Some Math formula

1. Geometry:

   • Area of a rectangle: $�=�\times �$
   • Area of a triangle: $�=\frac{1}{2}\times �\times ℎ$
   • Area of a circle: $�=�\times {�}^2$
   • Circumference of a circle: $�=2\times �\times �$
   • Volume of a cube: $�={�}^3$
   • Volume of a cylinder: $�=�\times {�}^2\times ℎ$

2. Algebra:

   • Quadratic formula: $�=\frac{-�\pm \sqrt{{�}^2-4��}}{2�}$
   • Slope-intercept form of a line: $�=��+�$
   • Distance formula: $�=\sqrt{(�2-�1{)}^2+(�2-�1{)}^2}$
   • Midpoint formula: $(\frac{�1+�2}{2},\frac{�1+�2}{2})$

3. Trigonometry:

   • Pythagorean theorem: ${�}^2+{�}^2={�}^2$ (for a right triangle)
   • Sine formula: $\sin (�)=\frac{\text{opposite}}{\text{hypotenuse}}$
   • Cosine formula: $\cos (�)=\frac{\text{adjacent}}{\text{hypotenuse}}$
   • Tangent formula: $\tan (�)=\frac{\text{opposite}}{\text{adjacent}}$

4. Calculus:

   • Derivative of a function: $\frac{��}{��}={\lim }_{ℎ\to 0}\frac{�(�+ℎ)-�(�)}{ℎ}$
   • Integration by parts: $\int ���=��-\int ���$
   • Fundamental theorem of calculus: ${\int }_{�}^{�}�(�)��=�(�)-�(�)$

5. Probability and Statistics:

   • Mean (average): $\text{Mean}=\frac{{\sum }_{�=1}^{�}{�}_{�}}{�}$
   • Standard deviation: $�=\sqrt{\frac{{\sum }_{�=1}^{�}({�}_{�}-\text{Mean}{)}^2}{�}}$
   • Binomial probability: $�(�=�)=\left(\genfrac{}{}{0px}{}{�}{�}\right)\cdot {�}^{�}\cdot (1-�{)}^{�-�}$

6. Number Theory:

   • Prime factorization: Every integer greater than 1 either is a prime number itself or can be factorized into a unique set of prime numbers.
   • Greatest Common Divisor (GCD): The largest positive integer that divides each of the integers.
   • Least Common Multiple (LCM): The smallest positive integer that is divisible by both integers.