\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{Eunicornz}
\pdfinfo{
  /Title (algebra-1-semester-exam.pdf)
  /Creator (Cheatography)
  /Author (Eunicornz)
  /Subject (Algebra 1 semester exam Cheat Sheet)
}

% Lengths and widths
\addtolength{\textwidth}{6cm}
\addtolength{\textheight}{-1cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{D40000}
\definecolor{LightBackground}{HTML}{FCEFEF}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Algebra 1 semester exam Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Eunicornz} via \textcolor{DarkBackground}{\uline{cheatography.com/33171/cs/10332/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Eunicornz \\
  \uline{cheatography.com/eunicornz} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 12th January, 2017.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.18988 cm} x{2.78712 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Data Analysis}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Five Number Summaries}}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
{\emph{Minimum (MinX)}} & the smallest number in the data \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\emph{1st quartile (Q\textasciicircum{}1\textasciicircum{})}} & the median of the lower half of the data \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
{\emph{Median (Med)}} & the middle of the data \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
{\emph{3rd quartile (Q\textasciicircum{}3\textasciicircum{})}} & median of the upper half of the data \tn 
% Row Count 8 (+ 2)
% Row 5
\SetRowColor{white}
{\emph{Maximum (MaxX)}} & the largest number in the data \tn 
% Row Count 10 (+ 2)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{\{\{bb\}\}} \tn 
% Row Count 11 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{\{\{bt\}\}{\bf{Other Data Analysis Terms}}} \tn 
% Row Count 12 (+ 1)
% Row 8
\SetRowColor{LightBackground}
{\emph{Mean(x̄)}} & ∑x / n (where n is the number of pieces in the data) \tn 
% Row Count 15 (+ 3)
% Row 9
\SetRowColor{white}
{\emph{Mode}} & the number that appears the most \tn 
% Row Count 17 (+ 2)
% Row 10
\SetRowColor{LightBackground}
{\emph{Range}} & the difference between the minimum and the maximum \tn 
% Row Count 20 (+ 3)
% Row 11
\SetRowColor{white}
{\emph{Standard Deviation(Sx or σx)}} & 1. find the mean (x̄) of the whole data set (∑x/n) 2.subtract each number from the mean and square it. 3.Find the mean of the squared differences. Your σx is the square root of the new mean. \tn 
% Row Count 29 (+ 9)
% Row 12
\SetRowColor{LightBackground}
σx & is standard deviation of the whole population. At the end of calculation, divide by "n" \tn 
% Row Count 33 (+ 4)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{x{2.18988 cm} x{2.78712 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Data Analysis (cont)}}  \tn
% Row 13
\SetRowColor{LightBackground}
Sx & standard deviation of a sample of the data. At the end of calculation, you divide it by "n-1" \tn 
% Row Count 5 (+ 5)
% Row 14
\SetRowColor{white}
{\emph{Mean Absolute Deviation (MAD)}} & 1. Find the mean of the data 2.Find the absolute difference between each value and the mean. Then find the mean of the absolute differences \tn 
% Row Count 12 (+ 7)
% Row 15
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{\{\{bb\}\}} \tn 
% Row Count 13 (+ 1)
% Row 16
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{\{\{bt\}\} {\bf{SOCS}}} \tn 
% Row Count 14 (+ 1)
% Row 17
\SetRowColor{LightBackground}
{\bf{{\emph{S}}hape}} & What is the {\emph{shape}} of the graph? \tn 
% Row Count 16 (+ 2)
% Row 18
\SetRowColor{white}
SPUGS! & You can find the shape of the graph with a histogram of the data set \tn 
% Row Count 20 (+ 4)
% Row 19
\SetRowColor{LightBackground}
1.Symmetric & the graph is symmetrical \tn 
% Row Count 22 (+ 2)
% Row 20
\SetRowColor{white}
2. Peaks & unimodal (1 peak), bimodal (2 peaks), or multimodal (3 or more peaks) \tn 
% Row Count 26 (+ 4)
% Row 21
\SetRowColor{LightBackground}
3. Uniform & all of the data are the same value \tn 
% Row Count 28 (+ 2)
% Row 22
\SetRowColor{white}
4. Gaps & In a histogram, there is a section that has nothing. \tn 
% Row Count 31 (+ 3)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{x{2.18988 cm} x{2.78712 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Data Analysis (cont)}}  \tn
% Row 23
\SetRowColor{LightBackground}
5. Skewness & skewed left: the tail points left skewed right: the tail points right \tn 
% Row Count 4 (+ 4)
% Row 24
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{\{\{bt\}\}} \tn 
% Row Count 5 (+ 1)
% Row 25
\SetRowColor{LightBackground}
{\bf{{\emph{O}}utliers}} & Are there any {\emph{outliers}} in the data set? \tn 
% Row Count 7 (+ 2)
% Row 26
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Outliers are more of a yes or no question} \tn 
% Row Count 8 (+ 1)
% Row 27
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{find the interquartile range, from Q\textasciicircum{}1\textasciicircum{} to Q\textasciicircum{}3\textasciicircum{}. multiply it by 1.5 and subtract/add from the mean. That is the borderline. Anything greater than the border line is an outlier} \tn 
% Row Count 12 (+ 4)
% Row 28
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{\{\{bb\}\}} \tn 
% Row Count 13 (+ 1)
% Row 29
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{From now on, it will be separated based on whether or not there is an outlier or not.}}} \tn 
% Row Count 15 (+ 2)
% Row 30
\SetRowColor{white}
a = no outlier & b = outlier \tn 
% Row Count 16 (+ 1)
% Row 31
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{\{\{bt\}\}} \tn 
% Row Count 17 (+ 1)
% Row 32
\SetRowColor{white}
{\bf{{\emph{C}}enter}} & What is the {\emph{center}} of the data set? \tn 
% Row Count 19 (+ 2)
