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\title{\vspace{-.5in}Final \hspace{1in} TMath 171 \hspace{1in}  Winter 2026}
\date{}


\begin{document}
\maketitle

\vspace{-0.9in}

\noindent As a reminder, you are welcome to use a non-internet accessing calculator (which includes Desmos Test Mode) and one 2-sided 8.5 in by 11 in sheet of notes. 

\begin{enumerate}
\item Consider the shaded part of the whole shown \\
on the right.

\begin{figure}[h]
\vspace{-1.1in} \hspace{4.5in}\includegraphics[alt={Circle cut into 8 equal-sized slices, three of which are shaded.}, height=3.3in]{FinalB.pdf}
\end{figure}

\vspace{-2.6in}
\begin{enumerate}
\item $[2]$ (FactionsActivity \#1)  Find a fraction for the \\
shaded part of the whole.
\vspace{.6in}

\item $[3]$ (\S5.2 \#20a) Find a common denominator \\
for the fraction in (a) and $\frac{5}{6}$.
\vspace{1in}

\end{enumerate}

\vspace{-.5in}

\item (ExtraPractice \S9.3 \#23) Two children go to school along the same road.Mary rode her bicycle but stopped to talk to a friend.  Joel walked half the distance and then jogged the rest of the way.  The following graphs show distance as a function of time for each of these students with the same scale on both axes.  

\begin{figure}[h]
\vspace{-.6in}\hspace{2.2in} \includegraphics[alt={The left graph has three line segments where the first and third line segments have the same slope. The first line segment begins at the origin and then stops at a horizontal line segment.  The right graph has two line segments. The first begins at the origin and has a lower slope than those on the left graph. The second line segment is more steep than the first but still not as steep as the slope in the left graph.  The function on the left stops at a higher x value and lower y value then the function on the right.}, height=3.0in]{finalA}
\end{figure}


\vspace{-2.8in}
\begin{enumerate}
\item $[3]$ Match each student \\
with a graph. Provide \\
some justification.

\vspace{1.1in}

%\item $[2]$ Which student took the least time to get to school? Justify your answer.
%\vspace{1.0in}

\item $[2]$ Which student lives closest to school? Justify your answer.
\vspace{1.0in}
\end{enumerate}


\item $[3]$ (Quiz7 \#1) Suppose you have a $\frac{3}{8}$-inch drill bit but the hole needs to be the next size down.  The set of drill bits is measured in sixteenths of an inch.  What size drill will you use? 

\vspace{1in}



\newpage
\item  If $n$ and $m$ have the prime factorizations: $n = 5 \times 7 \times 7$ and $m = 3 \times 5 \times 7$,
\begin{enumerate}
\item $[2]$ (ActivityGCF\#5) What is \emph{a} common factor of $n$ and $m$? 
\vspace{1in}
\item $[3]$ (\S4.2 \#14) What is the least common multiple of n and m?
\vspace{0.9in}

\end{enumerate}

\item (9.2 \#14) Consider the line that passes through (-2,4) and (3,0).

\begin{figure}[h]
\vspace{-.1in}\hspace{3.5in}\includegraphics[height=2.3in, alt={Set of axes ranging from -5 to 5 on both axes.}]{blank_5} 
\end{figure}

\vspace{-2.2in}
\begin{enumerate}
\item $[2]$ Graph the line on the axis.
\vspace{.3in}
\item $[3]$   Find the equation of the line.
\vspace{1.8in}
\end{enumerate}


\item $[5]$ (miniquiz \& fracActivity \#3) Perform the operations. Assume $a$ and $b$ are nonzero integers. Write your final answer in lowest terms. (Mixed numbers or improper fractions are both acceptable.)



\[\frac{3}{14}+\frac{10}{21} \hspace{1in} \frac{2}{ab}+\frac{1}{3a} \hspace{1in} \frac{4}{5a^2} \times \frac{a}{2a+1}\]

\vspace{1in}











\newpage

\item (\S9.1 \#6) Consider the balanced scales.


\begin{figure}[h]
\vspace{-.3in}\hspace{3.5in}\includegraphics[height=2.3in, alt={Scales in balance with 2 boxes and 3 balls on the left and 8 balls on the right.}]{FinalH} 
\end{figure}

\vspace{-2.2in}
\begin{enumerate}
\item $[2]$ Determine the number of chips \\
needed to replace each box in order \\
for the scales to balance. 
\vspace{.4in}
\item $[2]$ Let $x$ represent the number of \\
chips for each box, write the \\
corresponding equation that represents the scale.
\vspace{.4in}
\end{enumerate}

\item Consider the tile sequence to the right:

\begin{figure}[h]
\vspace{-.7in}\hspace{3.2in} \includegraphics[ alt={Three figures in the shape of a square arch. The first figure is 2 tiles high and 3 tiles across the top. Second figure is 3 tiles high and 4 tiles across the top. Third figure is 4 tiles high and 5 tiles across the top.}, height=1.9in]{FinalC}
\end{figure}

\begin{figure}[h]
\vspace{-.2in}\hspace{2.4in} \includegraphics[height=2.8in]{FinalD}
\end{figure}


\vspace{-4.4in}
\begin{enumerate}
\item $[3]$ (\S9.2 \#24a) Create an \\
input-output table with the \\
figure number and the\\
 number of tiles in each figure \\
 for the first 5 figures.

\vspace{2.7in}

\item $[2]$ (LinesActivity \#3)\\
Graph the coordinate \\
points on the axes.

\vspace{.2in}

\item $[3]$ (\S9.2 \#23) What figure will have 305 tiles? Provide some work so your process can be followed.
\vspace{1.3in}

\end{enumerate}


\newpage



\item Grade the work that follows.  The work may be correct or incorrect.  If correct, briefly justify why.  If incorrect, find the error(s) \& try to detect the reason for the error.

\begin{enumerate}
\item  $[3]$ (GCFActivity\#3))  

\begin{figure}[h]
\vspace{-.2in} \hspace{1in} \includegraphics[alt={The top has words, The greatest common factor of 140 and 84. A factor tree of 140 has branches 10 and 14, then leaves 2, 5, 2, and 7.  A factor tree of 84 has branches 6 and 14, then leaves 2, 3, 2, and 7.  The 14 is circled in each factor tree.  Beneath are the words, is 14 because 14 is the largest common factor on both factor trees.}, height=2.5in]{FinalE}   
\end{figure}

\item $[3]$ (ExtraPractice5.3 \#17)

\[ \frac{11}{12} \div \frac{1}{3}=\frac{33}{36}\div \frac{12}{36}= \frac{33 \div 12}{36 \div 36} = \frac{33 \div 12}{1}=\frac{33}{12}\]


\vspace{1.4in}



\item $[3]$ (Quiz6 \#1)

``The multiples of 140 are: 1,2,4,5,7,10,14,20,..."

\vspace{1.4in}

\end{enumerate}

\item $[1]$ What topic or concept did you study and prepare for, but not see on the exam?
\end{enumerate}

\end{document}
