Name: ___________________________________________ ____
1. 4𝑥𝑥 2 + 3𝑥𝑥 5 − 5
Write in standard form.
______________________________________________
Leading coefficient _______
4
2. 8𝑥𝑥 + 2𝑥𝑥 − 5𝑥𝑥
3
Degree________
Write in standard form.
______________________________________________
Leading coefficient _______
Degree________
3. Factor the following: 4𝑥𝑥 2 + 11𝑥𝑥 − 3
(
)(
4. Factor the following: 4𝑥𝑥 2 − 16
____(
)(
)
)
4
5 x = ___________ 6.
3
6 5 =__________
Write each expression using radical notation.
(
7. 4 xy 3
)
1
5
3
=_________ 8. (2)
9. Solve: √2𝑥𝑥 − 2 + 6 = 4
4
3
=________ _
𝑥𝑥 = _______
Algebra II 2015 – 2016
Write each logarithmic equation in exponential form.
10. log 1 25 = −2
5
11. log 4
1
256
= −4
____________________
_____________________
12. Condense: 6 log 7 𝑔𝑔 − 2 log 7 ℎ _________________
13. 4 log 3 𝑘𝑘 + 5 log 3 𝑙𝑙 + 6 log 3 𝑚𝑚
14. Expand:
15. log 7
Write each expression using rational exponents.
5.
Spring Semester Test review
6𝑎𝑎 1/2
𝑏𝑏
_________________
log 3 𝑝𝑝3 𝑞𝑞5 ____________________________
________________________________________
16. Solve: 4𝑥𝑥 = 6
x = ________
17. 2(73𝑥𝑥 ) + 5 = 91
x = ________
18. Make a table for five values of ‘x’, and the
resultant ‘y’, for the function 𝑓𝑓(𝑥𝑥) = 3(4)𝑥𝑥
X
0
Y
0.25
0.5
0.75
1
19. Solve: 3 log 4 (𝑥𝑥 + 4) = 9
𝑥𝑥 = _______
20. log 7 (4𝑥𝑥 + 5) = log 7 (6𝑥𝑥 − 7)
𝑥𝑥 = _______
21. Howard’s uncle gave him $1000 for his tenth
birthday. He invested it in an account that gives 8%
annually. Howard decided to leave it in the account
until it reached an amount of at least $2500. How
long did he leave the money in the account? [Hint:
Use the formula A = 𝑪𝑪(𝟏𝟏 + 𝒓𝒓)𝒕𝒕 ]
Leading Coefficient: _______
Degree: _______
End behavior:
Left side: as 𝑥𝑥 → −∞, 𝑓𝑓(𝑥𝑥) → _________
Right side: as 𝑥𝑥 → ∞, 𝑓𝑓(𝑥𝑥) → __________
23. 𝑓𝑓(𝑥𝑥) = −3𝑥𝑥 4 − 8𝑥𝑥 2
Leading Coefficient: _______
Degree: _______
End behavior:
Left side: as 𝑥𝑥 → −∞, 𝑓𝑓(𝑥𝑥) → _________
Right side: as 𝑥𝑥 → ∞, 𝑓𝑓(𝑥𝑥) → __________
22. 𝑓𝑓(𝑥𝑥) = 2𝑥𝑥 3 + 3𝑥𝑥 2 − 4𝑥𝑥
Identify whether the function graphed has an odd or even degree, the value of the degree, and if the
whether the leading coefficient is positive or negative.
24.
25.
26.
24. odd/even; degree____; pos/neg LC 25. odd/even; degree____; pos/neg LC 26. odd/even; degree____; pos/neg LC
Simplify:
27.
28.
3𝑥𝑥
∗
𝑥𝑥−2
∗
35𝑦𝑦
5𝑥𝑥
49𝑦𝑦
12𝑧𝑧
10𝑥𝑥
3𝑥𝑥 2 −12
Solve for ‘x’:
29.
𝑥𝑥
=
30.
𝑥𝑥
=
5
3
= __________𝑦𝑦 ≠ _____𝑧𝑧 ≠ _____
7
10
−2
𝑥𝑥+7
= ______________𝑥𝑥 ≠ _______
𝑥𝑥 = _________
𝑥𝑥 = __________
31. Use synthetic division to divide
3𝑥𝑥 3 − 4𝑥𝑥 2 + 2𝑥𝑥 − 5 by 𝑥𝑥 − 1.
What is the remainder?
32. Identify ALL of the asymptotes and hole
locations for the rational function.
𝑓𝑓(𝑥𝑥) =
𝑥𝑥 3 +𝑥𝑥 2 −2𝑥𝑥
2𝑥𝑥 3 +4𝑥𝑥 2 −6𝑥𝑥
Factor:
33. 𝑥𝑥 2 − 13𝑥𝑥 + 40 ________________________
34. 𝑥𝑥 2 + 𝑥𝑥 − 56
__________________
35. 𝑥𝑥 2 − 13𝑥𝑥
_________________
36. Find the roots of 𝑥𝑥 2 = 36
x = ________ ; x = _________
37. Express 8√−84 in terms of i.
_________________
38. Find the inverse for the function
Simplify each expression by rationalizing the
denominator.
41.
42.
