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The List of Algebric Formulas
| Formula Name | Formula |
| Quadratic Formula | $$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$$ |
| Slope of a Line | $$m=\frac{y_2-y_1}{x_2-x_1}$$ |
| Point-Slope Form | $$y-y_1=m(x-x_1)$$ |
| Slope-Intercept Form | $$y=mx+b$$ |
| Standard Form of a Line | $$Ax+By=C$$ |
| Distance Formula | $$d=\sqrt{(x_2-x_1)^2+(y_2-y_ |
| Midpoint Formula | $$M=\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right)$$ |
| Sum of a Geometric Series | $$S_n=a\frac{1-r^n}{1-r}$$ |
| Sum of an Arithmetic Series | $$S_n=\frac{n}{2}(a+l)$$ |
| Pythagorean Theorem | $$a^2+b^2=c^2$$ |
Trigonometric Values Table (Geometry)
| Angle (Degrees) | Angle (Radians) | Sine | Cosine | Tangent | |
| 0° | $$0$$ | $$0$$ | $$1$$ | $$0$$ | |
| 30° | $$\frac{\pi}{6}$$ | $$\frac{1}{2}$$ | $$\frac{\sqrt{3}}{2}$$ | $$\frac{1}{\sqrt{3}}$$ | |
| 45° | $$\frac{\pi}{4}$$ | $$\frac{\sqrt{2}}{2}$$ | $$\frac{\sqrt{2}}{2}$$ | $$1$$ | |
| 60° | $$\frac{\pi}{3}$$ | $$\frac{\sqrt{3}}{2}$$ | $$\frac{1}{2}$$ | $$\sqrt{3}$$ | |
| 90° | $$\frac{\pi}{2}$$ | $$1$$ | $$0$$ | $$\text{undefined}$$ |
Derivative Formula List
| Rule/Function | f(x) | f'(x) |
|---|---|---|
| Basic Rules | ||
| Constant Rule | c | 0 |
| Power Rule | ||
| Constant Multiple Rule | ||
| Sum Rule | ||
| Difference Rule | ||
| Product and Quotient Rules | ||
| Product Rule | ||
| Quotient Rule | ||
| Chain Rule | ||
| Chain Rule | ||
| Transcendental Functions | ||
| Exponential Function | ||
| Logarithmic Function | ||
| Trigonometric Functions | ||
| Sine Function | ||
| Cosine Function | ||
| Tangent Function | ||
| Cotangent Function | ||
| Secant Function | ||
| Cosecant Function |
Common Integration Formulas
Formula Name | Integration |
Power Rule | $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ |
Constant Rule | $$\int a \, dx = ax + C$$ |
Exponential Rule | $$\int e^x \, dx = e^x + C$$ |
Logarithmic Rule | $$\int \frac{1}{x} , dx = \ln(x)$$ |
Sine Rule | $$\int \sin(x) \, dx = -\cos(x) + C$$ |
Cosine Rule | $$\int \cos(x) \, dx = \sin(x) + C$$ |
Secant Squared Rule | $$\int \sec^2(x) \, dx = \tan(x) + C$$ |
Cosecant Squared Rule | $$\int \csc^2(x) \, dx = -\cot(x) + C$$ |
Secant Tangent Rule | $$\int \sec(x) \tan(x) \, dx = \sec(x) + C$$ |
Cosecant Cotangent Rule | $$\int \csc(x) \cot(x) \, dx = -\csc(x) + C$$ |
Exponential (Base a) Rule | $$\int a^x \, dx = \frac{a^x}{\ln(a)} + C$$ |
Integration by Parts | $$\int u \, dv = uv – \int v \, du$$ |
Substitution Rule | $$\int f(g(x)) g'(x) \, dx = \int f(u) \, du$$ |
Definite Integral | $$\int_a^b f(x) \, dx = F(b) – F(a)$$ |
