AnswersDHS Algebra 2 VGeometric Series

Geometric Series — Unit test Answers

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21
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Which geometric series converges?

A
StartFraction 1 Over 81 EndFraction + StartFraction 1 Over 27 EndFraction + one-ninth + one-third + ellipsis
Option A
B
1 + one-half + one-fourth + one-eighth + ellipsis
Option B
C
Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 7 (negative 4) Superscript n minus 1
Option C
D
Sigma-Summation Underscript n = 1 Overscript infinity EndScripts one-fifth (2) Superscript n minus 1
Option D
22
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A polynomial function has a root of –6 with multiplicity 1, a root of –2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?

A
The graph of the function is positive on (–6, –2).
B
The graph of the function is negative on (, 0).
Option B
C
The graph of the function is positive on (–2, 4).
D
The graph of the function is negative on (4, ).
Option D
23

A polynomial function has a root of –3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, and a root of 3 with multiplicity 2. If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?

A
mc015-1.jpg
Option A
B
mc015-2.jpg
Option B
C
mc015-3.jpg
Option C
D
mc015-4.jpg
Option D
24

What is the sum of the first seven terms of the geometric series?3 + 12 + 48 + 192 + ...

A
4,372
B
12,288
C
16,383
D
65,535
25

Which of the following is the complete list of roots for the polynomial function ?

Question illustration
A
–3 + 2i, –3 – 2i
B
–2, –4
C
–2, –4, –3 + 2i, –3 – 2i
D
–2, –4, –3 + 2i, 3 + 2i
26

Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
27

The polynomial function is graphed below.Which is a potential rational root of f(x) at point P?

Question illustration
A
The root at point P may be .
Option A
B
The root at point P may be .
Option B
C
The root at point P may be .
Option C
D
The root at point P may be .
Option D
28

A hospital sends an invoice to a patient. The patient schedules a payment plan in which she makes an initial payment of $1,451 the first month and then pays one-third of the previous month’s payment each of the following months until the invoice is paid in full. Approximately how much of the invoice will be paid after the fourth month?

A
$1,451.00
B
$2,095.89
C
$2,149.63
D
$2,167.54
29

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

Question illustration
A
–6, 6
B
–4, 1, 3
C
–3, –1, 4
D
1, 3
30

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?

A
, , , 5
Option A
B
, 1, , 11
Option B
C
, , , , , 5, 11
Option C
D
0, , , , , , 5, 11
Option D
31

Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots and 2?

Question illustration
A
f (x) = 3 x cubed minus 6 x squared minus 15 x + 30
Option A
B
f (x) = x cubed minus 2 x squared minus 5 x + 10
Option B
C
f (x) = 3 x squared minus 21 x + 30
Option C
D
f (x) = x squared minus 7 x + 10
Option D
32

Which polynomial function has a leading coefficient of 1, roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2?

A
f(x) = 2(x + 7)(x + 5)(x – 2)
B
f(x) = 2(x – 7)(x – 5)(x + 2)
C
f(x) = (x + 7)(x + 5)(x + 5)(x – 2)
D
f(x) = (x – 7)(x – 5)(x – 5)(x + 2)
33

Use synthetic division to solve (x4 – 1) ÷ (x – 1). What is the quotient?

A
x cubed minus x squared + x minus 1
Option A
B
x3
C
x cubed + x squared + x + 1
Option C
D
x3 – 2
34

Which of the following is the complete list of roots for the polynomial function ?

Question illustration
A
–3 + 2i, –3 – 2i
B
–2, –4
C
–2, –4, –3 + 2i, –3 – 2i
D
–2, –4, –3 + 2i, 3 + 2i
35

What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve.

A
x = StartFraction negative 4 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction
Option A
B
x = StartFraction negative 7 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction
Option B
C
x = –7 and x = –2
D
x = –1 and x = 4
36

A polynomial function has a root of –6 with multiplicity 1, a root of –2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?

A
The graph of the function is positive on (–6, –2).
B
The graph of the function is negative on (, 0).
Option B
C
The graph of the function is positive on (–2, 4).
D
The graph of the function is negative on (4, ).
Option D
37

If (x – 2k) is a factor of f(x), which of the following must be true?

A
f(2k) = 0
B
f(–2k) = 0
C
A root of f(x) is x = –2k.
D
A y intercept of f(x) is x = 2k.
38

A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his break, he paints half of the remaining unpainted portion and then takes another break. If he continues to paint half of the remaining unpainted portion between breaks, approximately what portion of the original wall will be painted when he takes his fifth break?

A
112.50 ft2
B
145.31 ft2
C
147.66 ft2
D
290.63 ft2
39

The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

A
She is incorrect because systems may have only complex solutions which are not visible on a graph.
B
She is incorrect because the solutions may have multiplicity greater than 1.
C
She is correct because all solutions are intersection points of the graphs.
D
She is correct because the solutions are irrational.
40

What are the solutions of the equation (x – 3)2 + 2(x – 3) – 8 = 0? Use u substitution to solve.

A
x = –5 and x = 1
B
x = –1 and x = 5
C
x = –1 and x = –7
D
x = 1 and x = 7

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