Maths Formulas for Class 11 & 12 – Algebra, Calculus, Trigonometry, Geometry [PDF]

Maths Formulas are essential for mastering Class 11 and 12 Mathematics, acing board exams, and excelling in competitive exams like JEE and CUET. Here, Hodu Academy brings you a chapter-wise collection of the most important Maths formulas from Algebra, Calculus, Trigonometry, Geometry, and more—your quick revision and score-boosting tool!

Use these formula sheets, mind maps, and short notes for Class 11 and 12 Maths to revise concepts, solve tough problems, and memorize shortcuts.
Whether you’re preparing for CBSE, ISC, or State boards—or targeting JEE or Olympiads—these tables are your essential last-minute revision resource!

Class 11 Maths Formula List

Class 11 Maths is the foundation for higher mathematics—covering Sets, Relations, Trigonometry, Complex Numbers, Quadratic Equations, Sequences & Series, Permutations & Combinations, Binomial Theorem, and basic Calculus. Here’s a table of the most important formulas to master:

Chapter Name Key Formulas & Concepts
Sets, Relations & Functions n(A∪B) = n(A) + n(B) – n(A∩B); Types of functions, Domain & Range
Trigonometric Functions sin²θ + cos²θ = 1, tanθ = sinθ/cosθ, Addition formulas, Graphs
Complex Numbers z = a + ib, |z| = √(a²+b²), Arg(z), (a+ib)(c+id) = (ac-bd) + i(ad+bc)
Quadratic Equations ax² + bx + c = 0; Roots: (-b±√(b²-4ac))/2a; Sum/Product of roots
Sequences & Series AP: nth = a + (n-1)d, Sum = n/2[2a+(n-1)d]; GP: nth = ar^(n-1), Sₙ = a(1-rⁿ)/(1–r)
Permutations & Combinations nPr = n!/(n–r)!, nCr = n!/[r!(n–r)!]
Binomial Theorem (a+b)ⁿ = Σ [nCr · a^(n–r) · b^r], General & Middle term
Straight Lines & Conic Sections y = mx + c, ax + by + c = 0, Circle: (x–h)²+(y–k)² = r², Parabola: y² = 4ax
Limits & Derivatives limₓ→ₐ f(x), d/dx (xⁿ) = nxⁿ⁻¹, d/dx (sinx) = cosx
Probability P(E) = n(E)/n(S), Mutually exclusive, Independent events

Class 11 Maths: Chapter-wise Formula Details

Note: Only chapters with significant formulas are included.

Sets, Relations & Functions
  • n(A∪B) = n(A) + n(B) – n(A∩B)
  • n(A×B) = n(A) × n(B)
  • Domain, Co-domain, Range definitions
Trigonometric Functions
  • sin²θ + cos²θ = 1, tan²θ + 1 = sec²θ, 1 + cot²θ = cosec²θ
  • sin(A±B) = sinAcosB ± cosAsinB
  • cos(A±B) = cosAcosB ∓ sinAsinB
Complex Numbers
  • z = a + ib, |z| = √(a²+b²), Arg(z) = tan⁻¹(b/a)
  • Conjugate: z̄ = a – ib
  • z₁z₂ = (a+ib)(c+id) = (ac–bd) + i(ad+bc)
Quadratic Equations
  • ax² + bx + c = 0; Roots: (-b±√(b²–4ac))/2a
  • Sum = –b/a, Product = c/a
  • Nature of roots: D = b²–4ac
Sequences & Series
  • AP: nth term = a + (n–1)d, Sum = n/2[2a + (n–1)d]
  • GP: nth term = ar^(n–1), Sum (r≠1): Sₙ = a(1–rⁿ)/(1–r)
Permutations & Combinations
  • nPr = n!/(n–r)!
  • nCr = n!/[r!(n–r)!]
Binomial Theorem
  • (a+b)ⁿ = Σ [nCr · a^(n–r) · b^r] (r=0 to n)
  • Middle term: n even, n/2+1; n odd, (n+1)/2-th term
Straight Lines & Conic Sections
  • y = mx + c, Distance formula: √[(x₂–x₁)²+(y₂–y₁)²]
  • Circle: (x–h)² + (y–k)² = r²
  • Parabola: y² = 4ax, Ellipse: (x²/a²) + (y²/b²) = 1
Limits & Derivatives
  • limₓ→ₐ f(x), d/dx (xⁿ) = nxⁿ⁻¹
  • d/dx (sinx) = cosx, d/dx (eˣ) = eˣ
Probability
  • P(E) = n(E)/n(S)
  • P(A∪B) = P(A) + P(B) – P(A∩B)

