Here are some fundamental formulas in mathematics:
Algebra
1. *Linear Equation*: ax + by = c
2. *Quadratic Equation*: ax^2 + bx + c = 0
3. *Polynomial Equation*: a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0 = 0
Geometry
1. *Pythagorean Theorem*: a^2 + b^2 = c^2
2. *Circle Area*: A = πr^2
3. *Circle Circumference*: C = 2πr
Trigonometry
1. *Sine*: sin(A) = opposite side / hypotenuse
2. *Cosine*: cos(A) = adjacent side / hypotenuse
3. *Tangent*: tan(A) = opposite side / adjacent side
Calculus
1. *Derivative*: f'(x) = lim(h → 0) [f(x + h) - f(x)]/h
2. *Integral*: ∫f(x) dx = F(x) + C
Statistics
1. *Mean*: μ = (Σx_i) / n
2. *Median*: M = middle value of data set
3. *Standard Deviation*: σ = √[(Σ(x_i - μ)^2) / (n - 1)]
Other Formulas
1. *Exponential Growth*: A = P(1 + r)^t
2. *Logarithm*: log_b(a) = x ⇔ b^x = a
3. *Permutation*: P(n, r) = n! / (n - r)!
4. *Combination*: C(n, r) = n! / (r!(n - r)!)
