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\author{rockcollector2}
\pdfinfo{
  /Title (quantitative-methods-midterm.pdf)
  /Creator (Cheatography)
  /Author (rockcollector2)
  /Subject (Quantitative Methods Midterm Cheat Sheet)
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\noindent
\begin{multicols}{3}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Quantitative Methods Midterm Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{rockcollector2} via \textcolor{DarkBackground}{\uline{cheatography.com/22080/cs/4425/}}}
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}rockcollector2 \\
  \uline{cheatography.com/rockcollector2} \\
  \end{tabulary}
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\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 19th June, 2015.\\
   Updated 11th May, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Fraction Rules}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Common Denominators \newline % Row Count 1 (+ 1)
a/b + c/d = ad + bc/bd \newline % Row Count 2 (+ 1)
Multiplication \newline % Row Count 3 (+ 1)
a/b * c/d = ac/bd \newline % Row Count 4 (+ 1)
Reciprocal \newline % Row Count 5 (+ 1)
1/(a/b) = b/a% Row Count 6 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Theory of Geometric Series}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{S = p + pr + pr\textasciicircum{}2\textasciicircum{} + pr\textasciicircum{}3\textasciicircum{} + ... + pr\textasciicircum{}n\textasciicircum{} \newline % Row Count 1 (+ 1)
Sr = p + pr + pr\textasciicircum{}2\textasciicircum{} + pr\textasciicircum{}3\textasciicircum{} + ... + pr\textasciicircum{}n\textasciicircum{} + pr\textasciicircum{}n+1\textasciicircum{} \newline % Row Count 3 (+ 2)
S - Sr = p - pr\textasciicircum{}n+1 \newline % Row Count 4 (+ 1)
S = p-pr\textasciicircum{}n+1\textasciicircum{}/1-r% Row Count 5 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Lines}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Given point (c,d) and slope m, the unique line that satisfies this is the set of all points (x,y) such that \newline % Row Count 3 (+ 3)
m = y-d/x-c \newline % Row Count 4 (+ 1)
slope is change in y/change in x \newline % Row Count 5 (+ 1)
Parallel, Perpendicular \newline % Row Count 6 (+ 1)
y=2x+4 and y=2x+3 are parallel \newline % Row Count 7 (+ 1)
y=2x+4 and 2y=4x+8 are same line \newline % Row Count 8 (+ 1)
y=2x+4 and y = 1/2x+6 meet perpendicularly \newline % Row Count 9 (+ 1)
Parallel lines never meet, same slope \newline % Row Count 10 (+ 1)
Perpendicular lines meet once at right angles and slopes are negative reciprocals% Row Count 12 (+ 2)
} \tn 
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Geometric Formulas}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{SOHCAHTOA \newline % Row Count 1 (+ 1)
SOH = sin(x) = a/c \newline % Row Count 2 (+ 1)
CAH = cos(x) = b/c \newline % Row Count 3 (+ 1)
TOA = tan(x) = a/b \newline % Row Count 4 (+ 1)
180 degrees = (pi)rad \newline % Row Count 5 (+ 1)
Divide arclength by radius to get radian measure \newline % Row Count 6 (+ 1)
Special Angles \newline % Row Count 7 (+ 1)
Degree   Radian   Cosine   Sine              Tangent \newline % Row Count 9 (+ 2)
0               0             1           0                      0 \newline % Row Count 11 (+ 2)
30          (pi)/6      sqrt3/2     1/2              1/sqrt3 \newline % Row Count 13 (+ 2)
45          (pi)/4        1/sqrt(2)  1/sqrt(2)         1 \newline % Row Count 15 (+ 2)
60          (pi)/3        1/2         sqrt(3)/2      sqrt(3) \newline % Row Count 17 (+ 2)
90          (pi)            0             1            undefined% Row Count 19 (+ 2)
} \tn 
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Quadratic Functions: Parabolas}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{f(x) = ax\textasciicircum{}2\textasciicircum{} + bx + c \newline % Row Count 1 (+ 1)
