How many formulas are there in Class 12 Maths?

Approximately 120–150 key formulas across all chapters. Calculus has the most (60+ formulas for differentiation, integration, and applications). Vectors & 3D Geometry have 20–25 formulas. Matrices & Determinants have 15–20. Probability has 10–15. Focus on Calculus first — it carries 35 out of 80 marks.

Which Maths chapter has the most marks in Class 12?

Calculus is the highest — 35 marks out of 80 (44% of the paper). This includes: Continuity & Differentiability, Applications of Derivatives, Integrals, Applications of Integrals, and Differential Equations. After Calculus: Vectors & 3D (14 marks), Matrices (10 marks), Probability (8 marks).

How to memorise so many Maths formulas?

Do not memorise — understand and practise. For integration: learn the base 15 formulas, then practise applying substitution and by-parts. For differentiation: learn the chain rule and 10 base derivatives. Write formulas by hand daily. Solve 5 problems per formula. Use spaced repetition: revise Day 1, 3, 7, 14.

Are these formulas enough for JEE Main too?

These cover the NCERT foundation which is common to both boards and JEE. JEE Main requires additional techniques: partial fractions (advanced), reduction formulas, complex integration methods, and 3D geometry advanced problems. For boards, these formulas are complete. For JEE, supplement with a reference book.

Maths Formulas Class 12 — 2026

Calculus carries 35/80 marks in Class 12 Maths — nearly half the paper. Master differentiation and integration formulas first. This is your complete formula sheet organised chapter-wise. Bookmark and review daily.

Relations & Functions

Concept	Key Formula / Fact
Types of Relations	Reflexive: (a,a) ∈ R ∀a. Symmetric: (a,b) ∈ R ⇒ (b,a) ∈ R. Transitive: (a,b) ∈ R and (b,c) ∈ R ⇒ (a,c) ∈ R. Equivalence = all three.
One-one (Injective)	f(a) = f(b) ⇒ a = b
Onto (Surjective)	Range = Codomain
Composition	(fog)(x) = f(g(x))

Inverse Trigonometric Functions

Formula	Domain / Range
sin⁻¹x + cos⁻¹x = π/2	x ∈ [−1, 1]
tan⁻¹x + cot⁻¹x = π/2	x ∈ ℝ
sin⁻¹(−x) = −sin⁻¹x	Odd function
cos⁻¹(−x) = π − cos⁻¹x	—
tan⁻¹x + tan⁻¹y = tan⁻¹((x+y)/(1−xy))	xy < 1
2tan⁻¹x = sin⁻¹(2x/(1+x²)) = cos⁻¹((1−x²)/(1+x²))	\|x\| ≤ 1

Matrices & Determinants

Formula	Description
(AB)' = B'A'	Transpose of product
(AB)⁻¹ = B⁻¹A⁻¹	Inverse of product
A⁻¹ = adj(A) / \|A\|	Inverse using adjoint (\|A\| ≠ 0)
\|adj(A)\| = \|A\|ⁿ⁻¹	For n×n matrix
A(adj A) = \|A\|·I	Matrix × adjoint = determinant × identity
\|AB\| = \|A\|·\|B\|	Determinant of product
Cramer's Rule: x = D₁/D, y = D₂/D	Solving equations using determinants

Differentiation

Function	Derivative
xⁿ	nxⁿ⁻¹
sin x	cos x
cos x	−sin x
tan x	sec²x
cot x	−cosec²x
sec x	sec x · tan x
cosec x	−cosec x · cot x
eˣ	eˣ
aˣ	aˣ · ln a
ln x	1/x
sin⁻¹x	1/√(1−x²)
cos⁻¹x	−1/√(1−x²)
tan⁻¹x	1/(1+x²)

Differentiation Rules

Rule	Formula
Product Rule	(uv)' = u'v + uv'
Quotient Rule	(u/v)' = (u'v − uv')/v²
Chain Rule	dy/dx = dy/du · du/dx
Logarithmic Differentiation	Take ln of both sides, then differentiate

Test these formulas with problems

Super Tutor has chapter-wise Class 12 Maths problems — Calculus, Vectors, Probability. Practise applying formulas, not just reading them.

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Integration

Function	Integral
xⁿ	xⁿ⁺¹/(n+1) + C (n ≠ −1)
1/x	ln\|x\| + C
eˣ	eˣ + C
aˣ	aˣ/ln a + C
sin x	−cos x + C
cos x	sin x + C
sec²x	tan x + C
cosec²x	−cot x + C
sec x · tan x	sec x + C
1/√(1−x²)	sin⁻¹x + C
1/(1+x²)	tan⁻¹x + C
1/(x√(x²−1))	sec⁻¹x + C

Special Integration Formulas

Type	Formula
∫1/(x²+a²) dx	(1/a) tan⁻¹(x/a) + C
∫1/(x²−a²) dx	(1/2a) ln\|(x−a)/(x+a)\| + C
∫1/√(a²−x²) dx	sin⁻¹(x/a) + C
∫1/√(x²+a²) dx	ln\|x + √(x²+a²)\| + C
∫eˣ[f(x)+f'(x)] dx	eˣ·f(x) + C
By Parts: ∫u·v dx	u∫v dx − ∫(u'∫v dx) dx. ILATE order: Inverse, Log, Algebraic, Trig, Exponential.

Applications of Derivatives

Application	Formula
Slope of tangent	m = dy/dx at (x₁, y₁)
Equation of tangent	y − y₁ = m(x − x₁)
Equation of normal	y − y₁ = (−1/m)(x − x₁)
Rate of change	dy/dt = (dy/dx)(dx/dt)
Maxima/Minima	f'(x) = 0 → find critical points. f''(x) > 0: minimum. f''(x) < 0: maximum.

Vectors & 3D Geometry

Formula	Description
\|a⃗\| = √(x²+y²+z²)	Magnitude of vector
a⃗·b⃗ = \|a\|\|b\|cosθ	Dot product
\|a⃗×b⃗\| = \|a\|\|b\|sinθ	Cross product magnitude
cosθ = (a⃗·b⃗)/(\|a\|\|b\|)	Angle between vectors
Line: r⃗ = a⃗ + λb⃗	Vector equation of line
(x−x₁)/a = (y−y₁)/b = (z−z₁)/c	Cartesian equation of line
Plane: r⃗·n⃗ = d	Vector equation of plane
ax + by + cz = d	Cartesian equation of plane
Distance from point to plane	\|ax₁+by₁+cz₁−d\| / √(a²+b²+c²)

Probability

Formula	Description
P(A\|B) = P(A∩B)/P(B)	Conditional probability
P(A∩B) = P(A)·P(B\|A)	Multiplication theorem
Bayes': P(Eᵢ\|A) = P(Eᵢ)·P(A\|Eᵢ) / ΣP(Eₖ)·P(A\|Eₖ)	Bayes' theorem
P(X=r) = ⁿCᵣ pʳ qⁿ⁻ʳ	Binomial distribution
Mean = np, Variance = npq	Binomial mean and variance

Linear Programming

5 easy marks. Steps: (1) Write objective function Z = ax + by. (2) Write constraints as inequalities. (3) Graph the constraints. (4) Find corner points of the feasible region. (5) Evaluate Z at each corner point. Maximum/minimum Z = answer. Always show the graph — diagram carries marks.

Formulas based on NCERT Class 12 Mathematics (2025–2026 syllabus). Some symbols simplified for readability. For complete proofs and derivations, refer to NCERT textbook. Useful for CBSE boards and as foundation for JEE Main. Last updated: February 2026.

Maths Formulas for Class 12 — Complete Formula Sheet 2026