University Neighborhood High School Algebra 2 Unit 5 Evaluation Worksheet

Hello,

I need this test completed fully and correctly. A graphing calculator may be needed.

If you need anything, please let me know.

Thank you!

B

Name
_________________________________
I.D. Number
_______________________
Unit 5 Evaluation
Evaluation 05
Second Year Algebra 2
(MTHH 040 059)
This evaluation will cover the lessons in this unit. It is open book, meaning you can use your syllabus
and other course materials. You will need to understand, analyze, and apply the information you
have learned in order to answer the questions correctly. To submit the evaluation by mail, follow the
directions on your Enrollment Information Sheet. To take the evaluation online, access the online
version of your course; use the navigation panel to access the prep page for this evaluation and
follow the directions provided. Note: A graphing calculator may be used on unit evaluations. You
may also use scratch paper to work out the solutions.
Multiple-Choice
Select the response that best completes the statement or answers the question.
_____ 1. A periodic function goes through 5 complete cycles in 4 minutes. What is the period of the
function?
1
min
5
1
b.
min
4
a.
c. 48 s
d. 75 s
_____ 2. The period of a periodic function is 8 s. How many cycles does it go through in 30 s?
a.
4
15
b. 3.75
c. 22
d. 240
_____ 3. Which of the following is not the graph of a periodic function?
a. I
b. II
c. III
d. both II and III
Unit 5 Evaluation
319
MTHH 040
_____ 4. The amplitude of a periodic function is 2.5 and its minimum value is 0. What is the
function’s maximum value?
a. −2.5
b. 0
c. 2.5
d. 5.0
_____ 5. Which angle in standard position is not coterminal with the others?
a. −190°
b. −170°
c. 190°
d. 550°
_____ 6. An angle drawn in standard position has a terminal side that passes through the point
( 2 , − 2 ). What is one possible measure of the angle?
a. 45°
b. 225°
c. 315°
d. 330°
_____ 7. An angle of 120° is in standard position. What are the coordinates of the point at which the
terminal side intersects the unit circle?
1 3
a.  ,
 2 2 


 1
3
b.   , 

 2
2 


3 1
,
c.  
 2 2 


 1 3
d.   ,
 2 2 


_____ 8. An angle of −225° is in standard position. Which points can lie on the terminal side of the
angle?
 2
2
,
I. 

 2
2 


2 2
,
II.  
 2 2 



2
2
,
III.  

 2
2 

IV. (−1, 1)
a. I and II
b. II and III
c. II and IV
d. I and III
Unit 5 Evaluation
320
MTHH 040
_____ 9. Which pairs of measurements represent the same angle measures?
7
radians
6
240°;
I.
II.
135°;
3
radians
4
III.
150°;
5
radians
6
a. I and II
b. I and III
c. II and III
d. I, II, and III
 5

_____ 10. What is the exact value of cos 
radians  ?
 4

a. −
3
2
2
2
1
c. −
2
2
d.
2
b. −
_____ 11. In a circle, an arc of length 8  cm is intercepted by a central angle of
2
radians. What
3
is the radius of the circle?
3
cm
16
16
b.
cm
3
a.
16 2
cm
3
d. 12 cm
c.
_____ 12. Two arcs have the same length. One arc is intercepted by an angle of
3
radians in a
2
circle of radius 15 cm. If the radius of the other circle is 25 cm, what central angle
intercepts the arc?
3
2
9
b.
10
7
c.
6
5
d.
3
a.
Unit 5 Evaluation
radians
radians
radians
radians
321
MTHH 040
_____ 13. Which value is not the same as the other three values?
a. sin 100°
b. sin 80°
c. sin −80°
d. sin −260°
_____ 14. What is the amplitude of y = 3 sin 4θ?
a.
4
3
b. 3
c. 4
d. 2 
_____ 15. Which answer choice describes y = −sin 2θ?
a. amplitude −1, period 4 
b. amplitude 1, period 
c. amplitude 2, period − 
d. amplitude 2  , period 1
_____ 16. Which function has a period of 4  and an amplitude of 8?
a. y = −8 sin 8θ
b. y = −8 sin
1
θ
2
c. y = 8 sin 2θ
d. y = 4 sin 8θ
_____ 17. Which of the following statement(s) is (are) true?
cos (θ) = cos (−θ)
I.
II.
cos (θ + 2  ) = cos (θ)
III.
cos
 = − cos 
a. I and II
b. II
c. I and III
d. I, II, and III
_____ 18. Which function has a period of 2  and an amplitude of 4?
a. f(x) = 2 cos 4θ
b. f(x) = 2 cos θ
c. f(x) = 4 cos 2θ
d. f(x) = 4 cos θ
Unit 5 Evaluation
322
MTHH 040
_____ 19. Which equation corresponds to the graph shown? The screen dimensions are
−4  ≤ x ≤ 4  and −2 ≤ y ≤ 2.
1
x
cos
2
4
1
b. y = cos 4x
2
x
c. y = 2 cos
4
a. y =
d. y = 2 cos 4x
_____ 20. Which equation has the same graph as y = − cos t ?
a. y = cos (−t)
b. y = sin (t –  )
c. y = cos (t –  )
d. y = − sin t
_____ 21. Which of the following values is not defined?
a. tan 0
b. tan 
c. tan
1
d.
tan
3
2

