Preparation for the second exam in 153


A useful quote for students
"It's one thing about the playoffs," Jeter said. "Every opportunity, every time you're up there, you have a chance to do something. You can't change anything that happened up to this point."


The exam will primarily concentrate on questions regarding material from lectures 11 through 20 of the syllabus. The reason for the phrasing "primarily concentrate" is that certainly some of the earlier material in the course (for example, differentiation!) will be needed to handle some of the questions in the exam. The course is quite cumulative. The textbook sections whose contents are emphasized on this exam are 3.8 through 3.11 and 4.1 through 4.9. This is a large amount of material, including most of the applications of derivatives.
The exam is scheduled for 80 minutes, from 1:40 PM to 3 PM on Thursday, November 19, in our usual lecture room. I will get to the classroom early and am willing to start early.


From the course coordinator
The course coordinator will be the primary writer of the uniform Math 151 final exam, intended for all sections of Math 151 and to be taken also by students in Math 153, so students should have some familiarity with the style of these problems.


From the instructor
I will write the exam you will take so you should be familiar with my "style".
The cover sheet for your exam will state:

Show your work. An answer alone may not receive full credit.
No texts, notes, or calculators may be used on this exam other than the formula sheet supplied with this exam.
Find exact values of standard functions such as e0 and sin(Π/2).
Otherwise do NOT "simplify" your numerical answers!

Here are some previous exams that I've given in Math 151, going backwards in time (most recent is first).


My old exam problems in relation to our syllabus
Here is a list of problems from those old exams "keyed" to each section of the syllabus. This may be useful to you. Please be aware, however, that with the increasing sophistication (!) of the course, a number of problems actually require ideas and computations from several sections.

Lecture Sections Topics My exam problems
11 3.8 Implicit differentiation A1  B2  C3
12 3.9, 3.10 Differentiation of inverse functions, exponentials, logarithms There are no specific problems testing this material, but there are many problems which build on this section's contents (those problems needing derivatives of such inverse functions as ln, arctan, and arcsin, for example -- there are many such).
13 3.11 Related rates A3  B3  C7
4 4.1, 4.8 Linear approximations, Newton's method A6  B4  C1  C2
15 4.2 Maxima and minima, critical points A2  B1
16 4.3, 4.4 Shape of a graph, Mean Value Theorem, first derivative test, concavity A4 A5  A8  B4 B7  B8  C1 C6
17 4.5Curve sketching, asymptotes A4 A5  B7
18 4.6Maxima and minima problems A2  B5  C5
19 4.7 Indeterminate forms, L'Hôpital's rule A7  B6  C8


My design criteria for calculus exams
I try to ask questions about most (hopefully all) important topics which were covered in the period to be tested. I try to avoid asking problems which require special "finicky" tricks, and do try to inquire about techniques which are broadly applicable.

I want to give, on any calculus exam, questions which require reading and writing graphical information, reading and writing symbolic information, reading and writing quantitative information ("numbers"), and, finally, some question(s) requiring students to exhibit some reasoning and explanation, appropriate to the level of the course and also recognizing the limited time of an exam. I certainly don't always "hit" this target but that's my aim.


Maintained by greenfie@math.rutgers.edu and last modified 9/26/2009.