Class 12 very important math notes

Basic Mathematics (Class 11
Mathematics)
1. Laws of Indices
• a^m × a^n = a^(m+n)
• a^m / a^n = a^(m−n)
• (a^m)^n = a^(mn)
• (ab)^n = a^n * b^n
• (a/b)^n = a^n / b^n


2. Surds and Radicals
• √a × √b = √(ab)
• √a / √b = √(a/b)
• (√a + √b)^2 = a + 2√(ab) + b
• (√a - √b)^2 = a - 2√(ab) + b


3. Logarithms
• log(ab) = log a + log b
• log(a/b) = log a - log b
• log(a^n) = n log a
• log_b a = log a / log b


4. Linear Equations
• General form: ax + b = 0
• Solution: x = -b/a (a ≠ 0)


5. Quadratic Equations
• General form: ax^2 + bx + c = 0
• Roots: x = [-b ± √(b² - 4ac)] / (2a)
• Discriminant (D) = b² - 4ac
• Nature of roots:
• - D > 0 → real and distinct
• - D = 0 → real and equal
• - D < 0 → complex conjugates