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\begin{document}
\noindent
\hfill{\small  \ Winter 2022\ \ Su}\


\noindent {\bf   {\large MATH 120  \ \ Midterm Exam 1}\\
\\
Tuesday February 1, 50 minutes during your quiz section:\\
{\small AA: 8:30-9:20am @SMI 405; \ \ AB: 9:30-10:20am @SMI 405;\ \  AD: 9:30-10:20am @SIG 227 }

{\small BA: 10:30-11:20am @SMI 405; \ \ BB: TuTh 11:30am-12:20pm @SMI 405}}\\ \\\\

Name: \frame{\rule{0pt}{1cm}\rule{8cm}{0pt}}  \ \ \ \ \   Quiz section:  \frame{\rule{0pt}{1cm}\rule{3cm}{0pt}} \\

7-digit UW ID: \frame{\rule{0pt}{1cm}\rule{5cm}{0pt}} \\\\




\noindent
{\bf Exam Instruction:}

\begin{itemize}

\item
{\bf You have 50 minutes to complete the four questions}.  Distribute your time wisely.

\item 
Show your work to earn full credit. If you can not completely solve a problem, providing reasonable work and steps may still earn you some partial credit. 

\item
Box \boxed{\textup{your final answer}} for each problem. 

\item
The last page is a scratch paper, tear it off and do NOT turn it in unless you have written down additional work on it to be graded.

\item
{\bf Do NOT write within 1 cm of the edge!} Your exam will be scanned for grading. If you run out of space, specify ``see scratch paper", then write you additional work on the scratch paper and turn it in together with your exam. 

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%Leave your answer in the exact form rather than a decimal approximation. For example, you may leave your answer as a fraction, a square root expression, an inverse trig function of an expression, etc.

\item
You can prepare one hand-written double-sided $8.5"\times11"$ page of notes and bring it to the exam. 

\item
You may use a basic calculator that can NOT graph or solve equation (e.g., TI-30X IIS).  All other electronic devices (e.g., cell phone, earbuds) are not allowed, and should be turned off and put away for the duration of the exam.

\item  You must finish the exam independently. {\bf Giving or receiving any assistance on the exam is considered cheating, which will result in a grade of zero for the exam.} There are multiple versions of the exam, do not discuss the exam questions with other students on the exam day.\\




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%\item 
%Please write your name AND your 7-digit UW ID number on the upper right corner of the first page of your work. If you don't know your 7-digit student number, please go to MyUW$\to$Unofficial Transcript (under the Academics block). Your student number appears in the upper left of the Transcript page.




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%Receive help from anyone else.
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%Share your work with your classmate.
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%Search or post the exam questions online to get help. 
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%Use an online calculator/tool to graph or perform calculus calculation. 
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%\item  During the exam, I will be holding a live zoom meeting (our regular class zoom link), joining the zoom meeting is encouraged but is not mandatory. You do not have to turn your camera on during the exam. The purpose of the zoom meeting is to provide an environment similar to an actual exam, you may ask questions via chat, and I can try to help with any technical issues occurred during the exam submission.

%\item  No late submission will be accepted. Be prepared to stop working on the exam questions at least 10 minutes before the exam ending time so you have enough time to take pictures, convert them to one single PDF file, and upload the file. If you encountered any technical difficulty uploading your file, please contact me through zoom chat or email at least 5 minutes before the exam ending time to receive permission to send me the PDF file right away.
\end{itemize}


\pagebreak




\begin{enumerate}

\item
(15 pts) A motion sensor can detect movement in a circular region with radius 5. Let the center of the circle be the origin of the $xy$--plane. A racoon walks along a straight path from the point $(1, 8)$ to the point $(-4, -7)$.

(a) Find the point at which the raccoon enters the circular region and the point at which it exits the circular region. The numbers in your answer should be exact, do not use calculator to round to decimal numbers. \\


\vspace{9.5cm}


(b) At which point along the path is the raccoon closest to the point $(5,0)$? The numbers in your answer should be exact, do not use calculator to round to decimal numbers. \\

\pagebreak

\item
(12 pts) Ava is 12 miles due east and 2 miles due north of her home, she starts driving along a straight path towards the library which is 7 miles north of her home at a speed of 65 miles per hour.  Let Ava's home be the origin of the $xy$--plane.


(a) Find parametric equations for the $x$ and $y$ coordinates of Ava $t$ hours after she started driving. The numbers in your answer should be exact, do not use calculator to round to decimal numbers.
\vspace{11cm}


(b) Find the distance (in miles) between Ava and her home 10 minutes after she started driving. Round your answer to have 2 decimal places. 





\pagebreak

\item
(12 pts) Here is the graph of a piecewise (multipart) function $f(x)$ and six given points, its left piece is a semicircle as in the picture; its right piece is a quadratic function passing through points $(-1,0)$, $(0,-2)$,$(1,2)$.  Find the piecewise (multipart) formula for $f(x)$.
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\item

(6 pts) Let $g(x)=|x+1|$, solve the equation $g(x)=2x+4$.
\vspace{4cm}



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scratch paper

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scratch paper

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\end{enumerate}

 \end{document}