4
_____ 22. What is the exact value of tan
7
?
6
a. − 3
b. 
3
3
c.
3
3
d.
3
Unit 5 Evaluation
323
MTHH 040
_____ 23. Which equation does not represent a vertical asymptote of the graph of y = tan θ?
a. θ = −

2
b. θ = 0
c. θ =

2
3
d. θ =
2
_____ 24. Which function has a period of 4  ?
a. y = tan 4θ
b. y = tan 2θ
1
θ
2
1
d. y = tan θ
4
c. y = tan
_____ 25. Which function is a phase shift of y = sin θ by 5 units to the left?
a. y = 5 sin θ
b. y = sin θ + 5
c. y = sin (θ + 5)
d. y = sin 5θ
_____ 26. Which function is a translation of y = cos θ by 5 units down?
a. y = −5 cos θ
b. y = cos θ – 5
c. y = cos (θ – 5)
d. y = cos (−5θ)
_____ 27. Which function is a translation of y = sin θ that is
a. y = sin (θ +
b. y = sin (θ +
c. y = sin (θ –
d. y = sin (θ –
Unit 5 Evaluation

3

2

2

3
)+
)+
)+
)–

3
units up and

2
units to the left?

2

3

3

2
324
MTHH 040
_____ 28. Suppose cos 45°. Find the exact value of sec θ.
2
a.
2
2
1
c.
2
3
d.
4
b.
_____ 29. Suppose tan (−30°). Find the exact value of cot θ.
3
a.
b. − 3
3
3
c.
d. −
3
3
_____ 30. Find csc 70°.
a. 0.3420
b. 0.9397
c. 1.0642
d. 2.9238
_____ 31. Write the measure of 270 in radians.
2
5
3
b.
2
a.
c.
d.

2

_____ 32. Write the measure of −3  radians in degrees.
a. −540
b. −360
c. −300
d. −60
_____ 33. The ____________ of a function is the length of one cycle.
a. amplitude
b. unit circle
c. period
d. phase shift
Unit 5 Evaluation
325
MTHH 040
_____ 34. A horizontal translation of a periodic function is a ____________.
a. sine function
b. cosine function
c. unit circle
d. phase shift
_____ 35. Which sketch in standard position represents −315?
a.
b.
c.
d.
_____ 36. Which sketch in standard position represents 240?
a.
b.
c.
d.
Unit 5 Evaluation
326
MTHH 040
_____ 37. Which sketch in standard position represents −340?
a.
b.
c.
d.
_____ 38. Which graph represents the function y = 2 cos x?
a.
b.
c.
d.
Unit 5 Evaluation
327
MTHH 040
_____ 39. Which graph represents the function y = 3 sin 2x?
a.
b.
c.
d.
_____ 40. Which graph represents the function y = −sin 3x?
a.
b.
c.
d.
Unit 5 Evaluation
328
MTHH 040
_____ 41. Which graph represents the function y = cos 4x?
a.
b.
c.
d.
_____ 42. Which graph represents the function y = −3 cos(x +
a.
b.
c.
d.
Unit 5 Evaluation
329
 ) + 3?
MTHH 040
_____ 43. Which graph represents the function y = 2 sin (2x –
a.
b.
c.
d.
_____ 44. Which graph represents the function y = −sin (x –
a.
b.
c.
d.
Unit 5 Evaluation
330

4

3
) – 2?
) + 1?
MTHH 040
_____ 45. Which graph represents the function y = 3 cos(3x +
a.
b.
c.
d.

2
) – 1?
_____ 46. Identify the amplitude and period of the function, y = 2 cos
x
.
4
a. 2, 8 
b. 2, 4 
c. 4, 2 
d. 2,

8
_____ 47. Identify the amplitude and period of the function, y =
a. 9,
1
sin 5x.
9
2
5
1
, 5
9
1 2
c. ,
9 5
b.
d. 5,
Unit 5 Evaluation

9
331
MTHH 040
_____ 48. Write the measure of 5  radians in degrees.
a. 900
b. 180
c. 36
d. 450
_____ 49. Write the measure of −45 in radians.
a.

4
b. 45 
c. −
d. −

2

4
_____ 50. Find the period and amplitude of this graph.
a. 4, 1.5
b. 4, 2
c. 1, 2.5
d. 2, 2
Carefully check your answers on this evaluation and make any corrections you feel are
necessary. When you are satisfied that you have answered the questions to the best of your
ability, transfer your answers to an answer sheet. Please refer to the information sheet that
came with your course materials.
Unit 5 Evaluation
332
MTHH 040