Class 10 NCERT Mathematics – Complete Formula Sheet
1. Real Numbers
•Euclid’s Division Lemma: a = bq + r, where 0 ≤ r < b
•HCF × LCM = Product of two numbers
2. Polynomials
•Quadratic Polynomial: ax² + bx + c
•α + β = −b/a
•αβ = c/a
3. Pair of Linear Equations in Two Variables
•ax + by + c = 0
•x/a + y/b = 1
•Cross-multiplication method
4. Quadratic Equations
•Standard form: ax² + bx + c = 0
•Quadratic Formula: x = (−b ± √(b² − 4ac)) / 2a
•Discriminant D = b² − 4ac
5. Arithmetic Progressions
•nth term: a■ = a + (n − 1)d
•Sum: S■ = n/2 [2a + (n − 1)d]
6. Triangles
•Similarity criteria: AAA, SAS, SSS
•Pythagoras Theorem: a² + b² = c²
•Area ratio of similar triangles = square of ratio of sides
7. Coordinate Geometry
•Distance formula: √[(x■ − x■)² + (y■ − y■)²]
•Midpoint formula: ((x■+x■)/2, (y■+y■)/2)
•Area of triangle = 1/2 |x■(y■−y■)+x■(y■−y■)+x■(y■−y■)|
