Top 100 Maths Formulas for Class 9, 10, 11 & 12 PDF: Complete Formula Sheet for Board Exams, JEE & NEET (2026)

Mathematics is one of the few subjects where a single formula can save several minutes during an exam. Whether you're preparing for CBSE board exams, state board exams, JEE, NEET, Olympiads, or school tests, remembering the right formula at the right time can make a significant difference in your score.

Many students understand concepts but struggle to recall formulas during exams. As a result, they lose marks in questions they could have solved easily. That's why having a well-organized math formula sheet is essential for quick revision and effective exam preparation.

In this guide, we've compiled the Top 100 Maths Formulas for classes 9, 10, 11, and 12 in one place. From Algebra and Geometry to Trigonometry, Coordinate Geometry, Mensuration, Probability, Statistics, and Calculus, this article covers the formulas students use most frequently in board exams and competitive exams.

Whether you're searching for a maths formulas PDF, Class 10 maths formula sheet, Class 12 calculus formulas, trigonometry formulas, or important algebra identities, you'll find everything here in a simple and easy-to-revise format.

Download Top 100 Maths Formulas PDF

Preparing for board exams, school tests, JEE, NEET, or other competitive exams? Download our complete Maths Formula Sheet PDF for quick revision anytime, anywhere.

The PDF includes important formulas from:

• Class 9 Mathematics

• Class 10 Mathematics

• Class 11 Mathematics

• Class 12 Mathematics

• Algebra

• Geometry

• Trigonometry

• Coordinate Geometry

• Mensuration

• Probability & Statistics

• Calculus

Download Maths Formulas PDF

Tip: Save the PDF on your phone or laptop so you can revise important formulas before exams, mock tests, and practice sessions.

Class 9 Maths Formulas

Algebraic Identities

• (a+b)² = a² + 2ab + b²

• (a-b)² = a² - 2ab + b²

• a²-b² = (a+b)(a-b)

• (a+b)³ = a³ + 3a²b + 3ab² + b³

• (a-b)³ = a³ - 3a²b + 3ab² - b³

• a³+b³ = (a+b)(a²-ab+b²)

• a³-b³ = (a-b)(a²+ab+b²)

• (a+b+c)² = a²+b²+c²+2ab+2bc+2ca

• (a-b-c)² = a²+b²+c²-2ab-2ac+2bc

• (x+a)(x+b) = x²+(a+b)x+ab

Geometry Formulas

• Area of Triangle = ½ × Base × Height

• Perimeter of Triangle = Sum of all sides

• Area of Rectangle = Length × Breadth

• Perimeter of Rectangle = 2(L+B)

• Area of Square = Side²

• Perimeter of Square = 4 × Side

• Area of Parallelogram = Base × Height

• Area of Rhombus = ½ × d₁ × d₂

• Area of Trapezium = ½(a+b)h

• Sum of Angles in a Triangle = 180°

Circle Formulas

• Circumference = 2πr

• Area of Circle = πr²

• Diameter = 2r

• Radius = Diameter ÷ 2

• Area of Sector = (θ/360) × πr²

Class 10 Maths Formulas

Trigonometry Formulas

• Sin θ = Perpendicular/Hypotenuse

• Cos θ = Base/Hypotenuse

• Tan θ = Perpendicular/Base

• Cot θ = Base/Perpendicular

• Sec θ = Hypotenuse/Base

• Cosec θ = Hypotenuse/Perpendicular

• Tan θ = Sin θ/Cos θ

• Cot θ = Cos θ/Sin θ

• Sin²θ + Cos²θ = 1

• Sec²θ = 1 + Tan²θ

• Cosec²θ = 1 + Cot²θ

Important Trigonometric Values

Coordinate Geometry Formulas

• Distance Formula = √[(x₂-x₁)² + (y₂-y₁)²]

• Midpoint Formula = [(x₁+x₂)/2, (y₁+y₂)/2]

• Section Formula = [(mx₂+nx₁)/(m+n)]

• Area of Triangle Using Coordinates = ½[x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)]

Statistics & Probability

• Mean = Sum of Observations ÷ Number of Observations

• Median = Middle Value

• Mode = Most Frequent Value

• Probability = Favorable Outcomes ÷ Total Outcomes

• 0 ≤ Probability ≤ 1

Class 11 Maths Formulas

Arithmetic Progression (AP) Formulas

• nth Term = a + (n−1)d

• Sum of n Terms = n/2 [2a + (n−1)d]

• Last Term = a + (n−1)d

• Sum of First n Natural Numbers = n(n+1)/2

• Sum of Squares of First n Natural Numbers = n(n+1)(2n+1)/6

• Sum of Cubes of First n Natural Numbers = [n(n+1)/2]²

Permutation and Combination Formulas

• nPr = n!/(n−r)!

