Review Guide for MAT187 Midterm Exam Part I. Spring 2017
Part 1 is worth 50% of your Midterm Exam grade. Syllabus approved calculators are NEEDED on this part of the exam so
be sure to bring yours! All work will be done on the test itself; you may NOT use any scratch paper. Partial credit WILL
be awarded for partially correct work so be sure to show ALL of your steps. Correct answers without the correct
corresponding work are worth nothing (this means answers that you obtain from your calculator that have no
corresponding written work will earn no points).
Section numbers have been provided by each topic so that you can go back through your NOTES, HOMEWORK and OLD
TESTS to find problems to practice. You can also go back to the class HELP page and view some of the relevant
supplemental readings and videos.
A. Use properties of logarithms to expand a given logarithmic expression (section 2.8). BE SURE TO SHOW MULTIPLE
STEPS OF WORK.
Log a
4a3b5
c6
B. Be able to find the domain of a logarithmic function. Write your answer using interval notation (section 2.7).
Log5  x 2  3x  4 
Log2 8  2 x 
C. Be sure that you KNOW the formulas for compound interest (the one where interest is compounded “n” times per
year and the one for “continuously” compounded interest) (section 2.6). You WILL need to use your calculator on this
problem to get the final answers (but you will be asked to show the “set up” for any problems given).
Investing $5000 for 8 years at 9% interest would yield how much money if interest is compounded…
A. Semiannually
B. Weekly
C. Daily
D. Continuously
D. Be able to work with rational functions (section 1.11). Know how to find various characteristics (like where a rational
function crosses its horizontal asymptote for example among other things that we studied) of a rational function
WITHOUT using your calculator!
x3  4 x 2  7 x  10
f  x 
x3  7 x  6
E. Solve a rational inequality and write your answer using interval notation (section 2.1)
x 2  x  2  x  1
 x  4  x  6 
5
4
0
F. Make sure that you understand piecewise defined functions (section 1.3 ).
For example….
x  2
x  3
 2
f  x    x  4  2  x  3 Can you find each of the following….
x  5
x3

f  3 ,
f 1 , the y-intercept, any x-intercepts, the graph of the function.
G. Make sure that you study all of the work we did with transformations of functions (section 1.4). Be able to “explain
in words” how you would transform the graph of y  g  x  in order to obtain the graph of y  g   x  3  2 . Also, if
you are given the graph of y  h  x  be able to draw the graph of y  h  x  3  2 for example!
On the blank set of axes sketch the graph of y  h  x  3  2
y  h  x
y   h  x  3  2
H. Be sure to study up on all of the work we did with synthetic division and solving polynomial equations
(sections 1.9, 1.10).
Develop a list of possible rational zeros for the following polynomial and then find all of them (show work)
f  x   6 x5  5x 4  42 x3  3x 2  32 x  12
I. Be able to solve an exponential equation (where you can make the bases the same) (section 2.9)
842 x  32
J. Be able to solve a logarithmic equation. (section 2.9)
Log2 x  Log2  x  2   3
K. Be able to complete the square to rewrite the equation of an ellipse OR a hyperbola in “graphing” form.
(sections 3.2, 3.3)
4 x2  9 y 2 16 x  18 y  11  0
OR 36 x2  y 2  24 x  6 y  41  0
NOTE: The sample problems provided here are NOT intended to be the only problems that you look at while preparing
for this Midterm exam. Be sure to READ the information provided after each alphabetic letter above and spend time
searching your old tests, notes and homework to review the mentioned topics. Make sure that you understand the
mathematics relevant to each topic NOT just how to do a set of particular problems!
It is unlikely that you will finish this test in the given amount of time unless you are EXCEPTIONALLY well prepared. You
have only 65 minutes to complete as much as you can. This test may prove to be very challenging unless you have taken
the necessary steps throughout the semester to learn all of the material we covered.