satformula

SAT Formula Sheet

The Pythagorean Theorem	\[ a^2+b^2=c^2 \]
The Distance Formula	\[ \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} \]
Circle Equation	\[ (x-a)^2+(y-b)^2=r^2 \]
Slope	\[ \frac{y_1-y_2}{x_1-x_2} \]
Perpendicular	\[ m_1\cdot m_2=-1 \]
Linear Equation	\[ \begin{array}{ccrcc} y&=&m&\cdot x+&b \\ y&=&\text{slope}&\cdot x+&y\text{-intecept} \end{array} \]
System of Linear Equations	\[ \begin{array}{rcl} y&=&m_1x+b_1 \\ y&=&m_2x+b_2 \end{array} \]
Midpoint	\[ \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right) \]
乘法公式	\[ \begin{array}{rcl} (a+b)^2 &=& a^2+2ab+b^2 \\ (a-b)^2 &=& a^2-2ab+b^2 \\ a^2-b^2 &=& (a+b)(a-b) \end{array} \]
Quadratic Formula	\[ax^2+bx+c=0\] \[ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \]
Discriminant	\[ax^2+bx+c=0\] \[ \begin{array}{rcl} b^2-4ac>0 & \Leftrightarrow & \text{two real solutions} \\ b^2-4ac=0 & \Leftrightarrow & \text{one real solution} \\ b^2-4ac\lt 0 & \Leftrightarrow & \text{no real solution} \end{array} \]
Translation	\(f(x)+1\) ↑ \(f(x+1)\) ← \(f(x)\) → \(f(x-1)\) ↓ \(f(x)-1\)
Vertex Form	\[ f(x)=a\left(x-\left(\frac{-b}{2a}\right)\right)^2+\text{extremum} \]
Vieta's Formulas	\[ax^2+bx+c=0\] \[ \begin{array}{rcl} x_1+x_2 &=& \frac{-b}{a} \\ x_1\cdot x_2 &=& \frac{c}{a} \end{array} \]
Exponential Laws	\(a^m a^n=a^{m+n}\) \(\frac{a^m}{a^n}=a^{m-n}\) \((ab)^m=a^m b^m\) \(\left(\frac{a}{b}\right)^m=\frac{a^m}{b^m}\) \((a^m)^n=a^{mn}\) \(a^{-1}=\frac{1}{a}\) \(a^{\frac{m}{n}}=\sqrt[n]{a^m}\)
Radian and Degree	\[ \pi=180^{\circ} \]
Arc Length	\[ 2\pi r\frac{\theta}{360^{\circ}} \]
Sector Area	\[ \pi r^2\frac{\theta}{360^{\circ}} \]
Volume of Sphere	\[ \frac{4}{3}\pi r^3 \]
Surface Area of Sphere	\[ 4\pi r^2 \]
Equilateral Triangle Area	\[ \frac{\sqrt{3}}{4}a^2 \]
Triangle Congruence Theorems	SSS, SAS, ASA, AAS, RHS
Triangle Similarity Theorems	AA, SSS, SAS
If two parallel lines are cut by a transversal, then	corresponding angles are congruent. alternate interior angles are congruent. consecutive interior angles are supplementary.
Trigonometric Functions	\[ \begin{array}{rcl} \sin{\theta} &=& \frac{\text{Opposite}}{\text{Hypotenuse}} \\ \cos{\theta} &=& \frac{\text{Adjacent}}{\text{Hypotenuse}} \\ \tan{\theta} &=& \frac{\text{Opposite}}{\text{Adjacent}} \end{array} \]
Trigonometric Functions	\[ \begin{array}{rcl} \sin{(90^{\circ}-\theta)} &=& \cos{\theta} \\ \cos{(90^{\circ}-\theta)} &=& \sin{\theta} \end{array} \]