Problem Set 12

Free-response problems are graded based on your ability to understand and to communicate that understanding of the material. Thus you must show your thought process. To receive full credit, solutions must be complete, legible, and well-organized. Trivial algebraic mistakes that might lead to an incorrect answer might not count against your grade for these problems. However, missing or incorrect explanations, even in the presence of a correct final answer, will be marked down.

The following general rubric will be used for grading each problem part:

• F: No substantial work. Simply writing a few equations or copying facts from the problem will not be awarded points.

• D: Some work, some evidence of knowledge about the material addressed, problem part started, but no significant understanding of the problem or progress shown. For example, pursuing a technically-feasible but non-preferred non-ideal approach to a solution, and then making major mistakes, will be graded in this way. Similarly, if the solution might be correct, but it is impossible to tell due to poorly presented thinking, the work will also be graded in this way.

• C: Meaningful progress toward a correct solution. Examples of this are:

  • pursuing a feasible but non-preferred or non-ideal approach with and making meaningful mistakes; pursuing a correct approach but making one or more major mistakes (including mistakes that may have cancelled each other out);
  • pursuing a correct approach to reach the correct solution but explaining that solution in a confusing manner, i.e. not showing a clear understanding of the reasoning behind the solution; or
  • submitting a solution that might be correct, but is difficult to grade.

• B: Largely correct solution that could benefit from improvement due to important flaws. Examples of this are:

  • pursuing a feasible but non-preferred or non-ideal approach correctly, or with only minor mistakes;
  • pursuing a correct approach but making one or more major mistakes;
  • pursuing a correct approach to reach the correct solution, but making major mistakes that have cancelled one another; or
  • pursuing a correct approach to reach the correct solution but explaining that solution in a confusing manner, not showing a clear understanding of the reasoning behind the solution, or submitting a solution that is difficult to grade.

• A: Exceptional, clear, exemplary solution. Such a solution will:

  • be developed through a preferred approach, with all work clearly labeled and explained well;
  • contain at worst trivial algebraic mistakes, and no sign errors whose origins are conceptual;
  • be easy to grade.

  Note that an A-level solution doesn't need to be long. It need only be based on an appropriate direct approach that is clearly indicated.