The first exam

The two versions of the exam had very similar statistical results. 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:

Discussion of the grading

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 (12 points)
a) (6 points) A Quotient Rule error loses 2 points. More minor errors lose a point.
b) (2 points) 1 point for each answer. Knowing that e⁰=1 is worth 1 point in this problem.
c) (2 points) For any correct equation of the line.
d) (2 points) Geometric slope and point are each worth 1 point: the line should look tangent.

Problem 2 (8 points)
1 point for g(1); 2 points for g´(x) and 1 point for for g´(1); 3 points for g´´(x) and 1 point for for g´´(1). 2 points off for an error in the Product Rule or the Chain Rule.

Problem 3 (10 points)
2 points for correctly instantiating [f(x+h)-f(x)]/h. This is mostly for substitution of x+h into f (or something equivalent). If this formula is not quoted correctly, then no credit can be earned in this problem (it is difficult to compute f´(x) from the definition when the definition isn't known!). If somehow the student writes 3–x+h instead of 3–(x+h) the student loses these 2 points, but they can be the only 2 points lost of the 10 if everything else is correctly done.
3 points for correctly combining the fractions.
2 points for cancelling the h's.
1 point for the answer, which must be the correct answer for the student's work.
2 points off if there is no mention of lim_h→0 in an otherwise correct solution.
The answer alone or the answer obtained algorithmically earns no credit.

Problem 4 (12 points) Each part is worth 4 points. Simple arithmetic errors lose 1 point each. Errors with the Product Rule or the Quotient Rule lose 2 points each.

Problem 5 (12 points)
The idea of taking the derivative and trying to find x so the derivative is 0 earns 3 points alone (if this can be read sufficiently clearly).
The correct derivative is worth 5 points. Solving for an x where f´(x)=0 earns the remaining 4 points.
Credit can be lost for assuming incorrect algebraic properties of logs or exponents.

Problem 6 (12 points)
4 points for the hypotenuse in terms of x (2 of these for the "legs" of the right triangle, and 2 of these for correctly using this information to get the hypotenuse).
3 points for the correct total length of the horizontal and vertical sides.
2 points for a correct formula for f(x).
3 points for a correct domain (with or without either or both endpoints). 1 of these points is earned for a specification of x>0 or x≥0.

Problem 7 (8 points)
The word continuous in relevant context earns 2 points. The phrase Intermediate Value Theorem in relevant context earns 2 points. This means that just scrawling (scrawl: "write in a hurried untidy way") the word "continuous" or the phrase "Intermediate Value Theorem" will not necessarily earn credit. 1 point is earned for a function value which is positive, and 1 point is earned for a function value which is negative. Finally, an explicit correct answer supported by the student's work earns 2 points (an interval of the form [0,something] in a similar context earns 1 point).
Comment The problem statement contains the following:

You must give evidence supporting your assertion -- the interval given can be any valid interval. The evidence should include specific vocabulary and results from this course.

Problem 8 (12 points)
a) (5 points) Factoring the top and bottom is worth 3 points. Cancellation and evaluation earns the remaining 2 points, 1 of which is for the answer.
b) (2 points) A correct answer earns 1 point. Some support (the word "continuous" or the phrase "plugging in") earns a second point.
c) (5 points) A correct answer earns 1 point. Some analysis (or even just acknowledgment!) of absolute value earns 2 points, and then algebra using this gets 2 more points.

Problem 9 (14 points)
a) (7 points) Restricting attention to 0 and 2 is worth 1 point. 2 points for getting a constraint at 0. 2 points for a similar constraint at 2. 2 points for solving and reporting correct values of A and B.
b) (7 points) The graph should be continuous (2 points). 2 points for the line segments (each correct line segment earns 1 point). 3 points for an increasing, correctly curved parabolic arc (not curved: 2 points off).

Maintained by greenfie@math.rutgers.edu and last modified 10/9/2009.