ALG



ALG. 2 FINAL EXAM REVIEW PACKET AND ANSWERS

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. An irrational number can ________ be expressed as a quotient of integers.

|a. |always |b. |sometimes |c. |never |

____ 2. Use the vertical-line test to determine which graph represents a function.

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 3. A biologist took a count of the number of migrating waterfowl at a particular lake, and recounted the lake’s population of waterfowl on each of the next six weeks.

|Week |0 |1 |2 |3 |4 |5 |6 |

|Population |585 |582 |629 |726 |873 |1,070 |1,317 |

|a. |Find a quadratic function that models the data as a function of x, the number of weeks. |

|b. |Use the model to estimate the number of waterfowl at the lake on week 8. |

|a. |[pic]; 1,614 waterfowl |

|b. |[pic]; 2,679 waterfowl |

|c. |[pic]; 1,961 waterfowl |

|d. |[pic]; 2,201 waterfowl |

____ 4. Identify the graph of the complex number [pic].

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

To which sets of numbers does the number belong?

____ 5. [pic]

|a. |integers, rational numbers, real numbers |

|b. |rational numbers, real numbers |

|c. |irrational numbers, real numbers |

|d. |rational numbers, irrational numbers, real numbers |

Name the property of real numbers illustrated by the equation.

____ 6. [pic]

|a. |Associative Property of Multiplication |

|b. |Distributive Property |

|c. |Commutative Property of Addition |

|d. |Associative Property of Addition |

____ 7. [pic]

|a. |Distributive Property |

|b. |Associative Property of Multiplication |

|c. |Commutative Property of Multiplication |

|d. |Associative Property of Addition |

Short Answer

8. Write the ordered pairs for the relation. Find the domain and range.

[pic]

Solve the system by graphing.

9. [pic]

10. [pic]

Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.

11. [pic]

12. [pic]

Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q.

13. [pic]

14. Use a graphing calculator to solve the equation [pic]. If necessary, round to the nearest hundredth.

15. Simplify [pic] using the imaginary number i.

Write the number in the form a + bi.

16. [pic]

17. Find [pic].

Simplify the expression.

18. [pic]

19. [pic]

20. Find the missing value to complete the square.

[pic]

Solve the quadratic equation by completing the square.

21. [pic]

22. [pic]

Rewrite the equation in vertex form.

23. [pic]

Use the Quadratic Formula to solve the equation.

24. [pic]

25. [pic]

26. Classify –3x5 – 2x3 by degree and by number of terms.

27. Classify –7x5 – 6x4 + 4x3 by degree and by number of terms.

28. Write the polynomial [pic] in standard form.

29. Use a graphing calculator to find a polynomial function to model the data.

|x |1 |2 |3 |4 |5 |6 |7 |8 |9 |10 |

|f(x) |12 |4 |5 |13 |9 |16 |19 |16 |24 |43 |

30. Write the expression (x + 6)(x – 4) as a polynomial in standard form.

31. Write 4x3 + 8x2 – 96x in factored form.

32. Divide [pic] by x + 3.

Divide using synthetic division.

33. [pic]

34. [pic]

35. In ΔXYZ, ∠Y is a right angle and [pic]. Find cos X in fraction and in decimal form. Round to the nearest hundredth, if necessary.

[pic]

36. In ΔXYZ, ∠Y is a right angle and [pic]. Find sin Z in fraction and in decimal form. Round to the nearest hundredth, if necessary.

[pic]

Find the length x. Round to the nearest tenth.

37. [pic]

38. [pic]

Find the angle measure to the nearest tenth of a degree.

39. [pic]

40. [pic]

41. [pic]

In [pic], [pic] is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.

42. a = 3.4, c = 5.8

43. Use the Law of Sines. Find b to the nearest tenth.

[pic]

44. Use the Law of Sines. Find [pic] to the nearest tenth.

[pic]

45. Use the Law of Cosines. Find b to the nearest tenth.

[pic]

46. Use the Law of Cosines. Find [pic] to the nearest tenth of a degree.

[pic]

47. In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.

|a. |Find a quadratic model for the data in the table. |

|b. |Use the model to estimate the population of bacteria at 9 hours. |

|Time (hours) |0 |1 |2 |3 |4 |5 |6 |

|Population (1000s) |5.1 |3.03 |1.72 |1.17 |1.38 |2.35 |4.08 |

Graph the number on a number line.

48. [pic]

49. [pic]

Simplify by combining like terms.

50. [pic]

51. Find the perimeter of the figure. Simplify the answer.

[pic]

Solve the equation.

