AnswersDHS Algebra 2 VGeometric Series

Geometric Series — Unit test Answers

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1
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Which statement about the polynomial function g(x) is true?

A
If all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
B
If all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
C
If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.
D
If the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.
2
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What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

Question illustration
A
–24, –3, 12
B
–12, 3, 24
C
–4, –2, 3
D
–3, 2, 4
3

A savings account pays 2% interest compounded annually. If $1,200 is deposited initially and again at the first of each year, how much money will be in the account three years after the initial deposit?

A
$1,248.48
B
$2,472.48
C
$3,672.48
D
$3,745.93
4

A rectangular prism with a volume of 400 cubic centimeters has the dimensions x + 1 centimeters, 2x centimeters, and x + 6 centimeters. The equation can be used to find x. What is the length of the longest side? Use a graphing calculator and a system of equations to find the answer.

Question illustration
A
4 centimeters
B
5 centimeters
C
8 centimeters
D
10 centimeters
5

What are the solutions of the equation x4 – 5x2 – 36 = 0? Use factoring to solve.

A
x = ±2 and x = ±3
B
x = ±2i and x = ±3
C
x = ±2 and x = ±3i
D
x = ±2i and x = ±3i
6

Which second degree polynomial function f(x) has a lead coefficient of 3 and roots 4 and 1?

A
f(x) = 3x2 + 5x + 4
B
f(x) = 3x2 + 15x + 12
C
f(x) = 3x2 – 5x + 4
D
f(x) = 3x2 – 15x + 12
7

You can use a system of equations to graph and solve the polynomial equation . Which statement is true?

Question illustration
A
The system has one solution, and the equation has three zeroes.
B
The y-coordinates of the solutions to the system and the zeroes of the equation are not equal.
C
The x-coordinates of the solutions to the system and the zeroes of the equation are not equal.
D
The equation has one zero, and the system has three solutions.
8

Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?

Question illustration
A
f(x) = x(x – a)2(x – b)4
B
f(x) = x(x – a)3(x – b)2
C
f(x) = x4(x – a)(x – b)2
D
f(x) = x2(x – a)5(x – b)
9

Which fraction represents the decimal 0.8888...?

A
StartFraction 80 Over 99 EndFraction
Option A
B
StartFraction 1,111 Over 1,250 EndFraction
Option B
C
Eight-ninths
Option C
D
Nine-eighths
Option D
10

According to the Rational Root Theorem, the following are potential roots of f(x) = 6x4 + 5x3 – 33x2 – 12x + 20., –2, 1, Which is an actual root of f(x)?

Question illustration
A
Negative five-halves
Option A
B
–2
C
1
D
Ten-thirds
Option D
11

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

Question illustration
A
–2, –1, 0, 2
B
–2, 0, 1, 2
C
–1, 0
D
0, 1
12

Which polynomial function could be represented by the graph below?

Question illustration
A
f(x) = x2 + x – 2
B
f(x) = 2x2 + 2x – 4
C
f(x) = x2 – x – 2
D
f(x) = 2x2 –2x – 4
13

A bungee jumper falls 97.2 feet before bouncing back up at the end of his bungee cord. Then he falls 64.8 feet before bouncing up again. On his third descent, he falls 43.2 feet before going back up. What is the total distance the bungee jumper drops after five falls if the distances continue in this pattern? (Do not include the distance traveled up.)

A
234.0 ft
B
253.2 ft
C
789.8 ft
D
1,281.8 ft
14

One root of a third degree polynomial function f(x) is –5 + 2i. Which statement describes the number and nature of all roots for this function?

A
f(x) has two real roots and one imaginary root.
B
f(x) has two imaginary roots and one real root.
C
f(x) has three imaginary roots.
D
f(x) has three real roots.
15

Which polynomial function has x-intercepts –1, 0, and 2 and passes through the point (1, –6)?

A
f(x) = x3 – x2 – 2x
B
f(x) = 3x3 – 3x2 – 6x
C
f(x) = x3 + x2 – 2x
D
f(x) = 3x3 + 3x2 – 6x
16

What are the solutions of the equation (x + 2)2 – 2(x + 2) – 15 = 0? Use u substitution to solve.

A
x = –7 and x = 1
B
x = –5 and x = 3
C
x = –3 and x = 5
D
x = –1 and x = 7
17

You can use a system of equations to graph and solve the polynomial equation . Which statement is true?

Question illustration
A
The system has one solution, and the equation has three zeroes.
B
The y-coordinates of the solutions to the system and the zeroes of the equation are not equal.
C
The x-coordinates of the solutions to the system and the zeroes of the equation are not equal.
D
The equation has one zero, and the system has three solutions.
18

A savings account pays 2% interest compounded annually. If $1,200 is deposited initially and again at the first of each year, how much money will be in the account three years after the initial deposit?

A
$1,248.48
B
$2,472.48
C
$3,672.48
D
$3,745.93
19

One root of a third degree polynomial function f(x) is –5 + 2i. Which statement describes the number and nature of all roots for this function?

A
f(x) has two real roots and one imaginary root.
B
f(x) has two imaginary roots and one real root.
C
f(x) has three imaginary roots.
D
f(x) has three real roots.
20

What are the solutions of the equation (x + 2)2 + 12(x + 2) – 14 = 0? Use u substitution and the quadratic formula to solve.

A
x = negative 8 plus-or-minus 5 StartRoot 2 EndRoot
Option A
B
x = negative 6 plus-or-minus 5 StartRoot 2 EndRoot
Option B
C
x = negative 4 plus-or-minus 5 StartRoot 2 EndRoot
Option C
D
x = negative 2 plus-or-minus 5 StartRoot 2 EndRoot
Option D

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