50 Maths Formulas

50 Maths Formulas PDFs for all the concepts covered under different classes (6, 7, 8, 9, 10, 11, and 12), as per the CBSE syllabus are provided here by our expert teachers. To solve mathematical problems easily, students should learn and remember the basic formulas based on certain fundamentals such as algebra, arithmetic, and geometry.

The basic Math formulas include arithmetic operations, where we learn to add, subtract, multiply and divide. Also, algebraic identities help to solve equations. The important formulas are related to algebra, Pythagoras theorem, series and sequence, mensuration, calculus, probability and statistics, trigonometry, matrices, etc.

50 Maths Formulas for Classes 6 to 12th

Math formulas for Class 6

‘Undefined’ refers to anything divided by zero
If the total of the digits is a multiple of three, the number is divisible by three.
A number is divisible by two if it contains the digits 0, 2, 4, 6, or 8.
A variable represents a condition in an equation. An equation has two sides, known as the Left-Hand Side and the Right-Hand Side, which are separated by an equal (=) sign.
A polygon is a simple closed figure created by line segments. A triangle is a polygon with three sides. Quadrilaterals are polygons with four sides.
The perimeter of a Square = 4 × Length of its side
Perimeter of a Rectangle = 2 × (Length + Breadth)
The perimeter of an Equilateral triangle = 3 × Length of a side
Area of a Rectangle = length × breadth

Maths formulas for Class 7

Profit Percentage = (Profit / Cost price) × 100
Loss Percentage = (Loss/ Cost price) × 100
Simple Interest = (Principal × Rate × Time) / 100
Amount = Principal + Interest
Percentage Change= (Change / Original Amount) × 100
Product of rational numbers = (Product of Numerators) / (Product of Denominators)
First Rational Number × (Reciprocal of other Rational Number)
Law of Product: am × an = am+n
Law of Quotient: am/an = am-n
Law of Zero Exponent: a0 = 1
Law of Negative Exponent: a-m = 1/am
Law of Power of a Quotient: (a/b)m = am/bm
Law of Power of a Power: (am)n = amn
Law of Power of a Product: (ab)m = ambm
Perimeter of a Rectangle = 2 × (Length + Breadth)
Area of Rectangle = Length × Breadth
Area of a Square = Side2
Area of Triangle = 1/ 2 × Base × Height
The perimeter of a Square = 4 × Side
Area of a Parallelogram = Base × Height
Area of a circle = πr2
Circumference of a circle = π d, where ‘d’ is the diameter of a circle and π = 22/7 or 3.14

Math Formulas for Class 8

Additive inverse of rational number: a/b = -b/a
Multiplicative Inverse of a/b = c/d , if a/b × c/d = 1
Distributives a(b – c) = ab – ac
Simple Interest = (Principal × Rate × Time) / 100
Amount = Principal + Interest
Compound Interest formula = Amount – Principal, Amount in case the interest is calculated annually = Principal ( 1 + Rate/100)n, where ‘n’ is the period.
Probability of the occurrence of an event = Number of outcomes that comprise an event/ Total number of outcomes

Maths Formulas for Class 9

Topics	Math Formulas
Real Numbers	√ab = √a √b √(a/b) = √a / √b (√a + √b) (√a – √b) = a – b (√a + √b)2 = a + 2√ab + b (a + √b) (a – √b) = a2 – b (a + b) (a – b) = a2 – b2
Geometry Formulas
Rectangle	Area of Rectangle A = Length x Width Perimeter of Rectangle P = 2(Length + Width)
Triangle	Area of Triangle, A = ½ x Breadth x Height Perimeter of Triangle, P = Sum of all the three sides of a triangle
Circle	Area of Circle, A = πr² The perimeter of circle, P = 2 πr
Parallelogram	Area of Parallelogram, A = Breadth x Height Perimeter of Parallelogram, P = 2( a+ b) (Here. a = side, b = base )
Trapezoid	Area of Trapezoid A = ½ x Height x (b₁ x b₂) Perimeter of Trapezoid, P = Sum of all the sides of a trapezoid
Cuboid	Surface Area (A) = (lb + bh + hl), ([l = length, b = Breadth, h = height] Volume V = Length x Breadth x Height
Cylinder	Surface area of Cylinder A = 2πr( h + r) [r = radius of the circular cylinder, H = height of a cylinder] The volume of Cylinder V = πr²H
Cube	The surface area of Cube. A = 6 side² Volume of a Cube V = Side³
Sphere	Surface Area of a Sphere A = 4πr² The volume of a Cube V = 4/3πr³
Cone	Surface area of a Cone (A) = πr( L + r) [l = slant height , r = Radius of base] Volume of a Cone (V )= ½ πr²
Heron’s Formula	Area of Triangle with 3 sides = √s(s-a)(s-b)(s-c) Here, s = semi-perimeter, and A,b, and c are the sides of a triangle. Semi Perimeter, S = ( a + b + c)/2
Polynomial Formula	P (x) = anxn + an- 1xn- 1 – an- 2xn- 1 + …… ax + a0
Algebra Identities	(x + θ) (x – θ) = x² – θ² (x + β)² = x² + β² + 2 x β (x – β)² = x² + β² – 2 x β (x – α)(x + θ) = x² + (θ – α)x – xθ (x – α)(x – θ) = x² – (α + θ)x + αq (x + α)(x + θ) = x² + (α + θ)x + αθ (x + α)(x – θ) = x² + (α – θ)x – αθ (α + β + θ)² = α² + β² + θ² + 2αβ + 2βθ + 2αθ (α + β – θ)² = α² + β² + θ² + 2αβ – 2βθ – 2αθ (α – β + θ)² = α² + β² + θ²- 2αβ – 2βθ + 2αθ (α – β – θ)² = α² + β² + θ² – 2αβ + 2βθ – 2αθ (α + θ)³ = α³ + θ³ + 3αθ(α + θ) (x)³ + (β)³ = ( x + β) (x² – xβ + β) (x)³ – (β)³ = ( x + β) (x² – xβ + β)
Statistics	Mean : Total number of observations/sum of all observations Median: ((n+1)/2)th observations = odd observations ((n/2)th + ((n/2)+1)th)/2 observations for even observations Mode: The most often occurring value in a data set

