How many formulas are there in Class 12 Maths?

It depends on how you count them, but most of them sit in Calculus: derivatives, standard integrals, definite-integral properties and differential equations. Calculus is also where the marks are: 35 of the 80 marks in the CBSE paper. Learn the Calculus formulas first, then Vectors and 3D Geometry.

Which Maths chapter has the most marks in Class 12?

Calculus. In CBSE's 2026-27 course structure the 80-mark paper is split as Calculus 35, Vectors and 3D Geometry 14, Algebra (matrices and determinants) 10, Relations and Functions 8, Probability 8 and Linear Programming 5. In ISC 2027, Calculus is also 35 of 80, followed by Relations and Functions and Algebra (10 each).

How do I memorise so many Maths formulas?

Understand and practise rather than memorise. For integration, learn the standard integrals, then practise substitution, partial fractions and integration by parts. For differentiation, learn the chain rule and the basic derivatives. Write formulas by hand daily, solve a few problems with each one, and revise on day 1, 3, 7 and 14.

Are these formulas enough for JEE Main too?

They cover the NCERT foundation that board exams and JEE Main share. JEE Main questions need faster, deeper problem-solving and cover Class 11 topics too, so use this sheet as a base and check NTA's current JEE Main syllabus for the full topic list.

Class 12 Maths Formulas — Chapter-Wise Sheet

Calculus carries 35 of the 80 marks in the CBSE Class 12 Maths paper, nearly half. Master differentiation and integration first. This is the full formula sheet from the NCERT Class 12 textbooks, chapter by chapter; rows marked “not in CBSE 2026-27” are topics CBSE no longer assesses, which other boards may still include.

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

CBSE's 2026-27 syllabus covers definitions, domains, ranges, principal value branches and graphs:

Function	Domain	Principal value range
sin⁻¹x	[−1, 1]	[−π/2, π/2]
cos⁻¹x	[−1, 1]	[0, π]
tan⁻¹x	ℝ	(−π/2, π/2)
cot⁻¹x	ℝ	(0, π)
sec⁻¹x	ℝ − (−1, 1)	[0, π] − {π/2}
cosec⁻¹x	ℝ − (−1, 1)	[−π/2, π/2] − {0}

The identities below are not in the CBSE 2026-27 syllabus, but ISC and some state boards still include properties of inverse trigonometric functions:

Formula	Valid for
sin⁻¹x + cos⁻¹x = π/2	x ∈ [−1, 1]
tan⁻¹x + cot⁻¹x = π/2	x ∈ ℝ
sin⁻¹(−x) = −sin⁻¹x	x ∈ [−1, 1]
cos⁻¹(−x) = π − cos⁻¹x	x ∈ [−1, 1]
tan⁻¹x + tan⁻¹y = tan⁻¹((x+y)/(1−xy))	xy < 1
2tan⁻¹x = sin⁻¹(2x/(1+x²))	\|x\| ≤ 1
2tan⁻¹x = cos⁻¹((1−x²)/(1+x²))	x ≥ 0

Matrices & Determinants

Formula	Description
(AB)' = B'A'	Transpose of a product
(AB)⁻¹ = B⁻¹A⁻¹	Inverse of a product
A⁻¹ = adj(A) / \|A\|	Inverse using the adjoint (\|A\| ≠ 0)
A(adj A) = (adj A)A = \|A\|·I	Matrix × adjoint = determinant × identity
\|adj(A)\| = \|A\|ⁿ⁻¹	For an n×n matrix
\|AB\| = \|A\|·\|B\|	Determinant of a product
AX = B ⇒ X = A⁻¹B	Solving linear equations by the matrix method (\|A\| ≠ 0)
Area of triangle = ½ \|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)\|	The same value as ½ × the absolute value of the determinant with rows (x₁, y₁, 1), (x₂, y₂, 1), (x₃, y₃, 1)
Cramer's rule: x = D₁/D, y = D₂/D	Not in CBSE 2026-27, which uses the matrix method

Continuity & Differentiability

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 · log a
log x	1/x
sin⁻¹x	1/√(1−x²)
cos⁻¹x	−1/√(1−x²)
tan⁻¹x	1/(1+x²)

