1. The quadratic formula: $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ 2. Pythagorean theorem: $$a^2+b^2=c^2$$ 3. Area of a circle: $$A=\pi r^2$$ 4. Circumference of a circle: $$C=2\pi r$$ 5. Slope of a line: $$m=\frac{y_2-y_1}{x_2-x_1}$$ 6. Equation of a line: $$y=mx+b$$ 7. Distance formula: $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$ 8. Midpoint formula: $$M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$ 9. Compound interest: $$A=P\left(1+\frac{r}{n}\right)^{nt}$$ 10. Simple interest: $$I=Prt$$ 11. Area of a triangle: $$A=\frac{1}{2}bh$$ 12. Volume of a sphere: $$V=\frac{4}{3}\pi r^3$$ 13. Volume of a cylinder: $$V=\pi r^2h$$ 14. Volume of a cone: $$V=\frac{1}{3}\pi r^2h$$ 15. Law of sines: $$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$$ 16. Law of cosines: $$c^2=a^2+b^2-2ab\cos C$$ 17. Exponential growth: $$N=N_0e^{rt}$$ 18. Logarithm definition: $$\log_b a=c \iff b^c=a$$ 19. Change of base formula: $$\log_b a=\frac{\log_c a}{\log_c b}$$ 20. Derivative definition: $$f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$ 21. Power rule: $$\frac{d}{dx}x^n=nx^{n-1}$$ 22. Product rule: $$\frac{d}{dx}(uv)=u'v+uv'$$ 23. Quotient rule: $$\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{u'v-uv'}{v^2}$$ 24. Chain rule: $$\frac{d}{dx}f(g(x))=f'(g(x))g'(x)$$ 25. Integral of power: $$\int x^n dx=\frac{x^{n+1}}{n+1}+C$$ 26. Area under curve: $$\int_a^b f(x) dx$$ 27. Euler's formula: $$e^{i\theta}=\cos \theta + i \sin \theta$$ 28. Binomial theorem: $$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k}b^k$$ 29. Sum of arithmetic series: $$S_n=\frac{n}{2}(a_1+a_n)$$ 30. Sum of geometric series: $$S_n=a_1\frac{1-r^n}{1-r}$$ 31. Standard deviation: $$\sigma=\sqrt{\frac{1}{N}\sum_{i=1}^N (x_i-\mu)^2}$$ 32. Permutations: $$P(n,r)=\frac{n!}{(n-r)!}$$ 33. Combinations: $$C(n,r)=\frac{n!}{r!(n-r)!}$$ 34. Binomial probability: $$P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}$$ 35. Normal distribution PDF: $$f(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$ 36. Distance formula in 3D: $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$$ 37. Dot product: $$\mathbf{a}\cdot\mathbf{b}=|a||b|\cos \theta$$ 38. Cross product: $$\mathbf{a}\times\mathbf{b}=|a||b|\sin \theta \mathbf{n}$$ 39. Magnitude of vector: $$|\mathbf{v}|=\sqrt{v_1^2+v_2^2+v_3^2}$$ 40. Equation of a circle: $$(x-h)^2+(y-k)^2=r^2$$ 41. Equation of ellipse: $$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$$ 42. Equation of hyperbola: $$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$$ 43. Heron's formula: $$A=\sqrt{s(s-a)(s-b)(s-c)}$$ where $$s=\frac{a+b+c}{2}$$ 44. Newton's second law: $$F=ma$$ 45. Kinematic equation: $$v=v_0+at$$ 46. Kinematic equation: $$s=v_0t+\frac{1}{2}at^2$$ 47. Kinematic equation: $$v^2=v_0^2+2as$$ 48. Ideal gas law: $$PV=nRT$$ 49. Ohm's law: $$V=IR$$ 50. Wave speed: $$v=f\lambda$$