52. [pic]

53. [pic]

54. [pic]

Solve the equation or formula for the indicated variable.

55. [pic], for t

56. [pic], for U

Solve the inequality. Graph the solution set.

57. 2 + 2k ≤ 8

58.

2(4y – 5) < –10

Solve the compound inequality. Graph the solution set.

59. 4x – 5 < –17 or 5x + 6 > 31

60. Suppose [pic] and [pic].

Find the value of [pic].

61. Graph the equation [pic].

Find the slope of the line through the pair of points.

62. [pic]

63. (6, 12) and (–6, –2)

Write in standard form an equation of the line passing through the given point with the given slope.

64. slope = –8; (–2, –2)

65. Find the point-slope form of the equation of the line passing through the points (–6, –4) and (2, –5).

Find the slope of the line.

66. [pic]

67. [pic]

Find an equation for the line:

68. through (–7, –4) and vertical.

69. Graph the equation of y = |x| translated 4 units up.

Find the value of y for a given value of x, if y varies directly with x.

70. If y = 166 when x = 83, what is y when x = 23?

71. If y = 4.8 when x = 2.4, what is y when x = 2.05?

72. A balloon takes off from a location that is 158 ft above sea level. It rises 56 ft/min. Write an equation to model the balloon’s elevation h as a function of time t.

Graph the absolute value equation.

73. [pic]

Without graphing, classify each system as independent, dependent, or inconsistent.

74. [pic]

Solve the system by the method of substitution.

75. [pic]

Use the elimination method to solve the system.

76. [pic]

77. [pic]

Solve the system of inequalities by graphing.

78. [pic]

79. [pic]

Find a quadratic model for the set of values.

80. (–2, 8), (0, –4), (4, 68)

81.

|x |–2 |0 |4 |

|f(x) |1 |–3 |85 |

82. Write [pic] in vertex form.

Factor the expression.

83. [pic]

84. [pic]

85. [pic]

86. [pic]

87. [pic]

Solve the equation by finding square roots.

88. [pic]

ALG. 2 FINAL EXAM REVIEW PACKET - 1

Answer Section

MULTIPLE CHOICE

1. ANS: C 1-1 Properties of Real Numbers

2. ANS: C 2-1 Relations and Functions

3. ANS: C 5-1 Modeling Data With Quadratic Functions

4. ANS: B 5-6 Complex Numbers

5. ANS: B 1-1 Properties of Real Numbers

6. ANS: B 1-1 Properties of Real Numbers

7. ANS: B 1-1 Properties of Real Numbers

SHORT ANSWER

8. ANS:

{(–2, 5), (–1, 2), (0, 1), (1, 2), (2, 5)}; domain: {–2, –1, 0, 1, 2}; range: {1, 2, 5}

2-1 Relations and Functions

9. ANS:

[pic]

(–5, –4)

3-1 Graphing Systems of Equations

10. ANS:

[pic]

no solutions

3-1 Graphing Systems of Equations

11. ANS:

linear function

linear term: [pic]

constant term: –6

5-1 Modeling Data With Quadratic Functions

12. ANS:

quadratic function

quadratic term: [pic]

linear term: [pic]

constant term: –6

5-1 Modeling Data With Quadratic Functions

13. ANS:

(–1, –2), x = –1

P'(0, –1), Q'(–3, 2)

5-1 Modeling Data With Quadratic Functions

14. ANS:

0.87, –2.07

5-5 Quadratic Equations

15. ANS:

[pic]

5-6 Complex Numbers

16. ANS:

[pic]

5-6 Complex Numbers

17. ANS:

[pic]

5-6 Complex Numbers

18. ANS:

[pic]

5-6 Complex Numbers

19. ANS:

[pic]

5-6 Complex Numbers

20. ANS:

1

5-7 Completing the Square

21. ANS:

[pic]

5-7 Completing the Square

22. ANS:

[pic]

5-7 Completing the Square

23. ANS:

[pic]

5-7 Completing the Square

24. ANS:

[pic], [pic]

5-8 The Quadratic Formula

25. ANS:

[pic] [pic]

5-8 The Quadratic Formula

26. ANS:

quintic binomial

6-1 Polynomial Functions

27. ANS:

quintic trinomial

6-1 Polynomial Functions

28. ANS:

[pic]

6-1 Polynomial Functions

29. ANS:

f(x) = 0.08x4 – 1.73x3 + 12.67x2 – 34.68x + 35.58

6-1 Polynomial Functions

30. ANS:

x2 + 2x – 24

6-2 Polynomials and Linear Factors

31. ANS:

4x(x – 4)(x + 6)

