\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{{[}deleted{]}} \pdfinfo{ /Title (maths.pdf) /Creator (Cheatography) /Author ({[}deleted{]}) /Subject (Maths 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}{A30000} \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{Maths Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{{[}deleted{]}} via \textcolor{DarkBackground}{\uline{cheatography.com/40341/cs/12411/}}} \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}{[}deleted{]} \\ \uline{cheatography.com/deleted-40341} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Published 17th August, 2017.\\ Updated 17th August, 2017.\\ 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{2.09034 cm} x{2.88666 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Probability Terms}} \tn % Row 0 \SetRowColor{LightBackground} Sample space & The set of all possible outcomes (e.g 1,2,3,4,5,6 on a normal dice) \tn % Row Count 3 (+ 3) % Row 1 \SetRowColor{white} Equally likely outcomes & A situation in which all outcomes have the same chance of occuring \tn % Row Count 6 (+ 3) % Row 2 \SetRowColor{LightBackground} Mutually exclusive events & These events have no outcomes in common \tn % Row Count 8 (+ 2) % Row 3 \SetRowColor{white} Non mutually exclusive events & These events have at least one outcome in common \tn % Row Count 11 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}--} \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{Probability can be expressed in fraction, decimal or percentage form.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Complementary Events}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Luke's chance of clearing the high jump is 7/10. Luke's chance of not clearing the high jump is?} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}1 (10) - 7/10 = 3/10 P(not clearing the high jump)} \tn % Row Count 4 (+ 4) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{We have a bag with 9 red marbles, 2 blue marbles, and 3 green marbles. What is the probability of not selecting a blue marble?} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Number of total marbles = 14 \{\{nl\}\} Blue marbles = 2 \{\{nl\}\} 1 (14) - 2 = 12/14 P(non blue marbles)} \tn % Row Count 10 (+ 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}{Probability Information}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{A "standard" deck of playing cards consists of 52 Cards in each of the 4 suits of Spades, Clubs (black suite), Hearts, and Diamonds (red suite). Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. Ace may or may not be higher than King.\{\{nl\}\}\{\{nl\}\}To convert 12 hour time to 24 hour time follow these rules. For AM times, leave the times the same except for single digit hours in which a 0 is written at the front. For PM times, add 12 to the hour digits.% Row Count 10 (+ 10) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Time Zones}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{What is the time in London, when it is 9am in Sydney? (Sydney is 10 hours ahead)} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}London time = Sydney time - 10 hours \{\{nl\}\} 9am - 10h = 11pm in London} \tn % Row Count 4 (+ 4) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{What is the time in Sydney, when it is 9am in London? (London is 10 hours behind)} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Sydney time = London time + 10 hours \{\{nl\}\} 9am + 10h = 7pm in Sydney} \tn % Row Count 8 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.54287 cm} x{3.43413 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Volume of Prisms}} \tn % Row 0 \SetRowColor{LightBackground} Rectangular prisms & Length x Width x Height \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} Triangular prisms & Area of triangle x Height \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} Any other prism & Area x Height (area of the cross section and height is the height of the prism) \tn % Row Count 7 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}--} \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{If the question tells you to, find the area of the shape's cross section and then times the amount by the height to get the volume. \{\{nl\}\} \{\{nl\}\} Remember to add cubed units to the answer.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Conversions}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Image could not be loaded.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.64241 cm} x{3.33459 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Area of Plane Shapes}} \tn % Row 0 \SetRowColor{LightBackground} Rectangle & Width x Height (or wh) \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} Square & a$^{\textrm{2}}$ (a = length of side) \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} Triangle & 1/2 x Base x Height (or bh) \tn % Row Count 4 (+ 2) % Row 3 \SetRowColor{white} Trapezium & 1/2 x (side a+ side b) \tn % Row Count 5 (+ 1) % Row 4 \SetRowColor{LightBackground} \seqsplit{Parallelogram} & Base x Height (or bh) \tn % Row Count 6 (+ 1) % Row 5 \SetRowColor{white} Rhombus/Kite & Side A x Side B / 2 \tn % Row Count 7 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{For a composite shape, split the shape into already known shapes and use their respective methods to find the area (add the areas together). \{\{nl\}\}\{\{nl\}\} Remember to add squared units with the answer.