AnswersNC-Math 4 CRUnit Test

Unit Test — Unit test Answers

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Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–1 + i) + (21 + 5i)?

A
(–1 + i) + (21 + 5i) + 0
B
–1 + (i + 21) + 5i
C
(–1 + 21) + (i + 5i)
D
–(1 – i) + (21 + 5i)
2
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In triangle ABC, AB = 90 in., BC = 80 in., and angle B measures 50°. What is the approximate perimeter of the triangle?

A
242.4 in.
B
265.3 in.
C
308.3 in.
D
324.1 in.
3

Caleb and Emily are standing 100 yards from each other. Caleb looks up at a 45° angle to see a hot air balloon. Emily looks up at a 60° angle to see the same hot air balloon. Approximately how far is the hot air balloon off the ground?

A
44.3 yd.
B
63.4 yd.
C
73.2 yd.
D
89.7 yd.
4

Review the graph.

Question illustration
A
quadrant I
B
quadrant II
C
quadrant III
D
quadrant IV
5

A child designs a flag in the shape of a rhombus, as shown in the diagram below. Which expression can be used to determine the side length of the rhombus?

Question illustration
A
StartFraction 10 over cosine 30 degree EndFraction.
Option A
B
StartRoot 800 minus 800 cosine 30 degree EndRoot.
Option B
C
40 cosine 30 degree.
Option C
D
StartRoot 400 minus 40 cosine 30 degree EndRoot.
Option D
6

Let z = and .Which statement describes the geometric construction of the product zw on the complex plane?

Question illustration
A
Stretch z by a factor of 3 and rotate radians counterclockwise.
Option A
B
Stretch z by a factor of 3 and rotate radians counterclockwise.
Option B
C
Stretch z by a factor of 24 and rotate radians counterclockwise.
Option C
D
Stretch z by a factor of 24 and rotate radians counterclockwise.
Option D
7

The angle measures in a triangle are in the ratio 1:3:5. The longest side of the triangle measures 5 inches. What is the approximate perimeter of the triangle?

A
9.0 in.
B
9.4 in.
C
11.1 in.
D
12.7 in.
8

Let z = and .What is the product of zw?

Question illustration
A
40 (cosine (StartFraction pi Over 16 EndFraction) + I sine (StartFraction pi Over 16 EndFraction) )
Option A
B
76 (cosine (StartFraction pi Over 16 EndFraction) + I sine (StartFraction pi Over 16 EndFraction) )
Option B
C
40 (cosine (StartFraction 3 pi Over 16 EndFraction) + I sine (StartFraction 3 pi Over 16 EndFraction) )
Option C
D
76 (cosine (StartFraction 3 pi Over 16 EndFraction) + I sine (StartFraction 3 pi Over 16 EndFraction) )
Option D
9

The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 34i. Which statement must be true about the complex numbers?

A
The complex numbers have equal imaginary parts.
B
The complex numbers have equal real parts.
C
The complex numbers have opposite imaginary parts.
D
The complex numbers have opposite real parts.
10

Given w = and , what is w – z expressed in polar form?

Question illustration
A
StartRoot 2 EndRoot (cosine (StartFRaction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 EndFraction) )
Option A
B
StartRoot 2 EndRoot (cosine (StartFraction 3 pi Over 4 EndFraction) + I sine (StartFraction 3 pi Over 4 EndFraction) )
Option B
C
StartRoot 2 EndRoot (cosine (StartFraction 5 pi Over 4 EndFraction) + I sine (StartFraction 5 pi Over 4 EndFraction) )
Option C
D
StartRoot 2 EndRoot (cosine (StartFraction 7 pi Over 4 EndFraction) + I sine (StartFraction 7 pi Over 4 EndFraction) )
Option D
11

Solve: over the interval .

Question illustration
A
StartFraction pi Over 2 EndFraction
Option A
B
StartFraction 2 pi Over 3 EndFraction
Option B
C
StartFraction 3 pi Over 4 EndFraction
Option C
D
StartFraction 5 pi Over 6 EndFraction
Option D
12

Which expression is equivalent to cos(103°)cos(54°) – sin(103°)sin(54°)?

A
sin(49°)
B
cos(49°)
C
sin(157°)
D
cos(157°)
13

Review the incomplete steps in the derivation of the tangent sum identity.Which action can be taken to the expression in Step 3 to give an expression for Step 4?

Question illustration
A
divide both the numerator and denominator by sin(x)sin(y)
B
divide both the numerator and denominator by sin(x)cos(y)
C
divide both the numerator and denominator by cos(x)sin(y)
D
divide both the numerator and denominator by cos(x)cos(y)
14

Consider w1 = 4 + 2i and w2 = –1 – 3i. Which graph represents the sum w1 + w2?

A
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line goes from (0, 0) to point (3, negative 5).
Option A
B
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line goes from (0, 0) to point (3, negative 1).
Option B
C
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line goes from (0, 0) to point (5, 5).
Option C
D
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line goes from (0, 0) to point (5, 1).
Option D
15

Review the four points on the complex plane.

Question illustration
A
A
B
B
C
C
D
D
16

Given z1 = and , what is the value of z1 – z2?

Question illustration
A
cos(0) + isin(0)
B
cos(0) – isin(0)
C
cos() + isin()
Option C
D
cos() – isin()
Option D
17

A plane took off at a 15° angle to the ground and flew in Sydney’s direction. She is standing at a point 25 miles from the point where the plane took off. If the plane has traveled 20 miles in the air, about how far is Sydney from the airplane? Round your answer to the nearest whole number.

A
8 mi.
B
15 mi.
C
28 mi.
D
59 mi.
18

What is the exact value of sin(264°)cos(6°) + cos(264°)sin(6°)?

A
–1
B
Negative one-half
Option B
C
0
D
1
19

Let z = 9 – 2i and zw = 25 + 70i.What is w?

A
1 + 8i
B
1 – 8i
C
–1 + 8i
D
–1 – 8i
20

Which equation demonstrates the multiplicative identity property?

A
(negative 3 + 5 i) + 0 = negative 3 + 5 i
Option A
B
(negative 3 + 5 i ) (1) = negative 3 + 5 i
Option B
C
(negative 3 + 5 i) (negative 3 + 5 i) = negative 16 minus 30 i
Option C
D
(negative 3 + 5 i) (3 minus 5 i) = 16 + 30 i
Option D

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