6-2 Polynomials and Linear Factors

32. ANS:

[pic], R –93

6-3 Dividing Polynomials

33. ANS:

[pic]

6-3 Dividing Polynomials

34. ANS:

[pic], R –38

6-3 Dividing Polynomials

35. ANS:

[pic]

14-3 Right Triangles and Trigonometric Ratios

36. ANS:

[pic]

14-3 Right Triangles and Trigonometric Ratios

37. ANS:

48.3

14-3 Right Triangles and Trigonometric Ratios

38. ANS:

72.0

14-3 Right Triangles and Trigonometric Ratios

39. ANS:

11.7°

14-3 Right Triangles and Trigonometric Ratios

40. ANS:

86.1°

14-3 Right Triangles and Trigonometric Ratios

41. ANS:

82.8°

14-3 Right Triangles and Trigonometric Ratios

42. ANS:

[pic] = 54.1°, [pic] = 35.9°, b = 4.7

14-3 Right Triangles and Trigonometric Ratios

43. ANS:

23.1

14-4 Area and the Law of Sines

44. ANS:

73.8°

14-4 Area and the Law of Sines

45. ANS:

63.2

14-5 The Law of Cosines

46. ANS:

33.9°

14-5 The Law of Cosines

47. ANS:

|a. |[pic] |

|b. |13,830 bacteria |

5-1 Modeling Data With Quadratic Functions

48. ANS:

[pic]

1-1 Properties of Real Numbers

OBJ: 1-1.1 Graphing and Ordering Real Numbers

49. ANS:

[pic]

1-1 Properties of Real Numbers

50. ANS:

[pic]

1-2 Algebraic Expressions

51. ANS:

10x + 2y

1-2 Algebraic Expressions

52. ANS:

[pic]

1-3 Solving Equations

53. ANS:

x = [pic] or x = [pic]

1-5 Absolute Value Equations and Inequalities

54. ANS:

[pic]i, [pic]i

5-6 Complex Numbers

55. ANS:

[pic]

1-3 Solving Equations

56. ANS:

[pic]

1-3 Solving Equations

57. ANS:

k ≤ 3

[pic]

1-4 Solving Inequalities

58. ANS:

y < 0

[pic]

1-4 Solving Inequalities

OBJ: 1-4.1 Solving and Graphing Inequalities

59. ANS:

x < –3 or x > 5

[pic]

1-4 Solving Inequalities

OBJ: 1-4.2 Compound Inequalities

60. ANS:

[pic]

2-1 Relations and Functions

61. ANS:

[pic]

2-2 Linear Equations

62. ANS:

[pic]

2-2 Linear Equations

63. ANS:

[pic]

2-2 Linear Equations

64. ANS:

8x + y = –18

2-2 Linear Equations

65. ANS:

y + 4 = [pic](x + 6)

2-2 Linear Equations

66. ANS:

[pic]

2-2 Linear Equations

67. ANS:

0

2-2 Linear Equations

OBJ: 2-2.2 Writing Equations of Lines

68. ANS:

x = –7

2-2 Linear Equations

69. ANS:

[pic]

2-6 Families of Functions

70. ANS:

46

2-3 Direct Variation

71. ANS:

4.1

2-3 Direct Variation

72. ANS:

h = 56t + 158

2-4 Using Linear Models

OBJ: 2-4.1 Modeling Real-World Data

73. ANS:

[pic]

2-5 Absolute Value Functions and Graphs

74. ANS:

dependent

3-1 Graphing Systems of Equations

75. ANS:

(0, –5)

3-2 Solving Systems Algebraically

76. ANS:

(5, 3)

3-2 Solving Systems Algebraically

77. ANS:

(0, –2)

3-2 Solving Systems Algebraically

78. ANS:

[pic]

3-3 Systems of Inequalities

79. ANS:

[pic]

3-3 Systems of Inequalities

80. ANS:

[pic]

5-1 Modeling Data With Quadratic Functions

81. ANS:

[pic]

5-1 Modeling Data With Quadratic Functions

82. ANS:

[pic]

5-3 Translating Parabolas

83. ANS:

[pic]

5-4 Factoring Quadratic Expressions

84. ANS:

[pic]

5-4 Factoring Quadratic Expressions

85. ANS:

[pic]

5-4 Factoring Quadratic Expressions

86. ANS:

[pic]

5-4 Factoring Quadratic Expressions

87. ANS:

[pic]

5-4 Factoring Quadratic Expressions

88. ANS:

[pic], –[pic]

5-5 Quadratic Equations

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