% Row 33
\SetRowColor{LightBackground}
a & mean \tn 
% Row Count 20 (+ 1)
% Row 34
\SetRowColor{white}
b & median \tn 
% Row Count 21 (+ 1)
% Row 35
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{\{\{bt\}\}} \tn 
% Row Count 22 (+ 1)
% Row 36
\SetRowColor{white}
{\bf{{\emph{S}}pread}} & What is the {\emph{spread}} of the data set? \tn 
% Row Count 24 (+ 2)
% Row 37
\SetRowColor{LightBackground}
a & Standard Deviation \tn 
% Row Count 25 (+ 1)
% Row 38
\SetRowColor{white}
b & IQR, range, and five number summary \tn 
% Row Count 27 (+ 2)
% Row 39
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{\{\{bb\}\}} \tn 
% Row Count 28 (+ 1)
% Row 40
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{\{\{bt\}\}} \tn 
% Row Count 29 (+ 1)
% Row 41
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{In the end, add an explanation to your data set, analyzing using all of the information}}} \tn 
% Row Count 31 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.63781 cm} x{2.33919 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Simplified Algebraic Expressions}}  \tn
% Row 0
\SetRowColor{LightBackground}
1.) No double signs & 3x - 4 not 3x +- 4 \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
2.) Variables are in Alphabetical order & 3a + 8f - 5g not - 5g + 8f + 3a \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
3.) Exponents are in decreasing order & - 2x\textasciicircum{}5\textasciicircum{} + 6y\textasciicircum{}3\textasciicircum{} not 6y\textasciicircum{}3\textasciicircum{} - 2x \textasciicircum{}5\textasciicircum{} \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
4.) No coefficients of 1 & y = 7 not 1y = 7 \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
5.) No denominators of 1 & x = 9 not x/1 = 9 \tn 
% Row Count 9 (+ 2)
% Row 5
\SetRowColor{white}
6.) Variables before constants & x + 5 not 5+x \tn 
% Row Count 11 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{3.03597 cm} x{1.94103 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Tolerances}}  \tn
% Row 0
\SetRowColor{LightBackground}
degree of error \{\{fa-arrow-right\}\} & level of acceptability \tn 
% Row Count 2 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.84149 cm} x{3.13551 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{3 Types of Linear Equations}}  \tn
% Row 0
\SetRowColor{LightBackground}
Conditional Equations & have exactly {\bf{one}} solution \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Identity Equations & have an {\bf{infinite}} amount of solutions \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Contradictory Equations & have {\bf{no}} solutions \tn 
% Row Count 6 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.46195 cm} p{0.66832 cm} x{1.46195 cm} p{0.58478 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{4}{x{5.377cm}}{\bf\textcolor{white}{Functions}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Yes a Function}} &  & {\bf{Not a function}} &  \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
x\{\{br\}\} & y \{\{br\}\} & \{\{bl\}\}x & \{\{bl\}\}y \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
0 & 5 & 0 & 4 \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
1 & 4 & 3 & {\bf{3}} \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
2 & 3 & 3 & {\bf{8}} \tn 
% Row Count 7 (+ 1)
% Row 5
\SetRowColor{white}
3 & 2 & 7 & 4 \tn 
% Row Count 8 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}----}
\SetRowColor{LightBackground}
\mymulticolumn{4}{x{5.377cm}}{{\emph{*}}*}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}----}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.18988 cm} x{2.78712 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Frequency Tables}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Relative}} & setting up to what part of wholes (decimals or percents) \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
{\bf{Joint Relative Frequency}} & the section in blue \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{Marginal Relative Frequency}} & the section in red \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
{\bf{Grand Total}} & the bottom right corner of the table \tn 
% Row Count 9 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Frequency Table Example}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/eunicornz_1483140770_Frequencytable.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Refer to Frequency Tables}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{7 step Algebraic Method for Word Problems}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{1.) {\bf{List}} all important information} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{2.) {\bf{Assign}} a variable} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{3.) Write an {\bf{expression}}} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{4.) Write an {\bf{equation}}} \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{5.) {\bf{Solve}} the equation} \tn 
% Row Count 5 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{7 step Algebraic Method for Word Problems}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{1.) {\bf{List}} all important information} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{2.) {\bf{Assign}} a variable} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{3.) Write an {\bf{expression}}} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{4.) Write an {\bf{equation}}} \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{5.) {\bf{Solve}} the equation} \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{6.) {\bf{Check}} equation} \tn 
% Row Count 6 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{7.) Write the answer as a {\bf{complete sentence}}} \tn 
% Row Count 7 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}