CBSE Class 6 to 12 Maths Formulas - Important Math Formulas

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Math formulas are really helpful for students when dealing with tricky math problems. They make it easier and faster to find solutions. By using basic math formulas, students can tackle complex problems using different methods. Getting good marks in math is achievable with consistent hard work and smart study strategies. The key is to carefully read the problem, figure out what it's asking, and then find the right math formulas for the solution.

For those preparing for competitive exams, having all the important math formulas in one place can be useful for better understanding the subject. Our expert teachers have compiled formulas for different classes (6, 7, 8, 9, 10, 11, and 12) according to the CBSE syllabus. To solve math problems easily, students should learn and remember basic formulas based on fundamentals like algebra, arithmetic, and geometry.

While addition, subtraction, multiplication, and division are straightforward, more advanced topics like derivation, calculus, and geometry require specific formulas. At Physics Wallah, we offer a unique way of solving math problems, helping students understand how equations come into existence. This approach makes it easier to memorise and apply the formulas effectively. It's a better way to grasp and use math formulas for problem-solving.

CBSE Class 6 to 12 Maths Formulas

Math Formulas for Class 6

  1. Divisibility Rule for Three: If the sum of the digits in a number is a multiple of three, then the number itself is divisible by three.

  2. Divisibility Rule for Two: A number is divisible by two if it contains any of the digits 0, 2, 4, 6, or 8.

  3. Variable in an Equation: In an equation, a variable represents a condition. The equation is divided into two sides, referred to as the Left-Hand Side and the Right-Hand Side, separated by an equal (=) sign.

  4. Polygon and Triangle: A polygon is a closed figure formed by connecting line segments. Specifically, a triangle is a polygon characterized by having three sides. Quadrilaterals are polygons with four sides.

  5. The Perimeter of a Square: To find the perimeter of a square, multiply the length of one side by 4.

  6. The Perimeter of a Rectangle: The perimeter of a rectangle is computed by adding twice its length to twice its breadth.

  7. The Perimeter of an Equilateral Triangle: The perimeter of an equilateral triangle is determined by tripling the length of one of its sides.

  8. Area of a Rectangle: The area of a rectangle is found by multiplying its length and breadth.

Math Formulas for Class 7

  1. Profit Percentage: Profit Percentage is calculated as (Profit / Cost price) × 100.

  2. Loss Percentage: Loss Percentage is calculated as (Loss / Cost price) × 100.

  3. Simple Interest: Simple Interest is calculated as (Principal × Rate × Time) / 100.

  4. Amount: The total Amount is the sum of Principal and Interest.

  5. Percentage Change: Percentage Change is calculated as (Change / Original Amount) × 100.

  6. Product of Rational Numbers: The product of rational numbers is calculated as (Product of Numerators) / (Product of Denominators).

  7. Law of Product: am × an = am+n

  8. Law of Quotient: am/an = am-n

  9. Law of Zero Exponent: a^0 = 1

  10. Law of Negative Exponent: a^(-m) = 1/a^m

  11. Law of Power of a Quotient: (a/b)^m = a^m/b^m

  12. Law of Power of a Power: (a^m)^n = a^(mn)

  13. Law of Power of a Product: (ab)^m = a^m b^m

  14. The perimeter of a Rectangle: The perimeter of a rectangle is calculated as 2 times the sum of its length and breadth.

  15. Area of Rectangle: The area of a rectangle is calculated as the product of its length and breadth.

  16. Area of a Square: The area of a square is calculated as the square of its side.

  17. Area of Triangle: The area of a triangle is calculated as 1/2 times the product of its base and height.

  18. The perimeter of a Square: The perimeter of a square is calculated as 4 times its side.

  19. Area of a Parallelogram: The area of a parallelogram is calculated as the product of its base and height.

  20. Area of a Circle: The area of a circle is calculated as πr^2.

  21. Circumference of a Circle: The circumference of a circle is calculated as πd, where 'd' is the diameter of the circle and π ≈ 3.14.

Math Formulas for Class 8

  1. Additive Inverse of Rational Number: a/b = -b/a

  2. Multiplicative Inverse: Multiplicative Inverse of a/b = c/d, if a/b × c/d = 1

  3. Distributive Property: a(b – c) = ab – ac

  4. Simple Interest: Simple Interest is calculated as (Principal × Rate × Time) / 100.

  5. Amount: The total Amount is the sum of Principal and Interest.

  6. Compound Interest Formula: Compound Interest is calculated as Amount – Principal. Amount in case the interest is calculated annually = Principal(1 + Rate/100)^n, where 'n' is the period.

