Prob 1: Several people didn't simplify the fractions correctly or had simple algebraic errors.
Prob 2: Several people did not use the product rule correctly in either part. Several people did not isolate the dy/dx terms and end up with a single dy/dx on the left and an expression (without a derivative) on the right.
Prob 3: Very few people received full credit on this problem,
even though it was on the third midterm and everyone had a copy of the
answer. A number of people tried to take the derivative of b,
which must be zero, since b is a constant (normally 90 ft).
Many did not label the diamond so that it was difficult for them (or
for the grader) to understand which variable related to which
distance (or other value).
Several people attempted to take the square root of a sum and obtain
the square roots of the individual components. The square root of
1+1 is the square root of 2 which is about 1.41..., but the square
root of 1 added to the square root of 1 is 2.
Prob 4: No consistent errors.
Prob 5:
A couple of students seemed not know how to "define" a function at a
specific point to give a specific value.
Prob 6: No consistent errors.
Prob 7: Many did not indicate on the diagram where the shadow was (on the ground on the opposite side of the man from where the light is, and not parallel to the curb). The length of the shadow is obtained via a similar triangle diagram with the lamppost and man as vertical legs and the distance from the base of the lamppost to the tip of the shadow being the horizontal leg. The pythagorean theorem is used to get the (moveable) distance from the man to the lamppost, but it is the "normal" 2-D version.
Prob 8: Some tried to differentiate the length of the ladder and get a non-zero number.
Prob 9:
a) Must be done by multiplying (and dividing) by the conjugate.
Then, when dividing top and bottom by x, inside the square
root, the x "turns into" an x2.
NOTE: One can NOT use L'Hopital's rule unless one has
a fraction!
The correct answer is 0.
b) If one uses L'Hopital's rule without first dividing out (top and
bottom) an x then one must use the product rule
for xsin(x) in the numerator.
Prob 10: As on the similar problem on the sample final exam, to "solve a differential equation" means to find the integral, and then compute the value of C based on the additional information (in this case, the values x=1, y=1). Several people had arithmetic problems getting the correct value of the constant(s).
Prob 11: This was one step simpler than a similar problem on the sample final.
Prob 12: Some people had problems with simple substitution.
Some people forgot the basic rules that
(1) one cannot "take out" a variable (expression/function) from within an integral;
(2) one should NEVER have TWO different variables inside the
same integral;
(3) when one has two functions of x MULTIPLIED (or divided) inside an
integral, one can NOT integrate them independently (of course, a
correct substitution may change this into a single function of
u).
If one is tempted to use (1) or has used a substitution resulting in (2),
the substitution is incorrect.
Some people used derivative rules rather than
integration rules!
A few forgot to add "+C" at each integration result.
In (a) several people did not use the denominator correctly. The
expression should have been separated into three fractions and a
"simplification" should have been performed to reduce each fraction to
a form that would make it easy to integrate. Some people "added" the
denominator to the numerator (with a negative exponent): if
anything, it should have been multiplied.
final nfinal
224 71
222 70
222 70
217 67
213 65
212 64
210 63
206 61
203 59
199 56
198 56
197 55
197 55
195 54
194 54
192 52
189 51
171 40
161 35
158 33
156 32
152 29
150 28
134 19
123 13
MAXIMUM 250 100
x
x
x x
x x
x x x
x x x x
x x x x x x
x x x x x x
120- 140- 160- 180- 200- 220-
139 159 179 199 219 239
(2) (4) (2) (8) (6) (3)
This page is maintained by Dennis C. Smolarski, S.J.
Email: dsmolarski "at" scu.edu
© Copyright 2011 Dennis C. Smolarski, SJ, All rights reserved.
Last changed: 8 December 2011.