This is “Review Exercises and Sample Exam”, section 5.7 from the book Beginning Algebra (v. 1.0). For details on it (including licensing), click here.

For more information on the source of this book, or why it is available for free, please see the project's home page. You can browse or download additional books there. You may also download a PDF copy of this book (81 MB) or just this chapter (5 MB), suitable for printing or most e-readers, or a .zip file containing this book's HTML files (for use in a web browser offline).

Has this book helped you? Consider passing it on:
Creative Commons supports free culture from music to education. Their licenses helped make this book available to you.
DonorsChoose.org helps people like you help teachers fund their classroom projects, from art supplies to books to calculators.

5.7 Review Exercises and Sample Exam

Review Exercises

Rules of Exponents

Simplify.

1. 7376

2. 5956

3. y5y2y3

4. x3y2xy3

5. 5a3b2c6a2bc2

6. 55x2yz55xyz2

7. (3 a 2 b 42 c 3)2

8. (2 a 3b4 c 4)3

9. 5x3y0(z2)32x4(y3)2z

10. (25x6y5z)0

11. Each side of a square measures 5x2 units. Find the area of the square in terms of x.

12. Each side of a cube measures 2x3 units. Find the volume of the cube in terms of x.

Introduction to Polynomials

Classify the given polynomial as a monomial, binomial, or trinomial and state the degree.

13. 8a31

14. 5y2y+1

15. 12ab2

16. 10

Write the following polynomials in standard form.

17. 7x25x

18. 5x213x+2x3

Evaluate.

19. 2x2x+1, where x=3

20. 12x34, where x=13

21. b24ac, where a=12, b=3, and c=32

22. a2b2, where a=12 and b=13

23. a3b3, where a=2 and b=1

24. xy22x2y, where x=3 and y=1

25. Given f(x)=3x25x+2, find f(2).

26. Given g(x)=x3x2+x1, find g(1).

27. The surface area of a rectangular solid is given by the formula SA=2lw+2wh+2lh, where l, w, and h represent the length, width, and height, respectively. If the length of a rectangular solid measures 2 units, the width measures 3 units, and the height measures 5 units, then calculate the surface area.

28. The surface area of a sphere is given by the formula SA=4πr2, where r represents the radius of the sphere. If a sphere has a radius of 5 units, then calculate the surface area.

Adding and Subtracting Polynomials

Perform the operations.

29. (3x4)+(9x1)

30. (13x19)+(16x+12)

31. (7x2x+9)+(x25x+6)

32. (6x2y5xy23)+(2x2y+3xy2+1)

33. (4y+7)(6y2)+(10y1)

34. (5y23y+1)(8y2+6y11)

35. (7x2y23xy+6)(6x2y2+2xy1)

36. (a3b3)(a3+1)(b31)

37. (x5x3+x1)(x4x2+5)

38. (5x34x2+x3)(5x33)+(4x2x)

39. Subtract 2x1 from 9x+8.

40. Subtract 3x210x2 from 5x2+x5.

41. Given f(x)=3x2x+5 and g(x)=x29, find (f+g)(x).

42. Given f(x)=3x2x+5 and g(x)=x29, find (fg)(x).

43. Given f(x)=3x2x+5 and g(x)=x29, find (f+g)(2).

44. Given f(x)=3x2x+5 and g(x)=x29, find (fg)(2).

Multiplying Polynomials

Multiply.

45. 6x2(5x4)

46. 3ab2(7a2b)

47. 2y(5y12)

48. 3x(3x2x+2)

49. x2y(2x2y5xy2+2)

50. 4ab(a28ab+b2)

51. (x8)(x+5)

52. (2y5)(2y+5)

53. (3x1)2

54. (3x1)3

55. (2x1)(5x23x+1)

56. (x2+3)(x32x1)

57. (5y+7)2

58. (y21)2

59. Find the product of x21 and x2+1.

60. Find the product of 32x2y and 10x30y+2.

61. Given f(x)=7x2 and g(x)=x23x+1, find (fg)(x).

62. Given f(x)=x5 and g(x)=x29, find (fg)(x).

63. Given f(x)=7x2 and g(x)=x23x+1, find (fg)(1).

64. Given f(x)=x5 and g(x)=x29, find (fg)(1).

Dividing Polynomials

Divide.

65. 7y214y+287

66. 12x530x3+6x6x

67. 4a2b16ab24ab4ab

68. 6a624a4+5a23a2

69. (10x219x+6)÷(2x3)

70. (2x35x2+5x6)÷(x2)

71. 10x421x316x2+23x202x5

72. x53x428x3+61x212x+36x6

73. 10x355x2+72x42x7

74. 3x4+19x3+3x216x113x+1

75. 5x4+4x35x2+21x+215x+4

76. x44x4

77. 2x4+10x323x215x+302x23

78. 7x417x3+17x211x+2x22x+1

79. Given f(x)=x34x+1 and g(x)=x1, find (f/g)(x).

80. Given f(x)=x532 and g(x)=x2, find (f/g)(x).

81. Given f(x)=x34x+1 and g(x)=x1, find (f/g)(2).

82. Given f(x)=x532 and g(x)=x2, find (f/g)(0).

Negative Exponents

Simplify.