Class 12 Maths Formula List

Class 12 Maths focuses on advanced topics: Calculus, Vectors, 3D Geometry, Matrices, Determinants, Probability, and Linear Programming. Use this table for your quick revision:

Chapter Name Key Formulas & Concepts
Relations & Functions Types of relations, Domain & Range, Types of functions (one-one, onto)
Inverse Trigonometric Functions sin⁻¹x + cos⁻¹x = π/2, tan⁻¹x + cot⁻¹x = π/2, Properties of inverses
Matrices Matrix addition, multiplication, Transpose, Determinant, Inverse
Determinants Determinant of 2×2, 3×3 matrices, Properties, Cramer's Rule
Continuity & Differentiability d/dx (f(g(x))) = f'(g(x))·g'(x) (Chain rule), Derivatives of log, exp, trig
Application of Derivatives Maxima/Minima, Rate of change, Tangents & Normals
Integrals ∫xⁿdx = xⁿ⁺¹/(n+1)+C, ∫eˣdx = eˣ+C, ∫1/x dx = ln|x|+C, Definite integrals
Differential Equations dy/dx = f(x), Variable separable, Linear, Homogeneous equations
Vectors & 3D Geometry a·b = |a||b|cosθ, a×b, Equation of line/plane, Direction cosines
Probability Bayes' theorem, Mean/Variance of Binomial distribution, P(A∪B)
Linear Programming Objective function, Constraints, Graphical solution method

Class 12 Maths: Chapter-wise Formula Details

Note: Only chapters with significant formulas are included.

Relations & Functions
  • Definition of relation & function, Types: one-one, onto, bijection
  • Domain, Range, Co-domain
Inverse Trigonometric Functions
  • sin⁻¹x + cos⁻¹x = π/2
  • tan⁻¹x + cot⁻¹x = π/2
  • Principal values & graphs
Matrices
  • Matrix operations: addition, multiplication, Transpose, Inverse
  • Determinant: |A| for 2×2, 3×3
Determinants
  • Determinant of 2×2, 3×3 matrices
  • Cramer's Rule, Properties of determinants
Continuity & Differentiability
  • d/dx (f(g(x))) = f'(g(x))·g'(x) (Chain rule)
  • Derivatives of log, exp, trigonometric functions
Application of Derivatives
  • Maxima & Minima: f'(x)=0, f''(x) test
  • Rate of change, Tangent/Normal at (x₀,y₀): y–y₀ = m(x–x₀)
Integrals
  • ∫xⁿdx = xⁿ⁺¹/(n+1) + C, ∫eˣdx = eˣ+C, ∫sinx dx = –cosx + C
  • Definite integrals: ∫ₐᵇ f(x) dx
Differential Equations
  • dy/dx = f(x), General solution
  • Variable separable, Homogeneous, Linear DEs
Vectors & 3D Geometry
  • Vector addition, Scalar/Dot product: a·b = |a||b|cosθ
  • Cross product: a×b, Equation of line/plane
Probability
  • Bayes’ theorem: P(A|B) = P(A∩B)/P(B)
  • Mean, Variance of Binomial, Poisson distributions
Linear Programming
  • Objective function: Z = ax + by
  • Constraints: ax + by ≤ c, Graphical solution

