I recommend that, after you finish the homework through Chapter 4, section 4, you take this sample test just like a test. Make a note of which problems you feel confident you worked correctly and which you didn't.

Then, since no answers or solutions are provided here, you may want to show your work to a tutor or the instructor for comments on whether you are doing the problems correctly.

Before they will discuss this with you, you must first, for each problem,

1. identify which section of the text has problems similar to this
2. find an odd-numbered problem that is similar to this one
3. work it (or find it in the homework that you have already worked)
4. check your answer
5. make a judgment about whether your solution to the sample test problem is correct

Bring all of that work with you when you come to the tutor or instructor.

Materials allowed: Calculator or Winplot software, scratch paper

Show all your work on blank paper. Your work, as well as your answers, is graded. Make sure your final answer to each part of the problem is clearly indicated.

If the answer to the problem is an integral, don't just give a numerical value for the integral. Be sure that you indicate what integral you are computing, in correct integral notation, and then, if you do an approximation, tell how many subdivisions, the right- and left-hand sums, and your best approximation of the integral. Make your approximations correct to at least one decimal place for full credit.

Make sure that the problems are in order on the test or that there is a clear note in the appropriate place saying where to find the work and the solution.

1. (18 pts) Find the derivative of each of these functions:

a.

b.

c.

2. (18 pts) In a certain country, the population P (in millions) in t years after 1980 is given by the function

a. Find the formula for the rate of change of the population.

b. What are the units of the rate of change of the population?

c. Find the rate of change of the population in 1992.

3. (10 points) For , find the equation of the tangent line at .

4. (18 pts) The graph on the next page represents Janet's velocity while she is biking near a lake. She starts at a point 5 miles from the lake, and the positive direction is away from the lake.

(Web version: I'll put this graph in as soon as I learn how to do that. In the meantime, you can look in the textbook. I don't have the textbook with me as I write this, but I remember that this was problem number 14 from either section 3.3, 3.4, or maybe the Chapter 3 Review.)

a. Use this graph to approximate her distance from the lake at several different times. (A fairly rough approximation is fine. Show enough work that I can see what you're doing, but don't spend much time making the approximation really accurate. The main purpose of this part of the problem is to give you info for the next parts of this problem.)

b. Exactly when is Janet farthest from the lake?

c. Approximately how far is she from the lake at her farthest point?

d. Exactly when is Janet closest to the lake?

e. Approximately how far is she from the lake at her closest point?

f. When is her acceleration zero?

5. (18 pts) For

a. Find

b. Find with right- and left- sums.

c. Find using the Fundamental Theorem of Calculus.

6. (18 pts) For

a. Find the average value of f over the interval from 1 to 3.

b. Find the area between the graph and the x axis between and .

c. Find

7. (Extra credit - 6 points) The period, T, of a pendulum is given in terms of its length, l, by , where g is the acceleration due to gravity (a constant). Find the derivative of T with respect to l.