Precalculus Test Out Practice Exam

Part 3 Test 1 Time: 3 hours


  1. (1,e) is a point on the graph of tex2html_wrap_inline149 . If the graph of f(x) is shifted so that it is superimposed on the graph of f(6-x)+9, where is the point (1,e) located after the shift?


    Answer: The point is (5,e+9).

  2. When does

    displaymath125


    Answer: They are equal when x>3.

  3. A total of $1,000 is invested at 10%, compounded monthly for five years. What is the balance after five years? What is the effective rate?


    Answer: The balance after 5 years is approximately $1,645.31. The effective rate is 10.47%.

  4. If you start an experiment with four cells that double every minute, write an equation with base e that describes the number of cells present at any time.


    Answer: The equation is tex2html_wrap_inline161 .

  5. If you start an experiment with four cells that double every minute, write an equation with base 6 that describes the number of cells present at any time.


    Answer: The equation is tex2html_wrap_inline163 .

  6. Find the inverse of the function tex2html_wrap_inline165 . If the domain needs to be restricted to find the inverse state the restricted domain. If the domain does not need to be restricted to find the inverse, explain.


    Answer: tex2html_wrap_inline167 with domain: x>2. The domain of f does not need to be restricted since the function is already a one-to-one function.

  7. Find the exact solution for x in the equation

    displaymath126


    Answer: The exact solution is tex2html_wrap_inline175 .

  8. What is the domain of the function

    displaymath127


    Answer: The domain is the set tex2html_wrap_inline177 .

  9. Find the exact solution(s) to the equation

    displaymath128


    Answer: There is no solution because of domain restriction.

  10. Write

    displaymath129

    as one term.


    Answer: tex2html_wrap_inline179 .

  11. Find the exact value of

    displaymath130


    Answer: The exact value is 6.

  12. Find the exact solution(s) to the equation

    displaymath131


    Answer: The exact solution is tex2html_wrap_inline181 .

  13. Find the exact solution(s) to the equation

    displaymath132


    Answer: The exact solution is x=6.

  14. Which balance is largest after five years? Answer: The largest balance is $1,000 at 10.3% compounded monthly.

  15. On a college campus of 5,000 students, one student returned from vacation with a contagious flu virus. The spread of the virus through the student body is given by

    displaymath133

    where y is the total number of students infected after t days. The college will cancel classes when 40% or more of the students are ill. After how many days will the college cancel classes?


    Answer: Approximately after 10 days.

  16. Find the equation of the circle that passes through the points (2,1) (6,5) and (0,-5). Write the equation in standard form.


    Answer: tex2html_wrap_inline189 .

  17. Write the equation of the parabola that passes through the points (2,9), (-2,29) and (1,5). Write the equation in standard form.


    Answer: tex2html_wrap_inline191 .

  18. Solve the following set of equations for x, y and z:

    eqnarray55


    Answer: tex2html_wrap_inline193 , y=22 and tex2html_wrap_inline197 .

  19. What is the maximum value of the function

    displaymath134


    Answer: The maximum value is f(x)=39.

  20. What is the equation of the line that passes through the points of intersection of the two circles

    displaymath135

    Write the equation of the line in the form ax+by+c=0, where the values a, b, and c are the exact values, not approximations.


    Answer: tex2html_wrap_inline203 .


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Wed Jul 16 12:33:29 MDT 1997

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