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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.
c.
y
4
4
2
2
–4
–4
O
–2
y
2
4
–2
x
O
2
4
x
2
4
x
–2
–2
–4
–4
b.
–4
____
–2
y
4
4
2
2
O
2
4
–4
x
–2
O
–2
–2
–4
–4
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.
b.
c.
d.
____
d.
y
; 1,614 waterfowl
; 2,679 waterfowl
; 1,961 waterfowl
; 2,201 waterfowl
4. Identify the graph of the complex number
.
a.
c.
Imaginary Axis
Imaginary Axis
4
4
2
2
Real Axis
–4
b.
–2
O
2
Real Axis
–4
4
–2
O
–2
–2
–4
–4
d.
Imaginary Axis
–2
4
4
2
2
O
2
4
Imaginary Axis
–4
–2
–2
–4
–4
2
15
a. integers, rational numbers, real numbers
b. rational numbers, real numbers
c. irrational numbers, real numbers
d. rational numbers, irrational numbers, real numbers
5. 
Name the property of real numbers illustrated by the equation.
____
____
O
–2
To which sets of numbers does the number belong?
____
6.
a.
b.
c.
d.
Associative Property of Multiplication
Distributive Property
Commutative Property of Addition
Associative Property of Addition
a.
b.
c.
d.
Distributive Property
Associative Property of Multiplication
Commutative Property of Multiplication
Associative Property of Addition
4
Real Axis
Real Axis
–4
2
7.
Short Answer
8. Write the ordered pairs for the relation. Find the domain and range.
2
4
y
4
2
–4
–2
O
2
x
4
–2
–4
Solve the system by graphing.
9.
10.
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant
terms.
11.
12.
Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q.
y
13.
8
4
Q
–8
–4
O
P
4
8
x
–4
–8
14. Use a graphing calculator to solve the equation
hundredth.
15. Simplify
using the imaginary number i.
Write the number in the form a + bi.
. If necessary, round to the nearest
16.
17. Find
.
Simplify the expression.
18.
19.
20. Find the missing value to complete the square.
Solve the quadratic equation by completing the square.
21.
22.
Rewrite the equation in vertex form.
23.
Use the Quadratic Formula to solve the equation.
24.
25.
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
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
by x + 3.
Divide using synthetic division.
33.
34.
35. In XYZ, Y is a right angle and
nearest hundredth, if necessary.
. Find cos X in fraction and in decimal form. Round to the
Z
25
20
X
Y
36. In XYZ, Y is a right angle and
. Find sin Z in fraction and in decimal form. Round to the nearest
hundredth, if necessary.
Z
5
4
X
Y
Find the length x. Round to the nearest tenth.
37.
59
x
55 °
38.
x
42°
80
Find the angle measure to the nearest tenth of a degree.
39.
40.
41.
In
tenth.
,
is a right angle. Find the remaining sides and angles. Round your answers to the nearest
42. a = 3.4, c = 5.8
43. Use the Law of Sines. Find b to the nearest tenth.
C
31
b
42°
64°
B
A
44. Use the Law of Sines. Find
to the nearest tenth.
C
69
67°
B
72
45. Use the Law of Cosines. Find b to the nearest tenth.
A
C
60
b
48°
B
A
85
46. Use the Law of Cosines. Find
to the nearest tenth of a degree.
C
17
22
B
A
30
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)
Population (1000s)
0
1
2
3
4
5
6
5.1
3.03
1.72
1.17
1.38
2.35
4.08
Graph the number on a number line.
48.
49.
Simplify by combining like terms.
50.
51. Find the perimeter of the figure. Simplify the answer.
x+y
2x
4x
y
2x
x
Solve the equation.
52.
53.
54.
Solve the equation or formula for the indicated variable.
55.
, for t
56.
, 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
Find the value of
61. Graph the equation
and
.
.
.
Find the slope of the line through the pair of points.
62.
y
8
4
–8
–4
O
4
8
x
–4
–8
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.
67.
y
4
2
–4
–2
O
2
4
x
–2
–4
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.
Without graphing, classify each system as independent, dependent, or inconsistent.
74.
Solve the system by the method of substitution.
75.
Use the elimination method to solve the system.
76.
77.
Solve the system of inequalities by graphing.
78.
79.
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
Factor the expression.
83.
84.
85.
86.
in vertex form.
87.
Solve the equation by finding square roots.
88.
