UNIT
3
MIXED REVIEW
UNIT 3
MIXED REVIEW
Assessment Readiness
Assessment Readiness
• Online Homework
• Hints and Help
• Extra Practice
1. Identify the transformations of the graph of f(x) = x 3 that produce the graph of
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the function g(x) = -2(x - 5) . Select the correct statement.
ASSESSMENT AND INTERVENTION
A. When compared to f(x), the graph of g(x) is not reflected across the x-axis.
B. When compared to f(x), the graph of g(x) is vertically compressed by a
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factor of _
.
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C. When compared to f(x) the graph of g(x) is translated 5 units to the right.
D. When compared to f(x), the graph of g(x) is translated 5 units vertically.
2. Consider the polynomial 3x 3 + 9x - 12x. Select the correct statement.
A. The polynomial cannot be factored as it is written.
B. The completely factored polynomial is 3x(x - 3)(x + 4).
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C. At an intermediate step, the factored polynomial is 3x(3x + 9x - 2).
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Assign ready-made or customized practice tests to
prepare students for high-stakes tests.
D. 3x can be factored out of every term.
ADDITIONAL RESOURCES
3. Consider the factored polynomial 3x(x - 2)(5x + 2). Which of the following is
equivalent to this polynomial? Select the correct answer.
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A. (3x 2 - 6x)(5x + 2)
C. 15x - 24x 2 + 12x
Assessment Resources
B. 3x(x 2 - 8x - 4)
• Leveled Unit Tests: Modified, A, B, C
• Performance Assessment
4. Consider the polynomial function g(x) = 3x 3 + 6x - 9x. Select the correct
statement.
A. The polynomial has no common monomial.
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AVOID COMMON ERRORS
B. The polynomial has only real roots.
© Houghton Mifflin Harcourt Publishing Company
Item 6 Some students have a hard time recognizing
the difference between a local maximum or
minimum, and a global maximum or minimum.
Remind students that not all graphs have global or
local maximums or minimums, but for the ones that
do, these values will occur at the turning points of the
graph. Also, you may wish to review the definitions
of global maximum, global minimum, local
maximum, and local minimum.
D. 3x(5x 2 - 5x - 2)
C. The polynomial has only complex roots.
D. The roots of the polynomial are 0, −3, 1, 3.
5. Identify the zeros of m(x) = x - 16. Select the correct answer.
1
A. ± _
C. 2 ± 2i
2
B. 0
D. ± 2, ± 2i
4
Unit 3
Texas Essential Knowledge and Skills
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Items
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Unit 3
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Algebra 2 TEKS
Mathematical Processes TEKS
1
A2.6.A
A2.1.F
2
A2.7.E
A2.1.F
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A2.7.B
A2.1.F
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A2.7.D
A2.1.D
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A2.7.D, A2.7.E
A2.1.F
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6. Use a graphing calculator to graph the function f(x) = -x(x + 1)(x - 4) , and
then use the graph to determine the number of turning points, global
maximums and minimums, and local maximums and minimums that are not
global. (Lesson 6.2)
2
PERFORMANCE TASKS
There are three different levels of performance tasks:
According to the graph, there are three turning points, one local maximum,
* Novice: These are short word problems that
require students to apply the math they have learned
in straightforward, real-world situations.
one local minimum, and one global maximum.
7. Ms. Flores grows tomatoes on her farm. The price per pound of tomatoes
can be modeled by P(x) = 20x + 4. If the total income that she wants to
earn from tomatoes for one year can be modeled by
ℓ(x) = 60x 3 - 8x 2 + 136x + 28, write a polynomial that can be used to model
the number of pounds of tomatoes Ms. Flores needs to grow in one year.
(Lesson 7.4)
** Apprentice: These are more involved problems
that guide students step-by-step through more
complex tasks. These exercises include more
complicated reasoning, writing, and open ended
elements.
ℓ(x) ÷ P(x) = (60x 3 - 8x 2 + 136x + 28) ÷ (20x + 4 )= 3x 2 - x + 7
To get the total number of pounds of tomatoes, divide the total income for
the year by the price per pound.
