Tamil Nadu Class 9 Maths Formula and Concept Bank — Samacheer Kalvi
Complete formula bank for Class 9 Maths Samacheer Kalvi with all formulas, identities, theorems, and key concepts from every chapter.
Updated 11 May 20263 min read
Chapter 1 — Set Language
Formula
Expression
Union count
n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
Three-set union
n(A ∪ B ∪ C) = n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)
Power set
n(P(A)) = 2^n(A)
Proper subsets
2^n(A) − 1
De Morgan's Law 1
(A ∪ B)' = A' ∩ B'
De Morgan's Law 2
(A ∩ B)' = A' ∪ B'
Chapter 2 — Real Numbers
Formula
Expression
Surd multiplication
√a × √b = √(ab)
Surd division
√a / √b = √(a/b)
Conjugate rationalisation
(a+√b)(a−√b) = a² − b
Exponent product
aᵐ × aⁿ = aᵐ⁺ⁿ
Exponent power
(aᵐ)ⁿ = aᵐⁿ
Fractional exponent
a^(1/n) = ⁿ√a
Negative exponent
a⁻ⁿ = 1/aⁿ
Chapter 3 — Algebra
Identity
Expression
Cube expansion +
(a+b)³ = a³ + 3a²b + 3ab² + b³
Cube expansion −
(a−b)³ = a³ − 3a²b + 3ab² − b³
Sum of cubes
a³+b³ = (a+b)(a²−ab+b²)
Difference of cubes
a³−b³ = (a−b)(a²+ab+b²)
Three variable square
(a+b+c)² = a²+b²+c²+2ab+2bc+2ca
Three variable cubes
a³+b³+c³−3abc = (a+b+c)(a²+b²+c²−ab−bc−ca)
Remainder Theorem
Remainder of p(x)÷(x−a) = p(a)
Factor Theorem
(x−a) is factor ↔ p(a) = 0
Chapter 5 — Coordinate Geometry
Formula
Expression
Distance formula
d = √[(x₂−x₁)² + (y₂−y₁)²]
Midpoint
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Section (internal)
P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
Centroid
G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)
Chapter 6 — Trigonometry
Identity
Expression
Pythagorean 1
sin²θ + cos²θ = 1
Pythagorean 2
1 + tan²θ = sec²θ
Pythagorean 3
1 + cot²θ = cosec²θ
Complementary sin/cos
sin(90°−θ) = cosθ; cos(90°−θ) = sinθ
Complementary tan/cot
tan(90°−θ) = cotθ; cot(90°−θ) = tanθ
Chapter 7 — Mensuration
Shape
LSA
TSA
Volume
Cuboid
2h(l+b)
2(lb+bh+lh)
lbh
Cube
4a²
6a²
a³
Cylinder
2πrh
2πr(r+h)
πr²h
Cone
πrl
πr(r+l)
(1/3)πr²h
Sphere
—
4πr²
(4/3)πr³
Hemisphere
2πr²
3πr²
(2/3)πr³
Slant height: l = √(r² + h²)
Chapters 8–9 — Statistics and Probability
Formula
Expression
Mean (grouped)
Σfx / Σf
Median (grouped)
L + [(N/2−cf)/f] × h
Mode (grouped)
L + [(f₁−f₀)/(2f₁−f₀−f₂)] × h
Empirical relationship
Mode = 3 Median − 2 Mean
Probability
P(E) = n(E)/n(S)
Complement
P(E') = 1 − P(E)
Frequently Asked Questions
Print or copy this page into your notebook. Before each revision session, read through it. In the final week, test yourself by covering the right column and trying to recall each formula from memory.