Differentiation Rules

Rule	Formula
Continuity at x = a	lim(x→a) f(x) = f(a)
Product rule	(uv)' = u'v + uv'
Quotient rule	(u/v)' = (u'v − uv')/v²
Chain rule	dy/dx = dy/du · du/dx
Parametric form	dy/dx = (dy/dt) / (dx/dt)
Logarithmic differentiation	Take log of both sides, then differentiate (useful for y = u(x)^v(x))
Second-order derivative	d²y/dx² = d/dx (dy/dx)

Test these formulas with problems

Super Tutor has chapter-wise Class 12 Maths practice quizzes — Calculus, Vectors, Probability and more — so you practise applying formulas, not just reading them.

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Applications of Derivatives

Application	Formula
Rate of change	dy/dt = (dy/dx)(dx/dt)
Increasing / decreasing	f'(x) > 0 on an interval: increasing. f'(x) < 0: decreasing.
Maxima / minima	Find critical points where f'(x) = 0. Second derivative test: f''(x) < 0 gives a local maximum, f''(x) > 0 a local minimum. First derivative test: f' changes from + to − at a maximum, − to + at a minimum.
Tangent and normal at (x₁, y₁)	Slope m = dy/dx; tangent y − y₁ = m(x − x₁); normal y − y₁ = (−1/m)(x − x₁). Not in CBSE 2026-27; ISC still includes tangents and normals.

Integrals

Function	Integral
xⁿ	xⁿ⁺¹/(n+1) + C (n ≠ −1)
1/x	log\|x\| + C
eˣ	eˣ + C
aˣ	aˣ/log a + C
sin x	−cos x + C
cos x	sin x + C
tan x	log\|sec x\| + C
cot x	log\|sin x\| + C
sec x	log\|sec x + tan x\| + C
cosec x	log\|cosec x − cot 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 (x > 1)

Special Integrals

Integral	Result
∫1/(x²−a²) dx	(1/2a) log\|(x−a)/(x+a)\| + C
∫1/(a²−x²) dx	(1/2a) log\|(a+x)/(a−x)\| + C
∫1/(x²+a²) dx	(1/a) tan⁻¹(x/a) + C
∫1/√(x²−a²) dx	log\|x + √(x²−a²)\| + C
∫1/√(a²−x²) dx	sin⁻¹(x/a) + C
∫1/√(x²+a²) dx	log\|x + √(x²+a²)\| + C
∫√(x²−a²) dx	(x/2)√(x²−a²) − (a²/2) log\|x + √(x²−a²)\| + C
∫√(x²+a²) dx	(x/2)√(x²+a²) + (a²/2) log\|x + √(x²+a²)\| + C
∫√(a²−x²) dx	(x/2)√(a²−x²) + (a²/2) sin⁻¹(x/a) + C
∫eˣ[f(x) + f'(x)] dx	eˣ·f(x) + C
By parts: ∫u·v dx	u∫v dx − ∫(u'∫v dx) dx. Choose u in ILATE order: Inverse, Logarithmic, Algebraic, Trigonometric, Exponential.

Definite Integrals

Property	Formula
Fundamental theorem	∫ₐᵇ f(x) dx = F(b) − F(a), where F'(x) = f(x)
Swapping limits	∫ₐᵇ f(x) dx = −∫ᵇₐ f(x) dx
Splitting the interval	∫ₐᵇ f(x) dx = ∫ₐᶜ f(x) dx + ∫ᶜᵇ f(x) dx
King's property	∫ₐᵇ f(x) dx = ∫ₐᵇ f(a+b−x) dx; in particular ∫₀ᵃ f(x) dx = ∫₀ᵃ f(a−x) dx
Even and odd functions	∫₋ₐᵃ f(x) dx = 2∫₀ᵃ f(x) dx if f is even; 0 if f is odd
Repeating interval	∫₀²ᵃ f(x) dx = 2∫₀ᵃ f(x) dx if f(2a−x) = f(x); 0 if f(2a−x) = −f(x)

Applications of Integrals

Area	Formula
Between a curve and the x-axis	A = ∫ₐᵇ y dx (take the absolute value of parts below the axis)
Between a curve and the y-axis	A = ∫ x dy, from y = c to y = d
Circle x² + y² = r²	πr²
Ellipse x²/a² + y²/b² = 1	πab

