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algebra1_solutions.tex
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algebra1_solutions.tex
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\documentclass{article}
\usepackage{amsfonts}
\usepackage{amsmath,multicol,eso-pic}
\begin{document}
\title{Algebra 101 worksheet 1 Solutions}
\date{\vspace{-5ex}}
\maketitle
\section{Linear equations}
\begin{enumerate}
\item$$c =\frac{L}{27} - \frac{W}{27}$$
\item$$L =\frac{19 - h}{K + 6}$$
\item
\item$$y =\frac{- W + q}{k - n}$$
\item$$t =\frac{X - z}{P - 1}$$
\item$$M =\frac{- k + n}{N - Q}$$
\item
\item$$u =\frac{x - 19}{q - 2}$$
\item$$D =\frac{V - y}{Q - g}$$
\item$$r =\frac{q}{25} - \frac{13}{25}$$
\item$$Y =\frac{6 - a}{e - 6}$$
\item$$X =- \frac{25}{12}$$
\item$$k =\frac{G + 20}{q - 11}$$
\item$$a =\frac{- Q + R}{R + 18}$$
\item$$z =\frac{M + 1}{X + 25}$$
\item$$V =\frac{f}{10} - \frac{3}{2}$$
\item$$N =\frac{25}{S - T}$$
\item$$m =\frac{- V + n}{q - 18}$$
\item$$D =\frac{9}{h + 21}$$
\item$$k =\frac{n - 22}{b + 23}$$
\end{enumerate}
\section{Quadratic equations}
\begin{enumerate}
\item$$x = -23, x = -20$$
\item$$x = 0, x = \frac{4}{15}$$
\item$$x = - \frac{9}{5}, x = 0$$
\item$$x = \frac{1}{2} - \frac{\sqrt{11} i}{10}, x = \frac{1}{2} + \frac{\sqrt{11} i}{10}$$
\item$$x = - \frac{\sqrt{38} i}{6}, x = \frac{\sqrt{38} i}{6}$$
\item$$x = - \frac{\sqrt{91}}{7}, x = \frac{\sqrt{91}}{7}$$
\item$$x = - \frac{\sqrt{3} i}{3}, x = \frac{\sqrt{3} i}{3}$$
\item$$x = - \frac{9}{14} - \frac{\sqrt{3} i}{14}, x = - \frac{9}{14} + \frac{\sqrt{3} i}{14}$$
\item$$x = - \frac{\sqrt{30} i}{6}, x = \frac{\sqrt{30} i}{6}$$
\item$$x = - \frac{7}{29}$$
\item$$x = 3 - \frac{\sqrt{41}}{2}, x = 3 + \frac{\sqrt{41}}{2}$$
\item$$x = 5, x = 10$$
\item$$x = 2, x = 20$$
\item$$x = -5, x = 18$$
\item$$x = -26, x = 20$$
\item$$x = - \frac{11}{25}, x = 0$$
\item$$x = -9, x = -2$$
\item$$x = -7, x = 8$$
\item$$x = - \frac{9}{34} - \frac{\sqrt{327} i}{34}, x = - \frac{9}{34} + \frac{\sqrt{327} i}{34}$$
\item$$x = 2, x = 5$$
\end{enumerate}
\section{Compute the derivative}
\begin{enumerate}
\item$$\frac{- \sin{\left(x \right)} + \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}}$$
\item$$\frac{-14 + \frac{1}{2 \sqrt{x}}}{\sqrt{x}} - \frac{\sqrt{x} - 14 x + 15}{2 x^{\frac{3}{2}}}$$
\item$$\frac{e^{x} - \sin{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\left(e^{x} + \cos{\left(x \right)}\right) \left(- \tan^{2}{\left(x \right)} - 1\right)}{\tan^{2}{\left(x \right)}}$$
\item$$\frac{30 x + \tan^{2}{\left(x \right)} + 5}{x} - \frac{15 x^{2} + 4 x + \tan{\left(x \right)}}{x^{2}}$$
\item$$\frac{1 - \sin{\left(x \right)}}{3 x^{3} - 15 x^{2} - 24} + \frac{\left(x + \cos{\left(x \right)}\right) \left(- 9 x^{2} + 30 x\right)}{\left(3 x^{3} - 15 x^{2} - 24\right)^{2}}$$
\item$$\frac{\left(\sqrt{x} + \tan{\left(x \right)}\right) \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{\tan^{2}{\left(x \right)} + 1 + \frac{1}{2 \sqrt{x}}}{\cos{\left(x \right)}}$$
\item$$\frac{20 - \sin{\left(x \right)}}{x} - \frac{20 x + \cos{\left(x \right)} + 11}{x^{2}}$$
\item$$\frac{- \sin{\left(x \right)} + \cos{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) \left(- \tan^{2}{\left(x \right)} - 1\right)}{\tan^{2}{\left(x \right)}}$$
\item$$\frac{-24 + \frac{1}{2 \sqrt{x}}}{x} - \frac{\sqrt{x} - 24 x}{x^{2}}$$
\item$$- \frac{54 x^{2}}{- 18 x^{3} - 11 x^{2}} + \frac{\left(54 x^{2} + 22 x\right) \left(- 18 x^{3} - 24\right)}{\left(- 18 x^{3} - 11 x^{2}\right)^{2}}$$
\end{enumerate}
\end{document}