ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
1.2-1 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
1
1.2-2 If f ( x) 
4
x  8 , what is f ( x) ?
3
(A)
f ( x) 
3
( x  8)
4
(B)
f ( x) 
3
x 8
4
(C)
f ( x) 
4
x6
3
(D)
f ( x) 
4
( x  8)
3
1.4-1 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) 
2014–2015
Clark County School District
1
x
( g f )( x)
Page 1 of 22
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
3.4-1 Simplify (3- 4i) + (5- 6i) .
(A)
(B)
(C)
(D)
8+10i
-9 - 38i
8-10i
6 -10i
3.4-2 Simplify (1- 3i) - (-3+ 7i) .
(A)
(B)
(C)
(D)
4 -10i
4 + 4i
18 +16i
-2 + 4i
3.6-1 (3.3) Solve the quadratic equation by taking the square root.
4 x 2  5  1
6
2
(A)
x
(B)
x
(C)
x
i 6
2
(D)
x
6
4
6
4
2014–2015
Clark County School District
Page 2 of 22
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
3.7-1 (3.1, 3.5) 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
3.7-2 (3.3) Show that (3  i) is a root of x  6 x  10  0 .
2
3.7-3 (3.3, 3.6) Solve x  25  0 over the set of complex numbers.
(A)
25i
(B)
5
(C)
5i
(D)
25
3.7-4 (3.2, 3.5) 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
2014–2015
Clark County School District
Page 3 of 22
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
3.7-5 (3.1, 3.5) What is the equation of the parabola shown?
(A)
y  4 x 2
(B)
y  2 x 2
(C)
1
y   x2
2
(D)
1
y   x2
4
2
3.7-6 (3.3) Factor 9 x  121 .
(A)
(3x  11)(3x  11)
(B)
(3x  11)(3x  11)
(C)
(3x  11i)(3x  11i)
(D)
(3x  11i)(3x  11i)
2
3.7-7 Solve the equation 6 x  24 x  126 by factoring.
(A)
x  7 or x  3
(B)
x  7 or x  3
(C)
x  7
(D)
x3
2014–2015
Clark County School District
Page 4 of 22
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
3.7-8 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
3.7-9 Which of the following is a factor of (a  1)2  b2 ?
(A)
a  b 1
(B)
a b
(C)
a 1
(D)
a  b 1
3.8-1 (3.3, 3.7) Which of the following quadratic equation has no real roots?
(A)
2 x2  7 x  9  0
(B)
2 x2  7 x
(C)
2 x2  7 x  9  0
(D)
2 x2  7 x  9  0
2
3.8-2 (3.2) Find the vertex of y = x + 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
2014–2015
Clark County School District
Page 5 of 22
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
3.8-3 (3.1) Consider the function f ( x)  x2  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  .
2
3.8-4 For what values of c will 3x  2 x  c  0 have exactly one distinct real root?
(A)

3
2
(B)

1
3
(C)
1
3
(D)
2
3
3.9-1 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
2
3.9-2 (3.8)
Given the general form of a quadratic equation x  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?
2014–2015
Clark County School District
Page 6 of 22
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
3.13-1(3.5) 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.
3.14-1 (3.4, 3.7) 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?
3.14-2 (3.5, 3.13) Several values of the quadratic function f ( x) are given in the table.
2014–2015
Clark County School District
Page 7 of 22
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
x
f ( x)
4
96
2
24
0
0
4
96
9
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
3.14-3 (3.8) 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) .
3.14-4 (3.1, 3.13) 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
2014–2015
Clark County School District
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Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
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.
4.2-1 What is the 4th term of the expanded binomial (2 x  1) 6 ?
(A)
240x3
(B)
60x3
(C)
240 x3
(D)
160 x3
4.2-2 Suppose xy  9 and ( x  y)2  21 . What is x2  y 2 ?
