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% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
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% Document Info
\author{Phoebe Zhang (Phoebe12)}
\pdfinfo{
  /Title (8f-discovery-april-20th-2.pdf)
  /Creator (Cheatography)
  /Author (Phoebe Zhang (Phoebe12))
  /Subject (8F Discovery April 20th (2) Cheat Sheet)
}

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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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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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\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{8F Discovery April 20th (2) Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Phoebe Zhang (Phoebe12)} via \textcolor{DarkBackground}{\uline{cheatography.com/30133/cs/8929/}}}
\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}Published 20th April, 2017.\\
   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}}  \\
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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}}




\begin{document}
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Algebra Test Cheat Sheet}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{21/04/2017} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Mordialloc College} \tn 
% Row Count 2 (+ 1)
% Row 2
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\mymulticolumn{2}{x{5.377cm}}{Discovery 8F} \tn 
% Row Count 3 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Vocabulary}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Expression: A number sentence without an equal sign. Has at least two terms and one operation.} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Coefficient: A number that does not stand by itself. It is attached to the variable.} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Constant: A number that stands by itself.} \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Term: Each part of an expression separated by an operation.} \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Variable: A letter that stands for a particular numerical value.} \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}{Reminders}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{The number comes before the letter.} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{You do not need to write the multiplication sign.} \tn 
% Row Count 2 (+ 1)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{FOIL}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{{\bf{F}}irst {\bf{O}}utside {\bf{I}}nside {\bf{L}}ast} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{eg. (a + 4)(a + 7)} \tn 
% Row Count 2 (+ 1)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{= a\textasciicircum{}2\textasciicircum{} + 7a + 4a + 28} \tn 
% Row Count 3 (+ 1)
% Row 3
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\mymulticolumn{1}{x{5.377cm}}{= a\textasciicircum{}2\textasciicircum{} + 11a + 28} \tn 
% Row Count 4 (+ 1)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Substitution}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{To replace a pronumeral with a given value.} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{eg. 2y + 3} \tn 
% Row Count 2 (+ 1)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{If y was1, then the expression would be} \tn 
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% Row 3
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\mymulticolumn{1}{x{5.377cm}}{2 x 1 + 3} \tn 
% Row Count 4 (+ 1)
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Expanding and Factorising Expressions}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{To expand an expression, multiply each term in the bracket by the number on the outside.} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{eg. 2(y + 2x) = 2y + 4x} \tn 
% Row Count 3 (+ 1)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{To factorise an expression, find a common factor to place outside of the brackets.} \tn 
% Row Count 5 (+ 2)
% Row 3
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\mymulticolumn{1}{x{5.377cm}}{eg. 3(2x + 7) = 6x + 21} \tn 
% Row Count 6 (+ 1)
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\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Number Laws}}  \tn
% Row 0
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\mymulticolumn{2}{x{5.377cm}}{{\bf{Commutative Law}}} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{2}{x{5.377cm}}{The Commutative Law refers to the order in which two numbers may be added, subtracted, multiplied or divided.} \tn 
% Row Count 4 (+ 3)
% Row 2
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\mymulticolumn{2}{x{5.377cm}}{It holds true for addition and multiplication but not subtraction and division.} \tn 
% Row Count 6 (+ 2)
% Row 3
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\mymulticolumn{2}{x{5.377cm}}{{\bf{Associative Law}}} \tn 
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% Row 4
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\mymulticolumn{2}{x{5.377cm}}{The Associative Law refers to the order in which three numbers may be added, subtracted, multiplied or divided, taking two at a time.} \tn 
% Row Count 10 (+ 3)
% Row 5
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\mymulticolumn{2}{x{5.377cm}}{Like the Commutative Law, it holds true for addition and multiplication but not subtraction and division.} \tn 
% Row Count 13 (+ 3)
% Row 6
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\mymulticolumn{2}{x{5.377cm}}{{\bf{Identity Law}}} \tn 
% Row Count 14 (+ 1)
% Row 7
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\mymulticolumn{2}{x{5.377cm}}{The Identity Law states that when a zero is added to a number/any number is multiplied by one, the original number remains unchanged.} \tn 
% Row Count 17 (+ 3)
% Row 8
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\mymulticolumn{2}{x{5.377cm}}{{\bf{Inverse Law}}} \tn 
% Row Count 18 (+ 1)
% Row 9
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\mymulticolumn{2}{x{5.377cm}}{The Inverse states that when a number is added to its additive inverse/multiplied by its reciprocal, the result is one.} \tn 
% Row Count 21 (+ 3)
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Inverse Operations and Backtracking}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Inverse operations are reverse operations that undo each other.} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Addition (+) and subtracting (-) are inverse operations. Multiplication (x) and division (÷) are also inverse operations.} \tn 
% Row Count 5 (+ 3)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{When backtracking, you have to work backwards with reverse BODMAS and inverse operations.} \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{eg. 2x - 3 = 19} \tn 
% Row Count 8 (+ 1)
% Row 4
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\mymulticolumn{1}{x{5.377cm}}{19 + 3 ÷ 2 = x} \tn 
% Row Count 9 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{∴ x = 10.5} \tn 
% Row Count 10 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Indices and Index Notation}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Indices is the plural form of index. An index is a shorthand way of writing a repeated multiplication.} \tn 
% Row Count 3 (+ 3)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{It is written as a small number to the right and above the base number.} \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{The base is the number that is being multiplied and the index (plural indices) is the number of times it is multiplied.} \tn 
% Row Count 8 (+ 3)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{In this example: 82 = 8 × 8 = 64} \tn 
% Row Count 9 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Other names for index are exponent or power.} \tn 
% Row Count 10 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Index notation is similar to expanded notation, but going one step further and writing multiples of 10 as indices.} \tn 
% Row Count 13 (+ 3)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{eg. 3,657,428 in index notation would be (3 x 10\textasciicircum{}6\textasciicircum{}) + (6 x 10\textasciicircum{}5\textasciicircum{}) + (5 x 10\textasciicircum{}4\textasciicircum{}) + (7 x 10\textasciicircum{}3\textasciicircum{}) + (4 x 10\textasciicircum{}2\textasciicircum{}) + (2 x 10\textasciicircum{}1\textasciicircum{}) + (8 x 10\textasciicircum{}0\textasciicircum{}).} \tn 
% Row Count 16 (+ 3)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Usually, indexes of 1 and 0 are not included in index notation. This is because 10\textasciicircum{}1\textasciicircum{} is equal to 10 and 10\textasciicircum{}0\textasciicircum{} is equal to 1.} \tn 
% Row Count 19 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Like and Unlike Terms}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Terms containing exactly the same pronumerals, regardless of order, are called like terms.} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Unlike terms are terms that have different variables.} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Examples of like terms:} \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{12 x and 7 x} \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{12 and 7} \tn 
% Row Count 7 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{12mno and 12mon} \tn 
% Row Count 8 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Examples of unlike terms:} \tn 
% Row Count 9 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{12x and 7m} \tn 
% Row Count 10 (+ 1)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{12x and 7} \tn 
% Row Count 11 (+ 1)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{12x and 7x$^{\textrm{2}}$} \tn 
% Row Count 12 (+ 1)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{When simplifying expressions, we can add or subtract like terms only. Expressions which do not have like terms cannot be added or subtracted.} \tn 
% Row Count 15 (+ 3)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{eg. 5{\bf{x}} + 3{\bf{x}} - 7 + 8{\bf{x}} = 16{\bf{x}} - 7} \tn 
% Row Count 16 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}