- Handed out Tuesday March 9
- Due at class time Thursday March 11
- Test to be written in one sitting of at most 2
hours
- Closed-book. You may use
calculators for ordinary arithmetic (only).
- Covers HWK 1 - HWK 11
- Sections covered: 12.1 - 12.6, 13.1 - 13.4, 14.1 - 14.5,
14.7
For about 50-60% of the test, the quizzes and HWK should give you
a reasonable indication of what kind of problems to expect. Realize
that you wrote the HWK quite soon after beginning a
particular topic, so some of the problems you did were
to begin
familiarizing yourself with the new concepts and techniques. Such
problems are less likely to appear on a test, which
you are writing
after having worked with (most of) the material for a longer period
of time and in more contexts.
Some of the test problems will be designed in part to test whether
you can apply what you have learned to a somewhat new situation.
Some of the test questions may be short-answer questions.
Two good ways to prepare for the test (different, but
complementary; both are advisable):
- Work lots of problems.
- Create an outline for each section, using your notes and the
readings in the text and your HWK, and then shrink your outlines
to a single one-page summary. Make sure you know what you've put on your summary.
If you want a list of topics covered, you can use the study guides
for the quizzes. Many of the items listed there can almost be crossed
off because you will be very familiar with them by now. Others may
not have been used as much and may require more review and
practice.
You can also use the quiz guides, along with the HWK assignments, to
choose some basic practice problems.
To practice applying what you know to somewhat less familiar
contexts, I suggest you choose problems from the following list.
Don't attempt to complete all of these problems!
- 12.1 p566: 15, 18, 31, 33, 34
Answers for evens. 18: a line parallel to the x-axis and
comprising points (x,4,2) for all real numbers x. 34: (a,b,c) = (1, -3/2, -1/2); f(x,y,z) =
d2 - 7/2.
- 12.2 p572: 8, 9, 14, 15, 16, 21
Answers for evens. 8. z decreases as x increases; z
increases as y increases. 16. a is IV, b is IX, c is VII,
d is I, e is VIII, f is II, g is VI, h is III, i is V
- 12.3 p581: 10, 13, 15, 20, 21, 26, 27, 28, 29
Answers for evens. 10.a is III, b is I, c is V, d is II, e
is IV. 20. a is I, b is IV, c is II, d is III. 26.
a is II, b is IV, c is VI, d is I, e is V, f is III. 28.
Partial answers. For a, use the same picture except change the
contour-level labels appropriately. Ditto for b. For c, shift the
diagram appropriately relative to the two axes. For d reflect the
diagram about the y-axis.
- 12.4 p588: 13, 15, 17, 23, 29, 30
- 12.5 p594: 5, 8, 9, 19, 22, 24, 29, 31
Answers for evens. 8. yes 22. ellipsoid centered at
origin; obtained from unit sphere with same center by stretch in
y-direction by a factor of 2. 24. g(x,y,z) = 2x+3y-z is one
of many possible correct answers.
- 12.6 p598: 11, 12, 14, 18, 20, 22
Answers for some evens. 14. No. 20. Show that the
only point (a,0) where f is continuous is the point (3,0).
22. No such value for c.
- Ch 12 Review Exs/Probs p600: 4, 7, 9, 11, 12, 13, 15,
17, 19, 20
- Ch 12 Check Understanding p602: 8, 10, 12, 16, 18, 20,
22, 24, 26, 28, 30, 32, 34, 36, 48, 50, 60
Answers. 8 True 10 True 12 True 16
False 18 False 20 False 22 True 24
True 26 False 28 True 30 True 32
True 34 False 36 True 48 False 50
False 60 True
- 13.1 p612: 28b, 29. Answer for 28b:
6i+8j
- 13.2 p619: 9, 21
- 13.3 p627: 11, 19, 21, 24, 25, 36, 37
Answers for evens. 24. Square root of 2; about 0.32.
- 13.4 p634: 12, 17
Answers for evens. 12. approx 2.05.
- Ch 13 Review Exs/Probs p635: 14, 19, 27, 32
Answers for evens. 14. a. t=1; b. no values for t. c. all
values for t. 32. Numbers are messy. Just figure out a plan
of attack. If you really want to know, the answer is approximately
7.0710i + 2.5882j + 6.580k.
- Ch 13 Check Understanding p637: 2, 4, 8, 10, 16, 18,
20, 30, any odds
Answers for evens: 2 False 4 False 8 False
10 False 16 True 18 False 20 True 30
False
- 14.1 p644: 8, 14, 15
Answer for 8. (a) negative, negative (b) negative, negative
- 14.2 p649: 38, 43, 44
Partial answer for 44. Yes. There are lots.
- 14.3 p657: 16. Answer: approx 136.09 derees C
- 14.4 p663: some from 43-47, 48, 49, 50, 52, 54, 56,
67, 68, 69
Answers for selected evens. 52. a. -3.268. b. -4.919.
56. 5/square root of 2 68. larger at P than at Q
- 14.5 p671: 17, 19, 25, 29, 31
- Not included: 14.6
- 14.7 p686: 27, 31, 33, 37, 41
- Ch 14 Review Exs/Probs p695: 26-33, 35, 37, 48, 51,
54
- Ch 14 Check Understanding p698: Choose some.
Questions?
Come to the problem sessions. Come to my office. Send
me e-mail. Post on the FirstClass Q&A conference for the
course. To ask about a particular problem from the text, please give
page or section number, give problem number, and make your question
as specific as you can.
Go back to the top
- Alexia Sontag,
Mathematics
- Wellesley College
- Date Created: June 28, 1999
- Last Modified: March 7, 2004
- Expires: June 30, 2004