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.05965 cm} p{0.4577 cm} x{2.05965 cm} } \SetRowColor{DarkBackground} \mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Volume and Capacity Conversions}} \tn % Row 0 \SetRowColor{LightBackground} \{\{literal\}\}Cubic Millimetres & mm$^{\textrm{3}}$ & \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \{\{literal\}\}Cubic Millimetres & cm$^{\textrm{3}}$ & \{\{ac\}\}1cm$^{\textrm{3}}$ = 1000m$^{\textrm{3}}$ \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} Cubic Metres & m$^{\textrm{3}}$ & \{\{ac\}\}1m$^{\textrm{3}}$ = 1000 000 cm$^{\textrm{3}}$ \tn % Row Count 6 (+ 2) % Row 3 \SetRowColor{white} Mililitre & mL & \{\{ac\}\}1mL = 1cm$^{\textrm{3}}$ \tn % Row Count 7 (+ 1) % Row 4 \SetRowColor{LightBackground} Litres & L & \{\{ac\}\}1L = 1000ml = 1000cm$^{\textrm{3}}$ \tn % Row Count 9 (+ 2) % Row 5 \SetRowColor{white} Kilolitres & kL & \{\{ac\}\}1kL = 1000L = 1m\textasciicircum{}3\textasciicircum{} \tn % Row Count 11 (+ 2) % Row 6 \SetRowColor{LightBackground} Megalitres & ML & 1ML = 1000kL = \{\{ac\}\}1000 000L \tn % Row Count 13 (+ 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 Notation}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{m x m} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}m\textasciicircum{}2\textasciicircum{}} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{5 x n x n x n} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}5n\textasciicircum{}3\textasciicircum{}} \tn % Row Count 4 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{When a pronumeral is multiplied by itself a number of times we can simplify the expression using index notation. \{\{nl\}\}\{\{nl\}\} Remember to substitute if necessary.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Dividing Algebraic Terms}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{30a / 2a} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Divide the numbers first, so 30 / 2 = 15. \{\{nl\}\} Next, cancel out the pronumerals. A goes into A, which gives us just 15.} \tn % Row Count 4 (+ 4) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{12ab / 6a\textasciicircum{}2\textasciicircum{}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Divide the numbers first, so 12 / 6 equals 2. Next, cancel out the pronumerals. A goes into A but B does not go into A. This gives us 2b / a.} \tn % Row Count 8 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Remember to always write the dividing algebraic terms in fraction form.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Factorising Algebraic Terms}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{3a + 12} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}3 x a + 3 x 4 is the expanded form. \{\{nl\}\} The factorised form is 3(a + 4).} \tn % Row Count 3 (+ 3) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{6m + 9} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}First, find the HCF. In this case, it is 3.\{\{nl\}\} \{\{nl\}\} Put the HCF out the front of a pair of brackets. Find what the HCF is multiplied by to get each term. \{\{nl\}\} \{\{nl\}\} So we end up getting 3(2m + 3)} \tn % Row Count 9 (+ 6) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Factorising is the reverse form of expanding. A good way to check your factorisation is by expanding your answer it to see if you get the original expression} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Adding and Subtracting Like Terms}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{5x - 2y - 3x + 7y} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Move the terms with the same pronumeral next to each other. So we get 5x - 3x - 2y + 7y \{\{nl\}\}\{\{nl\}\} Simplify and you get 2x + 5y} \tn % Row Count 4 (+ 4) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{7ab - 3bc + 2ab} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Move the terms with the same pronumeral next to each other. So we get 7ab + 2ab - 3bc \{\{nl\}\}\{\{nl\}\} Simplify and you get 9ab - 3bc} \tn % Row Count 8 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Only {\emph{like terms}} can be added or subtracted together.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Multiplying Algebraic Terms}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{10 x 3n} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}10 x 3 = 30 \{\{nl\}\} 30 x n = 30n} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{20n x 3mn} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}20 x 3 = 60 \{\{nl\}\} 60 x n x n x m = 60n\textasciicircum{}2\textasciicircum{}m} \tn % Row Count 4 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Remember to multiply the numbers first, then multiply the pro numerals (or add it to the end of the product). \{\{nl\}\}\{\{nl\}\}Negative and positive rules also apply to any problems.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Negative and Positive Rules}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/repeater13_1502786610_download.jpg}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Expanding Algebraic Terms}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{5(y + 3) + 2y} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}5 x y = 5y \{\{nl\}\} 5 x 3 = 15 \{\{nl\}\} 5y + 2y = 7y \{\{nl\}\} Expanded form is 7y + 15} \tn % Row Count 3 (+ 3) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{3(a + 4) + 2(5 - a)} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}3 x a = 3a \{\{nl\}\} 3 x 4 = 12 \{\{nl\}\}2 x 5 = 10 \{\{nl\}\} 2 x a = 2a \{\{nl\}\} 3a +- 2a = a \{\{nl\}\} 12 + 10 = 22 \{\{nl\}\} Expanded form is a + 22} \tn % Row Count 7 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{To write an expression without grouping symbols, multiply each term inside the grouping symbols by the term outside. \{\{nl\}\} \{\{nl\}\}Watch out for expressions that have negative signs outside the grouping symbols} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}