ALGEBRA II Honors
2013–2014 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
1. A student has learned that test scores in math are determined by this quadratic function:
s (t )  (t  6) 2  99
In the function, s is the score and t is the number of hours that a student spends on homework each
week.
a) How many hours must a student spend on homework to achieve maximum score?
b) What is the maximum score?
c) Based on the function, what will be the score if a student does no homework?
2. Show that ( 3  i ) is a root of x2  6 x  10  0 .
3. Solve x2  25  0 over the set of complex numbers.
(A) 25i
(B) 5
(C) 5i
(D) 25
4. Which of the following quadratic equation has no real roots?
(A) 2x2  7 x  9  0
(B) 2x2  7 x
(C) 2x2  7 x  9  0
(D) 2x2  7 x  9  0
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5. According to the Fundamental Theorem of Algebra, how many roots does the following equation
have?
6 x2  4  11x
(A) 2
(B) 4
(C) 6
(D) 11
6. Function A and Function B are continuous quadratic functions.
Function A
Function B
f ( x)  x 2  x  6
Which function has a greater positive x-intercept?
(A) Function A
(B) Function B
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7. What is the equation of the parabola shown?
(A) y  4 x 2
(B) y  2 x 2
1
(C) y   x 2
2
1
(D) y   x 2
4
8. Factor 9 x2  121 .
(A) (3x  11)(3 x  11)
(B) (3x  11)(3 x  11)
(C) (3x  11i)(3x  11i)
(D) (3x  11i)(3x  11i)
9. Solve the equation 6x2  24x  126 by factoring.
(A) x  7 or x  3
(B) x  7 or x  3
(C) x  7
(D) x  3
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10. Solve the quadratic equation by taking the square root.
4 x2  5  1
6
2
(A) x 
(B) x 
6
4
(C) x  
i 6
2
(D) x 
6
4
11. Solve the equation by using the quadratic formula.
2 x2  5x  3  0
(A) x = 1 or x = -6
(B) x =
1
or x = -3
2
(C) x 
1
or x  1
3
12. Simplify (3- 4i) + (5- 6i) .
(A) 8+10i
(B) -9 - 38i
(C) 8-10i
(D) 6 -10i
13. Simplify (1- 3i) - (-3+ 7i) .
(A) 4 -10i
(B) 4 + 4i
(C) 18 +16i
(D) -2 + 4i
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14. Find the vertex of y = x 2 + 2x - 3 and state if it is a maximum or a minimum.
(A) (-1, -4); maximum
(B) (-1, -4); minimum
(C) (-4, -1); maximum
(D) (-4, -1); minimum
15. The height of Carl, the human cannonball, is given by h(t )  16t 2  56t  40 where h is in feet
and t is in seconds after the launch.
a) What was his height at the launch?
b) What is his maximum height?
c) How long before he lands in the safety net, 8 feet above the ground?
16. What is the solution set of y 2  2 y  3 y  14 ?
(A) y  7
(B) y  2 or y  7
(C) 7  y  2
(D) 2  y  7
17. Which of the following is a factor of (a  1) 2  b 2 ?
(A) a  b 1
(B) a  b
(C) a 1
(D) a  b  1
18. Consider the function f ( x)  x 2  2 x  48.
a) Determine the roots of the function. Show your work.
b) The vertex of g  x  is the point (3, 30). Write the function rule for g in vertex form.
c) Explain how f  x  transformed to become g  x  .
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SEMESTER 1
19. Several values of the quadratic function f ( x) are given in the table.
x
f ( x)
4
2
0
96
24
0
4
9
96
486
The function g ( x ) is given by g ( x)  ( x  2) 2  3 . Which function has the greater maximum for
which value of x ?
(A) f ( x); for x  0
(B) f ( x); for x  6
(C) g ( x); for x  2
(D) g ( x); for x  3
20. Which statement best describes these two functions?
f  x   x2  x  4
g  x   3x 2  3x  7
(A) The maximum of f ( x) is less than the minimum of g ( x ) .
(B) The minimum of f ( x) is less than the maximum of g ( x ) .
(C) The maximum of f ( x) is greater than the minimum of g ( x ) .
(D) The minimum of f ( x) is greater than the maximum of g ( x ) .
21. Given the general form of a quadratic equation x2  bx  c  0 , determine the effect of each
condition on the solutions.
a)
b)
c)
d)
b0
c0
c0
What is needed for the solutions to have imaginary parts?