5
____________
2
3x
____________
7
Solve each radical equation
43. √𝑥𝑥 − 9 = 5
𝑥𝑥 = ______________
44. 2√𝑥𝑥 = √𝑥𝑥 + 9
𝑥𝑥 = ______________
Determine whether each equation below
represents a growth or decay relationship and
determine the rate of change.
45. 𝑦𝑦 = 3(0.75)𝑥𝑥
Growth
Decay
Rate of change ________
𝑓𝑓(𝑥𝑥) = 4𝑥𝑥 + 12
46. 𝑓𝑓(𝑥𝑥) = 0.5(1.23)𝑥𝑥 Growth
Decay
Rate of change ________
𝑓𝑓(𝑥𝑥) = _________________
State whether each graph shows exponential
growth or decay.
39. {(2, 5), (7, 3)} is the inverse relation of
the function {(5, 2)(3, 7)} True or False
40. The test that will tell you if any y-values
are repeated. If the function fails this test, its
inverse is not a function.
A) vertical line test
B) horizontal line test
C) inverse function
D) function
47. Growth
Decay
Write the equation that matches the
information in each problem.
51. Marisa invests $300 at a bank that offers
5% compounded annually.
𝑦𝑦 = _________________________________
48. Growth
Decay
Solve each exponential word problem
49. The number of flowers in a garden is
decreasing at a rate of about 2% each year.
If in one year there are 50,000 flowers in the
garden, and the equation used to model this
situation is 𝑦𝑦 = 50,000(1 − .02)𝑥𝑥 , how many
flowers will there be in 5 years?
52. Marco bought a new car at a cost of
$25,000. The car depreciates approximately
15% of its value each year.
𝑦𝑦 = _________________________________
53. Do long division:
(2𝑥𝑥 3 − 7𝑥𝑥 2 + 9𝑥𝑥 − 4) ÷ (2𝑥𝑥 − 1)
𝑦𝑦 = ______________________
50. In 1985, there were 285 cell phone
subscribers in the small town of Centerville.
The number of subscribers increased by
75% per year after 1985. Using the equation
𝑦𝑦 = 285(1.75)𝑥𝑥 find the number of cell phone
subscribers in Centerville in 1994. (Hint:
How many years passed between 1985 and
1994?)
𝑦𝑦 = ______________________
= _________________________________
54. Do synthetic division:
(2𝑥𝑥 3 + 5𝑥𝑥 2 + 9) ÷ (𝑥𝑥 + 3)
= ____________________________________
55. Write the equation whose graph can be
obtained from the graph of 𝑦𝑦 = 𝑥𝑥 2 by a
stretch of 5, and a vertical shift of 4 units up.
56. Consider the graph of 𝑓𝑓(𝑥𝑥) = 𝑥𝑥 3 . It is
shifted 3 units to the left, then reflected
across the x-axis, and finally shifted 8 units
down. What is the resulting equation?
57. What can you know about the graph of
the function 𝑓𝑓(𝑥𝑥) = 4(𝑥𝑥 + 3)2 − 7 ?
58.
60.
𝑥𝑥−2
−1
7𝑥𝑥+28
8𝑥𝑥 2 −24𝑥𝑥
59.
∗
1
𝑥𝑥
+
8
7𝑥𝑥+28
66.
6
𝑥𝑥 2 −9
=1−
1
𝑥𝑥+3
67.
3𝑥𝑥−4
𝑥𝑥+4
=
4𝑥𝑥
𝑥𝑥+4
3
68. Solve: (8𝑥𝑥) �2 − 2 = 6
69. For 𝑓𝑓(𝑥𝑥) = 3𝑥𝑥 − 2 𝑎𝑎𝑎𝑎𝑎𝑎
1
Solve for ‘x’
𝑥𝑥
Solve and give domain restrictions
𝑔𝑔(𝑥𝑥) = 𝑥𝑥 + 4, give the composition
3
𝑥𝑥
function 𝑓𝑓�𝑔𝑔(𝑥𝑥)� = ___________
2
61.
𝑥𝑥+1
3𝑥𝑥+6
∗
6𝑥𝑥+12
𝑥𝑥 2 −1
70. Match the function with its inverse:
Quadratic, exponential, square root,
logarithm
Use the function 𝒇𝒇(𝒙𝒙)
next four questions.
=
62. What is the domain?
63. Vertical Asymptotes?
64. Holes?
65. Horizontal Asymptote?
𝟒𝟒𝒙𝒙𝟐𝟐
𝒙𝒙𝟐𝟐 −𝟗𝟗
for the
Write the following parent functions and give the
domain and range and the transformation equation
(using a, h, and k) for each.
71. Linear:
72. Quadratic:
73. Cubic
74. Cube Root:
75. Exponential:
76. Logarithmic:
77. Reciprocal:
Simplify the following expressions:
78. (16𝑚𝑚2 + 12𝑚𝑚𝑚𝑚 − 8𝑛𝑛2 ) − (9𝑚𝑚2 − 21𝑛𝑛2 )
79. (5𝑎𝑎 + 6𝑏𝑏)(8𝑎𝑎 − 9𝑏𝑏)
80. (5𝑟𝑟 3 + 5𝑟𝑟 − 8) + (7𝑟𝑟 2 − 9)