Mathematics 2122-001
Calculus for Life Sciences II
Fall 2002
Test #1
Instructor: Dr. Alexandra Shlapentokh

1. Consider the picture of the unit circle above. is a point on the unit circle. The -coordinate of is _
(a) the .
(b) the .
(c) the .
(d) the .
(e) None of the above
2. This problem refers to the same picture as Problem # 1 . is a point on the unit circle. The -coordinate of is
(a) the .
(b) the .
(c) the .
(d) the .
(e) None of the above
(Hint: the degree measures of and add up to 180 degrees.)
3. Differentiate
(a)
(b)
(c)
(d)
(e) None of the above
4. Differentiate
(a)
(b)
(c)
(d)
(e) None of the above
5. Differentiate
(a)
(b)
(c)
(d)
(e) None of the above
6. Differentiate
(a)
(b)
(c)
(d)
(e) None of the above
7. Differentiate
(a)
(b)
(c)
(d)
(e) None of the above
8. One of the following graphs is the graph of . Which graph is it? _
(a)
(b)
(c)
(d)
(e)
9. This question refers to the graphs from Problem # 8 . One of these graphs is the graph of . Which graph is it?
10. One of the following graphs is the graph of . Which graph is it? _
(a)
(b)
(c)
(d)
(e)
11. This question refers to the graphs in Problem # 10 . One of the graphs in that problem is the graph of . Which graph is it?
12. This question refers to the graphs in Problem # 10 . One of the graphs in that problem is the graph of . Which graph is it?
13. This question refers to the graphs in Problem # 10 . One of the graphs in that problem is the graph of . Which graph is it?
14. Convert into radians. Round off your answer to two decimal points.
(a) 0.93 radians
(b) 0.87 radians
(c) 0.76 radians
(d) Angle of does not have a radian measure,
(e) None of the above
15. Convert 10 radians into degrees. Round off your answer to two decimal points.
(a) 100.3
(b) 323.12
(c) 572.96
(d) 10 radian angle cannot be measured in degrees.
(e) None of the above
16. What is the length of the arc of a circle of radius 3 inches rounded off to two decimal points, if the radian measure of the central angle corresponding to the arc is radians?
(a) 1.88 in
(b) 1.92 in
(c) 2.02 in
(d) This arc does not have length.
(e) None of the above
17. What is the length of the arc of a circle of radius 3 inches rounded off to two decimal points, if the degree measure of the central angle corresponding to the arc is degree?
(a) 1.32
(b) 1.23
(c) 1.64
(d) 1.57
(e) None of the above
18. What is the exact area of a sector of a circle of radius 3 inches, if the radian measure of the central angle corresponding to the arc is ?
(a) square inches.
(b) square inches
(c) Such a sector does not have an area.
(d) square inches.
(e) None of the above
19. What is the exact area of a sector of a circle of radius 3 inches, if the degree measure of the central angle corresponding to the arc is degree?
(a) square inches
(b) square inches
(c) Such a sector does not have an area.
(d) square inches
(e) None of the above
20. Suppose that is a central angle of a unit circle in the second quarter and is . Then is
(a) equal to .
(b) impossible to determine from these data.
(c) equal to .
(d) equal to .
(e) None of the above
21. Suppose that is a central angle of a unit circle in the fourth quarter and is . Then is
(a) equal to .
(b) impossible to determine from these data.
(c) equal to .
(d) equal to .
(e) None of the above
22. Determine which of the following equalities are true for all measured in radians.
(a)
(b)
(c)
(d)
(e) None of the above
23. Determine which of the following equalities are true for all measured in radians.
(a)
(b)
(c)
(d)
(e) None of the above
24. Determine which of the following equalities are true for all measured in radians.
(a)
(b)
(c)
(d)
(e) None of the above
25.
(a) =1.
(b) =0.
(c) does not exist.
(d) =1/2.
(e) None of the above
26.
(a) =1.
(b) =0.
(c) does not exist.
(d) =1/2.
(e) None of the above
27.
(a) =1.
(b) =2.
(c) does not exist.
(d) =3.
(e) None of the above
28.
(a) =1.
(b) =0.
(c) does not exist.
(d) =1/2.
(e) None of the above
29. Rounded off to two decimal points,
(a) 0.39
(b) 0.40
(c) 0.41
(d) 0.42
(e) None of the above
30. Compute the cotangent of 15 radians and round off your answer to two decimal points.
(a) -1.16
(b) -1.17
(c) -1.18
(d) - 1.19
(e) None of the above
Key
1 a, 2 b, 3 a, 4 a, 5 d, 6 a, 7 b, 8 c, 9 d, 10 d, 11 a, 12 b, 13 c, 14 b, 15 c, 16 a, 17 d, 18 b, 19 b, 20 c, 21 a, 22 d, 23 c, 24 b, 25 a, 26 b, 27 d, 28 d, 29 a, 30 b