AnswersCUSD Advanced Math A 5.0Distance and Midpoints in the Complex Plane

Distance and Midpoints in the Complex Plane — Unit test Answers

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1
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The following statements concern the modulus. Which statement is false?

A
The modulus represents the distance between the complex number and the origin.
B
The algorithm to find the modulus is based on the Pythagorean theorem.
C
The modulus is sometimes negative because of the computations with i.
D
The modulus is an extension of the absolute value in the complex plane.
2
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Which statements about the function are true? Select three options.

A
The vertex of the function is at (–4,–15).
B
The vertex of the function is at (–3,–16).
C
The graph is increasing on the interval x > –3.
D
The graph is positive only on the intervals where x 1.
E
The graph is negative on the interval x < –4.
3

An isosceles triangle’s altitude will bisect its base. Which expression could be used to find the area of the isosceles triangle above?

Question illustration
A
StartFraction start root 40 end root . start root 40 end root over 2 EndFraction
Option A
B
StartFraction start root 40 end root . start root 68 end root over 2 EndFraction
Option B
C
StartFraction start root 232 end root . start root 288 end root over 2 EndFraction
Option C
D
StartFraction start root 232 end root . start root 164 end root over 2 EndFraction
Option D
4

What is the greatest possible integer value of x for which is an imaginary number?

Question illustration
A
3
B
4
C
5
D
6
5

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x?

A
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 15 EndRoot Over 11 EndFraction
Option A
B
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction 2 StartRoot 15 EndRoot Over 11 EndFraction
Option B
C
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot Over 11 EndFraction
Option C
D
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot i Over 11 EndFraction
Option D
6

Which equation is an example of the commutative property of multiplication?

A
(4 + 2i) = (2i + 4)
B
(4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i)
C
(4 + 2i)(3 – 5i) = (4 + 2i)(3 – 5i)(1)
D
(4 + 2i) = (4 + 2i + 0)
7

What is the y-value of the vertex of the function f(x)=−(x+8)(x−14)?

A
3
B
6
C
112
D
121
8

A point of the form 25 +bi is 37 units from 13 – 31i. What is the value of b?

A
4
B
6.6
C
36.6
D
40.6
9

The following statements are about finding a midpoint of a segment in the complex plane. Which statement is false?

A
The midpoint is the average of the endpoints.
B
First add the endpoints and then multiply by 1/2.
C
First subtract the endpoints and then divide by 2.
D
The midpoint of complex conjugates will lie on the x-axis.
10

If the discriminant of a quadratic equation is 4, which statement describes the roots?

A
There are two complex roots.
B
There are two real roots.
C
There is one real root.
D
There is one complex root.
11

Which point shows the location of 5 – 2i on the complex plane below?

Question illustration
A
point A
B
point B
C
point C
D
point D
12

What is the sum of 12 – 5i and –3 + 4i?

A
–16 + 63i
B
9 – i
C
9 – 9i
D
15 – 9i
13

Solve for in the equation .

Question illustration
A
x = 3 plus-or-minus StartRoot 23 EndRoot
Option A
B
x = 3 plus-or-minus StartRoot 51 EndRoot
Option B
C
x = 3 plus-or-minus StartRoot 41 EndRoot
Option C
D
x = 3 plus-or-minus StartRoot 5 EndRoot
Option D
14

What are the values of x in the equation x2 – 6x + 9 = 25?

A
x = –2 or x = 8
B
x = –1 or x = –11
C
x = 1 or x = 11
D
x = 2 or x = –8
15

Which pair of complex numbers has a real-number product?

A
(1 + 3i)(6i)
B
(1 + 3i)(2 – 3i)
C
(1 + 3i)(1 – 3i)
D
(1 + 3i)(3i)
16

What is the value of i 20+1?

A
1
B
–1
C
–i
D
i
17

Which function has a vertex on the y-axis?

A
f(x) = (x – 2)2
B
f(x) = x(x + 2)
C
f(x) = (x – 2)(x + 2)
D
f(x) = (x + 1)(x – 2)
18

For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?

A
0
B
9
C
12
D
16
19

Solve for in the equation .

Question illustration
A
x = negative 11 plus-or-minus StartFraction 25 Over 2 EndFraction
Option A
B
x = negative eleven-halves plus-or-minus StartFraction 25 Over 2 EndFraction
Option B
C
x = negative 11 plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Option C
D
x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Option D
20

For what values of m does the graph of y = mx2 – 5x – 2 have no x-intercepts?

A
m greater-than negative StartFraction 25 Over 8 EndFraction
Option A
B
m less-than negative StartFraction 25 Over 8 EndFraction
Option B
C
m less-than StartFraction 25 Over 8 EndFraction
Option C
D
m greater-than StartFraction 25 Over 8 EndFraction
Option D

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