Formula Cheat Sheet for CBSE Class 10 Mathematics
Official 100% syllabus-accurate formula sheet for exam revision.
1. Real Numbers
Euclid's Division Lemmaa = bq + r, where 0 ≤ r < b
HCF × LCM IdentityHCF(a,b) × LCM(a,b) = a × b
Irrationality Conditionp is prime & p|a² ⇒ p|a
2. Polynomials & Quadratic Equations
Sum of Zeroes (α+β)α + β = −b/a
Product of Zeroes (αβ)αβ = c/a
Quadratic Formulax = (−b ± √(b²−4ac)) / 2a
Discriminant NatureΔ = b²−4ac: Δ>0 (real & distinct), Δ=0 (equal)
3. Arithmetic Progressions
n-th Term (a<sub>n</sub>)an = a + (n − 1)d
Sum of n Terms (S<sub>n</sub>)Sn = n/2 [2a + (n − 1)d]
Sum (First & Last)Sn = n/2 (a + l)
4. Trigonometry
Pythagorean Identity 1sin²θ + cos²θ = 1
Pythagorean Identity 21 + tan²θ = sec²θ
Pythagorean Identity 31 + cot²θ = csc²θ
5. Coordinate Geometry
Distance Formulad = √[(x²−x¹)² + (y²−y¹)²]
Section FormulaP = ((m¹x²+m²x¹)/(m¹+m²), (m¹y²+m²y¹)/(m¹+m²))
Midpoint FormulaM = ((x¹+x²)/2, (y¹+y²)/2)