Mathematics 2121-003
Calculus for Life Sciences I
Spring 05
Dr. A. Shlapentokh
Test #1

1. Which of the following statements is correct ?
(a)
(b)
(c)
(d)
(e) None of the above
2. One of the following graphs is the graph of , where is a real number. Which one is it?
(a)
(b)
(c)
(d)
(e)
3. One of the above graphs is the graph of , where is a real number. Which one is it?
(a)
(b)
(c)
(d)
(e)
4. One of the above graphs is the graph of , where is a real number. Which one is it?
(a)
(b)
(c)
(d)
(e)
5. One of the above graphs is the graph of , where is a real number. Which one is it?
(a)
(b)
(c)
(d)
(e)
6. Let . What is ?
(a)
(b)
(c)
(d)
(e) None of the above.
7. Let . What is ?
(a) 7
(b)
(c) The function is not defined at
(d)
(e) None of the above.
8. Find the domain of the function .
(a)
(b)
(c)
(d)
(e) None of the above
9. Find the domain of the function .
(a) Domain: .
(b) Domain: .
(c) Domain: .
(d) Domain: .
(e) None of the above.
10. Solve: .
(a) .
(b) .
(c) .
(d) or .
(e) None of the above.
11. Find the domain of , where is a real number.
(a) .
(b) .
(c) .
(d) .
(e) None of the above.
12. Find the domain of , where is a positive real number.
(a) .
(b) .
(c) .
(d) .
(e) None of the above.
13. Find the slope of the line passing through the points and .
(a) 2
(b) 1
(c) 0
(d) does not exist
(e) None of the above.
14. Which of the following lines does not have a slope ?
(a) Line passing through the points (2,4) and (4,7).
(b) Line passing through the points (3,2) and (3,5).
(c) Line passing through the points (0,2) and (5,2).
(d) Line passing through the points (1,2) and (7,6).
(e) All of the lines above have slope.
15. Write down an equation of the line passing through the points (1,7) and (2,5).
(a)
(b)
(c) .
(d)
(e) None of the above.
16. Write down an equation of the line passing through the points (13,3) and (13,4).
(a) .
(b) .
(c) .
(d) .
(e) None of the above.
17. Write down an equation of the line passing through the points (2,2) and (4,2).
(a) .
(b) .
(c) .
(d) .
(e) None of the above.
18. Find the slope and the -intercept of the line with the equation .
(a) Slope=-2, -intercept = -12.
(b) Slope = -2, -intercept = 12.
(c) Slope = 2, -intercept = -12.
(d) Slope = 1/2, -intercept = -12.
(e) None of the above
19. Suppose a line has the slope equal to . Then which of the following statements is true about points on ?
(a) For each unit increase in , we have that will increase by of a unit.
(b) For each unit increase in , we have that will decrease by units.
(c) For a 5 unit increase in , we have that will increase by units.
(d) For a 5 unit increase in , we have that will decrease by units.
(e) None of the above
20. Write down an equation of a line with -intercept equal to and slope equal to .
(a) .
(b) .
(c) .
(d) Such a line does not exist.
(e) None of the above.
21. A nurse is mixing two solutions. The first solution contains 0.5 mg of substance A per ounce of solution. The second solution contains 1.0 mg of substance A per ounce of solution. In what proportions should the two solutions be mixed together to obtain a solution containing 0.75 mg of substance A per ounce?
(a) For each mg of the first solution, the nurse should use 3 mg of the second solution.
(b) For each mg of the first solution, the nurse should use 2 mg of the second solution.
(c) Solutions should mixed in equal proportions.
(d) For each 2 mg of the first solution, the nurse should use 1 mg of the second solution.
(e) None of the above.
22. One of the following graphs might be the graph of . Which one is it?
(a)
(b)
(c)
(d)
(e) None of the above
23. The graph of the inequality
(a) consists of all the point on the line .
(b) consists of all the points above the line .
(c) consists of all the points above the line and on the line .
(d) consists of all the points below the line .
(e) None of the above
24. The graph of the inequality
(a) consists of all the point on the line .
(b) consists of all the points to the right of the line and on the line .
(c) does not exist
(d) consists of all the points below the line .
(e) None of the above
25. Which of the following statements are true?
(a) Parabola has two distinct positive -intercepts.
(b) Parabola has two distinct negative -intercepts.
(c) Parabola has no -intercepts.
(d) Parabola intersects -axis in only one point.
(e) None of the above
26. Which of the equations below is an equation of the circle centered at and with the radius equal to 2? Here is a real number.
(a) .
(b) .
(c) .
(d) .
(e) None of the above.
27. What is the center and the radius of the circle , if are positive real numbers?
(a) Such a circle does not exist.
(b) Center is at , radius is .
(c) Center is at , radius is .
(d) Center is at , radius is .
(e) None of the above.
28. Let , let . What is the formula and the domain for ?
(a) . Domain: .
(b) The composition does not exist.
(c) . Domain: .
(d) . Domain: all real numbers.
(e) None of the above.
29. Let let . What is the formula and the domain for ?
(a) . Domain: .
(b) . Domain: .
(c) . Domain: .
(d) . Domain: .
(e) None of the above.
30. Compute .
(a) 33
(b) 0
(c)
(d)
(e) None of the above
31. Compute .
(a) 1/6
(b) 0
(c)
(d)
(e) None of the above
32. Compute .
(a) 50
(b) 0
(c)
(d)
(e) None of the above
33. Compute .
(a) 0
(b)
(c) 1
(d)
(e) None of the above
34. Compute .
(a) 2
(b)
(c) -2
(d)
(e) None of the above
35. Let , where is a fixed real number. What is the average rate of change of between and for any ?
(a)
(b)
(c)
(d) Cannot be determined.
(e) None of the above
36. Find the increment of the function in the interval .
(a) 4
(b) 3
(c) 2
(d) 1
(e) None of the above
37. Let . Let . Find the corresponding .
(a) -25
(b) 25
(c) -27
(d) 27
(e) None of the above
38. Let . Find the average rate of change of in the interval .
(a)
(b)
(c)
(d)
(e) None of the above
39. Compute .
(a)
(b) 5/3
(c) -2
(d) 2
(e) None of the above
40. Compute .
(a) 0
(b)
(c) The limit does not exist.
(d) 3
(e) None of the above
41. Suppose , where . Then
(a) cannot be determined from these data.
(b) does not exist.
(c) is always 6
(d) is .
(e) None of the above
42. Suppose , where . Then
(a) cannot be determined from these data.
(b) does not exist.
(c) is .
(d) is .
(e) None of the above
43. Suppose . Then
(a) cannot be determined from these data.
(b) does not exist.
(c) is always 0
(d) is .
(e) None of the above
44. Suppose , where . Then
(a) cannot be determined from these data.
(b) does not exist.
(c) is always .
(d) is .
(e) None of the above
45. Compute .
(a) The limit does not exist.
(b)
(c)
(d)
(e) None of the above
Key
1c, 2a, 3b, 4d, 5e, 6b, 7b, 8e, 9e, 10d, 11c, 12d, 13a, 14b, 15c, 16b, 17b, 18c, 19d, 20e, 21c, 22a, 23d, 24b, 25c, 26a, 27d, 28e, 29c, 30c, 31a, 32b, 33c, 34c, 35a, 36a, 37c, 38a, 39b, 40d, 41d, 42d, 43a, 44c, 45b. _