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% Document Info
\author{ceyre}
\pdfinfo{
  /Title (year-10-algebra.pdf)
  /Creator (Cheatography)
  /Author (ceyre)
  /Subject (Year 10 Algebra 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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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Year 10 Algebra Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{ceyre} via \textcolor{DarkBackground}{\uline{cheatography.com/128194/cs/47197/}}}
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}ceyre \\
  \uline{cheatography.com/ceyre} \\
  \end{tabulary}
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\columnbreak
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 19th October, 2025.\\
   Updated 19th October, 2025.\\
   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{multicols*}{2}

\begin{tabularx}{8.4cm}{x{1.84 cm} x{6.16 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Algebra Vocabulary}}  \tn
% Row 0
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Terms & A term is separated by a + or - sign \{\{nl\}\} E.g: 5x-3y+2 \{\{nl\}\} There are 3 terms in this equation: \{\{nl\}\}5x, -3y and 2 \tn 
% Row Count 4 (+ 4)
% Row 1
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\seqsplit{Coefficient} & The number in front. \{\{nl\}\}E.g: In the term 5y, y's coefficient is 5 \tn 
% Row Count 7 (+ 3)
% Row 2
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Constant & Constant is the single number which does not have any letters or numbers attached to it. \tn 
% Row Count 10 (+ 3)
% Row 3
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Like terms & Terms including {\emph{exactly}} the same letter or combination of letters.\{\{nl\}\}E.g: 6p, 8p and 5p are like terms\{\{nl\}\}ab, 10ab and -2ab are like terms \tn 
% Row Count 15 (+ 5)
% Row 4
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Unlike terms & Terms which have different letters or combination of letters.\{\{nl\}\}E.g: 3x and 3y are unlike terms \tn 
% Row Count 19 (+ 4)
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Simplifying Expressions}}  \tn
% Row 0
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{\bf{Rule}} & {\bf{Example}} \tn 
% Row Count 1 (+ 1)
% Row 1
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Any numbers in the expression are multiplied. & 5 X 6x = 30x \tn 
% Row Count 4 (+ 3)
% Row 2
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Numbers are placed in front of letters when multiplying. & x X 3y = 3xy \tn 
% Row Count 7 (+ 3)
% Row 3
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If there is more than one letter they are written in \{\{nl\}\}alphabetical order.\{\{nl\}\}Numbers can be multiplied separately, then multiply letters. & 2q X 7p = 14pq\{\{nl\}\}\{\{nl\}\}6p X 3p\{\{nl\}\}= 6 X 3 X p X p\{\{nl\}\}=18p\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 15 (+ 8)
% Row 4
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Like terms can be grouped together and then added or \{\{nl\}\}subtracted. \{\{nl\}\}{\bf{Remember}}, the + and - signs go with \{\{nl\}\}the terms on their {\emph{right}}. & Simplify:\{\{nl\}\}2x + y - x + 8y\{\{nl\}\}=(2x - x) + (y + 8y)\{\{nl\}\}= x + 9y \tn 
% Row Count 23 (+ 8)
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\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Power Rules}}  \tn
% Row 0
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p\textasciicircum{}4\textasciicircum{} means p multiplied by itself {\emph{four}} times & p\textasciicircum{}4\textasciicircum{} \{\{nl\}\}= p X p X p X p \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
Simplify as powers and then multiply by \{\{nl\}\}each other & x X x X y X y \{\{nl\}\}= x\textasciicircum{}2\textasciicircum{}y\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 6 (+ 3)
% Row 2
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When multiplying expressions with the \{\{nl\}\}{\bf{same base}} (letter), we {\bf{add the powers}}. & x\textasciicircum{}2\textasciicircum{} X x\textasciicircum{}5\textasciicircum{} \{\{nl\}\}= x\textasciicircum{}2+5\textasciicircum{}\{\{nl\}\}=x\textasciicircum{}7\textasciicircum{} \tn 
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% Row 3
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When dividing expressions with the \{\{nl\}\}{\bf{same base}}, we can {\bf{subtract the powers}}. & 20x\textasciicircum{}4\textasciicircum{} ÷ 10x \{\{nl\}\}= 20x\textasciicircum{}4-1\textasciicircum{} ÷ 10\{\{nl\}\}=2x\textasciicircum{}3\textasciicircum{} \tn 
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When it is a "power of a power", {\bf{multiply}} the powers & (p\textasciicircum{}4\textasciicircum{})\textasciicircum{}2\textasciicircum{} \{\{nl\}\}= p\textasciicircum{}4\textasciicircum{}\textasciicircum{}x\textasciicircum{}\textasciicircum{}2\textasciicircum{} \{\{nl\}\}= p\textasciicircum{}8\textasciicircum{} \tn 
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Power of 0 is always {\bf{equal to 1}} & p\textasciicircum{}0\textasciicircum{}=1, 4\textasciicircum{}0\textasciicircum{}=1, 2768\textasciicircum{}0\textasciicircum{}=1 \tn 
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\mymulticolumn{1}{x{8.4cm}}{The goal of solving an equation is to get the {\bf{letter term}} on the {\bf{left}} of the = sign and the {\bf{number/value}} on the {\bf{right}}.\{\{nl\}\}{\bf{Remember}} if a number or term is moved across the equals, then you must use the opposite operation.% Row Count 5 (+ 5)
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% Row 0
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\mymulticolumn{2}{x{8.4cm}}{Multiply each term in the brackets by the outside term.\{\{nl\}\}Then add together and simplify.} \tn 
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Examples: \{\{nl\}\}8(c + d - e)\{\{nl\}\}= 8 X c + 8 X d - 8 X e\{\{nl\}\}=8c + 8d - 8e & \{\{nl\}\}4x(2x - 5)\{\{nl\}\}=(4x X 2x) + (4x X -5)\{\{nl\}\}=8x\textasciicircum{}2\textasciicircum{} - 20x \tn 
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Factorising}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{1) Find the Highest Common Factor (number that divides in all terms equally) of all terms.  Write this outside the brackets.} \tn 
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% Row 1
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\mymulticolumn{1}{x{8.4cm}}{2) Divide each term by the HCF, putting result in the brackets.} \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Calculating Gradients of a Line}}  \tn
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\hhline{>{\arrayrulecolor{DarkBackground}}-}
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% That's all folks
\end{multicols*}

\end{document}