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22. The amount of fuel F (in billions of gallons) used by trucks from 1990 through 2009 can be
approximated by the function F  f (t )  20.5  0.035t 2 where t  0 represents 1990.
a) Describe the transformation of the common function f (t )  t 2 . Then sketch the graph over the
interval 0  t  19.
f (19)  f (0)
b) Find and interpret
.
19  0
c) Rewrite the function so that t  0 represents 2000. Explain how you got your answer.
d) Use the model from part (c) to predict the amount of fuel used by trucks in 2015. Does your
answer seem reasonable? Explain.
23. Use the graph provided to choose the best description of what the graph represents.
Height (ft)
Time (s)
(A) A ball I dropped from a height of 42 feet and lands on the ground after 3 seconds.
(B) A ball is dropped from a height of 42 feet and lands on the ground after 1.5 seconds.
(C) A ball is shot up in the air and reaches a height of 42 feet after 1 second.
(D) A ball is shot up in the air, reaches a height of 42 feet, and lands on the ground after 1.5
seconds.
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24. The table lists all the real roots of a 5th degree polynomial p ( x ) and the multiplicity of each root.
x
3
Multiplicity
1
1
1
1
2
2
1
Which general factorization correctly represents p ( x ) ?
(A) a( x  3)( x  1) 2 ( x  2)
(B) a( x  3)( x  1)3 ( x  2)
(C) a( x  3)( x  1)( x  1) 2 ( x  2)
(D) a( x  3)( x  1)3 ( x  2)
25. A 4th degree polynomial with real coefficients is found to have exactly two distinct real roots.
What must be true about the other two roots?
(A) One root is real and the other is imaginary.
(B) Both roots must be real.
(C) Both roots are imaginary roots that are complex conjugates.
(D) All the roots have been found.
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26. Consider the graph of p ( x ) below. Which general factorization correctly represents p ( x ) .
Which general factorization correctly represents p ( x ) ?
(A) a( x  3)( x  2)( x  4)
(B) a( x  3)( x  2)( x  4)
(C) a( x  3)( x  2)( x  4)
(D) a( x  3)( x  2)( x  4)
27. The graph of p ( x ) is shown below.
Which general factorization correctly represents p ( x ) ?
(A) 4( x  3)( x  2)( x  4)
(B) 6( x  3)( x  2)( x  4)
(C)
1
( x  3)( x  2)( x  4)
4
(D) 4( x  3)( x  2)( x  4)
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28. Use the graph of p ( x ) to answer questions.
a) True or False: The leading term of p ( x ) , when written in standard form, is positive.
b) True or False: From the graph, p (3)  0 . The multiplicity of the factor ( x  3) is even. Explain
your answer.
29. If f ( x)  2 x 4  7 x 3  3x 2  8 x  4 , find the possible rational roots of f ( x) .
(A) x  1, 4
(B) x  1,  4
1
(C) x   ,  1,  2
2
1
(D) x   ,  1,  2,  4
2
30. Given polynomial q( x) , q (4)  6 . Which statement is correct?
(A) x  4 is not a root
(B) x  4 is a root
(C) ( x  4) is a factor
(D) ( x  4) is not a factor
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31. Consider p ( x)  2 x 4  x3  11x 2  5 x  5 .
a) Show that x  5 and x   5 are zeros of p ( x ) .
b) Completely factor p ( x ) where all the coefficients are rational numbers.
c) h( x) is p ( x ) translated 4 units right and 2 units up. What is the equation of h( x) ?
32. p( x)  3x5  13x 4  19 x3  17 x 2  16 x  4
a) Show that p (2) is a root.
b) Factor p ( x ) completely
c) If f ( x)  p ( x  3) , what are the real roots of f ( x) ?
33. Given the polynomial p( x)  x 4  3x3  12 x  16 :
a) Show that p (2i ) is a root.
b) What other root must also be a root of p ( x ) ? Explain.
c) Factor p ( x ) completely.
34. Consider p( x)  x 4  2.5 x3  7.5 x 2  15 x  9 .
a) Show that x   6 are roots of p ( x ) , then write p ( x ) as the appropriate factorizations at this
point.
b) Factor p ( x ) completely.
c) Let q ( x)  p (4 x) . List out the roots of q( x) .
d) Let f ( x) be p ( x ) vertically stretched by 2, translated 2 units to the right and 4 units up. Write
out the algebraic relationship between f ( x) and p ( x ) .
35. What is the 4th term of the expanded binomial (2 x  1) 6 ?
(A) 240x3
(B) 60x3
(C) 240 x3
(D) 160 x3
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36. For what values of c will 3x2  2 x  c  0 have exactly one distinct real root?