10th Class Maths Formulas List

Topics	Math Formulas
Arithmetic Formulas	an = a + (n – 1) d, where an is the nth term. Sn= n/2 [2a + (n – 1)d]
Trigonometry Formulas	sin(90° – A) = cos A cos(90° – A) = sin A tan(90° – A) = cot A cot(90° – A) = tan A sec(90° – A) = cosec A cosec(90° – A) = sec A sin θ cosec θ = 1 cos θ sec θ = 1 tan θ cot θ = 1 sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos2 θ ⇒ cos2 θ = 1 – sin2 θ cosec2 θ – cot2 θ = 1 ⇒ cosec2 θ = 1 + cot2 θ ⇒ cot2 θ = cosec2 θ – 1 sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
Area and Volume Formulas	The volume of Sphere = 4/3 ×π r3 Lateral Surface Area of Sphere (LSA) = 4π r2 Total Surface Area of Sphere (TSA) = 4πr2 The volume of the Right Circular Cylinder = πr2h Lateral Surface Area of Right Circular Cylinder (LSA) = 2×(πrh) Total Surface Area of Right Circular Cylinder (TSA) = 2πr×(r + h) The volume of Hemisphere = ⅔ x (πr3) Lateral Surface Area of Hemisphere (LSA) = 2πr2 Total Surface Area of Hemisphere (TSA) = 3πr2 The volume of Prism = B × h Lateral Surface Area of Prism (LSA) = p × h
Circle Formula	The tangent to a circle equation x2 + y2 = a2 for a line y = mx + c is given by the equation y = mx ± a √ [1+ m2]. The tangent to a circle equation x2 + y2 = a2 at (a1,b1) is xa1 + yb1 = a2

11th Maths Formulas

(a+b)2 = a2 + b2 + 2ab
(a-b)2 = a2 + b2 – 2ab
(a+b) (a-b) = a2 – b2
(x + a)(x + b) = x2 + (a + b)x + ab
(x + a)(x – b) = x2 + (a – b)x – ab
(a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – b3 – 3ab(a – b)
(x – a)(x + b) = x2 + (b – a)x – ab
(x – a)(x – b) = x2 – (a + b)x + ab
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
(x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
(x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
(x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
x2 + y2 =½ [(x + y)2 + (x – y)2]
(x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
x3 + y3= (x + y) (x2 – xy + y2)
x3 – y3 = (x – y) (x2 + xy + y2)
x2 + y2 + z2 -xy – yz – zx = ½ [(x-y)2 + (y-z)2 + (z-x)2]
sin (90° – θ) = cos θ
cos (90° – θ) = sin θ
tan (90° – θ) = cot θ
cot (90° – θ) = tan θ
sec (90° – θ) = cosecθ
cosec (90° – θ) = secθ
sin²θ + cos² θ = 1
sec²θ = 1 + tan²θ for 0° ≤ θ < 90°
Cosec²θ = 1 + cot² θ for 0° ≤ θ ≤ 90°

Math formulas For Class 12th

Topics	Math formulas
Trigonometry Formulas	sin-1(-x) = – sin-1x tan-1x + cot-1x = π / 2 sin-1x + cos-1 x = π / 2 cos-1(-x) = π – cos-1x cot-1(-x) = π – cot-1x
Calculus Formulas	∫ f(x) dx = F(x) + C Power Rule: ∫ xn dx = (xn+1) / (n+1) + C. (Where n ≠ -1) Exponential Rules: ∫ ex dx = ex + C ∫ ax dx = ax / ln(a) + C ∫ ln(x) dx = x ln(x) – x + C Constant Multiplication Rule: ∫ a dx = ax + C, where a is the constant. Reciprocal Rule: ∫ (1/x) dx = ln(x)+ C Sum Rules: ∫ [f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx Difference Rules: ∫ [f(x) – g(x)] dx = ∫f(x) dx – ∫g(x) dx ∫k f(x) dx = k ∫f(x) dx, , where k is any real number. Integration by parts: ∫ f(x) g(x) dx = f(x) ∫ g(x) dx – ∫[d/dx f(x) × ∫ g(x) dx]dx ∫cos x dx = sin x + C ∫ sin x dx = -cos x + C ∫ sec2 x dx = tan x + C ∫ cosec2 x dx = -cot x + C ∫ sec x tan x dx = sec x + C ∫ cosec x cot x dx = – cosec x + C
Vector Formulas	A + B = B + A (Commutative Law) A + (B + C) = (A + B) + C (Associative Law) (A • B )= \|P\| \|Q\| cos θ ( Dot Product ) (A × B )= \|P\| \|Q\| sin θ (Cross Product) k (A + B )= kA + kB A + 0 = 0 + A (Additive Identity)
Geometry Formulas	Cartesian equation of a plane: lx + my + nz = d Distance between two points P(x1, y1, z1) and Q(x2, y2, z2): PQ = √ ((x1 – x2)2 + (y1 – y2)2 + (z1 – z2)2)

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