Mathematics 2121-01
Calculus for Life Sciences I
Fall 02
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 . Which one is it?
(a)
(b)
(c)
(d)
(e)
3. Let . What is ?
(a)
(b)
(c)
(d)
(e) None of the above.
4. Let . What is ?
(a) 2
(b)
(c) 1
(d)
(e) None of the above.
5. Find the domain of the function .
(a)
(b)
(c)
(d)
(e) None of the above
6. Find the domain of the function .
(a) Domain: .
(b) Domain: .
(c) Domain: .
(d) Domain: .
(e) None of the above.
7. Solve: .
(a) .
(b) .
(c) .
(d) or .
(e) None of the above.
8. Solve: .
(a) or .
(b) or .
(c) .
(d) .
(e) None of the above.
9. Find the domain of .
(a) .
(b) .
(c) .
(d) .
(e) None of the above.
10. Find the domain of .
(a) .
(b) .
(c) .
(d) .
(e) None of the above.
11. Find the slope of the line passing through the points and .
(a) 1/3
(b) 3
(c)
(d)
(e) None of the above.
12. Which of the following lines does not have slope ?
(a) Line passing through the points (2,3) and (3,3).
(b) Line passing through the points (2,2) and (2,3).
(c) Line passing through the points (1,2) and (-1,2).
(d) Line passing through the points (1,2) and (0,2).
(e) All of the lines above have slope.
13. Write down an equation of the line passing through the points (1,2) and (3,4).
(a)
(b)
(c) .
(d)
(e) None of the above.
14. Write down an equation of the line passing through the points (2,3) and (2,4).
(a) .
(b) .
(c) .
(d) .
(e) None of the above.
15. Write down an equation of the line passing through the points (2,6) and (4,6).
(a) .
(b) .
(c) .
(d) .
(e) None of the above.
16. Find the slope and the -intercept of the line with the equation .
(a) Slope=-1/2, -intercept = 3.
(b) Slope = 1/2, -intercept = 3.
(c) Slope = 2, -intercept = -3.
(d) Slope = -2, -intercept = -3.
(e) None of the above
17. Write down an equation of a line with -intercept equal to and slope equal to -2.
(a) .
(b) .
(c) .
(d) .
(e) None of the above.
18. A nurse is mixing two solutions. The first solution contains 0.1 mg of substance A per ounce of solution. The second solution contains 0.3 mg of substance A per ounce of solution. In what proportions should the two solutions be mixed together to obtain a solution containing 0.2 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.
19. One of the following graphs is the graph of . Which one is it?
(a)
(b)
(c)
(d)
(e)
20. 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
21. 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
22. At most one of the graphs below is the graph of

Which graph is it?
(a)
(b)
(c)
(d)
(e) None of the above
23. A lab assistant is preparing a meal for a lab gerbil. The meal will consist of two types of food. The first type of food has 7 calories and 10 mg of vitamin A per ounce. The second type of food has 5 calories and 30 mg of vitamin per ounce. The gerbil has to get at least 200 mg of vitamin but no more than 20 calories. Describe all the food combinations which can be fed to the gerbil.
(a) Let be the number of ounces of the first and second food type respectively.


(b) Let be the number of ounces of the first and second food type respectively.


(c) Let be the number of ounces of the first and second food type respectively.


(d) Let be the number of ounces of the first and second food type respectively.


(e) None of the above.
24. Which of the following statements are true ?
(a) Parabola has two positive -intercepts.
(b) Parabola has two negative intercepts.
(c) Parabola has no -intercepts.
(d) Parabola intersects -axis in only one point.
(e) None of the above
25. Which of the equations below is an equation of the circle centered at (1,4) and with the radius equal to 2 ?
(a) .
(b) .
(c) .
(d) .
(e) None of the above.
26. What is the center and the radius of the circle ?
(a) Center is at (2,-3), radius is .
(b) Center is at (-2,-3), radius is .
(c) Center is at (2,3), radius is .
(d) Center is at (-2,-3), radius is .
(e) None of the above.
27. Let , let . What is the formula and the domain for ?
(a) . Domain: all real numbers.
(b) . Domain: .
(c) . Domain: all real numbers.
(d) . Domain: .
(e) None of the above.
28. Let let . What is the formula and the domain for ?
(a) . Domain: .
(b) . Domain: .
(c) . Domain: .
(d) . Domain: .
(e) None of the above.
29. Let . Find such that .
(a) , .
(b) .
(c) , .
(d) .
(e) None of the above.
30. At most one of the following graphs is the graph of . Which one is it?
(a)
(b)
(c)
(d)
(e) None of the above
31. Compute .
(a) 3/5
(b) 0
(c)
(d)
(e) None of the above
32. Compute .
(a) 3/5
(b) 0
(c)
(d)
(e) None of the above
33. Compute .
(a) 3/5
(b) 0
(c)
(d) 5/3
(e) None of the above
34. Compute .
(a) 0
(b)
(c) 2
(d)
(e) None of the above
35. Compute .
(a) -1
(b)
(c) -2
(d)
(e) None of the above
36. Let . What is the average rate of change of between and for any ?
(a) 1
(b) 2
(c) 4
(d) 5
(e) None of the above
37. Find the increment of the function in the interval .
(a) 4
(b) 3
(c) 2
(d) 1
(e) None of the above
38. Let . Let . Find the corresponding .
(a) -25
(b) 25
(c) -27
(d) 27
(e) None of the above
39. Find the average rate of change for the function in the interval .
(a) -2/3
(b) 1/3
(c) -1/3
(d) 1/4
(e) None of the above
40. Let . Find the average rate of change of in the interval .
(a)
(b)
(c)
(d)
(e) None of the above
41. Let . Find .
(a)
(b)
(c)
(d)
(e) None of the above
42. During the initial stage of an epidemic the number of infected people was growing is growing according to the formula , where is measured in days and is the number of infected individuals. Find the average rate of growth of the infected population between t=2 and t= 4 days.
(a) 13 people
(b) 13 people/day
(c) 10 people/day
(d) 26 people
(e) None of the above
KEY
1(b), 2(d), 3(c), 4(b), 5(e), 6(b), 7(d), 8(e), 9(c), 10(e), 11(a), 12(b), 13(c), 14(a), 15(b), 16(a), 17(a), 18(c), 19(a), 20(d), 21(b), 22(e), 23(a), 24(c), 25(a), 26(a), 27(c), 28(c), 29(b), 30(c), 31(c), 32(a), 33(b), 34(c), 35(c), 36(d), 37(a), 38(c), 39(c), 40(a), 41(c), 42(b)