(A) 
3
2
(B) 
1
3
(C)
1
3
(D)
2
3
37. Write a cubic function that passes through the following points: (-2, 0) (3, 0) (-1, 0) and (1, 2).
(A) y  x3  7 x  6
(B) y   x3  7 x  6
(C) y 
1 3 7
x  x 1
6
6
1
7
(D) y   x3  x  1
6
6
38. How many possible rational zeros exist for the polynomial function y  3x 6  9 x 2  4 x  12 ?
(A) 9
(B) 12
(C) 18
(D) 24
39. Suppose xy  9 and ( x  y ) 2  21 . What is x 2  y 2 ?
(A) 3
(B) 12
(C) 36
(D) 81
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40. Which graph represents f ( x)  x5  6 x3  9 x ?
(A)
(B)
(C)
(D)
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41. Divide ( x 4  2 x3  7)  ( x 2  1) using long division.
(A) x 2  2 x  1 
6
x 1
(B) x2  2 x  1 
2x  6
x2  1
(C) x2  2 x  1 
2x  6
x2  1
(D) x2  2 x  1 
2x  6
x2  1
2
42. This polynomial function has at least one rational root.
p( x)  x 4  kx 2  9
a) What are all the possible integer values of k ? Show your work or explain how you know.
b) What are all the possible real roots of the function? Show your work or explain how you know.
43. The volume V ( x ) and height ( h ) of the prism is given. Find a polynomial expression for the area
of the base ( B ) in terms of x . (Hint: V  Bh )
h  x2
V ( x)  2 x3  5 x 2  4
(A) 2x2  x  2
(B) 2x2  4 x  4
(C) x  6
(D) x2  5x  3
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44. Consider the function f ( x)  3x3  9 x 2  3x  9 .
a) Use the leading coefficient and degree of f ( x) to describe the end behavior.
b) Write the rule for the function g ( x)  f ( x) , and describe the transformation.
c) Describe the end behavior of g ( x ) . How does the end behavior of g ( x ) relate to the
transformation of f ( x) ?
45. Use the information in the table.
Interval
(, 2)
Value of f(x)
Negative
(2,1)
(1, 4)
Positive
Negative
(4, )
Positive
a) What are the three real zeros of the polynomial function f ?
b) What can be said about the behavior of the graph of f at x  0 ?
c) What is the least possible degree of f ? Explain. Can the degree of f ever be even? Explain.
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46. The town of Frostburg experienced a bit of a heat wave during January of this year. The graph
below shows the curve of best fit that represents the low temperature of every day in January.
A newspaper journalist is writing a story on the weather and needs to report some information. He
needs a bit of guidance with interpreting the graph.
1) Write a few sentences describing the key characteristics of the graphs as it relates to the
context of the problem. Be sure to include domain, range, intervals where the function
increases and decreases, x and y intercepts, and any other important information
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46. (cont.…)
The graph below shows the curve of best fit that represents the low temperature of every day in
February.
2) Three different models have been proposed that could be used to determine the temperature
for a particular date in February. The models are given below:
Model 1:
y  ax 2  bx  c
Model 2:
y  a( x  3)( x  9)( x  20) 2
Model 3:
y  a( x  3)( x  9)( x  20) 2
Which model would best describe the low temperatures for February? Explain why you chose
that model.
The weather in July showed a related pattern to the weather in February. The curve of best fit for July is
shown below:
3) Explain the relationship between the graph for February and the graph for July. Use that
relationship to create an equation for the temperatures in July.
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47. If f (x) = x 2 -1 and g(x) = x -1 , which expression represents
(A)
x
(B)
x -1
(C)
x +1
f (x)
for x  1 ?
g(x)
1
(D)
x +1
48. Which value of x makes this equation true?
4
9(x - 7) 3 = 9
(A) 1
(B) 7
(C) 8
(D) 34
49. Solve for x :
3
4x  1  5
(A) x  31
(B) x  6
(C) x  31
(D) No real solution
50. Solve for x .
x  7  x 1
(A) x  5 and x  10
(B) x  5
(C) x  10
(D) No real solutions
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51. Solve for x .
x 3  x  3
(A) x  4
(B) x  6
(C) x  9
(D) No real solutions
52. Identify the x and y intercepts of the function f ( x)  3 x  8 .
(A) (8,0) and (0,-2)
(B) (2,0) and (0,2)
(C) (8,0) and (0,8)
(D) (-2,0) and (0,8)
53. Which is the domain of the function f ( x)  5 x  4  3 ?
(A) {x | x  4}
(B) {x | x  3}
(C) {x | x  0}
(D) {x | x  }
54. Compare the graph of y  6  3 x with the graph of its parent function f ( x)  3 x .
(A) Shifts 6 units down
(B) Reflects across the x-axis and shifts 6 units down
(C) Reflects across the x-axis and shifts 6 units up
(D) Reflects across the y-axis and shifts 6 units up
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55. If 3 12 x  28  4 , what is the value of x 3 ?