(A)
3
(B)
12
(C)
36
(D)
81
4.3-1 The table lists all the real roots of a 5th degree polynomial p ( x) and the
multiplicity of each root.
x
Multiplicity
3
1
1
1
1
2
2
1
Which general factorization correctly represents p ( x) ?
(A)
a( x  3)( x  1)2 ( x  2)
2014–2015
Clark County School District
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Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
(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)
4.3-2 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.
4.4-1 Divide ( x 4  2 x3  7)  ( x2  1) using long division.
(A)
x2  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
4.4-2 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
2014–2015
Page 10 of 22
V ( x)  2 x  5 x  4
3
Clark County School District
2
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
(A)
2 x2  x  2
(B)
2 x2  4 x  4
(C)
x6
(D)
x2  5x  3
4.4-3 Write an expression that represents the width of a rectangle with length x  5 and
area x3  12 x 2  47 x  60 .
(A)
x3  7 x 2  12 x
(B)
x 2  7 x  12
x 2  17 x  38  x50
5
ALGEBRA II(C)
Honors
2013–2014 SEMESTER
EXAMS
x 2  17 x  132  720
(D)
x 5
PRACTICE MATERIALS
SEMESTER 1
(4.3)graph
Use of
the pgraph
answer questions
p ( x) to
28.4.6-1
Use the
answer
questions.
( x) toof
a) True or False: The leading term of p ( x) , when written in standard form, is
a) True orpositive.
False: The leading term of p ( x) , when written in standard form, is positive.
b) 2014–2015
True or False: From the graph, p(-3) Page
The
multiplicity of the factor Revised
even. Explain
= 0 . 11
( x + 3) is
of 22
July 2014
your answer.
Clark County School District
29. If f ( x ) = 2 x 4 + 7 x 3 + 3 x 2 - 8 x - 4 , find the possible rational roots of f ( x) .
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
b) True or False: From the graph, p(3)  0 . The multiplicity of the factor
( x  3) is even. Explain your answer.
4.6-2 (4.3) Which graph represents f ( x)  x5  6 x3  9 x ?
2014–2015
Clark County School District
Page 12 of 22
Revised July 2014
ALGEBRA II Honors
2013–2014 SEMESTER EXAMS
PRACTICE
MATERIALS
ALGEBRA
II
SEMESTER
1 SEMESTER EXAMS
2014–2015
PRACTICE MATERIALS
40.SEMESTER
Which graph1represents f ( x) = x 5 - 6 x 3 + 9 x ?
(A)
(B)
(C)
(D)
2013–2014
2014–2015
Clark County School District
Clark County School District
Page 13 of 29
Page 13 of 22
Revised November 2013
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
4.7-1 (4.6) Use the information in the table.
Interval
Value of f(x)
(, 2)
Negative
(2,1)
Positive
(1, 4)
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.
4.8-1 According to the Fundamental Theorem of Algebra, how many roots does the
following equation have?
6 x 2  4  11x
(A)
2
(B)
4
(C) II6Honors
ALGEBRA
2013–2014
EXAMS
(D) SEMESTER
11
PRACTICE MATERIALS
SEMESTER
4.9-1(
4.3, 4.6)1Consider the graph of p ( x) below. Which general factorization correctly
represents p ( x) .
26. Consider the graph of p ( x) below. Which general factorization correctly represents p ( x) .
Which general factorization correctly represents p ( x) ?
Which general factorization correctly represents p ( x) ?
2014–2015
(A)
a( x + 3)( x - 2)( x - 4) Page 14 of 22
(B)
a( x + 3)( x + 2)( x + 4)
(C)
a( x - 3)( x + 2)( x - 4)
(D)
a ( x - 3)( x - 2)( x - 4)
Clark County School District
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
Which general factorization correctly represents p ( x) ?
x x3)(
x  x2)(
(A)(A) a( xa+(3)(
- 2)(
- x4) 4)
x x3)(
 x2)(
(B) (B) a( xa+(3)(
+ x2)(
+ x4) 4)
x x3)(
 x2)(
(C) (C) a( xa-(3)(
+ x2)(
- x4) 4)
x x3)(
 x2)(
(D)(D) a( xa-(3)(
- x2)(
- x4) 4)
) is shown below.