Zeros given by the quadratic formula: \newline % Row Count 2 (+ 1)
-b +/- sqrt(b\textasciicircum{}2\textasciicircum{} - 4ac)/2a \newline % Row Count 3 (+ 1)
Coordinate point (-b/2a,( -b\textasciicircum{}2\textasciicircum{} +4ac)/4a)% Row Count 4 (+ 1)
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Geometric Equations}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Circles: Circumference 2(pi)r   Area (pi)r\textasciicircum{}2\textasciicircum{} \newline % Row Count 1 (+ 1)
Cylinders: Surface area 2(pi)r x h + 2(pi)r\textasciicircum{}2\textasciicircum{}   Volume: (pi)r\textasciicircum{}2\textasciicircum{}h \newline % Row Count 3 (+ 2)
Sphere: Surface area 4(pi)r\textasciicircum{}2\textasciicircum{}  Volume 4/3(pi)r\textasciicircum{}3\textasciicircum{}% Row Count 4 (+ 1)
} \tn 
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Negative Exponents}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{a\textasciicircum{}-m\textasciicircum{} = 1/a\textasciicircum{}m\textasciicircum{} \newline % Row Count 1 (+ 1)
1/a\textasciicircum{}-m\textasciicircum{} = a\textasciicircum{}m\textasciicircum{}% Row Count 2 (+ 1)
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Trigonometric Identities}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{cos\textasciicircum{}2\textasciicircum{}x + sin\textasciicircum{}2\textasciicircum{}x = 1 \newline % Row Count 1 (+ 1)
tan\textasciicircum{}-1\textasciicircum{}x = arctan x \newline % Row Count 2 (+ 1)
cot(x) = 1/tan x \newline % Row Count 3 (+ 1)
e\textasciicircum{}10\textasciicircum{} = cos x + isin x% Row Count 4 (+ 1)
} \tn 
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Secant, Cosecant, Cotangent}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Secant: 1/cos(x) \newline % Row Count 1 (+ 1)
Cosecant = 1/sin(x) \newline % Row Count 2 (+ 1)
Cotangent = 1/tan(x) = cos(x)/sin(x)% Row Count 3 (+ 1)
} \tn 
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Unit Circle}}  \tn
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\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/rockcollector2_1434672893_21 unit circle.png}}} \tn 
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Pythagorean Theorem}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{a\textasciicircum{}2\textasciicircum{} + b\textasciicircum{}2\textasciicircum{} = c\textasciicircum{}2\textasciicircum{}% Row Count 1 (+ 1)
} \tn 
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Exponential Rules}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{exp(a)exp(b) = exp(a+b) \newline % Row Count 1 (+ 1)
{[}exp(a){]}\textasciicircum{}b = exp(ab) \newline % Row Count 2 (+ 1)
exp(-a) = 1/exp(a) \newline % Row Count 3 (+ 1)
Domain: all real numbers \newline % Row Count 4 (+ 1)
Range: all positive numbers% Row Count 5 (+ 1)
} \tn 
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Absolute Values}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Absolute Values often generate "and" and "or" situations. \newline % Row Count 2 (+ 2)
Examples: \newline % Row Count 3 (+ 1)
|x|\textless{}1: -1\textless{}x and x\textless{}1   -1\textless{}x\textless{}1 \newline % Row Count 4 (+ 1)
|x|\textgreater{}1: x\textgreater{}1 or x\textless{}-1 \newline % Row Count 5 (+ 1)
|2x+3|\textgreater{} 1: 2x+3\textgreater{}1 or -(2x+3)\textgreater{}1 \newline % Row Count 6 (+ 1)
x\textgreater{}-1 or x\textless{}-2% Row Count 7 (+ 1)
} \tn 
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Multiplication and Scientific Notation}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Multiplication and Division: \newline % Row Count 1 (+ 1)
- Convert into scientific notation \newline % Row Count 2 (+ 1)
- Add/subtract exponents \newline % Row Count 3 (+ 1)
- Multiply/divide coefficients \newline % Row Count 4 (+ 1)
- Convert to scientific notation \newline % Row Count 5 (+ 1)
