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{\bf date:} the $18^{\rm th}$ of September, 1998 

{\bf place:} room 221 Hayes

{\bf time:} 8:30-9:20

{\bf 111 - Exam I}

This exam contains 10 problems worth 10 points each. You may use only a
blank sheet of paper, a pencil, a rubber gum eraser, a ruler and a
small calculator. You can use your calculator only to add, substract,
multiply or divide two numbers. This exam is taken under the honor
code. \\

{\bf Name:}
\\

{\bf Recommendation}

{\it Never give a "solitaire" answer without justifying it by previous
calculations or reasoning. } \newpage {\bf Problems} \\

{\bf 1.} Calculate $f'(25)$ if $f(x)=2x^{1.5}$. 

{\bf 2.} Write down the equation of the line passing through the points
$(1,2)$ and $(3,-4)$, and draw this line as accurate as possible.

{\bf 3.} Decide whether the lines $y=2x-1$ and $y=-\frac{1}{2}x+3$ are
parallel, perpendicular or neither, and calculate the coordinates of an
intersection point.

{\bf 4.} Simplify as much as possible the following algebraic
expression: $$ \frac{x^{\frac{1}{2}}y^3x^2}{y^2x^{\frac{3}{2}}} $$

{\bf 5.} Factor the polynomial $x^2-7x+5$. ({\it Hint: First use the
quadratic formula to find the roots.})

{\bf 6.} Calculate and bring to the simplest form you can the
composition $f(g(x))$ where $f(x)=x^2+3x+1$ and $g(x)=x-2$.

{\bf 7.} An amount of \$1783 is deposited at 4.5\% interest per year.
If this interest is computed monthly, what will be the amount after $2$
years?

{\bf 8.} Let $f(x)=x^2-2x+3$ be a function, and let $M$ be a point on
the graph of this function having one coordinate $x=2$. Write down the
equation of the tangent line to the graph at $M$. ({\it Hint: First
calculate the $y$-coordinate of $M$, and the slope of the graph at
$M$}.)



{\bf 9.} Let $f(x)=\frac{2}{x-1}$ be a function. Calculate $f'(3)$
using the definition with limits.

{\bf 10.} Suppose that a vehicle is traveling on a line and its
position function is given by $s=3t^2-t+5$ feet, where $t$ is time in
seconds. Calulate the velocity and the acceleration at $t=2$ seconds.
({\it Hint: First calculate the velocity and the acceleration at any
instant.) \\



{\bf Good luck!}


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