AnswersCommon Core Algebra II A-ICSimplifying Rational Expressions

Simplifying Rational Expressions — Unit test Answers

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1
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What is the quotient in simplest form? Assume .

Question illustration
A
Negative StartFraction m Superscript 12 Baseline n Superscript 6 Baseline Over 2 EndFraction
Option A
B
Negative StartFraction m Superscript 27 Baseline n Superscript 8 Baseline Over 2 EndFraction
Option B
C
6 m Superscript 12 Baseline n Superscript 6 Baseline
Option C
D
8 m Superscript 12 Baseline n Superscript 6 Baseline
Option D
2
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The resistance, R, to electricity of a cylindrical-shaped wire is given by the equation , where p represents the resistivity of the wire’s material, L represents the length of the wire, and d represents the diameter of the wire. What happens to the resistance of the wire as the diameter approaches 0?

Question illustration
A
The resistance approaches 0.
B
The resistance approaches .
Option B
C
The resistance approaches L.
D
The resistance approaches infinity.
3

Riley makes a mistake in step 2 while doing her homework. What was her mistake? Step 1: Step 2: Step 3: Step 4:

Question illustration
A
She added the two fractions incorrectly.
B
She used the wrong common denominator.
C
She did not distribute the negative correctly.
D
She did not multiply the first fraction by a factor.
4

Which statement is true about the discontinuities of the function f(x)?

Question illustration
T
There is a hole at x = 2.
T
There are asymptotes at x = 0 and x = –1.
T
There are asymptotes at x = 0 and x = –1 and a hole at .
Option T
T
There are holes at x = 0 and x = –1 and an asymptote at x = 2.
5

A certain company has a fixed cost of $200 per day. It costs the company $3.10 per unit to make its products. The company is tracking its average cost to make x units using . Which statement is true?

Question illustration
A
The horizontal asymptote of y = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.
B
The horizontal asymptote of y = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.
C
The vertical asymptote of x = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.
D
The vertical asymptote of x = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.
6

Which expression is equivalent to ? Assume .

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

Using V = lwh, what is an expression for the volume of the following rectangular prism?

Question illustration
A
StartFraction 15 Over 2 x EndFraction
Option A
B
StartFraction 3 x + 12 Over 2 x + 8 EndFraction
Option B
C
StartFraction 15 Over 2 x + 2 EndFraction
Option C
D
Fifteen-eighths
Option D
8

Which expression is equivalent to the following complex fraction?

Question illustration
A
StartFraction y + x Over y minus x EndFraction
Option A
B
StartFraction (y minus x) (y + x) Over x squared y squared EndFraction
Option B
C
StartFraction x squared y squared Over (y + x) (y + x) EndFraction
Option C
D
StartFraction y minus x Over y + x EndFraction
Option D
9

For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1?

Question illustration
a
a = –1, m = 0
a
a = 1, m = 0
a
a = –1, m = 1
a
a = 1, m = 1
10

What is the quotient in simplified form? Assume .

Question illustration
A
Negative StartFraction 4 a Superscript 12 Baseline b Superscript 8 Baseline Over 5 EndFraction
Option A
B
Negative StartFraction 4 a Superscript 32 Baseline b Superscript 5 Baseline Over 5 EndFraction
Option B
C
StartFraction a Superscript 12 Baseline b Superscript 8 Baseline Over 80 EndFraction
Option C
D
StartFraction a Superscript 32 Baseline b Superscript 5 Baseline Over 80 EndFraction
Option D
11

What is the product?

Question illustration
A
StartFraction k + 1 Over k squared EndFraction
Option A
B
StartFraction k minus 1 Over k squared EndFraction
Option B
C
StartFraction negative 1 Over k EndFraction
Option C
D
StartFraction 1 Over k EndFraction
Option D
12

Which expression is equivalent to ?

Question illustration
A
StartFraction 1 Over x EndFraction
Option A
B
StartFraction 1 Over x Superscript 5 Baseline EndFraction
Option B
C
StartFraction 1 Over x Superscript 9 Baseline EndFraction
Option C
D
StartFraction 1 Over x Superscript 24 Baseline EndFraction
Option D
13

Which graph represents the function ?

Question illustration
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 3, and the horizontal asymptote is at y = negative 2.
Option A
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens down and to the left in quadrants 2 and 3. A vertical asymptote is at x = 3, and the horizontal asymptote is at y = negative 2.
Option B
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens down and to the left in quadrants 2 and 3. A vertical asymptote is at x = negative 3, and the horizontal asymptote is at y = 2.
Option C
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1 , and the other curve opens down and to the left in quadrants 2, 1, and 4. A vertical asymptote is at x = 3, and the horizontal asymptote is at y = 2.
Option D
14

For the inverse variation equation , what is the value of p when V = ?

Question illustration
A
Option
Option A
B
Option
Option B
2
2
3
32
15

What are the vertical and horizontal asymptotes for the function ?

Question illustration
A
vertical asymptote: x = 1horizontal asymptote: none
B
vertical asymptote: x = 1horizontal asymptote: y = 0
C
vertical asymptote: x = –2, x = 3horizontal asymptote: y = 0
D
vertical asymptote: x = –2, x = –3horizontal asymptote: none

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