Class 10 notes math

Here are Class 10 Math Notes — full and comprehensive, covering all major chapters:

📚 Class 10 Mathematics — Full Notes

Chapter 1: Real Numbers

Key Concepts:

Euclid's Division Lemma: For any two positive integers a and b, there exist unique integers q and r such that: a = bq + r, where 0 ≤ r < b

Euclid's Division Algorithm: Used to find HCF of two numbers by repeatedly applying the lemma.

Fundamental Theorem of Arithmetic: Every composite number can be expressed as a product of primes in a unique way (ignoring order).

HCF × LCM = Product of two numbers

Irrational Numbers: √2, √3, π, etc. cannot be expressed as p/q

Decimal Expansions:

Terminating: denominator has only factors of 2 and 5

Non-terminating repeating: rational but denominator has other prime factors

Chapter 2: Polynomials

Types: Linear (degree 1), Quadratic (degree 2), Cubic (degree 3)

Zeroes of a Polynomial: Values of x where p(x) = 0

Relationship between zeroes and coefficients (Quadratic: ax² + bx + c):

Sum of zeroes (α + β) = −b/a

Product of zeroes (αβ) = c/a

For cubic ax³ + bx² + cx + d:

α + β + γ = −b/a

αβ + βγ + γα = c/a

αβγ = −d/a

Division Algorithm: p(x) = g(x) × q(x) + r(x)

Chapter 3: Pair of Linear Equations in Two Variables

General form: a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0

Conditions:

| Condition | Type | Graph |

|-----------|------|-------|

| a₁/a₂ ≠ b₁/b₂ | Unique solution | Intersecting lines |

| a₁/a₂ = b₁/b₂ = c₁/c₂ | Infinite solutions | Coincident lines |

| a₁/a₂ = b₁/b₂ ≠ c₁/c₂ | No solution | Parallel lines |

Methods of Solving: Graphical, Substitution, Elimination, Cross-multiplication