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\title{\textbf{Math 010 Fall 21 Test 1}}

\date{\vspace{-1in}}

\begin{document}
\begin{center}
    {\textbf{\Large Math 010 Practice Problems for Test 1 Fall 2022}}
\end{center}
\begin{singlespacing}
The following are examples of potential exam questions. It is recommended that you show all work while doing these problems. No problem requires a calculator but you are welcome to use one.

\begin{enumerate}
\item 
No work necessary for this one problem. 
"Basic" computation
\begin{enumerate}
\item Compute $2+5$
\item Compute $7-3$
\item Compute $-2+6$
\item Compute $1-(-4)$
\item Compute $3\cdot (-2)$
\item Compute $(-1)\cdot (-5)$
\item Compute $-6\div 3$
\item Compute $-8\div (-4)$
\end{enumerate}

\item
Simplify by factor trees

\begin{enumerate}
\item Simplify the fraction: $\frac{3}{9}$
\item Simplify the fraction: $\frac{100}{180}$
\item Simplify the fraction: $\frac{336}{392}$
\end{enumerate}


\item 
Computing with common denominators

\begin{enumerate}
\item Compute and simplify $\frac{1}{2}+\frac{1}{2}$
\item Compute and simplify $\frac{3}{5}-\frac{2}{5}$
\item Compute and simplify $\frac{5}{4}-\frac{3}{4}$
\item Compute and simplify
$\frac{1}{6}-(-\frac{1}{6})$
\end{enumerate}

\item 
Computing with uncommon denominators
\begin{enumerate}
\item Compute and simplify $\frac{1}{2}+\frac{1}{3}$
\item Compute and simplify $\frac{3}{4}-\frac{2}{5}$
\item Compute and simplify $\frac{5}{2}-\frac{3}{4}$
\item Compute and simplify
$\frac{1}{6}-(-\frac{1}{2})$
\end{enumerate}

\item 
Computing with mult and div
\begin{enumerate}
\item Compute and simplify
$\frac{1}{2}\cdot \frac{2}{3}$
\item Compute and simplify
$\frac{1}{2}\cdot(-\frac{3}{4})$
\item Compute and simplify
$\frac{1}{6}\div\frac{3}{4}$
\item Compute and simplify
$\frac{1}{2}\div (-\frac{6}{7})$
\end{enumerate}



\item 
Compound fractions
\begin{enumerate}
\item Compute and simplify $\frac{\frac{1}{3}+\frac{2}{3}}{\frac{1}{2}-\frac{5}{2}}$
\item Compute and simplify $\frac{\frac{1}{2}\cdot\frac{2}{3}}{\frac{1}{2}+\frac{1}{3}}$
\item Compute and simplify $\frac{\frac{1}{3}+\frac{3}{9}}{\frac{1}{2}-\frac{3}{4}}$
\item Compute and simplify $\frac{\frac{1}{2}+\frac{2}{7}}{\frac{1}{5}+\frac{3}{2}}$
\end{enumerate}

\item 
Solve linear equations.
\begin{enumerate}
\item Solve for x: $x+3=5$
\item Solve for x: $2x-3=5$
\item Solve for x: $\frac{1}{2}x+4=5$
\item Solve for x: $3x-2x+3=5-2$
\item Solve for x: $14-20=12x-x-5x$
\item Solve for x: $-4(x-3)-5=27$
\item Solve for x: $4x-2=2x+8$

\end{enumerate}

\item 
Solving and interpreting inequalities
\begin{enumerate}
	\item Solve the inequality, graph the solution, and write the solution in interval notation: $x+3<5$
	\item Solve the inequality, graph the solution, and write the solution in interval notation: $2x-3\geq5$
	\item Solve the inequality, graph the solution, and write the solution in interval notation: $\frac{1}{2}x+4>5$
	\item Solve the inequality, graph the solution, and write the solution in interval notation: $6x\leq 11x+15$\\

	
	
\end{enumerate}

\item 
Compute with exponents
\begin{enumerate}
\item Compute and simplify $2^3$
\item Compute and simplify $3^2+2^3$
\item Compute and simplify $1^{999}$
\item Compute and simplify $72^1+2^2$
\item Compute and simplify $9^{99999}\cdot 9^{-100000}$
\item Simplify $(2x)^2-4x^2$
\end{enumerate}


\item
Compute with radicals
\begin{enumerate}
\item Compute $\sqrt{4}$
\item Compute $\sqrt{16}$
\item Compute $\sqrt[3]{8}$
\item Compute $\sqrt[999]{3^{999}}$
\item Simplify $\sqrt{16a^2}$
\item Simplify $\sqrt{a^4}$
\item Simplify $\sqrt[3]{27a^9}$
\end{enumerate}



\end{enumerate}

\end{singlespacing}
\end{document}
