Basic Cheatsheet Template

Cheatsheet Content

### How to Use This Template This is a basic structure to get you started. You can ask me to: - **Add new sections** on specific topics (e.g., "Add a section on derivatives"). - **Elaborate on existing points** (e.g., "Expand on the properties of vectors"). - **Remove sections** (e.g., "Remove the matrices section"). - **Change the level of detail** (e.g., "Make this more advanced" or "Simplify the explanations"). - **Format content** (e.g., "Add an example for matrix multiplication"). ### Mathematics Basics #### Constants & Notations - $\pi \approx 3.14159$ - $e \approx 2.71828$ - $i = \sqrt{-1}$ - $\sum$ (Summation) - $\int$ (Integral) - $\lim$ (Limit) #### Fundamental Formulas - **Quadratic Formula:** For $ax^2 + bx + c = 0$, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ - **Pythagorean Theorem:** $a^2 + b^2 = c^2$ ### Common Functions #### Polynomials - **General Form:** $P(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0$ - **Degree:** Highest power of $x$. #### Exponential & Logarithmic - **Exponential:** $f(x) = a^x$ - **Logarithmic:** $f(x) = \log_a(x)$ - **Properties:** - $\log_a(xy) = \log_a(x) + \log_a(y)$ - $\log_a(x/y) = \log_a(x) - \log_a(y)$ - $\log_a(x^p) = p \log_a(x)$ ### Geometry Formulas #### 2D Shapes - **Circle:** - Area: $A = \pi r^2$ - Circumference: $C = 2\pi r$ - **Rectangle:** - Area: $A = lw$ - Perimeter: $P = 2(l+w)$ - **Triangle:** - Area: $A = \frac{1}{2}bh$ #### 3D Shapes - **Sphere:** - Volume: $V = \frac{4}{3}\pi r^3$ - Surface Area: $A = 4\pi r^2$ - **Cube:** - Volume: $V = s^3$ - Surface Area: $A = 6s^2$