Semester Exam Review

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Semester Exam Review

• Calculator skills and example problems

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Solving Equations
SOLVE FOR X
Enter each side of the equation as its own
function
Create a window that allows you to see all
intersections
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Use the 2nd button and the TRACE button to access
the CALCULATE menu. Select option 5.
Move your cursor to one point of intersection and
hit ENTER three times. Repeat this process for
other points on intersection in order to find all
solutions.
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Finding Maximum and Minimum values of a Function
and Intervals on Which a Function is Decreasing
or Increasing.
Graph the function shown
After hitting ZOOM 4, you will notice that you
cannot see the entire graph. Instead of merely
zooming out (which will make your graph skinny
and difficult to navigate), try adjusting the
window so that you can see more above and below
the x-axis.
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Use the 2nd and TRACE button to access the
CALCULATE menu.
Then follow the on-screen directions to move your
cursor to a point to the left and a point to the
right of where you see the maximum point.
Hit the ENTER button again to indicate your
Guess and you see that the maximum value of
15.75 occurs at x -1.5.
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Repeat this process to find the minimum point.
Once you have established the x-values for the
maximum and minimum points on the graph, you can
see that the function is decreasing inbetween
them, so you would say that the function is
decreasing on the interval -1.5, .666.
Remember, you dont use y-values when you are
talking about where something happens on a
graph. Then, since you can see the function is
increasing everywhere else, and you know the
domain of a polynomial is all real numbers, you
would say that the function is increasing on the
intervals (-8,-1.5 and .666, 8).
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How to Create an Appropriate Viewing Window
Given the equation for simple harmonic motion,
find the maximum displacement, the value of d
when t 4, and the least positive value of t for
which d 0.

• An appropriate viewing window must take into
  account the range of y-values possible and the
  sector of the domain at which you wish to look.
• Since we can see the amplitude is 6 and that
  there is no vertical shift, we adjust Ymin and
  Ymax accordingly.
• Since we want to look at positive values for
  time, up to at least 4 seconds, we adjust Xmin
  and Xmax accordingly.

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Create an appropriate viewing window for the
function that models the exponential growth of a
substance, y, after t years. Make sure you can
use your window to find when the amount has
reached 10,000.
Since t is represented by x in the calculator, we
want to make Xmin 0 (there is no negative time).
We dont know how many years it will take to
reach an amount of 10,000, so we take a guess,
and can make is larger or smaller later if
necessary. Since we see the initial amount is
2745, we can make that our Ymin. Since we are
trying to find when the amount is 10,000, make
your Ymax more than that.
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Regressions on Calculator

• The amount of money, in billions of dollars,
  spent on advertising in the United States per
  year is given in the table below. Find a
  quadratic regression to model this data, using t
  0 as 1990. Use this model to predict spending
  in the year 2007.

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• After entering the input values into L1 and the
  output values into L2, run a quadratic regression
  using these two lists, and storing the equation
  into Y1.

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Next, turn on the plot view by using the 2nd and
the Y buttons.
Make sure the Xlist is using the list with your
input values and the Ylist is using the list with
your output values. Tun the Plot On and hit
ZOOM 9. This should give you a nice pretty
picture of your data points. You will also see
the equation graphed, and the curve should fit
the data points fairly closely.
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When you hit the TRACE button, your calculator
displays in the top, left corner which function
it is tracing. If you see P1, you know it is
tracing the data points. Hit the down arrow to
switch to the equation stored in Y1.
In order to made the prediction for 2007, you can
trace to the point where x 17, but if you try
to type in 17 at this point, you will get an
error message because x 17 is not within your
window range.
To remedy this situation, change the Xmax on your
WINDOW settings to something larger than 17.
Then go back to the graph and trace to x17. You
can then conclude that spending is predicted to
be 271.723 billion dollars in 2007, according to
this model.
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The other option for calculating the amount of
spending in 2007 would be to use the main screen
of your calculator and the VARS button.
Your calculator understands function notation,
and reads this as evaluate the function in Y1
for an input of 17. Either method gives you the
same answer. Dont forget UNITS!
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After you finish the non-calculator part of the
exam, you will be asked to show your proctor this
screen in order to receive the calculator part of
the exam
Clearing the RAM on your calculator will erase
all lists, equations, and programs. If you have
data or programs that you do not want to lose,
please see Ms. Winkler before the day of the exam
and she will save those for you and return them
to you after the exam.
Press 2nd and the to enter the MEM menu.
Show your screen to the proctor so that you can
begin the second part of the exam. Your screen
may say TI-83 or TI-84, and may have a number
other than 2.41.