\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{Lumokoii} \pdfinfo{ /Title (applied-math-11.pdf) /Creator (Cheatography) /Author (Lumokoii) /Subject (Applied Math 11 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}{A30202} \definecolor{LightBackground}{HTML}{FCF7F7} \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{Applied Math 11 Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{Lumokoii} via \textcolor{DarkBackground}{\uline{cheatography.com/204607/cs/43622/}}} \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}Lumokoii \\ \uline{cheatography.com/lumokoii} \\ \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 June, 2024.\\ 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{1.78503 cm} x{1.78503 cm} x{1.00694 cm} } \SetRowColor{DarkBackground} \mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Formules Finances}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{I est Intérêt Simple (\$ gagner)}} & {\bf{{\emph{Interet Composee}}}} & M = C x (1+t/n)\textasciicircum{}(nd) \tn % Row Count 3 (+ 3) % Row 1 \SetRowColor{white} {\bf{ C est le Capital (investi ou emprunte)(\$)}} & {\bf{ Interet Simple}} & {\bf{I = CTD}} \tn % Row Count 7 (+ 4) % Row 2 \SetRowColor{LightBackground} {\bf{ T est Taux d'intérêt simple (décimal)}} & {\bf{{\emph{Intérêt Seulement}}}} & {\bf{I = M-C}} \tn % Row Count 10 (+ 3) % Row 3 \SetRowColor{white} {\bf{D est Duree en annees}} & {\bf{ΣInt (1, n) pour calculer interet}} & \tn % Row Count 13 (+ 3) % Row 4 \SetRowColor{LightBackground} {\bf{M est la Valeur Capitalisée}} & {\bf{Interet / Argent Investi}} = Taux de Rendement & \tn % Row Count 17 (+ 4) % Row 5 \SetRowColor{white} {\bf{N est periodes d'intérêt composé par an}} & {\bf{{\emph{Regle de 72}}}} & {\bf{ \seqsplit{(annees)} = 72/t(\%)}} \tn % Row Count 21 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}---} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Finances}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{N:}} Nombres de periodes d'intérêt ou de paiement (selon la valeur P/Y)} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{I\% :}} Taux d'intérêt annuel (en \%)} \tn % Row Count 3 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{PV:}} Valeur actialisée ( capital: investi ou emprunté)} \tn % Row Count 5 (+ 2) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{PMT:}} Versement regulier (0 si aucun)} \tn % Row Count 6 (+ 1) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{FV:}} Valeur Capitalisée (de l'investissement ou la dette)} \tn % Row Count 8 (+ 2) % Row 5 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{P/Y:}} Nombre de périodes de versements par année (Affecte N)} \tn % Row Count 10 (+ 2) % Row 6 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{C/Y:}} Nombre de fois que l'intérêt est composée par année} \tn % Row Count 12 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.59264 cm} x{3.38436 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Exponentielles y = a(b)\textasciicircum{}x}} \tn % Row 0 \SetRowColor{LightBackground} ABS x (y=0) & 0 (Aucun, c'est asymptote) \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} ORD y (x=0) & A \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \seqsplit{Comportement} & Section 4-1 \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} Domaine & {]}-∞,∞{[} \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} Image & {]}0,∞{[} \tn % Row Count 5 (+ 1) % Row 5 \SetRowColor{white} Si b \textgreater{} 1 & croissante \tn % Row Count 6 (+ 1) % Row 6 \SetRowColor{LightBackground} Si 0 \textless{} b \textgreater{} 1 & decroissante \tn % Row Count 7 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.73735 cm} x{2.23965 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fonctions Log y = a+b ln(x)}} \tn % Row 0 \SetRowColor{LightBackground} Nombre d'ABS & 1 \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} ORD & Aucune \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} Comportement & 1-4 ou 4-1 \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} Domaine & {]}0,∞{[} \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} Image & {]}-∞,∞{[} \tn % Row Count 5 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.28942 cm} x{2.68758 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fonctions Constantes y = k}} \tn % Row 0 \SetRowColor{LightBackground} ABS & 0 ou infini (si y = 0) \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} ORD & a ou b \tn % Row Count 3 (+ 1) % Row 2 \SetRowColor{LightBackground} Comportement & 2-1 ou 3-4 \tn % Row Count 4 (+ 1) % Row 3 \SetRowColor{white} Change de direction & 0 \tn % Row Count 6 (+ 2) % Row 4 \SetRowColor{LightBackground} Domaine & {]}-∞,∞{[} \tn % Row Count 7 (+ 1) % Row 5 \SetRowColor{white} Image & k \tn % Row Count 8 (+ 1) % Row 6 \SetRowColor{LightBackground} Degre & 0 \tn % Row Count 9 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{3.4839 cm} x{1.4931 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fonctions Lineaires y = mx+b}} \tn % Row 0 \SetRowColor{LightBackground} ABS & 1 \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} ORD & b \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} Comportement & 2-4 ou 3-1 \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} Changement de direction & 0 \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} Domaine & {]}-∞,∞{[} \tn % Row Count 5 (+ 1) % Row 5 \SetRowColor{white} Image & {]}-∞,∞{[} \tn % Row Count 6 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{3.4839 cm} x{1.4931 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fonctions Quadratiques y = ax$^{\textrm{2}}$+bx+c}} \tn % Row 0 \SetRowColor{LightBackground} ABS & 0,1 ou 2 \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} ORD & c \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} Comportement & 2-1 ou 3-4 \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} Changement de Direction & 1 \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} Domaine & {]}-∞,c{]} \tn % Row Count 5 (+ 1) % Row 5 \SetRowColor{white} Image & {[}c,∞{[} \tn % Row Count 6 (+ 1) % Row 6 \SetRowColor{LightBackground} Axe de Symetrie & x=b \tn % Row Count 7 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{3.4839 cm} x{1.4931 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fonctions Cubiques y= ax$^{\textrm{3}}$ + bx$^{\textrm{2}}$ + cx + d}} \tn % Row 0 \SetRowColor{LightBackground} ABS & 1,2,ou 3 \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} ORD & d \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} Comportement & 2-4 ou 3-1 \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} Changement de Direction & 0 ou 2 \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} Domaine & {]}-∞,∞{[} \tn % Row Count 5 (+ 1) % Row 5 \SetRowColor{white} Image & {]}-∞,∞{[} \tn % Row Count 6 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.23965 cm} x{2.73735 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Regression Notes}} \tn % Row 0 \SetRowColor{LightBackground} Lineaire & LinReg (ax+b) Y1 \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} Quadratique & QuadReg Y1 \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} Cubique & CubicReg Y1 \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} Exponentielle & ExpReg Y1 \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} Logarithmique & LnReg Y1 \tn % Row Count 5 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.34379 cm} x{3.63321 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Example Exponentielle}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\bf{y= 1 000 (1,05)\textasciicircum{}x}}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} 1 000 = & Population initiale \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} 1,05 = & Taux de croissance \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{Fonction qui represente le changement de population dans un village} \tn % Row Count 5 (+ 2) \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}{Regression SInusoidale}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{y = a sin(bx+c) + d} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} A= & Etire et comprime la fonction Verticalement \tn % Row Count 4 (+ 3) % Row 2 \SetRowColor{LightBackground} B= & Etire et comprime la fonction Horizontalement \tn % Row Count 7 (+ 3) % Row 3 \SetRowColor{white} C= & Deplace la fonction sur l'axe Horizontal \tn % Row Count 9 (+ 2) % Row 4 \SetRowColor{LightBackground} D= & Deplace la fonction sur l'axe Vertical \tn % Row Count 11 (+ 2) % Row 5 \SetRowColor{white} Amplitude (A): (Max-Min)/2 & Mediane (D): (Max+Min)/2 \tn % Row Count 13 (+ 2) % Row 6 \SetRowColor{LightBackground} Periode: (2π)/b & Maximale: D+A \tn % Row Count 14 (+ 1) % Row 7 \SetRowColor{white} Pt de Depart: {[}-c/b), d{]} Coordonnees & Minimale: D-A \tn % Row Count 16 (+ 2) % Row 8 \SetRowColor{LightBackground} Est Sur la mediane, point le plus pres de 0 & Monte sur la courbe de gauche a droite \tn % Row Count 19 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}