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% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
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% Document Info
\author{Emergybuttonse}
\pdfinfo{
  /Title (math-9709-paper-1-as-level.pdf)
  /Creator (Cheatography)
  /Author (Emergybuttonse)
  /Subject (Math (9709): Paper 1, AS level Cheat Sheet)
}

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% Header and Footer
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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{Math (9709): Paper 1, AS level Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Emergybuttonse} via \textcolor{DarkBackground}{\uline{cheatography.com/207489/cs/44379/}}}
\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}Emergybuttonse \\
  \uline{cheatography.com/emergybuttonse} \\
  \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 16th September, 2024.\\
   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}
\raggedright
\raggedcolumns

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% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{1.84149 cm} x{3.13551 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Miscellaneous}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{When money is involved (i.e - money of a company) round off the answer to its significant figure which is usually three. Also, add '.00' (ex - 29.00) if value is only two digits long.} \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{triangle theories} \tn 
% Row Count 5 (+ 1)
% Row 2
\SetRowColor{LightBackground}
area of a triangle & 1/2 absin(C) \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
to find third side & a\textasciicircum{}2\textasciicircum{} = b\textasciicircum{}2\textasciicircum{} + c\textasciicircum{}2\textasciicircum{} - 2bc*cosA \tn 
% Row Count 9 (+ 2)
% Row 4
\SetRowColor{LightBackground}
to find angle & cosA = (b\textasciicircum{}2\textasciicircum{} + c\textasciicircum{}2\textasciicircum{} - a\textasciicircum{}2\textasciicircum{})/2bc \tn 
% Row Count 11 (+ 2)
% Row 5
\SetRowColor{white}
sin rule & a/sinA = b/sinB = c/sinC \tn 
% Row Count 12 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.89126 cm} x{3.08574 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Quadratics}}  \tn
% Row 0
\SetRowColor{LightBackground}
General formula & ax\textasciicircum{}2\textasciicircum{} + bx + c = 0 \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Discriminant & b\textasciicircum{}2\textasciicircum{} - 4ac \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Sum and product of roots & if roots are x\textasciitilde{}1\textasciitilde{} and x\textasciitilde{}2\textasciitilde{}\{\{nl\}\}x\textasciitilde{}1\textasciitilde{} + x\textasciitilde{}2\textasciitilde{} =-b/a\{\{nl\}\}x\textasciitilde{}1\textasciitilde{} * x\textasciitilde{}2\textasciitilde{}=c/a \tn 
% Row Count 5 (+ 3)
% Row 3
\SetRowColor{white}
Vertex & y = a(x-h)\textasciicircum{}2\textasciicircum{} + k\{\{nl\}\}coordinates of vertex:\{\{nl\}\}h = -b/2a\{\{nl\}\}Substitute h as x in the quadratic equation and find y \tn 
% Row Count 10 (+ 5)
% Row 4
\SetRowColor{LightBackground}
Axis of symmetry & x = -b/2a \tn 
% Row Count 12 (+ 2)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.14011 cm} x{2.83689 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Circular measures}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{types of circles} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
x\textasciicircum{}2\textasciicircum{} + y\textasciicircum{}2\textasciicircum{} = r\textasciicircum{}2\textasciicircum{} & (x-a)\textasciicircum{}2\textasciicircum{} + (y-b)\textasciicircum{}2\textasciicircum{} = r\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
x\textasciicircum{}2\textasciicircum{} + y\textasciicircum{}2\textasciicircum{} + 2gx + 2fx + c= 0 & radius = root of (g\textasciicircum{}2\textasciicircum{} + f\textasciicircum{}2\textasciicircum{} - c)\{\{nl\}\}center = -g,-f \tn 
% Row Count 6 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\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}{Functions}}  \tn
% Row 0
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Types of functions & One-to-many, many-to-one, one-to-one or many-to-many \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
Sequence of transformations & The order of vertical and horizontal transformations do not affect the graph. However the order of two vertical (or horizontal) transformations affects the final graph. \tn 
% Row Count 10 (+ 7)
% Row 2
\SetRowColor{LightBackground}
 & to do transformations, first convert f to {\bf{a {\emph{f}} (b(x + c)) + d}}\{\{nl\}\} Do all the transformations from left to right \tn 
% Row Count 15 (+ 5)
% Row 3
\SetRowColor{white}
Composition of functions & Doman of composition function depends on domain of first function\{\{nl\}\}Range of resultant function depends on range of second functions \tn 
% Row Count 21 (+ 6)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Functions - graphs}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/emergybuttonse_1726485951_img17_32.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Coordinate geometry}}  \tn
% Row 0
\SetRowColor{LightBackground}
Angle between two lines when slopes are given. & tan(θ) = Absolute value of (m\textasciitilde{}2\textasciitilde{}-m\textasciitilde{}1\textasciitilde{})/(1+m\textasciitilde{}2\textasciitilde{}m\textasciitilde{}1\textasciitilde{}) \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
gradient of y axis is undefined & gradient of x axis is 0 \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{If the question says 'at the same rate' it means that the lines are parallel} \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
when intersects x axis and y axis are given & x/a + y/b = 1 \tn 
% Row Count 10 (+ 3)
% Row 4
\SetRowColor{LightBackground}
considering general form of a line to be & Ax + By + C = 0 \tn 
% Row Count 12 (+ 2)
% Row 5
\SetRowColor{white}
Distance from a Point to a Line & d = {[}|Ax\textasciitilde{}0\textasciitilde{} + By\textasciitilde{}0\textasciitilde{} + C| / √(A\textasciicircum{}2\textasciicircum{} + B\textasciicircum{}2\textasciicircum{}){]} \tn 
% Row Count 15 (+ 3)
% Row 6
\SetRowColor{LightBackground}
The centroid of a Triangle & x coordinates - (x\textasciitilde{}1\textasciitilde{} + x\textasciitilde{}2\textasciitilde{} + x\textasciitilde{}3\textasciitilde{})/3 \tn 
% Row Count 17 (+ 2)
% Row 7
\SetRowColor{white}
 & y coordinates - (y\textasciitilde{}1\textasciitilde{} + y\textasciitilde{}2\textasciitilde{} + y\textasciitilde{}3\textasciitilde{})/3 \tn 
% Row Count 19 (+ 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}{Shoelace method for area}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/emergybuttonse_1726490911_SmartSelect_20240916_181430_Flexcil.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}