AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S1_2024Radical Equations and Extraneous Roots

Radical Equations and Extraneous Roots — Cumulative exam Answers

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1
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Which expression is equivalent to ?

Question illustration
A
5 StartRoot 3 EndRoot i
Option A
B
6 StartRoot 3 EndRoot i
Option B
C
7 StartRoot 3 EndRoot i
Option C
D
8 StartRoot 3 EndRoot i
Option D
2
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What is the value of 53i 9?

A
–125i
B
–15i
C
15i
D
125i
3

If m(x) = x2 + 3 and n(x) = 5x + 9, which expression is equivalent to (mn)(x)?

A
5x3 + 9x2 + 15x + 27
B
25x2 + 90x + 84
C
x2 + 5x + 12
D
5x2 + 24
4

For which pair of functions is ?

Question illustration
A
f(a) = a2 – 4 and
Option A
B
and g(a) = 2a – 2
Option B
C
f(a) = 5 + a2 and
Option C
D
f(a) = 3 – 3a and g(a) = 4a – 5
5

Which of the following graphs could be the graph of the function f(x) = x3 + 8?

A
mc019-1.jpg
Option A
B
mc019-2.jpg
Option B
C
mc019-3.jpg
Option C
D
mc019-4.jpg
Option D
6

Which two functions are inverses of each other?

A
,
Option A
B
,
Option B
C
,
Option C
D
,
Option D
7

What is the product? Assume

Question illustration
A
3 x StartRoot 5 EndRoot + 3 StartRoot 165 x EndRoot + 10 StartRoot 6 EndRoot
Option A
B
3 x StartRoot 5 EndRoot + 6 StartRoot 10 x EndRoot + 5 StartRoot 3 x EndRoot + 10 StartRoot 6 EndRoot
Option B
C
3 x StartRoot 5 EndRoot + 10 StartRoot 6 EndRoot
Option C
D
StartRoot 3 x EndRoot + 5 StartRoot 3 x EndRoot + 10 StartRoot 6 EndRoot
Option D
8

What is the following product?

Question illustration
A
–2
B
2
C
22 –
Option C
D
98 –
Option D
9

What is the value of (–3 + 3i) + (–2 + 3i)?

A
–5 – 6i
B
–5 + 6i
C
5 + 6i
D
5 – 6i
10

What is the solution to the equation ?

Question illustration
A
x = –3
B
x = –3 and x = 0
C
x = 0 and x = 3
D
x = 3
11

Which equation could generate the curve in the graph below?

Question illustration
A
y = 9x2 + 6x + 4
B
y = 6x2 – 12x – 6
C
y = 3x2 + 7x + 5
D
y = 2x2 + 8x + 8
12

What is the simplified form of the following expression?

Question illustration
A
2 StartRoot 2 EndRoot
Option A
B
5 StartRoot 2 EndRoot
Option B
C
9 StartRoot 2 EndRoot
Option C
D
15 StartRoot 2 EndRoot
Option D
13

What is the solution of ?

Question illustration
A
c = 0 and c = 3
B
all real numbers
C
all real numbers, except c ¹ 0 and c ¹ 3
D
no solution
14

Which expression is equivalent to (4 + 7i)(3 + 4i)?

A
–16 + 37i
B
12 – 28i
C
16 – 37i
D
37 + 16i
15

What is the following sum?

Question illustration
A
4 x (RootIndex 3 StartRoot 2 y EndRoot) + 12 x squared y (RootIndex 3 StartRoot 2 y squared EndRoot)
Option A
B
8 x (RootIndex 3 StartRoot x y EndRoot) + 12 x cubed y squared (RootIndex 3 StartRoot 6 y EndRoot)
Option B
C
16 x cubed y (RootIndex 3 StartRoot 2 y squared EndRoot)
Option C
D
48 x cubed y (RootIndex 3 StartRoot 2 y EndRoot)
Option D
16

A polynomial function has a root of –4 with multiplicity 4, a root of –1 with multiplicity 3, and a root of 5 with multiplicity 6. If the function has a positive leading coefficient and is of odd degree, which could be the graph of the function?

A
mc016-1.jpg
Option A
B
mc016-2.jpg
Option B
C
mc016-3.jpg
Option C
D
mc016-4.jpg
Option D
17

If the discriminant of a quadratic equation is equal to , which statement describes the roots?

Question illustration
A
There are two complex roots.
B
There are two real roots.
C
There is one real root.
D
There is one complex root.
18

The function that represents the average cost per person, including transportation, to a museum is . Which statement is true about the graph of the function?

Question illustration
A
The horizontal asymptote y = 0 means the cost approaches zero as the number of people increases.
B
The horizontal asymptote y = 8 means the average cost approaches $8 as the number of people increases.
C
The vertical asymptote x = 0 means the cost approaches zero as the number of people increases.
D
The vertical asymptote x = 8 means the cost approaches zero as the number of people increases.
19

The graph below shows the number of houses sold over x days. What is the average rate of change from day 2 to day 10?

Question illustration
A
Negative four-thirds
Option A
B
Negative three-fourths
Option B
C
6
D
8
20

What is the binomial expansion of (x + 2y)7?

A
2x7 + 14x6y + 42x5y2 + 70x4y3 + 70x3y4 + 42x2y5 + 14xy6 + 2y7
B
x7 + 14x6y + 42x5y2 + 70x4y3 + 70x3y4 + 42x2y5 + 14xy6 + y7
C
x7 + 7x6y + 21x5y2 + 35x4y3 + 35x3y4 + 21x2y5 + 7xy6 + y7
D
x7 + 14x6y + 84x5y2 + 280x4y3 + 560x3y4 + 672x2y5 + 448xy6 + 128y7

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