- 2.3E4 x 9.5E7/1.6E10 = 2.3x9.5/1.6E(4+7-10)% Row Count 6 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Logarithms}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Logarithms are the functional inverses of the exponential \newline % Row Count 2 (+ 2)
y = b\textasciicircum{}x is equivalent to logb(y) = x \newline % Row Count 3 (+ 1)
log(mn) = log(m) + log(n) \newline % Row Count 4 (+ 1)
log(m\textasciicircum{}n) = nlog(m) \newline % Row Count 5 (+ 1)
log(1/m) = -log(m) \newline % Row Count 6 (+ 1)
loga(m) = logb(m)/logb(a) \newline % Row Count 7 (+ 1)
exp(a)exp(b) = exp(ab) \newline % Row Count 8 (+ 1)
exp(-a) = 1/exp(a) \newline % Row Count 9 (+ 1)
e\textasciicircum{}2.3 = 10, e\textasciicircum{}12 = e\textasciicircum{}2.3*5.2 = (e\textasciicircum{}2.3)\textasciicircum{}5.2 = 10\textasciicircum{}5.2 = 2E5% Row Count 11 (+ 2)
} \tn 
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\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Function Variables}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Domain = valid inputs to function \newline % Row Count 1 (+ 1)
Range = what can the function produce \newline % Row Count 2 (+ 1)
Zeros or Roots = where is f(x)=0 \newline % Row Count 3 (+ 1)
Intersections = Where is f(x) = g(x) \newline % Row Count 4 (+ 1)
Local maximum is largest value around itself \newline % Row Count 5 (+ 1)
Local minimum is smallest value around itself \newline % Row Count 6 (+ 1)
Global is largest overall% Row Count 7 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Sine}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Sine is the y component as theta spins \newline % Row Count 1 (+ 1)
Domain is all real numbers \newline % Row Count 2 (+ 1)
Range -1\textless{}/ y \textless{}/ 1 \newline % Row Count 3 (+ 1)
Maxima at pi/2 + 2kpi, Minima at 3pi/2 + 2kpi \newline % Row Count 4 (+ 1)
Zeros at kpi \newline % Row Count 5 (+ 1)
Period 2pi% Row Count 6 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Cosine}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Cosine is the x component as theta spins \newline % Row Count 1 (+ 1)
Domain is all real numbers  \newline % Row Count 2 (+ 1)
Range is -1\textless{}/ y \textless{}/ 1 \newline % Row Count 3 (+ 1)
Max is 2kpi, Minima (2k + 1)pi \newline % Row Count 4 (+ 1)
Zeros at pi/2 + kpi \newline % Row Count 5 (+ 1)
Period is 2pi% Row Count 6 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Tangent}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Tangent is the slope of the line with angle theta \newline % Row Count 1 (+ 1)
Domain is all real numbers except pi/2 + kpi \newline % Row Count 2 (+ 1)
Range is all real numbers \newline % Row Count 3 (+ 1)
No max or min. asymptotes at undefined points \newline % Row Count 4 (+ 1)
Zeros at kpi \newline % Row Count 5 (+ 1)
Period is pi% Row Count 6 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Distance Between Points}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{The distance between two points on the plane is based on the Pythagorean Theorem \newline % Row Count 2 (+ 2)
|A-B| = sqrt((Xa-Xb)\textasciicircum{}2\textasciicircum{} +(Ya - Yb)\textasciicircum{}2\textasciicircum{}) \newline % Row Count 3 (+ 1)
A=(Xa,Ya) B=(Xb,Yb)% Row Count 4 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Basic Facts}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Total human population: 7 billion \newline % Row Count 1 (+ 1)
USA population: 300 million \newline % Row Count 2 (+ 1)
Distance from NY to LA: 2500 miles \newline % Row Count 3 (+ 1)
Distance to the moon: 2.4E5 miles \newline % Row Count 4 (+ 1)
Distance to the Sun: 1E8 miles \newline % Row Count 5 (+ 1)
Distance around the equator: 2.5E4 miles \newline % Row Count 6 (+ 1)
Area of the US: 4E6 square miles \newline % Row Count 7 (+ 1)
Surface area of the Earth: 2E8 square miles% Row Count 8 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}