83. (10)2

84. 102

85. 5x3

86. (5x)3

87. 17y3

88. 3x4y2

89. 2a2b5c8

90. (5x2yz1)2

91. (2x3y0z2)3

92. (10 a 5 b 3 c 25a b 2 c 2)1

93. ( a 2 b 4 c 02 a 4 b 3c)3

The value in dollars of a new laptop computer can be estimated by using the formula V=1200(t+1)1, where t represents the number of years after the purchase.

94. Estimate the value of the laptop when it is 1½ years old.

95. What was the laptop worth new?

Rewrite using scientific notation.

96. 2,030,000,000

97. 0.00000004011

Perform the indicated operations.

98. (5.2×1012)(1.8×103)

99. (9.2×104)(6.3×1022)

100. 4×10168×107

101. 9×10304×1010

102. 5,000,000,000,000 × 0.0000023

103. 0.0003/120,000,000,000,000

Sample Exam

Simplify.

1. 5x3(2x2y)

2. (x2)4x3x

3. (2 x 2 y 3)2x2y

4. a. (5)0; b. 50

Evaluate.

5. 2x2x+5, where x=5

6. a2b2, where a=4 and b=3

Perform the operations.

7. (3x24x+5)+(7x2+9x2)

8. (8x25x+1)(10x2+2x1)

9. (35a12)(23a2+23a29)+(115a518)

10. 2x2(2x33x24x+5)

11. (2x3)(x+5)

12. (x1)3

13. 81x5y2z3x3yz

14. 10x915x5+5x25x2

15. x35x2+7x2x2

16. 6x4x313x22x12x1

Simplify.

17. 23

18. 5x2

19. (2x4y3z)2

20. (2 a 3 b 5 c 2a b 3 c 2)3

21. Subtract 5x2y4xy2+1 from 10x2y6xy2+2.

22. If each side of a cube measures 4x4 units, calculate the volume in terms of x.

23. The height of a projectile in feet is given by the formula h=16t2+96t+10, where t represents time in seconds. Calculate the height of the projectile at 1½ seconds.

24. The cost in dollars of producing custom t-shirts is given by the formula C=120+3.50x, where x represents the number of t-shirts produced. The revenue generated by selling the t-shirts for $6.50 each is given by the formula R=6.50x, where x represents the number of t-shirts sold.

a. Find a formula for the profit. (profit = revenuecost)

b. Use the formula to calculate the profit from producing and selling 150 t-shirts.

25. The total volume of water in earth’s oceans, seas, and bays is estimated to be 4.73×1019 cubic feet. By what factor is the volume of the moon, 7.76×1020 cubic feet, larger than the volume of earth’s oceans? Round to the nearest tenth.

Review Exercises Answers

1: 79

3: y10

5: 30a5b3c3

7: 9a4b84c6

9: 10x7y6z7

11: A=25x4

13: Binomial; degree 3

15: Monomial; degree 3

17: x25x+7

19: 22

21: 6

23: −7

25: f(2)=24

27: 62 square units

29: 12x5

31: 8x26x+15

33: 8y+8

35: x2y25xy+7

37: x5x4x3+x2+x6

39: 7x+9

41: (f+g)(x)=4x2x4

43: (f+g)(2)=14

45: 30x6

47: 10y224y

49: 2x4y25x3y3+2x2y

51: x23x40

53: 9x26x+1

55: 10x311x2+5x1

57: 25y2+70y+49

59: x41

61: (fg)(x)=7x323x2+13x2

63: (fg)(1)=45

65: y22y+4

67: a+4b+1

69: 5x2

71: 5x3+2x23x+4

73: 5x210x+1+32x7

75: x3x+5+15x+4

77: x2+5x10

79: (f/g)(x)=x2+x32x1

81: (f/g)(2)=1

83: 1100

85: 5x3

87: y37

89: 2a2c8b5

91: x98z6

93: 8a6b3c3

95: $1,200

97: 4.011×108

99: 5.796×1019

101: 2.25×1020

103: 2.5×1018

Sample Exam Answers

1: 10x5y

3: 4x2y5

5: 60

7: 4x2+5x+3

9: 23a259

11: 2x2+7x15

13: 27x2y

15: x23x+1

17: 18

19: y64x8z2

21: 5x2y2xy2+1

23: 118 feet

25: 16.4