• nCr = n!/[r!(n−r)!]

• nCr = nC(n−r)

• nP0 = 1

• nC0 = 1

Binomial Theorem Formulas

• (a+b)² = a² + 2ab + b²

• (a−b)² = a² − 2ab + b²

• General Term = nCr aⁿ⁻ʳ bʳ

• Number of Terms in Expansion = n + 1

Straight Line Formulas

• Slope = (y₂−y₁)/(x₂−x₁)

• Equation of Line = y = mx + c

• Point-Slope Form = y−y₁ = m(x−x₁)

• Intercept Form = x/a + y/b = 1

Circle Formulas

• Standard Equation = (x−h)² + (y−k)² = r²

• Circle Center = (h,k)

• Radius = r

Sequence and Series Formulas

• Geometric Progression nth Term = arⁿ⁻¹

• Sum of GP = a(rⁿ−1)/(r−1)

• Infinite GP Sum = a/(1−r)

Logarithm Formulas

• log(ab) = log a + log b

• log(a/b) = log a − log b

• log(aⁿ) = n log a

• logₐ1 = 0

• logₐa = 1

Class 12 Maths Formulas

Differentiation Formulas

• d/dx(xⁿ) = nxⁿ⁻¹

• d/dx(sin x) = cos x

• d/dx(cos x) = −sin x

• d/dx(tan x) = sec²x

• d/dx(cot x) = −cosec²x

• d/dx(sec x) = sec x tan x

• d/dx(cosec x) = −cosec x cot x

• d/dx(eˣ) = eˣ

• d/dx(log x) = 1/x

Integration Formulas

• ∫dx = x + C

• ∫xⁿdx = xⁿ⁺¹/(n+1) + C

• ∫sin x dx = −cos x + C

• ∫cos x dx = sin x + C

• ∫sec²x dx = tan x + C

• ∫cosec²x dx = −cot x + C

• ∫eˣ dx = eˣ + C

• ∫1/x dx = ln|x| + C

Limits Formulas

• lim(x→0) sinx/x = 1

• lim(x→0) tanx/x = 1

• lim(x→0) (1−cosx)/x² = ½

• lim(x→∞) (1+1/x)ˣ = e

Matrix Formulas

For Matrix:

|a b|
|c d|

• Determinant = ad − bc

• Singular Matrix → Determinant = 0

• Non-Singular Matrix → Determinant ≠ 0

Probability Formulas

• P(A∪B) = P(A)+P(B)−P(A∩B)

• P(A|B) = P(A∩B)/P(B)

• P(A') = 1−P(A)

Vector Algebra Formulas

• Magnitude of Vector = √(x²+y²+z²)

• Dot Product = |A||B|cosθ

• Cross Product = |A||B|sinθ

3D Geometry Formulas

• Distance Formula = √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²]

• Midpoint Formula = [(x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2]

Relations and Functions Formulas

• Number of Relations = 2ⁿ

• Number of Functions = mⁿ

Inverse Trigonometric Formulas

• sin⁻¹x + cos⁻¹x = π/2

• tan⁻¹x + cot⁻¹x = π/2

• sec⁻¹x + cosec⁻¹x = π/2

Important Mensuration Formulas

Cube

• Volume = a³

• Total Surface Area = 6a²

• Lateral Surface Area = 4a²

• Diagonal = a√3

Cuboid

• Volume = l × b × h

• Total Surface Area = 2(lb + bh + lh)

• Lateral Surface Area = 2h(l + b)

• Diagonal = √(l²+b²+h²)

Cylinder

• Volume = πr²h

• Curved Surface Area = 2πrh

• Total Surface Area = 2πr(r+h)

Cone

• Volume = ⅓πr²h

• Curved Surface Area = πrl

• Total Surface Area = πr(l+r)

Sphere

• Volume = ⁴⁄₃πr³

• Surface Area = 4πr²

Hemisphere

• Volume = ⅔πr³

• Curved Surface Area = 2πr²

• Total Surface Area = 3πr²

Additional Important Maths Formulas

Quadratic Equations

• If ax² + bx + c = 0, then x = [-b ± √(b²-4ac)] / 2a

• Sum of Roots = -b/a

• Product of Roots = c/a

• Discriminant (D) = b² - 4ac

• Nature of Roots:

  • D > 0 → Real and Distinct

  • D = 0 → Real and Equal

  • D < 0 → Imaginary

Sets and Relations

• n(A∪B) = n(A) + n(B) - n(A∩B)

• n(A-B) = n(A) - n(A∩B)

• n(A') = n(U) - n(A)

• A∪Φ = A

• A∩Φ = Φ

Complex Numbers

• i² = -1

• i³ = -i

• i⁴ = 1

• z = a + ib

• |z| = √(a²+b²)

