MAT092 Algebra 1 Name______
Final Exam Review Questions
[NOTE: The actual final exam contains only 50 questions and more work space between them.]
1. Evaluate: a) ½79½ b) ½-26½ c) -½-41½ d) -½35½
______2. Evaluate:
3. Evaluate 5xz + y2 when x = -2, y = -8, and z = 4
4. Simplify: 3 + 2(7x + 10) - 5x
5. Simplify: -4(6x - 1)
For # 6 - 15: Solve the equations.
6. 7x - 21 = 42
7. 24x = 3
8. 3x + 10 = 15
9.
10. 9 - 5x = -11
11.
12. -9x = 33
13. 7x + 2 = 6 - 3x
14.
15. 4x + 3(10 + 2x) = x - 6
16. Translate the following expression into mathematical symbols:
The product of five less than a number and one-third of the number.
17. Eight is the sum of twice a number and twelve. Find the number.
______18. A rectangular picture frame has a perimeter of 80 inches. The length of the frame
is 24 inches. Find the width of the frame.
______19. A triangle includes a 62° angle and a 70° angle. What is the measure of the third
angle?
______20. What is the complement of a 75° angle?
______21. What is the supplement of a 20° angle?
22. Evaluate: 3-4
23. Write the numbers in Scientific Notation:
______a) 7,014,000,000,000,000
______b) 0.000000324
______c) 123.456
24. Write the numbers in standard form:
______a) 6.285 ´ 10-4
______b) 3.908 ´ 108
______c) 7.654 ´ 102
For # 25 - 35: Simplify. (Do all the indicated operations and write the answer in simplest form.)
25. (x2)6
26. y30 × y6
27. x 15
x 3
28. -9xy4 × 5x9y3
29. (3x4y)5
30. (x + 7)2
31. 12ab5c6
28a7b5c2
32. (7x2 + 9x - 2) - (4x2 - 6x - 3)
33. 2x3(8x2 - 4xy2 + 3)
34. (6x - 7)(2x + 3)
35. 18y5 - 30y3 + 6y2 + 12y
6y2
For # 36 - 46: Factor completely.
36. x2 - 11x + 24
37. x2 - 81
38. y2 + 14y - 32
39. 20x3 + 4x5
40. 3x2 + 19x + 20
41. 20x2 - 45
42. 4y2 + 16y + 12
43. x2 + 49
44. 10x3 - 14x2 + 15x - 21
45. 3x5 - 75x3
46. 8x2y - 18y3
47. Solve the equation: 8 = 2
7x + 1 9
Problems # 48 - 56 pertain to linear equations and graphs.
48. Write the y-intercept and slope of the line represented by the equation:
y = 6x - 11
49. Find the x-intercept: 10x + 3y = 4
50. Write the equation of the line with slope and y-intercept (0 , 7).
______51. Write the equation of the line that contains the points (1 , 9) and (5 , -3).
______52. Write the equation of the line that contains the point (-2 , 5) and has slope .
(see graph) 53. Graph: y = -2x + 3 [Use real graph paper!]
(see graph) 54. Graph: 3x - 5y = 15 [Use real graph paper!]
55. Find the slope of the line containing the points (-2 , 8) and (4 , 3).
56. Find the y-intercept: 6x - 4y = 12
57. Solve the system of equations using any appropriate method.
y = x - 8
4x + 3y = -3
58. Solve the system of equations using any appropriate method.
6x - 9y = 7
-4x + 6y = 5
59. Simplify:
60. Multiply and simplify:
61. Simplify:
62. Rationalize the denominator:
For # 63 - 65: Solve the equations.
63. x2 + 8x + 15 = 0
64. x2 - 9 = 3
65. 2x2 + 5x - 1 = 0
66. Find the length of the third side of the triangle:
13 12
?
MAT092 Algebra 1
Answer Key for Final Exam Review Questions
1. a) 79 b) 26 c) -41 d) -35 2. 16 3. 24 4. 23 + 9x (or 9x + 23) 5. -24x + 4
6. x = 9 7. x = 8. x = 9. x = -30 10. x = 4 11. x = 12. x =
13. x = 14. x = 16 15. x = -4 16.
17. x = - 2 [Translate the words as the equation: 8 = 2x + 12. Then solve.] 18. 16 inches
19. 48° 20. 15° 21. 160° 22. 23. a) 7.014 ´ 1015 b) 3.24 ´ 10-7 c) 1.23456 ´ 102
24. a) 0.0006285 b) 390,800,000 c) 765.4 25. x12 26. y36 27. x12 28. -45x10y7
29. 243x20y5 30. x2 + 14x + 49 31. 32. 3x2 + 15x + 1 33. 16x5 - 8x4y2 + 6x3
34. 12x2 + 4x - 21 35. 3y3 - 5y + 1 + 36. (x - 3)(x - 8) 37. (x + 9)(x - 9)
38. (y + 16)(y - 2) 39. 4x3(5 + x2) 40. (3x + 4)(x + 5) 41. 5(2x + 3)(2x - 3)
42. 4(y + 3)(y + 1) 43. prime 44. (5x - 7)(2x2 + 3) 45. 3x3(x + 5)(x - 5)
46. 2y(2x + 3y)(2x - 3y) 47. x = 5 48. y-intercept: (0 , -11) slope: 6 (or )
49. 50. 51. y = -3x + 12 52.
53. 54.
55. 56. (0 , -3) 57. (3 , -5) 58. inconsistent system (no solution)
59. 60. 61. 62. 63. x = -3 or x = -5
64. x = or x = 65. x = or x = 66. 5