8. Measurement A bottom for a box can be
made by cutting congruent squares from
each of the four corners of a piece
of cardboard. The volume of a box made
from an 8.5-by-11-inch piece of cardboard
would be represented by
v(x) = x(11 - 2x)(8.5 - 2x), where x is the
side length of one square.
A. Express the volume as a sum of
monomials.
B. Find the volume when x = 1 inch.
***Expert: These are open-ended, nonroutine
problems that, instead of stepping the students
through, ask them to choose their own methods for
solving and justify their answers and reasoning.
x
8.5 in.
x
SCORING GUIDES
11 in.
Item 8 (2 points)
a. 1 point for correct polynomial
A. 4x - 39x + 93.5x
3
2
b. 1 point for correct volume
Unit 3
© Houghton Mifflin Harcourt Publishing Company
B. 58.5 in 3
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Items
Texas Essential Knowledge and Skills
Algebra 2 TEKS
Mathematical Processes TEKS
6
A2.2.A
A2.1.D
7
A2.7.C
A2.1.E
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* Item integrates mixed review concepts from previous modules or a previous course.
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9. Astronomy The volume of several planets in cubic kilometers can be modeled
SCORING GUIDES
1
by v(d) = _
πd 3, where d is the diameter of the planet in kilometers. The mass
Item 9 (2 points)
M(d) = (3.96 × 10 12)d 3 - (6.50 × 10 17)d 2 + (2.56 × 10 )d - 5.56 × 10 25.
A. The density of a planet in kilograms per cubic kilometer can be found by
dividing the planet’s mass by its volume. Use polynomial division to find a
model for the density of a planet in terms of its diameter.
B. Use the model to estimate the density of Jupiter, with diameter
d = 142,984 km.
6
of each planet in kilograms in terms of diameter d can be modeled by
22
A. 1 point for correct model
B. 1 point for reasonable estimate
Item 10 (6 points)
2.376 × 10
A. D(d) = _________
+ ___________________________________
π
πd 3
13
A. 1 point for correct factoring
(-3.9 × 10 18)d 2 + (1.536 × 10 23)d - 3.336 × 10 26
B. 1.236 × 10 12 kg/km 3
B. 1 point for correct value
C. 1 point for correct value
1 point for correct interpretation
D. 2 points for explanation
10. Business The profit of a small business (in thousands of dollars) since it
was founded can be modeled by the polynomial
4
2
f(t) = -t + 44t 3 - 612t + 2592t, where t represents the number of years
since 1980.
A. Factor f(t) completely.
B. What was the company’s profit in 1985?
C. Find and interpret f(15).
D. What can you say about the company’s long-term prospects?
A. f(t) = -t(t - 8)(t - 18)(t - 18)
© Houghton Mifflin Harcourt Publishing Company
B. $2,535,000
C. f(15) = -945, the company lost $945,000 in 1995.
D. Possible answer: The company will continue to lose money after breaking
even in 1998.
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math in careers
MATH IN CAREERS
statistician According to data from the U.S. Census Bureau, the total number
of people in the United States labor force can be approximated by the function
T(x) = –0.011x 2 + 2x + 107, where x is the number of years since 1980 and T(x) is the
number of workers in millions. The number of women in the United States labor force can
be approximated by the function W(x) = –0.012x 2 + 1.26x + 45.5.
Statistician In this Unit Performance Task, students
can see how a statistician uses mathematics on
the job.
a. Use the function T(x) to estimate the number of workers in millions in 2010.
For more information about careers in mathematics
as well as various mathematics appreciation topics,
visit the American Mathematical Society
http://www.ams.org
b. Write a polynomial function M(x) that models the number of men in the labor force, and
explain how you found your function.
c. Use the function found in part b to estimate the number of male workers in
millions in 2010.
d. Explain how you could have found the answer to part c without using the function M(x).
a. 157.1
SCORING GUIDES
b. M(x) = 0.001x 2 + 0.74x + 61.5, M(x) = T(x) - W(x)
Task (6 points)
c. 84.6
a. 1 point for correct value
d. You can use the function W(x) to find the number of female
b. 1 point for correct function
1 point for explanation
workers in 2010 and subtract this value from the total number of
workers found in part a.
c. 1 point for correct value
d. 2 points for correct explanation
© Houghton Mifflin Harcourt Publishing Company
Unit 3
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