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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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