πr
Circle Area
A = πr²
Speed
Speed = Distance ÷ Time

Class 7 Mathematics

Middle School
Percentage
% = (Part/Whole) × 100
Profit Percentage
Profit% = (Profit/CP) × 100
Loss Percentage
Loss% = (Loss/CP) × 100
Simple Interest
SI = PRT/100
Identity
(a + b)² = a² + 2ab + b²
Identity
(a − b)² = a² − 2ab + b²
Identity
a² − b² = (a − b)(a + b)
Triangle Area
A = ½bh

Class 8 Mathematics

Middle School
Linear Equation
ax + b = c → x = (c − b)/a
Cube
a³ = a × a × a
Cube Root
∛a
Square Root
√a
Area of Trapezium
A = ½(a + b)h
Volume of Cube
V = a³
Volume of Cuboid
V = lwh
Surface Area of Cube
TSA = 6a²

Class 9 Mathematics

Secondary
Heron's Formula
Area = √[s(s−a)(s−b)(s−c)]
Distance Formula
d = √[(x₂−x₁)² + (y₂−y₁)²]
Midpoint Formula
((x₁+x₂)/2, (y₁+y₂)/2)
Surface Area of Sphere
SA = 4πr²
Volume of Sphere
V = 4/3 πr³
Volume of Cylinder
V = πr²h
Area of Circle
A = πr²
Probability
P(E) = Favourable outcomes / Total outcomes

Class 10 Mathematics

Secondary
Quadratic Formula
x = [−b ± √(b²−4ac)] / 2a
Discriminant
D = b² − 4ac
Arithmetic Progression
aₙ = a + (n−1)d
Sum of AP
Sₙ = n/2 [2a + (n−1)d]
Sine Ratio
sin θ = Perpendicular/Hypotenuse
Cosine Ratio
cos θ = Base/Hypotenuse
Tangent Ratio
tan θ = Perpendicular/Base
Mean
Mean = Σx/n
Probability
P(E) = Number of favourable outcomes / Total outcomes

Class 11 Mathematics

+1
Binomial Theorem
(a+b)ⁿ = Σ C(n,r)aⁿ⁻ʳbʳ
Permutation
ⁿPᵣ = n!/(n−r)!
Combination
ⁿCᵣ = n!/[r!(n−r)!]
AP nth Term
aₙ = a + (n−1)d
Sum of AP
Sₙ = n/2 [2a + (n−1)d]
Sum of GP
Sₙ = a(rⁿ−1)/(r−1), r ≠ 1
Distance Formula
d = √[(x₂−x₁)²+(y₂−y₁)²]
Slope
m = (y₂−y₁)/(x₂−x₁)
Equation of a Line
y − y₁ = m(x − x₁)

Class 12 Mathematics

+2
Derivative of xⁿ
d/dx(xⁿ) = nxⁿ⁻¹
Derivative of sin x
d/dx(sin x) = cos x
Derivative of cos x
d/dx(cos x) = −sin x
Derivative of eˣ
d/dx(eˣ) = eˣ
Derivative of ln x
d/dx(ln x) = 1/x
Integral of xⁿ
∫xⁿ dx = xⁿ⁺¹/(n+1) + C, n ≠ −1
Integral of 1/x
∫(1/x)dx = ln|x| + C
Integral of eˣ
∫eˣ dx = eˣ + C
Vector Magnitude
|a| = √(a₁²+a₂²+a₃²)
Dot Product
a·b = |a||b|cos θ
Probability Addition
P(A∪B) = P(A)+P(B)−P(A∩B)
Conditional Probability
P(A|B) = P(A∩B)/P(B)