AnswersNY-Algebra II Term 2 HillcrestUnit Test

Unit Test — Unit test Answers

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Which of the following are in the correct order from least to greatest?

A
, , 80°, , 38°
Option A
B
38°, 80°, , ,
Option B
C
38°, , 80°, ,
Option C
D
, 38°, 80°, ,
Option D
2
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Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 3 by 2 at (3 pi by 2, comma negative 3 by 2 ) and (negative pi by 2 by negative 3 by 2) and y equals negative 5 by 2 at ( pi by 2 comma negative 5 by 2) and (negative 3 pi by 2 comma negative 5 by 2).
Option A
B
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 at (3 pi by 2 comma negative 1) and (negative pi by 2 comma negative 1) and y equals negative 3 at (pi by 2 comma negative 3) and (negative 3 pi by 2 comma negative 3).
Option B
C
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 at (pi comma negative 1) and (negative pi comma negative 1) and y equals negative 3 at (0 comma negative 3).
Option C
D
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 point 8 at (0 comma negative 1 point 8) and y equals negative 2 point 2 at (pi comma negative 2 point 2) and (negative pi comma negative 2 point 2).
Option D
3

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
4

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
5

Which of the following is the equation of the function below?

Question illustration
A
y equal to 2 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.
Option A
B
y equal to 2 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) minus 1 right-square-bracket.
Option B
C
y equal to 0 point 5 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.
Option C
D
y equal to 0 point 5 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) right-square-bracket minus 1.
Option D
6

Haruto simplified the value below.Which statement explains whether Haruto is correct?

Question illustration
A
Haruto is correct because the angle is coterminal with and the reference angle is .
Option A
B
Haruto is correct because the angle is coterminal with , which is also the reference angle.
Option B
C
Haruto is not correct because the angle is coterminal with , and .
Option C
D
Haruto is not correct because the angle is coterminal with , and .
Option D
7

Suppose you want to transform the graph of the function into the graph of the function . Which transformations should you perform?

Question illustration
A
Reflect the graph of the first function across the x-axis, translate it units to the left, and translate it 2 units up.
Option A
B
Reflect the graph of the first function across the x-axis, translate it units to the right, and translate it 2 units up.
Option B
C
Reflect the graph of the first function across the line , translate it units to the left, and translate it 2 units up.
Option C
D
Reflect the graph of the first function across the line , translate it units to the right, and translate it 2 units up.
Option D
8

Which function describes the graph below?

Question illustration
A
f (x) = 6 cosine (x)
Option A
B
f (x) = 3 cosine (x) + 3
Option B
C
f (x) = 6 sine (x)
Option C
D
f (x) = 3 sine (x) + 3
Option D
9

If angle B measures 25°, what is the approximate perimeter of the triangle below?

Question illustration
A
10.3 units
B
11.8 units
C
22.1 units
D
25.2 units
10

What is the period of the function ?

Question illustration
A
units
Option A
B
units
Option B
C
units
Option C
D
units
Option D
11

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
12

What is 270° converted to radians?

A
StartFraction pi Over 6 EndFraction
Option A
B
StartFraction 3 Over 2 EndFraction
Option B
C
StartFraction 3 pi Over 2 EndFraction
Option C
D
3
13

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
14

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
15

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
16

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
17

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
18

What is the length of x in the diagram below?

Question illustration
A
StartFraction 5 Over StartRoot 3 EndRoot
Option A
B
StartFraction 10 Over StartRoot 3 EndRoot EndFraction
Option B
C
5 StartRoot 3 EndRoot
Option C
D
10
19

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
20

What is the simplest form of the expression below?

Question illustration
A
sec
Option A
B
cot
Option B
C
csc
Option C
D
tan
Option D

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