n(A ∪ B)
n(A) + n(B) − n(A ∩ B)
One sheet · NCERT · Board revision
Class 11 Mathematics Formula Sheet
41 formulas from Mathematics and Science, chapter by chapter. Search, filter, copy, or print. This is a revision sheet — not a replacement for the textbook derivation.
Practice questions aligned to NCERT topics used in CBSE classrooms. These are original exam-oriented questions for revision — not official CBSE board papers and not a guarantee of any exam question. Always match the textbook issued by your school and the latest PDFs on ncert.nic.in and cbseacademic.nic.in.
➗ Class 11 · Mathematics
Sets
De Morgan
(A ∪ B)′ = A′ ∩ B′, (A ∩ B)′ = A′ ∪ B′
➗ Class 11 · Mathematics
Trigonometric Functions
Radian
π rad = 180°
Identity
sin²x + cos²x = 1
sin(A±B)
sin A cos B ± cos A sin B
cos(A±B)
cos A cos B ∓ sin A sin B
➗ Class 11 · Mathematics
Complex Numbers and Quadratic Equations
Modulus
|z| = √(a² + b²) for z = a + ib
i²
i² = −1
Product of moduli
|z₁ z₂| = |z₁| |z₂|
From chapter list
|z1 z2|=|z1||z2|
➗ Class 11 · Mathematics
Permutations and Combinations
nPr
ⁿPᵣ = n! / (n − r)!
nCr
ⁿCᵣ = n! / [r! (n − r)!]
Symmetry
ⁿCᵣ = ⁿCₙ₋ᵣ
From chapter list
nCr = n! / r!(n−r)!
➗ Class 11 · Mathematics
Binomial Theorem
General term
Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ
➗ Class 11 · Mathematics
Sequences and Series
AP nth / sum
aₙ = a+(n−1)d, Sₙ = n/2 [2a+(n−1)d]
GP nth
aₙ = a rⁿ⁻¹
GP sum
Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1
Infinite GP
S∞ = a / (1 − r), |r| < 1
Sum of first n naturals
Σn = n(n+1)/2
Sum of squares
Σn² = n(n+1)(2n+1)/6
Sum of cubes
Σn³ = [n(n+1)/2]²
From chapter list
Sn=a(r^n−1)/(r−1)
➗ Class 11 · Mathematics
Straight Lines
Slope
m = tan θ = (y₂−y₁)/(x₂−x₁)
Point–slope
y − y₁ = m(x − x₁)
Distance point to line
d = |ax₁ + by₁ + c| / √(a² + b²)
From chapter list
d=|ax1+by1+c|/√(a²+b²)
➗ Class 11 · Mathematics
Conic Sections
Circle
(x − h)² + (y − k)² = r²
Parabola
y² = 4ax (standard)
Ellipse
x²/a² + y²/b² = 1
Hyperbola
x²/a² − y²/b² = 1
➗ Class 11 · Mathematics
Introduction to Three Dimensional Geometry
Distance 3D
d = √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²]
➗ Class 11 · Mathematics
Limits and Derivatives
d/dx (xⁿ)
n xⁿ⁻¹
d/dx (sin x)
cos x
d/dx (cos x)
−sin x
From chapter list
d/dx (sin x)=cos x
➗ Class 11 · Mathematics
Statistics
Variance
σ² = Σ(x − x̄)² / n
Standard deviation
σ = √variance
From chapter list
σ=√(Σ(x−x̄)²/n)
➗ Class 11 · Mathematics
Probability
Addition
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Conditional
P(A|B) = P(A ∩ B) / P(B)
Also open
FAQs
Are these all official board formulas?
They are the standard NCERT relations used in CBSE Maths and Science papers. Always match the edition issued by your school.
Why are some Biology items short?
Biology is mostly definitions. Only equations and standard ratios (photosynthesis, Hardy–Weinberg, growth models) sit on this sheet.
Will a formula come as-is in the exam?
Often the paper asks you to use a formula, not recite it. Practise a numerical or a derivation after you memorise the line.