4.9-2
(4.3,
4.6)of
Thep (graph
of p ( xbelow.
27. The
graph
x) is shown
p( x) ?
Which general
factorization
Which general
factorization
correctlycorrectly
representsrepresents
p( x) ?
x x3)(
x  x2)(
(A)(A) -4(x4(
- 3)(
- 2)(
- x4) 4)
x x3)(
 x2)(
(B) (B) 6( x 6(
- 3)(
+ x2)(
+ x4) 4)
(C) (C)
1 1 ( x  3)( x  2)( x  4)
( x + 3)( x - 2)( x - 4)
4 4
x x3)(
 x2)(
(D)(D) 4( x 4(
+ 3)(
+ x2)(
+ x4) 4)
2013–2014
4.9-3
9 of 29
Revised
2013
f ( x)November
4 , find
(4.3) If f ( x)  2 x 4  7 x3  3x 2  8x Page
the possible rational roots of
.
Clark County School District
(A)
x  1, 4
(B)
x  1,  4
(C)
1
x   ,  1,  2
2
(D)
1
x   ,  1,  2,  4
2
2014–2015
Clark County School District
Page 15 of 22
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
4.9-4 (4.3) 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
4.9-5 (4.3) p( x)  3x5  13x 4  19 x3  17 x2  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) ?
4.9-6 (4.3) 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.
4.9-7 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
(D)
1
7
y   x3  x  1
6
6
1 3 7
x  x 1
6
6
4.9-8 How many possible rational zeros exist for the polynomial function
y  3x6  9 x 2  4 x  12 ?
(A)
9
(B)
12
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Clark County School District
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SEMESTER 1
(C)
18
(D)
24
4.9-9 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.
4.11-1 (4.3, 4.9) Consider p( x)  2 x4  x3  11x2  5x  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 ) ?
4.11-2 (4.3, 4.9) Consider p( x)  x4  2.5x3  7.5x2  15x  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) .
4.11-3 (4.6) 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) ?
2014–2015
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Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
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SEMESTER 1
4.12-1 (4.6, 4.7) 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
2014–2015
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ALGEBRA II
2014–2015 SEMESTER EXAMS
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SEMESTER 1
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.
2014–2015
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Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
5.2-1 (5.1)
If f (x) = x 2 -1 and g(x) = x -1 , which expression represents
f (x)
g(x)
for x  1 ?
(A)
x
(B)
x -1
(C)
x +1
(D)
1
x +1
5.3-1 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)
5.3-2 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  }
5.4-1 (5.3) 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
2014–2015
Clark County School District
Page 20 of 22
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
5.5-1 (5.1, 5.2) Which value of x makes this equation true?
4
9(x - 7) 3 = 9
(A)
1
(B)
7
(C)
8
(D)
34
5.5-2 (5.1,5.2) Solve for x :
3
4x 1  5
(A)
x  31
(B)
x6
(C)
x  31
(D)
No real solution
5.5-3 Solve for x .
x  7  x 1
(A)
x  5 and x  10
(B)
x5
(C)
x  10
(D)
No real solutions
5.5-4 Solve for x .
x 3  x  3
(A)
x4
(B)
x6
(C)
x9
(D)
No real solutions
2014–2015
Clark County School District
Page 21 of 22
Revised July 2014
ALGEBRA II
2014–2015 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
5.5-5 (5.2) If 3 12 x  28  4 , what is the value of x3 ?
(A)
-8
(B)
3
(C)
12
(D)
27
5.6-1 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) 
(D)
a( x)  3 x  4 
3
x4
1
2
3
x  4 1
2
2014–2015
Clark County School District
1
2
Page 22 of 22
Revised July 2014