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%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
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% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
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% Document Info
\author{Phoebe Zhang (Phoebe12)}
\pdfinfo{
  /Title (8f-discovery-april-20th-1.pdf)
  /Creator (Cheatography)
  /Author (Phoebe Zhang (Phoebe12))
  /Subject (8F Discovery April 20th (1) Cheat Sheet)
}

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\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}}
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\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{8F Discovery April 20th (1) Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Phoebe Zhang (Phoebe12)} via \textcolor{DarkBackground}{\uline{cheatography.com/30133/cs/11092/}}}
\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}Phoebe Zhang (Phoebe12) \\
  \uline{cheatography.com/phoebe12} \\
  \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 20th April, 2017.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
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  \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}
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Integers}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Integers are positive whole numbers, negative whole numbers and zero.} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{When there is more than 1 operation, remember to use BODMAS.} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{When adding/subtracting, look at the symbols in the middle.} \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{When multiplying/dividing, look at the symbols next to the numbers.} \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
+ + = + & - - = + \tn 
% Row Count 9 (+ 1)
% Row 5
\SetRowColor{white}
+ - = - & - + = - \tn 
% Row Count 10 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.24425 cm} x{3.73275 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Indices}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{The {\bf{index}} is the small number above the {\bf{base}}.} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Example: 2\textasciicircum{}4\textasciicircum{} & 2 is the {\bf{base}}, 4 is the {\bf{index}}. \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{2\textasciicircum{}4\textasciicircum{} can also be written as 2 x 2 x 2 x 2.} \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{2\textasciicircum{}4\textasciicircum{} can also be written as 16, as 2 x 2 x 2 x 2 = 16. This is known as a {\bf{basic numeral}}.} \tn 
% Row Count 7 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.96117 cm} x{1.64772 cm} x{1.96811 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Reciprocals}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{3}{x{5.377cm}}{The reciprocal is simply: 1/number.} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{3}{x{5.377cm}}{Reciprocal: What to multiply a value by to get 1. It is also known as "Multiplicative Inverse".} \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{3}{x{5.377cm}}{Example: The reciprocal of 2 is $\frac{1}{2}$ (a half).} \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{3}{x{5.377cm}}{More Examples:} \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
Number & Reciprocal & As a decimal \tn 
% Row Count 6 (+ 1)
% Row 5
\SetRowColor{white}
5 & 1/5 & = 0.2 \tn 
% Row Count 7 (+ 1)
% Row 6
\SetRowColor{LightBackground}
8 & 1/8 & = 0.125 \tn 
% Row Count 8 (+ 1)
% Row 7
\SetRowColor{white}
1000 & 1/1000 & = 0.001 \tn 
% Row Count 9 (+ 1)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{3}{x{5.377cm}}{For fractions, flip the whole fraction over} \tn 
% Row Count 10 (+ 1)
% Row 9
\SetRowColor{white}
\mymulticolumn{3}{x{5.377cm}}{Example: The reciprocal of 3/4 is 4/3} \tn 
% Row Count 11 (+ 1)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{3}{x{5.377cm}}{Every number has a reciprocal except 0.} \tn 
% Row Count 12 (+ 1)
% Row 11
\SetRowColor{white}
\mymulticolumn{3}{x{5.377cm}}{Multiplying a number by its reciprocal gets us 1.} \tn 
% Row Count 13 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.9908 cm} x{2.9862 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Simplifying Expressions}}  \tn
% Row 0
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\mymulticolumn{2}{x{5.377cm}}{How to simplify an expression:} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{1. Remove brackets by multiplying factors.} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{2. Use index laws to remove brackets in terms with indices.} \tn 
% Row Count 4 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{3. Combine like terms by adding coefficients.} \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{4. Combine the constants.} \tn 
% Row Count 6 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Variable: A symbol for a number we don't know yet. It is usually a letter like x or y.} \tn 
% Row Count 8 (+ 2)
% Row 6
