AnswersGA-Advanced Algebra Concepts and Connections B ULHSUnit Test

Unit Test — Unit test Answers

25 verified answers1 views
1
Free Preview

What are the values of m and in the diagram below?

Question illustration
A
,
Option A
B
,
Option B
C
,
Option C
D
,
Option D
2
Free Preview

Which is the graph of y = cos(x) + 3?

A
On a coordinate plane, a cosine curve has a maximum of 3 and a minimum of negative 3.
Option A
B
On a coordinate plane, a cosine curve has a maximum of 4 and a minimum of negative 2.
Option B
C
On a coordinate plane, a cosine curve has a maximum of negative 2 and a minimum of negative 4.
Option C
D
On a coordinate plane, a cosine curve has a maximum of 6 and a minimum of negative 0.
Option D
3

The point P(x, y) is on the terminal ray of angle . If is between radians and radians and csc = , what are the coordinates of P(x, y)?

Question illustration
A
P(, –2)
Option A
B
P (, –2)
Option B
C
P(–2, )
Option C
D
P(–2, )
Option D
4

An object is attached to a spring that is stretched and released. The equation models the distance, d, of the object in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 6 inches above the rest position? Round to the nearest hundredth, if necessary.

Question illustration
A
0 seconds
B
1.38 seconds
C
4.62 seconds
D
8 seconds
5

Three trigonometric functions for a given angle are shown below.What are the coordinates of point (x, y) on the terminal ray of angle , assuming that the values above were not simplified?

Question illustration
A
(–5, 12)
B
(5, –12)
C
(–12, 5)
D
(12, –5)
6

The angle measures associated with which set of ordered pairs share the same reference angle?

A
(Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction , negative one-half), (negative one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option A
B
(one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half)
Option B
C
(Negative one-half, negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (One-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option C
D
(StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half), (one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option D
7

What is the range of y = –3sin(x) – 4?

A
all real numbers
Option A
B
all real numbers
Option B
C
all real numbers
Option C
D
all real numbers
Option D
8

Which shows all the exact solutions of ? Give your answer in radians.

Question illustration
A
and
Option A
B
and
Option B
C
, , , and
Option C
D
, , , and
Option D
9

The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation . Which of the following is the graph of this equation?

Question illustration
A
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (2, 8), and then decreases to (6, 2).
Option A
B
On a coordinate plane, a curve crosses the y-axis at (0, 8). It decreases to (4, 2), and then increases to (8, 8).
Option B
C
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (1, 8), and then decreases to (3, 2).
Option C
D
On a coordinate plane, a curve crosses the y-axis at (0, 5). It decreases to (2, 1), and then increases to (3, 8).
Option D
10

What is the equation of the graph below?

Question illustration
A
y = sine (x + 90 degrees)
Option A
B
y = cosine (x + 90 degrees)
Option B
C
y = sine (x + 45 degrees)
Option C
D
y = cosine (x + 45 degrees)
Option D
11

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.

A
h = negative 10 sine (StartFraction pi Over 15 EndFraction t) + 35
Option A
B
h = negative 10 sine (Pi t) + 35
Option B
C
h = 10 sine (StartFraction pi Over 15 EndFraction t) + 35
Option C
D
h = 10 sine (Pi t) + 35
Option D
12

Which of the following is the graph of y = cos(2x)?

A
mc008-1.jpg
Option A
B
mc008-2.jpg
Option B
C
mc008-3.jpg
Option C
D
mc008-4.jpg
Option D
13

What is the range of ?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
14

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.

A
h = 0.5 cosine (StartFraction pi Over 12 EndFraction t) + 9.5
Option A
B
h = 0.5 cosine (StartFraction pi Over 6 EndFraction t) + 9.5
Option B
C
h = cosine (StartFraction pi Over 12 EndFraction t) + 9
Option C
D
h = cosine (StartFraction pi Over 6 EndFraction t) + 9
Option D
15

Which of the following could be the equation of the function below?

Question illustration
A
y = negative 3 sine (2 (x + pi)) + 2
Option A
B
y = negative 3 sine (x + pi) + 2
Option B
C
y = 3 sine (4 (x minus pi)) + 4
Option C
D
y = 3 sine (2 (x + pi)) + 2
Option D
16

The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when and that the windmill turns counterclockwise at a constant rate.

Question illustration
A
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 10
Option A
B
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 30
Option B
C
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 10
Option C
D
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 30
Option D
17

Which of the following best explains the value of on the unit circle below?

Question illustration
A
The length opposite the angle is the vertical distance from the x-axis on the graph.
Option A
B
The length adjacent to the angle is the vertical distance from the x-axis on the graph.
Option B
C
The length opposite the angle is the horizontal distance from the y-axis on the graph.
Option C
D
The length adjacent to the angle is the horizontal distance from the y-axis on the graph.
Option D
18

Which is equivalent to ? Give your answer in radians.

Question illustration
A
0
B
mc026-2.jpg
Option B
C
mc026-3.jpg
Option C
D
mc026-4.jpg
Option D
19

Consider the relationship below, given .Which of the following best explains how this relationship and the value of sin can be used to find the other trigonometric values?

Question illustration
A
The values of sin and cos represent the legs of a right triangle with a hypotenuse of 1; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.
Option A
B
The values of sin and cos represent the angles of a right triangle; therefore, solving the relationship will find all three angles of the triangle, and then all trigonometric values can be found.
Option B
C
The values of sin and cos represent the angles of a right triangle; therefore, other pairs of trigonometric ratios will have the same sum, 1, which can then be used to find all other values.
Option C
D
The values of sin and cos represent the legs of a right triangle with a hypotenuse of –1, since is in Quadrant II; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.
Option D
20

Which of the following could be the equation of the function below?

Question illustration
A
y = 0.5 cosine (2 (x minus StartFraction pi Over 2 EndFraction)) + 2
Option A
B
y = 0.5 cosine (4 (x minus StartFraction pi Over 2 EndFraction)) minus 2
Option B
C
y = 0.5 cosine (4 (x + pi)) + 2
Option C
D
y = 0.5 cosine (2 (x minus pi)) minus 2
Option D

Did you find these answers helpful?

More from this Course

Quiz
25 verified answers

Unit Test

Quiz
25 verified answers

Unit Test

Quiz
10 verified answers

Simplifying Rational Expressions

Unit Test — Unit test Answers — GA-Advanced…