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Formula Sheet & Quick Facts
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Algebra & Powers
- \(a^m a^n = a^{m+n}\), \(\dfrac{a^m}{a^n}=a^{m-n}\), \((a^m)^n=a^{mn}\).
- \(a^{-n}=\dfrac{1}{a^n}\), \(a^{1/n}=\sqrt[n]{a}\).
- Quadratic formula: \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\); \(\Delta=b^2-4ac\).
Trig (Right Triangle)
- \(\sin\theta=\dfrac{\text{opp}}{\text{hyp}}\), \(\cos\theta=\dfrac{\text{adj}}{\text{hyp}}\), \(\tan\theta=\dfrac{\text{opp}}{\text{adj}}\).
- Law of Sines: \(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\), Law of Cosines: \(c^2=a^2+b^2-2ab\cos C\).
Sequences & Series
- Arithmetic: \(u_n=u_1+(n-1)d\), \(S_n=\dfrac{n}{2}(2u_1+(n-1)d)\).
- Geometric: \(u_n=u_1 r^{n-1}\), \(S_n=u_1\dfrac{1-r^n}{1-r}\) (if \(r\neq1\)).
Measurement
- Cylinder: \(V=\pi r^2 h\). Cone: \(V=\dfrac{1}{3}\pi r^2 h\). Sphere: \(V=\dfrac{4}{3}\pi r^3\).
- SA Sphere: \(4\pi r^2\), Right prism: \(SA=2A_b+P_b h\).
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