AnswersDSD-CR-Secondary Math III-Term 2Unit Test

Unit Test — Unit test Answers

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Which second degree polynomial function has a leading coefficient of 2 and roots –3 and 5?

A
f(x) = 2x2 + 4x – 30
B
f(x) = 2x2 + 2x – 15
C
f(x) = 2x2 – 4x – 30
D
f(x) = 2x2 – 2x – 15
2
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A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?

A
The graph of the function is positive on (2, 4).
B
The graph of the function is negative on (4, ).
Option B
C
The graph of the function is positive on (, –7).
Option C
D
The graph of the function is negative on (–7, –1).
3

What is the end behavior of the graph of the polynomial function f(x) = –x5 + 9x4 – 18x3?

A
As , and as , .
Option A
B
As , and as , .
Option B
C
As , and as , .
Option C
D
As , and as , .
Option D
4

If (x – 5) is a factor of f(x), which of the following must be true?

A
A root of f(x) is x = –5.
B
A root of f(x) is x = 5.
C
Both x = –5 and x = 5 are roots of f(x).
D
Neither x = –5 nor x = 5 is a root of f(x).
5

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)
6

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
7

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
8

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
9

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
10

Which expression is equivalent to 9x – (x – 8)(x + 1) + 10x?

A
mc009-1.jpg
Option A
B
mc009-2.jpg
Option B
C
mc009-3.jpg
Option C
D
mc009-4.jpg
Option D
11

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
12

Which geometric series diverges?

A
Three-fifths + three-tenths + three-twentieths + StartFraction 3 Over 40 EndFraction + ellipsis
Option A
B
Negative 10 + 4 minus eight-fifths + StartFraction 16 Over 25 EndFraction minus ellipsis
Option B
C
Sigma-Summation Underscript n = 1 Overscript infinity EndScripts two-thirds (negative 4) Superscript n minus 1
Option C
D
Sigma-Summation Underscript n = 1 Overscript infinity EndScripts (negative 12) (one-fifth) Superscript n minus 1
Option D
13

The price that a company charged for a computer accessory is given by the equation where x is the number of accessories that are produced, in millions. It costs the company $10 to make each accessory. The company currently produces 2 million accessories and makes a profit of 100 million dollars. What other number of accessories produced yields the same profit?

Question illustration
A
1.45 million
B
3.45 million
C
40 million
D
48 million
14

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

A
f(k) = 0
B
f(–k) = 0
C
A root of f(x) is x = k.
D
A y intercept of f(x) is x = –k.
15

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.

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