Rational exponent
a^{p/q} = (q√a)^p
One sheet · NCERT · Board revision
Class 9 Formula Sheet
51 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 9 · Mathematics
Number Systems
Laws of exponents
a^m · a^n = a^{m+n}, (a^m)^n = a^{mn}
From chapter list
a^(p/q) = (q√a)^p
➗ Class 9 · Mathematics
Polynomials
Remainder theorem
p(x) divided by (x − a) leaves remainder p(a)
Factor theorem
x − a is a factor iff p(a) = 0
From chapter list
p(x) = (x−a)q(x) + p(a)
➗ Class 9 · Mathematics
Linear Equations in Two Variables
Standard form
ax + by + c = 0
➗ Class 9 · Mathematics
Lines and Angles
Linear pair
Adjacent angles on a straight line sum to 180°
Vertically opposite
Vertically opposite angles are equal
➗ Class 9 · Mathematics
Triangles
Angle sum
A + B + C = 180°
Exterior angle
Exterior = sum of two remote interiors
➗ Class 9 · Mathematics
Quadrilaterals
Angle sum
Sum of interior angles = 360°
Mid-point theorem
Segment joining mid-points of two sides ∥ third side and half of it
➗ Class 9 · Mathematics
Circles
Angle in a semicircle
90°
Cyclic quadrilateral
Opposite angles sum to 180°
➗ Class 9 · Mathematics
Heron’s Formula
Semi-perimeter
s = (a + b + c) / 2
Heron
Δ = √[s(s−a)(s−b)(s−c)]
➗ Class 9 · Mathematics
Surface Areas and Volumes
Cuboid
TSA = 2(lb+bh+hl), V = lbh
Cube
TSA = 6a², V = a³
Cylinder
CSA = 2πrh, TSA = 2πr(h+r), V = πr²h
From chapter list
V_cuboid = l×b×h
➗ Class 9 · Mathematics
Statistics
Ungrouped mean
x̄ = Σx / n
From chapter list
mean = Σx/n for ungrouped
🔬 Class 9 · Science
Matter in Our Surroundings
Kelvin
K = °C + 273
🔬 Class 9 · Science
Is Matter Around Us Pure?
Mass percent
mass % = (mass of solute / mass of solution) × 100
🔬 Class 9 · Science
Atoms and Molecules
Mole
1 mol = 6.022 × 10²³ particles
Molar mass idea
Mass of 1 mole in grams = formula mass in u
🔬 Class 9 · Science
Structure of the Atom
Mass number
A = Z + N
Atomic number
Z = number of protons
🔬 Class 9 · Science
Motion
Speed
speed = distance / time
Velocity
v = displacement / time
Acceleration
a = (v − u) / t
Equation 1
v = u + at
Equation 2
s = ut + ½ at²
Equation 3
v² = u² + 2as
From chapter list
v = u + at; s = ut + ½at²; v² = u²+2as
🔬 Class 9 · Science
Force and Laws of Motion
Newton II
F = m a
Momentum
p = m v
Impulse
F Δt = Δp
From chapter list
F = ma; p = mv
🔬 Class 9 · Science
Gravitation
Universal law
F = G m₁ m₂ / r²
Weight
W = m g
Pressure in liquid
P = h ρ g
Density
ρ = m / V
From chapter list
W = mg; P = hρg
🔬 Class 9 · Science
Work and Energy
Work
W = F s cos θ
Kinetic energy
KE = ½ m v²
Potential energy
PE = m g h
Power
P = W / t
From chapter list
KE = ½mv²; PE = mgh
🔬 Class 9 · Science
Sound
Wave relation
v = f λ
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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.