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% Document Info
\author{simonereneehunter}
\pdfinfo{
  /Title (math-methods-wace-exam.pdf)
  /Creator (Cheatography)
  /Author (simonereneehunter)
  /Subject (MATH METHODS WACE EXAM Cheat Sheet)
}

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    {\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{MATH METHODS WACE EXAM Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{simonereneehunter} via \textcolor{DarkBackground}{\uline{cheatography.com/31686/cs/9661/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}simonereneehunter \\
  \uline{cheatography.com/simonereneehunter} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 29th October, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{4}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Exponential Growth}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{population of bacteria is known to increase in size by 50\% every 2 hours. There are 2000 bacteria in the population at 12 noon} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{i) the constant of proportionality correct to four decimal places} \tn 
\mymulticolumn{1}{x{3.833cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}k=0.5 t=2 a= 2000 : a= 2000e\textasciicircum{}kt\textasciicircum{} :  3000=2000e\textasciicircum{}2(k)\textasciicircum{}: k= 0.2027} \tn 
% Row Count 7 (+ 4)
% Row 2
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\mymulticolumn{1}{x{3.833cm}}{ii) the time when population will reach 8000} \tn 
\mymulticolumn{1}{x{3.833cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}a= 2000e\textasciicircum{}0.2027t\textasciicircum{} : 8000=2000e\textasciicircum{}0.2027t\textasciicircum{} : t= 6.84 : after 12 pm} \tn 
% Row Count 10 (+ 3)
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\par\addvspace{1.3em}

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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Binomial Distribution}}  \tn
% Row 0
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\mymulticolumn{1}{x{3.833cm}}{E(X) = np} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{3.833cm}}{Var(X)= npq} \tn 
% Row Count 2 (+ 1)
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\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Binomial}}  \tn
% Row 0
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\mymulticolumn{1}{x{3.833cm}}{Binomial experiment has 7 trials. prob. of successes is 0.4. what is the probability that:} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{3.833cm}}{X=3} \tn 
\mymulticolumn{1}{x{3.833cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}0.2903 (BinPDF)} \tn 
% Row Count 4 (+ 2)
% Row 2
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\mymulticolumn{1}{x{3.833cm}}{X is at least 3} \tn 
\mymulticolumn{1}{x{3.833cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}0.58009 (BinCDF)} \tn 
% Row Count 6 (+ 2)
% Row 3
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\mymulticolumn{1}{x{3.833cm}}{X is more than 5} \tn 
\mymulticolumn{1}{x{3.833cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}(go from 5.5)= 0.018842} \tn 
% Row Count 8 (+ 2)
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\begin{tabularx}{3.833cm}{X}
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Rate of Change}}  \tn
% Row 0
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\mymulticolumn{1}{x{3.833cm}}{ROC is modelled by d/dx= -x\textasciicircum{}2\textasciicircum{}+ e\textasciicircum{}0.4x\textasciicircum{}, where A is the area, x is the time- days from June 1st. on june 1st there was 6000m infested} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{i) the ROC in area on June 5th. ie when x=4} \tn 
\mymulticolumn{1}{x{3.833cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}-(4)\textasciicircum{}2\textasciicircum{} + e\textasciicircum{}0.4(4)\textasciicircum{}= -11.047 : 11m/sq} \tn 
% Row Count 5 (+ 2)
% Row 2
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\mymulticolumn{1}{x{3.833cm}}{ii) the date when ROC is a minimum} \tn 
\mymulticolumn{1}{x{3.833cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}f(x)0= 2x+0.4e\textasciicircum{}0.4x\textasciicircum{} solve: x=9.7 =10th June} \tn 
% Row Count 7 (+ 2)
% Row 3
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\mymulticolumn{1}{x{3.833cm}}{iii) what is the total change in area infested between June 1st and June 12th inclusive} \tn 
\mymulticolumn{1}{x{3.833cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}integral from 0 to 12 of -x\textasciicircum{}2\textasciicircum{} + e\textasciicircum{}0.4x\textasciicircum{} = -274.7 thus decreases by 275 m/sq} \tn 
% Row Count 11 (+ 4)
% Row 4
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\mymulticolumn{1}{x{3.833cm}}{iv) what is the total area infested by end of june 15th} \tn 
\mymulticolumn{1}{x{3.833cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}6000 + integral from 0 to 15 of -x\textasciicircum{}2\textasciicircum{} + e\textasciicircum{}0.4x\textasciicircum{} = 5881.1 m/sq} \tn 
% Row Count 15 (+ 4)
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% That's all folks
\end{multicols*}

\end{document}