ALG 2 CH
ALG. 2 CH. 5.5-5.8 TEST PRE-VIEW - QUADRATIC EQUATIONS & FUNCTIONS
CHAPTER REVIEW FOR CH. 5 TEST
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. The function [pic] models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second.
|a. |7.79 seconds |c. |0.25 seconds |
|b. |11.02 seconds |d. |5.51 seconds |
____ 2. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the length of the shorter base to be 3 yards greater than the height, and the length of the longer base to be 5 yards greater than the height. For what height will the garden have an area of 360 square yards? Round to the nearest tenth of a yard.
|a. |17.1 yards |c. |39.2 yards |
|b. |34.2 yards |d. |152.6 yards |
____ 3. –6 – [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 4. Identify the graph of the complex number [pic].
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Solve the equation.
____ 5. [pic]
|a. |14, 4 |c. |14, –14 |
|b. |–4, –14 |d. |–4, 4 |
____ 6. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 155 square yards. The situation is modeled by the equation [pic]. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard.
|a. |12.7 yards |c. |10.2 yards |
|b. |20.4 yards |d. |320 yards |
Short Answer
7. Determine the type and number of solutions of [pic].
8. Solve by factoring.
[pic] = 0
Solve the equation by finding square roots.
9. [pic]
10. [pic]
11. Simplify [pic] using the imaginary number i.
Write the number in the form a + bi.
12. [pic]
13. Find [pic].
14. Find the additive inverse of [pic].
Simplify the expression.
15. [pic]
16. [pic]
17. [pic]
18. [pic]
Use the Quadratic Formula to solve the equation.
19. [pic]
20. [pic]
21. [pic]
Rewrite the equation in vertex form.
22. [pic]
23. [pic]
24. Use a graphing calculator to solve the equation [pic]. If necessary, round to the nearest hundredth.
Solve the quadratic equation by completing the square.
25. [pic]
26. [pic]
27. [pic]
28. [pic]
Solve the equation.
29. [pic]
30. Find the missing value to complete the square.
[pic]
Essay
31. Use a graphing calculator to graph the function [pic].
|a. |What does the graph let you conclude about real number solutions of [pic]? Explain. |
|b. |Substitute [pic] for x in the equation [pic]. Simplify. Is the resulting equation true? Show your work. |
|c. |What conclusions can you state about solutions of [pic]? Explain. |
ALG 2 CH. 5.4-5-8 Quadratic Equations CHAPTER REVIEW FOR CH. 5 TEST
Answer Section
MULTIPLE CHOICE
1. ANS: D
2. ANS: A
3. ANS: B
4. ANS: B
5. ANS: B
6. ANS: C
SHORT ANSWER
7. ANS:
two real solutions
8. ANS:
–8, [pic]
9. ANS:
[pic], –[pic]
10. ANS:
[pic], [pic]
11. ANS:
[pic]
12. ANS:
[pic]
13. ANS:
[pic]
14. ANS:
[pic]
15. ANS:
[pic]
16. ANS:
[pic]
17. ANS:
–36
18. ANS:
[pic]
19. ANS:
[pic], [pic]
20. ANS:
[pic] [pic]
21. ANS:
[pic] [pic]
22. ANS:
[pic]
23. ANS:
[pic]
24. ANS:
0.87, –2.07
25. ANS:
[pic]
26. ANS:
[pic]
27. ANS:
[pic] [pic]
28. ANS:
[pic] [pic]
29. ANS:
[pic]i, [pic]i
30. ANS:
1
ESSAY
31. ANS:
|[4] |a. |The equation has no real number solutions. The graph of [pic] does not intersect the x-axis. |
| |b. |[pic] |
| | |Yes, [pic] is true. |
| |c. |[pic] has no real number solutions. But the equation does seem to have [pic] as a solution, because you get a |
| | |true equation when you substitute [pic] for x and simplify. |
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