Differential Equations

Type	Method
Order and degree	Order: the highest derivative present. Degree: the power of that derivative once the equation is a polynomial in derivatives.
Variable separable: dy/dx = f(x)g(y)	∫dy/g(y) = ∫f(x) dx + C
Homogeneous: dy/dx = F(y/x)	Put y = vx, so dy/dx = v + x(dv/dx), then separate variables
Linear: dy/dx + Py = Q	Integrating factor IF = e^(∫P dx); solution y·IF = ∫(Q·IF) dx + C
Linear in x: dx/dy + P₁x = Q₁	IF = e^(∫P₁ dy); solution x·IF = ∫(Q₁·IF) dy + C

Vectors & 3D Geometry

Formula	Description
\|a⃗\| = √(x² + y² + z²)	Magnitude of a vector
â = a⃗ / \|a⃗\|	Unit vector
r⃗ = (m b⃗ + n a⃗)/(m + n)	Position vector of the point dividing AB internally in the ratio m : n
a⃗·b⃗ = \|a\|\|b\|cosθ	Dot product; cosθ = (a⃗·b⃗)/(\|a\|\|b\|)
Projection of a⃗ on b⃗ = (a⃗·b⃗)/\|b⃗\|	Scalar projection
\|a⃗ × b⃗\| = \|a\|\|b\|sinθ	Cross product magnitude; area of parallelogram = \|a⃗ × b⃗\|, area of triangle = ½\|a⃗ × b⃗\|
l² + m² + n² = 1	Direction cosines of a line
Line: r⃗ = a⃗ + λb⃗	Vector equation of a line
(x−x₁)/a = (y−y₁)/b = (z−z₁)/c	Cartesian equation of a line
cosθ = \|a₁a₂ + b₁b₂ + c₁c₂\| / (√(a₁²+b₁²+c₁²) √(a₂²+b₂²+c₂²))	Angle between two lines
d = \|(a⃗₂ − a⃗₁)·(b⃗₁ × b⃗₂)\| / \|b⃗₁ × b⃗₂\|	Shortest distance between skew lines
d = \|b⃗ × (a⃗₂ − a⃗₁)\| / \|b⃗\|	Distance between parallel lines
Plane: r⃗·n̂ = d, or ax + by + cz = d	Not in CBSE 2026-27; check your board's syllabus
\|ax₁ + by₁ + cz₁ − d\| / √(a² + b² + c²)	Distance from a point to a plane. Not in CBSE 2026-27

Probability

Formula	Description
P(A\|B) = P(A∩B)/P(B)	Conditional probability (P(B) ≠ 0)
P(A∩B) = P(A)·P(B\|A)	Multiplication theorem
P(A∩B) = P(A)·P(B)	Independent events
P(A) = ΣP(Eᵢ)·P(A\|Eᵢ)	Theorem of total probability (E₁…Eₙ a partition of the sample space)
P(Eᵢ\|A) = P(Eᵢ)·P(A\|Eᵢ) / ΣP(Eₖ)·P(A\|Eₖ)	Bayes' theorem
P(X = r) = ⁿCᵣ pʳ qⁿ⁻ʳ; mean np, variance npq	Binomial distribution. Not in CBSE 2026-27; check your board's syllabus

Linear Programming

5 marks in the CBSE paper. Steps: (1) write the objective function Z = ax + by; (2) write the constraints as inequalities; (3) graph the constraints and shade the feasible region; (4) find the corner points of the feasible region; (5) evaluate Z at each corner point. The largest or smallest value is the answer; if the region is unbounded, check that the optimum really exists. Draw the graph neatly, because the feasible region is part of the answer.

Formulas are from the NCERT Class 12 Mathematics textbooks, with some symbols simplified for readability. Notes on what is and isn't assessed follow the CBSE 2026-27 syllabus; ISC and state boards differ, so check your own board's syllabus. Marks per unit are from CBSE's 2026-27 course structure and CISCE's ISC 2027 syllabus.

Class 12 Maths Formulas: Complete Chapter-Wise Formula Sheet