| Problem | #1 | #2 | #3 | #4 | #5 | #6 | #7 | #8 | Total |
|---|---|---|---|---|---|---|---|---|---|
| Max grade | 16 | 12 | 10 | 15 | 12 | 10 | 12 | 12 | 97 | Min grade | 2 | 0 | 0 | 1 | 0 | 4 | 5 | 2 | 52 | Mean grade | 13.44 | 7.8 | 4.22 | 11.56 | 8.2 | 9.08 | 9.68 | 7.68 | 74.16 | Median grade | 15 | 8 | 7 | 12 | 9 | 10 | 10 | 8 | 75 |
Numerical grades will be retained for use in computing
the final letter grade in the course.
Here are approximate letter grade assignments for this exam:
| Letter equivalent | A | B+ | B | C+ | C | D | F |
|---|---|---|---|---|---|---|---|
| Range | [85,100] | [75,84] | [70,74] | [65,69] | [55,64] | [50,54] | [0,49] |
Grading guidelines
Minor errors (such as a missing factor in a final answer, sign error,
etc.) will be penalized minimally. Students whose errors materially
simplify the problem will not be eligible for most of the
problem's credit.
The grader will read only what is written and not attempt to guess or
read the mind of the student.
The student should solve the problem given and should not invent
another problem and request credit for working on that problem.
Problem 1 (16 points)
a) (2 points) The region should be roughly three-sided with line
segments on the x- and y-axes and with a curvy concave down boundary
curve for the third side. If no label is present, any positive score
will be reduced by 1 point (a label was explicitly requested).
b) (4 points) Setting up the integral is worth 2 points, and
evaluating it with C correctly used is worth the other 2 points. 1
point will be given for an inderinite integral.
c) (8 points) Setting up the integral either dx or dy is worth 5
points. Computing it is worth the other 3 points. 3 points will be
given for an indefinite integral.
d) (2 points) Setting the answer in c) equal to 1 earns 1 point and
then solving the equation earns 1 point.
Problem 2 (12 points)
a) (4 points) 2 points for the substitution and 2 points
for antidifferentiation.
b) (8 points) 2 points for an initial substitution, then 5 points for
an integration by parts which "moves forward" and then 1 point for the
final answer. Integration by parts with the original variable is
certainly also valid, and will be scored appropriately. An integration
by parts which "pumps up" the powers earns 2 points only.
Problem 3 (10 points)
a) (3 points) 1 point for the largest value and 1 point for a reason,
and then 1 point for the limit answer.
b) (5 points) 2 points for setting up the mean or average value
integral correctly, 2 points for the antidifferentiation, and 1 point
for the limit answer.
c) (2 points) 1 point for the answer and 1 point for some explanation.
Problem 4 (15 points)
Proportional sides equation/information is worth 3 points. Density
information correctly used is worth 3 points. The distance to lift the
slice is worth 3 points. If either the density or the distance to lift
the slice is missing, the maximum which can be earned is 10 points. If
both are missing, the maximum which can be earned is 7 points.
Assembling this into a correct definite integral is worth 3 points
(essentially the student is penalized 2 of these 3 points if one of
desnity/distance is missing). The final computation is worth 3
points. A missing factor of Π loses a point.
Problem 5 (12 points)
3 points for a correct trig substitution, 3 more points for conversion
of the integral correctly into the trig "variable", 2 points for a
correct antidifferentiation, 2 points for converting correctly back to x, and 2 points for the answer.
Problem 6 (10 points)
2 points for writing the correct symbolic sum, and 2 points for
combining terms successfully. 1 point each for correct values of the
variables for a total of 3 points. 2 more points for correct
antidifferentiation, 1 for each term.
Problem 7 (12 points)
4 points for the (cos(x))2 antidifferentiation, 4 points for the
(cos(x))3
antidifferentiation, 2 points for correctly combining them, and 2 more
points for the final answer, including evaluating the trig functions
correctly.
Problem 8 (13 points)
a) (4 points) Writing the correct weights earns 1 point, getting
Δx correct earns 1 point, and using the correct function values
earns 2 points.
b) (7 points) Computing the first derivative earns 1 point, and
computing the second derivative earns 2 points. Estimation is worth 4
points.
c) (2 points) Setting up the inequality correctly is worth 1
point. Using it to get useful information about a correct N earns the
other point. If the inequality is incorrect, no points are earned in
this part. An equality with N loses 1 point.
Maintained by greenfie@math.rutgers.edu and last modified 10/9/2009.