ALG. 2 FINAL EXAM REVIEW PACKET - 1
Answer Section
MULTIPLE CHOICE
1. ANS: C
2. ANS: C
3. ANS: C
4. ANS: B
5. ANS: B
6. ANS: B
7. ANS: B
SHORT ANSWER
1-1 Properties of Real Numbers
2-1 Relations and Functions
5-1 Modeling Data With Quadratic Functions
5-6 Complex Numbers
1-1 Properties of Real Numbers
1-1 Properties of Real Numbers
1-1 Properties of Real Numbers
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:
y
8
4
–8
–4
O
4
8
x
–4
–8
(–5, –4)
3-1 Graphing Systems of Equations
10. ANS:
y
4
2
–4
–2
O
2
4
–2
–4
no solutions
3-1 Graphing Systems of Equations
11. ANS:
x
linear function
linear term:
constant term: –6
5-1 Modeling Data With Quadratic Functions
12. ANS:
quadratic function
quadratic term:
linear term:
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:
5-6 Complex Numbers
16. ANS:
5-6 Complex Numbers
17. ANS:
41
5-6 Complex Numbers
18. ANS:
5-6 Complex Numbers
19. ANS:
5-6 Complex Numbers
20. ANS:
1
5-7 Completing the Square
21. ANS:
5-7 Completing the Square
22. ANS:
5-7 Completing the Square
23. ANS:
5-7 Completing the Square
24. ANS:
1
, 2
5
5-8 The Quadratic Formula
25. ANS:
1
8
5-8 The Quadratic Formula
26. ANS:
quintic binomial
6-1 Polynomial Functions
27. ANS:
quintic trinomial
6-1 Polynomial Functions
28. ANS:
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:
, R –93
6-3 Dividing Polynomials
33. ANS:
6-3 Dividing Polynomials
34. ANS:
, R –38
6-3 Dividing Polynomials
35. ANS:
14-3 Right Triangles and Trigonometric Ratios
36. ANS:
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:
= 54.1°,
= 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.
b. 13,830 bacteria
5-1 Modeling Data With Quadratic Functions
48. ANS:
–5 –4 –3 –2 –1 0 1 2 3 4 5
1-1 Properties of Real Numbers
OBJ: 1-1.1 Graphing and Ordering Real Numbers
49. ANS:
–5 –4 –3 –2 –1 0 1 2 3 4 5
1-1 Properties of Real Numbers
50. ANS:
1-2 Algebraic Expressions
51. ANS:
10x + 2y
1-2 Algebraic Expressions
52. ANS:
1
2
2
1-3 Solving Equations
53. ANS:
1
x = 1 or x = 2
3
1-5 Absolute Value Equations and Inequalities
54. ANS:
4 4
 i, i
3 3
5-6 Complex Numbers
55. ANS:
1-3 Solving Equations
56. ANS:
1-3 Solving Equations
57. ANS:
k3
–8 –6 –4 –2
0
2
4
6
8
4
6
8
1-4 Solving Inequalities
58. ANS:
y0
–8 –6 –4 –2
0
2
1-4 Solving Inequalities
OBJ: 1-4.1 Solving and Graphing Inequalities
59. ANS:
x < –3 or x > 5
–8 –6 –4 –2
0
2
4
6
8
1-4 Solving Inequalities
OBJ: 1-4.2 Compound Inequalities
60. ANS:
4
2
7
2-1 Relations and Functions
61. ANS:
y
4
2
–4
–2
O
–2
–4
2-2 Linear Equations
62. ANS:
4
2-2 Linear Equations
63. ANS:
7
6
2-2 Linear Equations
64. ANS:
8x + y = –18
2-2 Linear Equations
65. ANS:
1
y + 4 =  (x + 6)
8
2-2 Linear Equations
66. ANS:
1

2
2-2 Linear Equations
67. ANS:
0
2
4
x
2-2 Linear Equations
OBJ: 2-2.2 Writing Equations of Lines
68. ANS:
x = –7
2-2 Linear Equations
69. ANS:
y
6
4
2
–6
–4
–2 O
–2
2
4
6
x
–4
–6
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:
y
16
12
8
4
–8
–4
O
4
8
x
–4
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:
y
6
4
2
–6
–4
–2 O
–2
2
4
6
x
–4
–6
3-3 Systems of Inequalities
79. ANS:
y
4
2
–4
–2
O
2
4
x
–2
–4
3-3 Systems of Inequalities
80. ANS:
5-1 Modeling Data With Quadratic Functions
81. ANS:
5-1 Modeling Data With Quadratic Functions
82. ANS:
5-3 Translating Parabolas
83. ANS:
5-4 Factoring Quadratic Expressions
84. ANS:
5-4 Factoring Quadratic Expressions
85. ANS:
5-4 Factoring Quadratic Expressions
86. ANS:
5-4 Factoring Quadratic Expressions
87. ANS:
5-4 Factoring Quadratic Expressions
88. ANS:
7, – 7
5-5 Quadratic Equations