Precalculus Test Out Practice Exam

Part 3	Test 1	Time: 3 hours

1. (1,e) is a point on the graph of . 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

   

   
   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 .

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 .

6. Find the inverse of the function . 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: 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

   

   
   Answer: The exact solution is .

8. What is the domain of the function

   

   
   Answer: The domain is the set .

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

   

   
   Answer: There is no solution because of domain restriction.

10. Write

    

    as one term.

    
    Answer: .

11. Find the exact value of

    

    
    Answer: The exact value is 6.

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

    

    
    Answer: The exact solution is .

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

    

    
    Answer: The exact solution is x=6.

14. Which balance is largest after five years?
    • $ 1,000 invested at 10 % compounded continuously.
    • $ 1,000 invested at 10.3 % compounded monthly.
    • $ 1,000 invested at 10.1 % compounded weekly

      
      

    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

    

    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: .

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: .

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

    

    
    Answer: , y=22 and .

19. What is the maximum value of the function

    

    
    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

    

    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: .

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Wed Jul 16 12:33:29 MDT 1997

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