Algebra 2 Final Exam Review Name______Date_____
1. Evaluate (27)23
2. 32x-6 +8=10
3. Rewrite 1114 using radical notation.
4. Evaluate the factorial expression 5!
5. Last year the Pride football team scored the following number of points in its 10 games.
Number of points: 17, 7, 28, 21, 24, 35, 14, 10, 31, 20.
Find the mean and the range of the data.
6. Nine people are entered in a race. If there are no ties, in how many ways can the first three places come out?
a) 472 b) 3
c) 504 d) 252
7. Identify all horizontal and vertical asymptotes of the graph of the following function: fx= -x3x3-8
8. Sketch the graph of the function
fx= x2x2-9
9. R varies jointly with S and the square of T.
If R is 21.6 when S = 0.3 and T = 3, find R when S = 0.5 and T =8.
10. A lunch menu consists of 3 different sandwiches, 3 different soups and 5 different drinks. How many choices are there for ordering a sandwich, a bowl of soup and a drink?
11. A college has six instructors qualified to teach a special computer lab course which requires two instructors to be present. How many different pairs of teachers could there be?
a) 20 b) 30
c) 15 d) 36
12. The intensity, l, of light received from a source varies inversely as the square of the distance, d, from the source. If the light intensity is 2 foot candles at 12 feet, find the light intensity at 14 feet. Round your answer to the nearest hundredth if necessary.
13. Let fx= x2+ 4 and gx=3x2. Find (f ⃘g)(x)
a) 3x4 + 12 b) 3x4 + 24x2 + 48
c) 9x4 + 4 d) 3x4 + 4
14. Let fx=1- x2 and g x=1-x. Find fx- g x
15. Find the inverse of the relation: (1,1), (2,2), (1,3), (4,4)
16. Write an equation for the inverse of the relation: y= -11x +9
17. Let fx= x2 +4 and gx=3x2. Find g(fx)
18. Let fx= -3x. Find f-1
19. Simplify 354
20. Add 6x+4+5x-4
a) 11x2-16 b) 11x-4
c) 11x+4 d) 11x-4x2-16
21. Add 9x+3+2x-3
22. Solve 14=83x+5
a) -73 b) -139
c) -179 d) -79
23. Solve x-7x+9=x+1x-4
24. Divide x2+7x+12x2-9÷x+4x-4
25. Simplify (-3x-2)-3
26. Simplify (-3c3d4e6)2
a) 9c5d6e8 b) 9c6d8e12 c) -9c5d6e8 d) -9c6d8e12
27. Find all the zeros of the function. fx=6x4- 7 x3- 9x2+ 7x +3
28. Find all the zeros of the function. fx= 2-4x+9x-13x-5
a) 98 ,12 ,56 b) -94 , -1 , -53
c) 94 , 1 , 53 d) -98 ,-12 ,-56
29. Evaluate log525
a) 12 b) 110
c) 2 d) 10
30. Factor completely 3x3+6x2+ 15x
a) 3x(x2+2x+ 5) b) 3(x3+ 2x2+ 5x)
c) x(3x2+6x+15) d) 3xx+2(x+5)
31. Find the domain and range of the function y= 4x - 4
32. List the zeros of the cubic function and tell which, if any, are double or triple zeros.
y= x+4x-3x-2
33. Solve cc-4 + 12c= 1
a) 2 b) 3 c) 4 d) 5
34. Simplify 3x36y3 ∙ y5x5
35. Simplify n2-9n+3 ∙ n2n-6
a) 2n b) n+3n-3 c) n2 d) 12n
36. Solve and check for extraneous solutions 3x-812 = 5
37. Solve and check for extraneous solutions 2y-7 = 11
38. 3x34 =192
39. x2+ 5 =3-x
40. 3x-3 =4
41. Find the missing term: x+32 = x2 + 6x+______
a) 9 b) 3 c) 12 d) 6
42. Identify the sequence as arithmetic, geometric or neither: 1, 4, 9, 16, 25, ……
43. Find the sum of the finite geometric series. Round your result to two decimal places.
n=110423n-1
44. Find the sum of the infinite geometric series
k=1∞414k-1
a) 203 b) 163 c) 1 d) 165
45. Find the common ratio of the geometric sequence 2, -8, 32, -128………..
46. Rewrite the equation in exponential form: log324= 25
47. Divide using synthetic division: 2x4-4x3-12x-16÷x-3
a) 2x2+2x+6+2 b) 2x3+2x2+6x+6+2
c) 2x3+2x2+6x+6+ 2x-3 d) 2x2+2x+6+ 2x-3
48. Factor completely with respect to the integers. 2x4-14x2+ 24
49. One of the zeros of the function fx= x4+ 2x3- 13x2- 38x-24 is x= -3.
Find the other zeros of the function.
50. What is the range of the function gx=2+ x+1
51. Find the sum of the series:
k=14k2-1
52. Perform the indicated operation: 3x+22x2-7x-4
53. Simplify 18 + 32
54. x25y1535
55. Last year, the personal best high jumps of track athletes in a nearby state were normally distributed with a mean of 205 cm and a standard deviation of 19 cm. What is the probability that a randomly selected high jumper has a personal best between 167 and 205 cm?
56. The duration of routine operations in a certain hospital has approximately a normal distribution with an average of 130 minutes and a standard deviation of 20 minutes. What percentage of operations last longer than 90 minutes?
1