(A) -8
(B) 3
(C) 12
(D) 27
56. In 1950, the city of San Jose had a population of 95,000. Since then, on average, it grows 4% per
year. What is the best formula to model San Jose’s growth?
(A) 95,000(1.04)t
(B) 95,000(0.96)t
(C) -.04t + 95,000
(D) .04t + 95,000
57. A biologist studying the relationship between the brain weight and body weight in mammals uses
the formula:
ln( wbody )  ln( wbrain )  669
Where wbody =body weight in grams and wbrain =brain weight in grams. What is the formula for the
body weight?
(A) wbody  ( wbrain )(e669 )
(B) wbody  ( wbrain )  (e669 )
(C) wbody  e( wbrain )( e
669 )
(D) wbody  669( wbrain )
58. Find the value of log 2 32 .
(A) 5
(B) 1024
(C) 16
(D) 4
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59. Given the sequence 1, 2, 4, 8, ….
Find the sum of the infinite series.
(A) 15
(B) 18
(C) 30
(D) 
60. During a flu outbreak, a hospital recorded 12 cases the first week, 54 cases the second week, and
243 cases the third week.
a) Write a geometric sequence to model the flu outbreak.
b) How many cases will occur in the sixth week if the hospital cannot stop the outbreak?
61. Which is the same function as f ( x)  ln
x
?
3
(A) g ( x)  ln x  ln 3
(B) g ( x) 
ln x
ln 3
(C) g ( x)  ln 3  ln x
(D) g ( x)  ln x  ln 3
62. Rewrite log9 92 x3  y in exponential form.
(A) 9 y  9(2 x  3)
(B) 9 y  92 x3
(C) y  2 x  3
(D) 9 y  18 x  27
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63. Given the geometric sequence with common ratio r , write a rule for the nth term of the sequence
4, -28, 196, -1372…
(A) an  7(4)n1
(B) an  4(7)n1
(C) an  7(4)n1
(D) an  4(7)n1
64. Choose the function that describes the graph below:
(A) f ( x)  log x  2
(B) f ( x)  log( x  2)
(C) f ( x)  log x  2
(D) f ( x)  log( x  2)
65. Sarai bought $400 of Las Vegas Cellular stock in January 2005. The value of the stock is expected
to increase by 6.5% per year.
a) Write a model to describe Sarai’s investment.
b) Use the graph to show when Sarai’s investment will reach $1100?
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66. Consider the function f ( x)  log x .
a)
b)
c)
d)
Identify the transformation applied to f ( x) to create g ( x)  log x  1 .
Identify the transformation applied to f ( x) to create h( x)  log(10 x) .
Compare the graphs of g ( x ) and h( x) . What do you notice?
Use the properties of logarithms to explain your answer to part c.
8
67. What is the value of  (15  4n) ?
n 3
(A) -42
(B) -17
(C) 88
(D) 363
68. What function is represented by the following graph?
(A) f ( x)  3x
(B) f ( x)  3x  2
(C) f ( x)  2  3x
3
(D) f ( x)  ( ) x
2
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PRACTICE MATERIALS
SEMESTER 1
69. The graph of the equation y  log(2 x  3) is translated right 3 units and down 3.5 units to form a
new graph. Which equation best represents the new graph?
(A) y  log(2 x  9)  3.5
(B) y  log(2 x  9)  3.5
(C) y  log(2 x  3)  3.5
(D) y  log(2 x  3)  3.5
70. John graphs the equation y  5 x . Lana graphs the equation y  5 x  2 . How does Lana’s graph
compare to John’s graph?
(A) Lana’s graph shifts 2 units downward
(B) Lana’s graph shifts 2 units upward
(C) Lana’s graph shifts 2 units to the left
(D) Lana’s graph shifts 2 units to the left
2013–2014
Clark County School District
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Revised November 2013
ALGEBRA II Honors
2013–2014 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
71. In a classic math problem a king wants to reward a knight who has rescued him from an attack.
The king gives the knight a chessboard and plans to place money on each square. He gives the
knight two options. Potion 1 is to place a thousand dollars on the first square, two thousand on the
second square, three thousand on the third square, and so on. Option 2 is to place one penny on the
first square, two pennies on the second, four on the third, and so on.
