Name: ________________________ Class: ___________________ Date: __________
Algebra II Honors Final Exam Review 2014-2015
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. Identify the graph of the complex number 3  2i.
a.
c.
b.
d.
2. Determine which binomial is a factor of 2x 3  14x 2  24x  20.
a. x + 5
b. x + 20
c. x – 24
1
d.
x–5
ID: A
Name: ________________________
____
ID: A
3. Which function matches the graph?
a.
y 
x5 5
c.
y 
x5 5
b.
y 
x5 5
d.
y 
x5 5
Short Answer
Factor the expression.
4. 15x 2  21x
5. 8x 2  12x  16
6. x 2  14x  48
7. 16x 2  40x  25
8. x 3  216
2
Name: ________________________
ID: A
9. x 4  20x 2  64
Graph the exponential function.
10. y  4 2
x
11. An initial population of 895 quail increases at an annual rate of 7%. Write an exponential function to model the
quail population.
12. Find the annual percent increase or decrease that y  0.35(2.3) x models.
13. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you
have in the account after 4 years?
Write the equation in logarithmic form.
14. 6 4  1, 296
3
Name: ________________________
ID: A
Evaluate the logarithm.
15. log 5
1
625
Graph the logarithmic equation.
16. y  log(x  1)  7
Write the expression as a single logarithm.
17. 5 log b q  2 log b y
18. 4 log x  6 log (x  2)
Expand the logarithmic expression.
19. log 3 11p 3
20. Use the properties of logarithms to evaluate log 3 9  log 3 36  log 3 4.
4
Name: ________________________
ID: A
21. Solve 15 2x  36. Round to the nearest ten-thousandth.
22. Solve
1
 64 4x  3 .
16
23. Solve log(4x  10)  3 .
24. Solve log(x  9)  log x  3 .
Write the expression as a single natural logarithm.
25. 3 ln x  2 lnc
26. Solve ln(2x  1)  8 . Round to the nearest thousandth.
Use natural logarithms to solve the equation. Round to the nearest thousandth.
27. 6e 4x  2  3
5
Name: ________________________
ID: A
Graph the function.
28. y 
x 1
29. y 
x3
30. Solve by factoring.
4x 2  28x  32 = 0
6
Name: ________________________
ID: A
Solve the equation by finding square roots.
31. 3x 2  21
32. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the length of the shorter base
to be 3 yards greater than the height, and the length of the longer base to be 5 yards greater than the height. For
what height will the garden have an area of 360 square yards? Round to the nearest tenth of a yard.
33. Simplify
175 using the imaginary number i.
Write the number in the form a + bi.
34.
4  10
35. Find the additive inverse of 7  5i.
Simplify the expression.
36. (1  6i)  (4  2i)
37. (6i)(6i)
Solve the equation.
38. 9x 2  16  0
39. x 2  18x  81  25
7
Name: ________________________
40.
ID: A
x  10  7  5
4
41. 4(3  x) 3  5  59
42. Find the missing value to complete the square.
x 2  2x  ____
Rewrite the equation in vertex form.
2
43. y  x  10x  16
44. The function P  h 2  60h  400 models the daily profit a barbershop makes from haircuts that include a
shampoo. Here P is the profit in dollars, and h is the price of a haircut with a shampoo. Write the function in
vertex form. Use the vertex form to find the price that yields the maximum daily profit and the amount of the
daily profit.
Use the Quadratic Formula to solve the equation.
45. 5x 2  9x  2  0
46. Classify –3x5 – 2x3 by degree and by number of terms.
47. Write the polynomial
6x 2  9x 3  3
in standard form.
3
8
Name: ________________________
ID: A
48. The table shows the number of llamas born on llama ranches worldwide since 1988. Find a cubic function to
model the data and use it to estimate the number of births in 1999.
Years since 1988
Llamas born (in thousands)
1
3
5
7
9
1.6
20
79.2
203.2
416
49. Write 4x3 + 8x2 – 96x in factored form.
50. Find the zeros of y  x(x  3)(x  2) . Then graph the equation.
51. Write a polynomial function in standard form with zeros at 5, –4, and 1.
52. Divide 3x 3  3x 2  4x  3 by x + 3.
Divide using synthetic division.
53. (x 4  15x 3  77x 2  13x  36)  (x  4)
54. Ian designed a child’s tent in the shape of a cube. The volume of the tent in cubic feet can be modeled by the
equation s 3  64  0, where s is the side length. What is the side length of the tent?
55. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation
x 3  x 2  7x  4  0 . Do not find the actual roots.
Find the roots of the polynomial equation.
56. x 3  2x 2  10x  136  0
9
Name: ________________________
ID: A
57. A polynomial equation with rational coefficients has the roots 5 
1, 4 
7 . Find two additional roots.
58. For the equation 2x 4  5x 3  10  0, find the number of complex roots and the possible number of real roots.
59. Find all zeros of 2x 4  5x 3  53x 2  125x  75  0.
60. In how many different orders can you line up 8 cards on a shelf?
Evaluate the expression.
61. 5!
62.
9
P4
63.
7
C6
64. There are 10 students participating in a spelling bee. In how many ways can the students who go
first and second in the bee be chosen?
65. The Booster Club sells meals at basketball games. Each meal comes with a choice of hamburgers, pizza, hot
dogs, cheeseburgers, or tacos, and a choice of root beer, lemonade, milk, coffee, tea, or cola. How many
possible meal combinations are there?
Use Pascal’s Triangle to expand the binomial.
66. (d  5) 6
10
Name: ________________________
67. Find all the real fourth roots of
ID: A
256
.
2401
Simplify the radical expression. Use absolute value symbols if needed.
36g 6
68.
69. The formula for the volume of a sphere is V 
4 3
 r . Find the radius, to the nearest hundredth, of a sphere
3
with a volume of 15 in.3.
70. Simplify
3
128a 13 b 6 . Assume that all variables are positive.
Divide and simplify.
3
71.
162
3
2
Rationalize the denominator of the expression. Assume that all variables are positive.
3
72.
73.
3
9
11
3 
6
3 
6
74. A garden has width
13 and length 7 13 . What is the perimeter of the garden in simplest radical form?
11
Name: ________________________
ID: A
Simplify.
75. 
5  3 36  6 5
4
76. 8 3
Multiply.

