Precalculus Test Out Practice Exam

Part 2	Test 2	Time: 3 hours

1. Simplify the expression to the from a+bi.

   
   Answer: .

2. Solve the equation for x. List the exact answer(s), not approximation(s). A decimal answer is not an exact answer; it is an approximation. No credit will be given for an approximation.

   
   Answer: The exact solutions are: .

3. A farmer wants to construct a rectangular livestock pen so that he maximizes the area with 14,884 feet of fencing. Find the exact dimensions of the pen.

   
   Answer: The fence should be a square with side length 3721 feet.

4. Why are the following not functions:
   • .

     
     Answer: This equation describes a circle, and therefore its graph fails the vertical line test.

   • .

     
     Answer: The points (6,0) and (6,-7/6) both lie on the graph of this equation, so the equation fails the vertical line test.

   • .

     
     Answer: This equation describes a vertical line. Vertical lines fail the vertical line test.

5. Find the exact solution(s) to the equation . Find the extraneous solution.

   
   Answer: The solution is . The extraneous solution is .

6. Find the exact solution(s) to the equation . Find the extraneous solution.

   
   Answer: The solutions are: and . The extraneous solutions are and .

7. Find the exact non-real solutions(s), if any, to the equation .

   
   Answer: The exact non-real solution is .

8. Solve for x.

   
   Answer: The solutions are the numbers satisfying ,

   
   or in interval notation, .

9. Solve for x.

   
   Answer: x>6.

10. Find the exact vertex of the parabola . (No decimals)

    
    Answer: The vertex is .

11. Find an equation of the parabola that has a vertex at (8,3) and passes through the point (4,1).

    
    Answer: .

12. Find the maximum height of a ball that follows the path defined by the equation .

    
    Answer: The maximum height is 9820.

13. Find an equation of a polynomial of degree 10 that has 3+i as a zero.

    
    Answer: .

14. Find the zeros of the polynomial .

    
    Answer: and .

15. Divide by x-6. What is the remainder?

    
    Answer: The remainder is 22.

16. What is the largest rational (exact) zero of the polynomial

    

    
    Answer: The largest zero is .

17. How many real zeros does the polynomial have?

    
    Answer: It has 3 real zeros, which are x=-2 and x=1 (double root).

18. Find an equation of the slant asymptote to the graph of

    

    
    Answer: y=x-6.

19. Is a zero of the polynomial

    

    
    Answer: Yes, it is a zero.

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

    
    Answer: There are two solutions:

    

    when the domain is restricted to the interval , or

    

    when the domain is restricted to the interval .

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Wed Jul 9 16:04:51 MDT 1997

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