  7. Probability: Probability of the occurrence of an event = Number of outcomes that comprise an event / Total number of outcomes.\

  8. 2D Geometry Shapes

Shape

Formula

Rectangle

Area of Rectangle (A) = Length × Width

Perimeter of Rectangle (P) = 2 × (Length + Width)

Triangle

Area of Triangle (A) = ½ × Base × Height

Perimeter of Triangle (P) = Sum of all three sides of the triangle

Circle

Area of Circle (A) = πr²

Perimeter of Circle (P) = 2πr

 

  1. 3D Geometry Shapes

3 Dimensional Shapes

Total Surface Area

Lateral/Curved Surface Area

Volume

Sphere

4πr²

4πr²

4/3(πr³)

Right Circular Cone

πr(l + r)

πrl

⅓(πr²h)

Cylinder

2πr(r + h)

2(π × r × h)

πr²h

Right Pyramid

Lateral Surface Area + Area of Base

½(Perimeter of Base × Slant Height)

⅓(Area of Base) × Height

Hemisphere

3πr²

2πr²

⅔(πr³)

Cuboid

2(lb + bh + hl)

2h(l + b)

l × b × h

Cube

6a²

4a²

Right Prism

Lateral Surface Area + 2(Area of End)

Perimeter of Base × Height

Area of Base × Height

Maths Formula for Class 9

Candidates can go through the list of Maths Formula for Class 9 from the below table:- 

Topics

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

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]

Volume of Cylinder V = πr²H

Cube

The surface area of Cube. A = 6 side²

Volume of a Cube V = Side³

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)

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)

Maths Formula for Class 10

Candidates can go through the list of Maths Formula for Class 10 from the below table:- 

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.

Maths Formula for Class 11

Candidates can go through the list of Maths Formula for Class 11

 from the below table:- 

Topics

Math Formulas

Algebra Formulas

a × (b + c) = a × b + a × c (Distributive property)

a + b = b + a (Commutative Property of Addition)

a × b = b × a (Commutative Property of Multiplication)

a + (b + c) = (a + b) + c (Associative Property of Addition)

a × (b × c) = (a × b) × c (Associative Property of Multiplication)

a + 0 = a (Additive Identity Property)

a × 1 = a(Multiplicative Identity Property)

a + (-a) = 0 (Additive Inverse Property)

a⋅(1/a) = 1 (Multiplicative Inverse Property)

a × (0) =0 (Zero Property of Multiplication)

Calculus Formulas

d/dx [f(x) + g (x)] = d/dx [f(x)] + d/dx [g(x)]

d/dx [f(x) – g (x)] = d/dx [f(x)] – d/dx [g(x)]

d/dx [f(x) × g (x)] = d/dx [f(x)] × [g(x)] + [f(x)] × d/dx [g(x)]

d/dx [f(x) / g (x)] = {d/dx [f(x)] × [g(x)] – [f(x)] × d/dx [g(x)]} / g(x)²

Geometry and Lines Formulas

Slope m = rise/run = Δy/Δx = y₂−y₁/x₂−x₁

Point-Slope Form y−y₁ = m (x−x₁)

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

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

sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

Maths Formula for Class 12

Candidates can go through the list of Maths Formula for Class 12 from the below table:- 

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 )=

(A × B )=

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)

Strategy for Maths 

  1. Know the entire CBSE syllabus for mathematics thoroughly.

  2. Allocate time for each topic according to its weightage in the exam.

  3. Focus on understanding the concepts rather than rote memorization.

  4. Candidates should solve a variety of problems regularly to strengthen their understanding and problem-solving skills.

  5. Refer to NCERT textbooks as they cover the CBSE syllabus comprehensively.

  6. Candidates should solve CBSE sample papers and previous years' question papers to get familiar with the exam pattern and types of questions asked.

  7. Taking mock tests helps candidates assess their preparation level and identify areas of improvement.

  8. Memorize important formulas and theorems as they are essential for solving problems quickly.

  9. Regularly revise the topics candidates have studied to reinforce their learning and retain information.

  10. Don't hesitate to ask teachers or peers for help if candidates have doubts or difficulties with any concept.

CBSE Class 6 to 12 Maths Formulas FAQs

Q1. How can I effectively use these formulas for exam preparation?

Ans. Understand the underlying concepts, practice regularly, create a formula sheet for quick reference, solve sample papers, take mock tests, and seek help when needed.

Q2. Can I rely solely on these formulas for exam preparation?

Ans. While these formulas are valuable, it's crucial to complement them with a deep understanding of concepts, regular practice, and problem-solving skills to handle different types of problems.

Q3. Where can I find additional study materials for CBSE mathematics?

Ans. Additional study materials can be found in CBSE-approved textbooks, reference books, online educational platforms like Physics Wallah, and resources provided by your school. However, NCERT textbooks are highly recommended.

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