Determinants

For

|a b|
|c d|

• Determinant = ad - bc

For

|a b c|
|d e f|
|g h i|

• Determinant = a(ei-fh)-b(di-fg)+c(dh-eg)

Matrices

• A + B = [aᵢⱼ + bᵢⱼ]

• A - B = [aᵢⱼ - bᵢⱼ]

• A(I) = A

• A(0) = 0

• A × A⁻¹ = I

Vector Algebra

• Unit Vector = A/|A|

• Projection of A on B = (A·B)/|B|

• A·A = |A|²

• A×A = 0

• A·B = B·A

Differential Equations

• dy/dx = f(x)

• General Solution = Particular Solution + Constant

• Order = Highest Order Derivative

• Degree = Highest Power of Derivative

• Variable Separable Form:

  • dy/dx = f(x)g(y)

Coordinate Geometry

• Equation of X-axis → y = 0

• Equation of Y-axis → x = 0

• Slope of Horizontal Line = 0

• Slope of Vertical Line = Undefined

• Distance Between Parallel Lines:

  • |c₁-c₂| / √(a²+b²)

Trigonometric Identities

• Sin(A+B) = SinA CosB + CosA SinB

• Sin(A-B) = SinA CosB - CosA SinB

• Cos(A+B) = CosA CosB - SinA SinB

• Cos(A-B) = CosA CosB + SinA SinB

• Tan(A+B) = (TanA + TanB)/(1-TanA TanB)

Additional Mensuration Formulas

• Area of Semicircle = ½πr²

• Perimeter of Semicircle = πr + 2r

• Area of Equilateral Triangle = (√3/4)a²

• Height of Equilateral Triangle = (√3/2)a

• Diagonal of Square = a√2

Statistics Formulas

• Mean = Σx/n

• Range = Highest Value - Lowest Value

• Variance = Σ(x-Mean)²/n

• Standard Deviation = √Variance

• Coefficient of Variation = (SD/Mean) × 100

Miscellaneous Formulas

• Simple Interest = (P×R×T)/100

• Amount = Principal + Interest

• Compound Amount = P(1+R/100)ⁿ

• Compound Interest = Amount - Principal

• Percentage = (Value/Total Value) × 100

Most Important Formulas to Revise Before Exams

While every formula has its importance, some are used more frequently than others. Before an exam, make sure you revise:

Algebra

• (a+b)²

• (a-b)²

• a²-b²

• a³+b³

• a³-b³

Trigonometry

• Sin²θ + Cos²θ = 1

• Sec²θ = 1 + Tan²θ

• Cosec²θ = 1 + Cot²θ

Coordinate Geometry

• Distance Formula

• Midpoint Formula

Calculus

• d/dx(xⁿ) = nxⁿ⁻¹

• ∫xⁿdx = xⁿ⁺¹/(n+1) + C

Probability

• P(A∪B) = P(A)+P(B)-P(A∩B)

Mensuration

• Area of Circle = πr²

• Volume of Cylinder = πr²h

• Surface Area of Sphere = 4πr²

How to Remember Maths Formulas More Effectively

Learning formulas becomes easier when you focus on understanding rather than memorization.

Maintain a Formula Notebook

Write important formulas chapter-wise in a separate notebook. Revising from a single source saves time before exams.

Practice Formula-Based Questions

Simply reading formulas is not enough. Use them while solving problems to improve retention.

Revise Regularly

A quick revision session of 10–15 minutes daily is often more effective than long revision sessions before an exam.

Understand the Logic

When you know where a formula comes from, it becomes much easier to remember and apply correctly.

Common Mistakes Students Make

• Memorizing formulas without understanding concepts

• Forgetting units in mensuration questions

• Mixing up trigonometric identities

• Skipping regular revision

• Using formulas incorrectly because of calculation errors

Being aware of these mistakes can help improve accuracy and avoid unnecessary loss of marks.

Frequently Asked Questions

Which maths formulas are most important for Class 10?

Algebraic identities, trigonometric identities, coordinate geometry formulas, probability formulas, and mensuration formulas are among the most important topics for Class 10 students.

Are these formulas useful for competitive exams?

Yes. Many of these formulas form the foundation for higher-level mathematics and are commonly used in competitive examinations.

How often should I revise formulas?

A short daily revision session is usually enough to keep formulas fresh in your memory.

Should I memorize formulas or understand them?

Understanding should always come first. Once the concept is clear, memorizing the formula becomes much easier.

Is it useful to keep a formula sheet?

Yes. A formula sheet helps students revise quickly before tests, assignments, and examinations.

Final Thoughts

Mathematics becomes much easier when important formulas are organized in one place. Instead of searching through multiple books and notebooks, students can use this guide as a quick reference whenever they need to revise.

Whether you are preparing for school exams, board exams, or simply strengthening your fundamentals, consistent revision and regular practice can make a noticeable difference in your performance.