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Mathematics

Algebra

Graded Assignment
Name:
MTH302B: Algebra II | Unit 8 | Lesson 4: Semester Test
Date:
Graded Assignment
Semester Test, Part 2
Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for
full credit.
(10 points)
1. Consider the function f(x) = x4 – 3x3 – 7x2 + 15x + 18.
Score
a. Find the possible rational roots of f(x) = 0.
b. Use synthetic division to divide f(x) by x – 3. Show all your work. Use your answer to
explain whether or not x – 3 is a factor of f(x).
c. Factor f(x) completely. Show all your work.
d. Sketch the graph of f(x) by plotting the x-intercepts, finding and plotting additional points on the graph, and
using what you know about the graph’s end behavior.
Answer:
(10 points)
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Copying or distributing without K12’s written consent is prohibited.
Page 1 of 4
Graded Assignment
2.
MTH302B: Algebra II | Unit 8 | Lesson 4: Semester Test
The population of frogs in a park is decreasing exponentially at a rate of 2% each year.
In the year 2006, the population was estimated to be 4800.
Score
a. Use the exponential decay formula to write an equation to model the situation.
b. Use your equation from Part a to predict the frog population in the year 2018.
c. Sketch the graph of the equation you wrote in Part a. Find its asymptote, domain, and range.
Answer:
(8 points)
3.
An office manager recorded the number of reams of paper that were used for a printer
each month for six months: 15, 10, 25, 19, 10, 17.
Score
a. Identify the five-number summary of the data set.
b. Draw the box-and-whisker plot.
c. Compute the standard deviation. Show all your work.
Answer:
© 2010 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 2 of 4
Graded Assignment
MTH302B: Algebra II | Unit 8 | Lesson 4: Semester Test
(10 points)
4.
A home furnishings store has two locations, one in the north and one in the south. The
matrices below show the costs of their most popular sheet set, in dollars, and the current
inventory of the sets in two colors at both locations.
T
w
i
n
Q
u
e
e
n
K
i
n
g
C
=
c
o
s
t
2
4 3
9 4
9
Northern Location
White Beige
Twin 6
N = Queen
8
King
7
11
4
3
Score
SouthernLocation
White Beige
Twin 14
S = Queen
1
King
5
13
6
8
a. Find CN and CS.
b. Tell which location has the greater dollar value of beige sheets in their inventory, and find the difference in
these dollar values.
c. Find CN + CS. Describe what each element in the matrix represents.
Answer:
© 2010 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 3 of 4
Graded Assignment
MTH302B: Algebra II | Unit 8 | Lesson 4: Semester Test
Your Score
© 2010 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
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