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\mymulticolumn{2}{x{5.377cm}}{Constant: A number on its own.} \tn 
% Row Count 9 (+ 1)
% Row 7
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\mymulticolumn{2}{x{5.377cm}}{Coefficient: A number used to multiply a variable.} \tn 
% Row Count 10 (+ 1)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Variables without a number have a coefficient of 1.} \tn 
% Row Count 12 (+ 2)
% Row 9
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Example: ax2 + bx + c} \tn 
% Row Count 13 (+ 1)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{x is a {\bf{variable}}, a and b are {\bf{coefficients}} and c is a {\bf{constant}}.} \tn 
% Row Count 15 (+ 2)
% Row 11
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  In other words, terms that are "like" each other. (Note: the coefficients can be different)} \tn 
% Row Count 19 (+ 4)
% Row 12
\SetRowColor{LightBackground}
Example: & −2{\bf{xy2}} \tn 
% Row Count 20 (+ 1)
% Row 13
\SetRowColor{white}
6{\bf{xy2}} & (1/3){\bf{xy2}} \tn 
% Row Count 21 (+ 1)
% Row 14
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{These are all like terms because the variables are all xy2} \tn 
% Row Count 23 (+ 2)
\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}{Prime and Composite Numbers}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{A prime number is a number that can be divided evenly only by 1, or itself.  And it must be a whole number greater than 1.} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{A composite number is a whole number that can be divided evenly by numbers other than 1 or itself.} \tn 
% Row Count 5 (+ 2)
\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}{Factors and Multiples}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Factors and multiples are both to do with multiplication:} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Factors are what we can multiply to get the number.} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Multiples are what we get after multiplying the number by an integer (not a fraction).} \tn 
% Row Count 6 (+ 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}{Index Laws}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{1. The numbers in index form with the same base can be multiplied together by being written in factor form first.} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Multiply: a\textasciicircum{}m\textasciicircum{} x a\textasciicircum{}n\textasciicircum{} = a\textasciicircum{}m + n\textasciicircum{}} \tn 
% Row Count 4 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{2. The numbers in index form with the same base can be divided first by being written in factor form.} \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Divide: a\textasciicircum{}m\textasciicircum{} ÷ a\textasciicircum{}n\textasciicircum{} = a\textasciicircum{}m - n\textasciicircum{}} \tn 
% Row Count 8 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{3. Any base that has an index power of 0 is equal to 1.} \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Zero Law: a\textasciicircum{}0\textasciicircum{} = 1} \tn 
% Row Count 11 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{4. Every number and variable inside the brackets should have its index multiplied by the power outside the brackets.} \tn 
% Row Count 14 (+ 3)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Powers: (a\textasciicircum{}m\textasciicircum{})\textasciicircum{}n\textasciicircum{} = a\textasciicircum{}m x n\textasciicircum{}} \tn 
% Row Count 15 (+ 1)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{5. Negative Indices: a\textasciicircum{}-3\textasciicircum{} = 1 ÷ a\textasciicircum{}3\textasciicircum{}} \tn 
% Row Count 16 (+ 1)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{6. Any number or variable that does not appear to have an index really has an index of one.} \tn 
% Row Count 18 (+ 2)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{7. Every number or variable inside the brackets must be raised to the power outside the brackets.} \tn 
% Row Count 20 (+ 2)
\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}{Factor Trees}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{A factor tree is a special diagram where you find the factors of a number, then the factors of those numbers, etc until you can't factor any more.} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{The ends are all the prime factors of the original number.} \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{A prime factor is a factor that is a prime number: one of the prime numbers that, when multiplied, give the original number.} \tn 
% Row Count 8 (+ 3)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Example: The prime factors of 15 are 3 and 5 (3×5=15, and 3 and 5 are prime numbers).} \tn 
% Row Count 10 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{There is only one (unique) set of prime factors for any number. This is called the Fundamental Theorem of Arithmetic.} \tn 
% Row Count 13 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}