n(A ∪ B)
n(A) + n(B) − n(A ∩ B)
One sheet · NCERT · Board revision
Class 11 Formula Sheet
88 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)
⚛️ Class 11 · Physics
Units and Measurements
Force dimension
[F] = M L T⁻²
Relative error
Δa / a
⚛️ Class 11 · Physics
Motion in a Straight Line
Constant a
v = u + at, s = ut + ½at², v² = u² + 2as
From chapter list
v=u+at
⚛️ Class 11 · Physics
Motion in a Plane
Projectile time of flight
T = 2 u sinθ / g
Maximum height
H = u² sin²θ / (2g)
Range
R = u² sin 2θ / g
Centripetal acceleration
a = v² / r = ω² r
⚛️ Class 11 · Physics
Laws of Motion
Newton II
F = dp/dt = m a
Friction
f ≤ μ N, f_k = μ_k N
From chapter list
f ≤ μN
⚛️ Class 11 · Physics
Work, Energy and Power
Work
W = F · s
KE
½ m v²
Power
P = F · v
From chapter list
P=F v; KE=½mv²
⚛️ Class 11 · Physics
System of Particles and Rotational Motion
Torque
τ = r × F = I α
Angular momentum
L = I ω
From chapter list
τ=Iα
⚛️ Class 11 · Physics
Gravitation
Escape speed
v_esc = √(2GM / R)
Orbital speed
v_o = √(GM / r)
g at height
g_h = g (R / (R+h))²
⚛️ Class 11 · Physics
Mechanical Properties of Solids
Young’s modulus
Y = (F/A) / (ΔL/L)
⚛️ Class 11 · Physics
Mechanical Properties of Fluids
Pressure
P = h ρ g
Bernoulli
P + ρ g h + ½ ρ v² = constant
Surface tension
T = F / l
⚛️ Class 11 · Physics
Thermal Properties of Matter
Linear expansion
ΔL = α L ΔT
Heat
Q = m c ΔT, Q = m L
⚛️ Class 11 · Physics
Thermodynamics
First law (NCERT)
ΔU = Q − W
Ideal gas
Cₚ − Cᵥ = R
⚛️ Class 11 · Physics
Kinetic Theory
rms speed
v_rms = √(3RT / M)
⚛️ Class 11 · Physics
Oscillations
SHM period (spring)
T = 2π √(m / k)
Simple pendulum
T = 2π √(l / g)
⚛️ Class 11 · Physics
Waves
Wave speed
v = f λ
🧪 Class 11 · Chemistry
Some Basic Concepts of Chemistry
Molarity
M = n / V_L
Mole
n = given mass / molar mass
🧪 Class 11 · Chemistry
Structure of Atom
Photon
E = h ν = hc / λ
From chapter list
E=hν
🧪 Class 11 · Chemistry
Thermodynamics
First law (chemistry)
ΔU = q + w, w = −PΔV
Gibbs
ΔG = ΔH − TΔS
🧪 Class 11 · Chemistry
Equilibrium
Kc
K_c = [C]^c [D]^d / [A]^a [B]^b
Water
K_w = 10⁻¹⁴ at 25°C
pH
pH = −log₁₀ [H⁺]
From chapter list
Kc = [C]^c[D]^d/[A]^a[B]^b
🧬 Class 11 · Biology
Photosynthesis in Higher Plants
Overall
6CO₂ + 12H₂O → C₆H₁₂O₆ + 6O₂ + 6H₂O (as in NCERT)
🧬 Class 11 · Biology
Respiration in Plants
RQ
RQ = CO₂ evolved / O₂ consumed
🧬 Class 11 · Biology
Breathing and Exchange of Gases
Vital capacity
VC = TV + IRV + ERV
🧬 Class 11 · Biology
Biomolecules
Enzyme (idea)
V depends on [S]; K_m is [S] at ½ V_max
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.