Math 95 Final Exam Practice Questions
Write each solution set in interval and set-builder notation, and graph it on a number line
1. 5𝑦 + 1 > 16
2. 2(𝑥 − 1) ≤ 3(𝑥 + 2)
3. 0.4𝑡 + 0.37 < 0.3(𝑡 + 2.1)
4. |4𝑥 + 12| < 8
5. |0.25𝑥 − 3| + 2 > 4
Solve each equation, making sure to identify whether solutions actually satisfy the original equation
6. |3𝑠 + 6| = 12
7. |2𝑥 + 1| = |𝑥 + 5|
8. |4 + 2𝑞| = |2𝑞 + 8|
9. 𝑥 2 − 16 = 6𝑥
10. 2𝑥 2 + 𝑥 − 6 = 0
11. 2𝑥 2 + 𝑥 − 5 = 0
12. 𝑥 2⁄3 − 3𝑥 1⁄3 + 2 = 0
13. √𝑤 − 1 = 3
14. 3√𝑦 + 1 = 3√2𝑦 − 4
15. 1 + √𝑥 = √2𝑥 + 1
16. √5𝑛 − 1 = 4 − 2𝑛
Graph each of the following, making sure to label your axes
17. 𝑦 ≤ 2𝑥 + 4
18. 𝑥 − 𝑦 > 5
19. 𝑦 = −2𝑥 2 + 6
1
20. 𝑓(𝑥) = 3 (𝑥 − 2)2 − 1
21. 𝑦 = −0.5𝑥 2 + 4𝑥 − 6
22. 𝑓(𝑥) = |𝑥 − 2| + 1
Identify the domain and range of each function
23.
24. {(−1, 3), (0, 2), (1, 3), (2, 6), (4, 18)}
Factor the polynomial completely
25. 𝑥 2 − 15𝑥 + 50
26. 2𝑥 2 + 7𝑥 + 3
27. 𝑥 3 + 7𝑥 2 − 18𝑥
28. 𝑥 2 − 36
29. 𝑥 2 + 16𝑥 + 64
Perform the indicated operation and simplify your answer as much as possible
30.
𝑛2 −6𝑛+9 𝑛2 +4𝑛+3
∙ 𝑛2 −3𝑛
𝑛2 −9
31.
3𝑥+2
5𝑥 2 −𝑥
32.
33.
34.
6𝑥 2 +𝑥−2
÷ 10𝑥2 +3𝑥−1
4𝑥+5
𝑥+4
−
𝑥+1
𝑥+1
4
5
+ 𝑦−3
𝑦+3
𝑎+6
𝑎−3
− 𝑎+3
𝑎 2 +7𝑎+12
35. √5𝑥 5 ∙ √20𝑥 3
36. 4√10𝑐 ∙ 2√6𝑐 4
37.
9√160
3√8
38. 4√24 − 6√54
2
39. (√2 + 1)
40. 3√6(2 − 3√6)
Compute the following, and write your answer in standard (𝒂 + 𝒃𝒊) form
41. (10 + 𝑖) − (2 − 13𝑖) + (6 − 5𝑖)
42. (5 − 2𝑖)(4 + 𝑖)
Find the intercepts (x and y) and vertex of each parabola
43. 𝑦 = 𝑥 2 − 𝑥 − 12
44. 𝑦 = 3𝑥 2 + 𝑥 − 2
45. 𝑦 = (𝑥 − 1)2 − 3
Solve each word problem, including the appropriate units with your answer
46. A toy rocket is launched with an initial velocity of 45 meters per second. The equation ℎ =
−4.9𝑡 2 + 45𝑡 describes the height, h, of the rocket in meters t seconds after being launched.
Round all values to the nearest hundredth.
a)
After how many seconds does the rocket reach its maximum height?
b)
What is the maximum height the rocket reaches?
c)
How long is the rocket in the air?
47. What are the length and width of a rectangle if the length exceeds the width by 14 inches and
the perimeter is 60 inches?
48. One integer is six less than three times another integer. The sum of the integers is -42. Find
the integers.