Algebra Formulas

Formula/Concept Explanation
Quadratic Formula Roots of ax² + bx + c = 0: x = [-b±√(b²–4ac)]/(2a)
Sum & Product of Roots Sum = –b/a, Product = c/a
AP/GP/HP nth term of AP: a + (n–1)d, GP: ar^(n–1), HP: 1/(a + (n–1)d)
Binomial Theorem (a+b)ⁿ = Σ [nCr · a^(n–r) · b^r]
nCr & nPr nCr = n!/[r!(n–r)!], nPr = n!/(n–r)!
Logarithm Properties logₐ(xy) = logₐx + logₐy; logₐ(x/y) = logₐx – logₐy; logₐxⁿ = n·logₐx

Trigonometry Formulas

Formula/Concept Explanation
sin²θ + cos²θ = 1 Fundamental identity for all θ
sin(A±B), cos(A±B) sin(A±B) = sinAcosB ± cosAsinB; cos(A±B) = cosAcosB ∓ sinAsinB
tan(A±B) tan(A±B) = (tanA±tanB)/(1∓tanA·tanB)
Double/Triple Angle sin2A = 2sinAcosA; cos2A = cos²A–sin²A; tan2A = 2tanA/(1–tan²A)
Sum to Product sinA + sinB = 2sin[(A+B)/2]cos[(A–B)/2]

Calculus Formulas

Derivative/Integral Result
d/dx (xⁿ) nxⁿ⁻¹
d/dx (sinx), d/dx (cosx) cosx, –sinx
d/dx (eˣ), d/dx (lnx) eˣ, 1/x
∫xⁿdx xⁿ⁺¹/(n+1) + C (n≠–1)
∫eˣdx, ∫1/x dx eˣ + C, ln|x| + C
Chain Rule d/dx f(g(x)) = f'(g(x))·g'(x)

Coordinate & 3D Geometry Formulas

Formula/Concept Explanation
Distance Formula Between points (x₁, y₁), (x₂, y₂): √[(x₂–x₁)²+(y₂–y₁)²]
Section Formula (mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n)
Circle Equation (x–h)² + (y–k)² = r²
Equation of Line y = mx + c, ax + by + c = 0
Direction Cosines cosα, cosβ, cosγ (l² + m² + n² = 1)
3D Geometry Equation of plane: ax + by + cz + d = 0

Important Maths Definitions & Tips

  • Set: A collection of well-defined objects.
  • Function: A rule that assigns each input exactly one output.
  • Domain & Range: Set of all possible inputs/outputs of a function.
  • Matrix: A rectangular array of numbers.
  • Determinant: A value that can be computed from the elements of a square matrix.
  • Derivative: Measures the rate of change; slope of a function.
  • Integral: Area under the curve of a function.
  • Probability: A measure of the likelihood of an event.

How to Study Maths Formulas Effectively?

  • Write important formulas and theorems for each chapter in a separate notebook.
  • Revise formulas daily and attempt practice problems using them.
  • Use flashcards for tricky formulas, standard results, and identities.
  • Try visualizing concepts—especially for coordinate geometry and calculus.
  • Solve previous years’ papers to master application of formulas.
  • Teach a friend or explain aloud to strengthen your memory.

Tip: Return to this page before every test for a lightning revision!

Frequently Asked Questions (FAQs) – Maths Formulas

  • Q1. How do I memorize so many maths formulas?
    Group formulas by topic, use regular practice, make summary sheets, and teach someone else for best retention.
  • Q2. Are these formulas sufficient for JEE, CUET, or Board Exams?
    Yes, these cover core CBSE/NCERT/ISC formulas that appear frequently in JEE, CUET, and board exams.
  • Q3. How to remember trigonometric identities?
    Use mnemonic devices, write identities repeatedly, and solve problems using them daily.
  • Q4. What are the most important chapters for formulas?
    Trigonometry, Calculus (Derivatives/Integrals), Algebra, and Coordinate Geometry.

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Last modified: Saturday, 5 July 2025, 1:17 PM