77.  7 


2   8 


2 

3
78. Write the exponential expression 3x 8 in radical form.
79. Write the radical expression
80. Write 8a 6 

7
8
in exponential form.
x 15
2
3
in simplest form.
81. The area of a circular trampoline is 112.07 square feet. What is the radius of the trampoline? Round to the
nearest hundredth.
Solve. Check for extraneous solutions.
82. 6x 
24  12x
83. Let f(x)  3x  6 and g(x)  5x  2 . Find f(x) + g(x).
12
Name: ________________________
ID: A
84. Let f(x)  x 2  2x  1 and g(x)  2x  4 . Find 2f(x) – 3g(x).
85. Let f(x)  3x  6 and g(x)  x  2 . Find
f
and its domain.
g
86. Let f(x)  2x  7 and g(x)  4x  3 . Find (f  g)(5).
87. Graph the relation and its inverse. Use open circles to graph the points of the inverse.
x
0
4
9
10
y
3
2
7
–1
13
Name: ________________________
ID: A
88. The Sears Tower in Chicago is 1454 feet tall. The function y  16t 2  1454 models the height y in feet of an
object t seconds after it is dropped from the top of the building.
a. After how many seconds will the object hit the ground? Round your answer to the nearest
tenth of a second.
b.
What is the height of the object 5 seconds after it is dropped from the top of the Sears
Tower?
89. State whether each situation involves a combination or a permutation.
a. 4 of the 20 radio contest winners selected to try for the grand prize
b. 5 friends waiting in line at the movies
c. 6 students selected at random to attend a presentation
14
ID: A
Algebra II Honors Final Exam Review 2014-2015
Answer Section
MULTIPLE CHOICE
1. B
2. D
3. B
SHORT ANSWER
4. 3x(5x  7)
2
5. 4(2x  3x  4)
6. (x  6)(x  8)
2
7. (4x  5)
8. (x  6)(x 2  6x  36)
9. (x  2)(x  2)(x  4)(x  4)
10.
11.
12.
13.
14.
f(x)  895(1.07) x
130% increase
$1,923.23
log 6 1, 296  4
15. –4
1
ID: A
16.
17. log b (q 5 y 2 )
18. none of these
19. log 3 11  3 log 3 p
20. 4
21. 0.6616
7
22.
12
495
23.
2
24. 0.0090
x3
25. ln 2
c
26. 1,490.979
27. –0.046
28.
2
ID: A
29.
30. –8, 1
7, – 7
31.
32. 17.1 yards
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
5i 7
10  2i
7  5i
5  8i
–36
4 4
 i, i
3 3
–4, –14
–6
–5, 11
1
y  (x  5) 2  9
2
44. P  (h  30)  500 ; $30; $500
1
45.
, 2
5
46. quintic binomial
47. 2x 2  3x 3  1
48. L(x)  0.5x 3  0.6x 2  0.3x  0.2 ; 741,600 llamas
49. 4x(x – 4)(x + 6)
3
ID: A
50. 0, 3, 2
51.
52.
53.
54.
55.
56.
f(x)  x 3  2x 2  19x  20
3x 2  12x  32, R –93
x 3  19x 2  x  9
4 feet
–4, –2, –1, 1, 2, 4
3 ± 5i, –4
57. 5  1, 4  7
58. 4 complex roots; 0, 2 or 4 real roots
3
59. 1, ,  5i
2
60. 40,320
61. 120
62. 3,024
63. 7
64. 90 ways
65. 30
66. d 6  30d 5  375d 4  2500d 3  9375d 2  18750d  15625
4
4
67.  and
7
7

3

68. 6 g
69. 1.53 in.
70. 4a 4 b 2 3 2a
71. 3 3 3
3
72.
99
11
73. 3  2 2
74. 16 13 units
75. 5 5  18
4
ID: A
76. 16
77. 54 
2
8
78. 3 x 3

15
79. 8x 7
a4
80.
4
81. 5.97 feet
82. 1
83. 2x – 4
84. 2x 2  2x  10
85. 3; all real numbers except x  2
86. –53
87.
88.
a. 9.5 seconds
b. 1,054 ft
89. a. combination
b. permutation
c. combination
5