Preparation for the first exam in 251:12-14 and 15-17

The exam will cover the material in lectures 1 through 9 of the syllabus. This is also the material covered in lectures 1 through 11 of the diary (but note, please, exclusions such as torsion). This is, roughly, the textbook material in chapters 12 and 13, and chapter 14 up to but not including optimization.
The exam is scheduled for 80 minutes. All 6 sections will take in their standard lecture meeting times on Tuesday, October 12 (sections 12, 13, and 14 from 3:20 to 4:40; sections 15, 16,and 17 from 10:20 to 11:40) in Hill 116.

No formula sheets and no calculators may be used on the exam.

More specifically, 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.
"Simplification" of answers is not necessary, but find exact values of standard functions such as e⁰ and sin(Π/2).

Here are some previous exams and review material that I've given in this course, going backwards in time (most recent is first).

A My first exam in spring 2010
This was given last semester covering the same subject matter with the same textbook. It represents the most recent insight into the types of questions I'd ask. Here are answers to that exam.
Please There is no guarantee that I will ask similar questions although a colleague once suggested that I should ask exactly the same questions but just change the answers! So all questions about eligible material linked to this page represent valid test items. Homework questions are also candidates.
B My first exam in fall 2008
This was given for a course using the same textbook and covering the almost the same material as the first exam here (optimization was not included, so problem 11 would not be eligible for this exam). Here are answers to that exam.
C My first exam in spring 2006
This was given for a course using a different textbook and a slightly different syllabus. Here are answers to that exam.
D A set of old review problems suitable for this first exam
And here are answers to most of these problems.

Old problems in relation to our syllabus
The problems contained in the links given above are listed here "keyed" to each section of the syllabus. This may be useful to you as you review these topics.

Lecture Sections and Topics My exam problems

1 12.1 Vectors in the Plane
12.2 Vectors in Three Dimensions B2

2 12.3 Dot Product and the Angle Between Two Vectors
12.4 The Cross Product A2 B4 B5 C1 C2 DG&H

3 12.5 Planes in Three-Space A1 C3 DC DS

4 13.1 Vector-Valued Functions
13.2 Calculus of Vector-Valued Functions A2 B1 DM DV

5 13.3 Arc Length and Speed
13.4 Curvature
13.5 Motion in Three-Space A7 B3 C4 C5 DF DN DO&P DL

6 14.1 Functions of Two or More Variables
14.2 Limits and Continuity in Several Variables B7 DA DQ DT

7 14.3 Partial Derivatives
14.4 Differentiability, Linear Approximation and Tangent Planes B8 C6 DI DW&X

8 14.5 The Gradient and Directional Derivatives A3&6 B10 C8 C9 DB DE DJ DW&X

9 14.6 The Chain Rule A4&5 B9 C7 DD DE DK DR DU DW&X

Lecture	Sections and Topics	My exam problems
1	12.1 Vectors in the Plane 12.2 Vectors in Three Dimensions	B2
2	12.3 Dot Product and the Angle Between Two Vectors 12.4 The Cross Product	A2 B4 B5 C1 C2 DG&H
3	12.5 Planes in Three-Space	A1 C3 DC DS
4	13.1 Vector-Valued Functions 13.2 Calculus of Vector-Valued Functions	A2 B1 DM DV
5	13.3 Arc Length and Speed 13.4 Curvature 13.5 Motion in Three-Space	A7 B3 C4 C5 DF DN DO&P DL
6	14.1 Functions of Two or More Variables 14.2 Limits and Continuity in Several Variables	B7 DA DQ DT
7	14.3 Partial Derivatives 14.4 Differentiability, Linear Approximation and Tangent Planes	B8 C6 DI DW&X
8	14.5 The Gradient and Directional Derivatives	A3&6 B10 C8 C9 DB DE DJ DW&X
9	14.6 The Chain Rule	A4&5 B9 C7 DD DE DK DR DU DW&X

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 9/26/2010.