Mathematics 2122-001
Calculus for Life Sciences II
Spring 05
Test #1
Instructor: Dr. Alexandra Shlapentokh

1. Consider the picture of the unit circle above and the acute angle formed by the rays and . Let be the point of the intersection of the unit circle and the ray . Then 1 over 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. Let be the same point on the unit circle as in Problem #1. Then the -coordinate of is
(a) the .
(b) the .
(c) the .
(d) the .
(e) None of the above
3. One of the graphs below is the graph of . Which graph is it? _
(a)
(b)
(c)
(d)
(e)
4. This question refers to the graphs in Problem # 3. One of the graphs in that problem is the graph of . Which graph is it?
(a)
(b)
(c)
(d)
(e)
5. This question refers to the graphs in Problem # 3. One of the graphs in that problem is the graph of . Which graph is it?
(a)
(b)
(c)
(d)
(e)
6. Which of the following statements are true.
(a) and have the same domain.
(b) and have the same domain.
(c) Both and are even.
(d) and have the same range.
(e) None of the above
7. Convert into radian measure. Round off your answer to two decimal points.
(a) 0.14
(b) 0.16
(c) 0.15
(d) Angle of does not have a radian measure.
(e) None of the above
8. Suppose the radian measure of an angle is 60. What is the degree measure of the angle? Round off your answer to two decimal points.
(a) 3500.89
(b) 3430.77
(c) 3720.96
(d) 60 radian angle cannot be measured in degrees.
(e) None of the above
9. An angle of has the radian measure equal to
(a)
(b)
(c)
(d) Not all angles have radian measure.
(e) None of the above
10. Angle whose radian measure is has the following degree measure:
(a)
(b)
(c)
(d) Not all angles have degree measure.
(e) None of the above
11. What is the length of the arc of a circle of radius 10 inches rounded off to two decimal points, if the radian measure of the central angle corresponding to the arc is radians?
(a) 8.98 in
(b) 13.94 in
(c) 6.04 in
(d) This arc does not have length.
(e) None of the above
12. What is the length of the arc of a circle of radius 4 inches, if the degree measure of the central angle corresponding to the arc is degrees?
(a) in
(b) in
(c) in
(d) in
(e) None of the above
13. What is the exact area of a sector of a circle of radius 2 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
14. What is the exact area of a sector of a circle of radius 1 inch, 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
15. Rounded off to two decimal points,
(a) 0.81
(b) 0.65
(c) 0.55
(d) 1.42
(e) None of the above
16. Compute the tangent of 32 radians and round off your answer to two decimal points.
(a) 0.66
(b) -0.66
(c) -1.38
(d) - 1.29
(e) None of the above
In Problems 17–24 differentiate the given function with respect to x.
17.
(a)
(b)
(c)
(d)
(e) None of the above
18.
(a)
(b)
(c)
(d)
(e) None of the above
19.
(a)
(b)
(c)
(d)
(e) None of the above
20.
(a)
(b)
(c)
(d)
(e) None of the above
21.
(a)
(b)
(c)
(d)
(e) None of the above
22.
(a)
(b)
(c)
(d)
(e) None of the above
23.
(a)
(b)
(c)
(d)
(e) None of the above
24. .
(a)
(b)
(c)
(d)
(e) None of the above
In Problems 25 – 28 determine the smallest positive period of the given function.
25.
(a) This function is not periodic.
(b)
(c)
(d)
(e) None of the above
26.
(a) This function is not periodic.
(b)
(c)
(d)
(e) None of the above
27.
(a) This function is not periodic.
(b)
(c)
(d)
(e) None of the above
28.
(a) 1
(b) 2
(c)
(d)
(e) None of the above
In Problems 29–30 determine the amplitude of the given function.
29.
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of the above
30.
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of the above
31. A certain variable varies sinusoidally between 2 and 6 with a period of 2 days. The variable reaches its highest value at 1 pm of the first day. (We assume the period starts at 12 am.) Find a formula for .
(a) , where is measured in hours and corresponds to 12 am.
(b) , where is measured in hours and corresponds to 12 am.
(c) , where is measured in hours and corresponds to 12 am.
(d) , where is measured in hours and corresponds to 12 am.
(e) None of the above
32. A certain varibale varies according to the formula . Then which of the statements below is true?
(a) At the variable reaches its highest value.
(b) The period of this variable is 3.
(c) The highest value of this variable is 7.
(d) The lowest value of this varibale is 5.
(e) None of the above
33. Suppose an antiderivative of is . Then
(a) cannot be determined.
(b) is .
(c) is .
(d) is .
(e) None of the above
34. Suppose has an antiderivative . Then
(a) has no other antiderivatives.
(b) has infinitely many antiderivatives.
(c) has one more antiderivative.
(d) has two more antiderivatives.
(e) None of the above
35. Let and be antiderivatives of the same function. Then
(a) is a constant.
(b) is equal to .
(c) is equal to .
(d) is equal to .
(e) None of the above
36. Suppose , where is a constant. Then any antiderivative of , where is a non-zero real number, is of the form
(a) .
(b) .
(c) , where is a constant.
(d) , where is a constant.
(e) None of the above
37. Suppose , where is a constant. Then any antiderivative of is of the form
(a) , where is a constant.
(b) , where is a constant.
(c) cannot be determined.
(d) , where is a constant.
(e) None of the above
In Problems 38–41 let be an antiderivative of the given function. Determine .
38.
(a) 5
(b) -5
(c) 0
(d) 1
(e) None of the above
39.
(a)
(b)
(c)
(d)
(e) None of the above
40.
(a)
(b)
(c)
(d)
(e) None of the above
41.
(a) 0
(b) 1
(c) 2
(d) 3
(e) None of the above
Key
1b, 2b, 3c, 4d, 5b, 6d, 7a, 8e, 9c, 10c, 11e, 12d, 13b, 14d, 15a, 16a, 17b, 18d, 19a, 20b, 21d, 22a, 23c, 24d, 25c, 26c, 27e, 28b, 29a, 30b, 31d, 32e, 33d, 34b, 35a, 36c, 37b, 38a, 39d, 40b, 41c.