Think about which offer sounds better and then answer these questions.
a) List the first five terms in the sequences formed by the given options. Identify each sequence as
arithmetic, geometric, or neither.
Option 1
Option 2
b) For each option, write a rule that tells how much money is placed on the nth square of the
chessboard and a rule that tells the total amount of money placed on squares one through n .
Option 1
Option 2
c) Find the amount of money placed on the 20th square of the chessboard and the total amount
placed on squares 1 through 20 for each option.
Option 1
Option 2
d) There are 64 squares on a chessboard. Find the total amount of money placed on the chessboard
for each option.
Option 1
Option 2
e) Which gives the better reward, Option 1 or Option 2? Explain why.
2013–2014
Clark County School District
Page 25 of 29
Revised November 2013
ALGEBRA II Honors
2013–2014 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
72. The loudness of sound is measured on a logarithmic scale according to the formula L  10 log(
I
),
I0
where L is the loudness of sound in decibels ( db ), I is the intensity of sound, and I 0 is the
intensity of the softest audible sound.
a) Find the loudness in decibels of each sound listed in the table.
b) The sound at a rock concert is found to have a loudness of 110 decibels. Where should this
sound be placed in the table in order to keep the sound intensities in order from least to greatest?
Sound
Intensity
Jet taking off
1015 I 0
Jackhammer
1012 I 0
Hairdryer
107 I 0
Whisper
103 I 0
Leaves rustling
102 I 0
Softest audible sound
I0
c) A decibel is
1
of a bel. Is a jet plane louder than a sound that measures 20 bels? Explain.
10
73. If log 4{log 2[log 3(3 x)]} 
1
, then what is x ?
2
(A) 81
(B) 48
(C) 27
(D) 9
74. Which equation has the same solution as log 4 ( x  7)  5 ?
(A) 4x7  5
(B) 5x7  5
(C) 54  x  7
(D) 45  x  7
2013–2014
Clark County School District
Page 26 of 29
Revised November 2013
ALGEBRA II Honors
2013–2014 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
75. Aaron invested $4000 in an account that paid an interest rate r compounded continuously. After
10 years he has $5809.81. The compound interest formula is A  Pert , where P is the principal
(the initial investment), A is the total amount of money (principal plus interest), r is the annual
interest rate, and t is the time in years.
a) Divide both sides of the formula by P and then use logarithms to rewrite the formula without
an exponent. Show your work.
b) Using your answer for part (a) as a starting point, solve the compound interest formula for the
interest rate r .
c) Use your equation from part (a) to determine the interest rate.
76. What is the inverse of f ( x)  2 x  9 ?
(A) f 1 ( x) 
x
9
2
(B) f 1 ( x) 
1
2x  9
(C) f 1 ( x) 
x 9
2
(D) f 1 ( x) 
2
x 9
77. If f ( x)  e x , then which of the following is f 1 (7) ?
(A) e7
(B) 7
(C) log 7
(D) ln 7
2013–2014
Clark County School District
Page 27 of 29
Revised November 2013
ALGEBRA II Honors
2013–2014 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
78. If f 1 ( x) 
4
x  8 , what is f ( x ) ?
3
3
(A) f ( x)  ( x  8)
4
(B) f ( x) 
3
x 8
4
(C) f ( x) 
4
x6
3
4
(D) f ( x)  ( x  8)
3
79. Which is the inverse of f ( x)  (2 x  1)3  4 ?
(A) a ( x)  3 2 x  1  4
(B) b( x) 
(C) a ( x) 
3
x4
1
2
3
x  4 1
2
(D) a( x)  3 x  4 
1
2
80. Which is the inverse of f ( x)  2log3 x ?
(A) f 1 ( x)  1.5 x
(B) f 1 ( x)  0.5(3) x
(C) f 1 ( x)  30.5 x
(D) f 1 ( x)  2(3) x
2013–2014
Clark County School District
Page 28 of 29
Revised November 2013
ALGEBRA II Honors
2013–2014 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
81. Which statement must be true if f and g are inverses of one another?
(A) ( f g )( x)  ( g f )( x)  x
(B) ( f g )( x)  f ( x) g ( x)  ( g f )( x)  g ( x) f ( x)  x
(C) ( f g )( x)  f ( g ( x))  ( g f )( x)  g ( f ( x))  x
(D) ( f g )( x) 
1
x
( g f )( x)
2013–2014
Clark County School District
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Revised November 2013