12th Grade Mathematics Formulae
1. Quadratic Formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] 2. Derivative of a Function: \[ \frac{d}{dx}\left[f(x)\right] = \lim_{\Delta x \to 0} \frac{f(x + \Delta x) - f(x)}{\Delta x} \] 3. Sum of an Arithmetic Progression (AP): \[ S_n = \frac{n}{2} \left[2a + (n-1)d\right] \] 4. Sum of a Geometric Progression (GP): \[ S_n = \frac{a(1 - r^n)}{1 - r} \quad (r \neq 1) \] 5. Area of a Triangle (Using Heron’s Formula): \[ A = \sqrt{s(s-a)(s-b)(s-c)} \quad \text{where} \ s = \frac{a+b+c}{2} \] 6. Standard Equation of a Circle: \[ (x - h)^2 + (y - k)^2 = r^2 \] 7. Distance Between Two Points: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] 8. Slope of a Line: \[ m = \frac{y_2 - y_1}{...