## Precalculus Test Out Practice Exam

Part 2 Test 1 Time: 3 hours

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

2. Solve the equation for x. List the exact answer(s), not approximation(s).

Answer: The exact solutions are: .

3. A picture frame has a total perimeter of 3 feet. The width of the frame is 0.62 times its height. Find the exact dimensions of the area of the frame.

Answer: The height of the frame is feet, its width is feet.

4. Which of the following is a function:
• .
• .
• 7x=6.

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

Answer: The exact solution is x=1.

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

Answer: The exact solutions are x=1, and x=-3.

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

Answer: The exact non-real solutions are: .

8. Solve for x.

Answer: The values of x that make the inequality true are the real numbers contained in the interval (-1,3).

9. Solve for x.

Answer: The values of x that make the inequality true are 5<x<15, or in interval notation, (5,15).

10. Find the exact vertex of the parabola .

11. Find an equation of the parabola that has its vertex at (2,3) and passes through the point (1,1).

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

Answer: The maximum height is 81.125.

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

Answer: One solution is the polynomial .

14. Find the zeros of the polynomial .

Answer: The zeros are: x=-5, x=4, and x=5.

15. Divide by x-4. What is the remainder?

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

Answer: The largest rational zero is .

17. How many real zeros does the polynomial have?

Answer: There are three real solutions, which are: x=-2, and x=1 (double solution).

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

19. Is a zero of the polynomial

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

when the domain is restricted to the interval , or

when the domain is restricted to the interval .

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Wed Jul 9 15:08:24 MDT 1997