exam3

=Examination 3=

This exam assesses the main topics of chapter 4, which focus mostly on applications of the derivative for analysis of functions and solving optimization problems. Part 1 will focus on differentiation skills and limits at infinity. Part 2 will involve more concept-rich questions that cover the range of topics in chapter 4. Overall, performance was uniformly strong on most questions, though I was surprised by a few. Specifically, question number six on part two (an optimization problem where one proves a minimum sum for a pair of "positive, real numbers") seemed to trip up most folks; I realized only after I began grading that they had interpreted the 'find two numbers' part of it as 'find two integers.' Therefore, most people did not engage this as a calculus problem (and lost most of the points as a result). Also worth noting was the common practice of not supplying enough work to justify answers given. This is not surprising behavior for younger mathematics students, so I saw the overall exam scores more as a referendum on students' reading skills and showing of work, and less a referendum on their deeper understanding of calculus. Yet, this gets at the age-old dilemma all mathematics teachers face -- how can we properly (i.e., accurately) assess what students understand without proper (i.e., complete, explicit) evidence, in the form of performances or worked-out problem solving? Aside from developing mind-reading abilities, I'm not sure that there's a reasonable alternative to helping students get better at supplying what teachers require.


 * PDFs of Exam 3 and its Answer Key:**
 * [[file:Math 151 (WN10) Exam 3.pdf]]
 * [[file:Math 151 (WN10) Exam 3 (KEY).pdf]]


 * PDFs of Exam 3 Review and its Answer Key:**
 * [[file:Math 151 exam 3 review v2.pdf]]
 * [[file:Math 151 exam 3 review (KEY) v2.pdf]]
 * Exam 3 In-Class Practice:**
 * [[file:Math 151 exam 3 practice.pdf]]
 * **Images of student-generated solutions:** **Exam_3_Practice_1; Exam_3_Practice_2; Exam_3_Practice_3; Exam_3_Practice_4)**


 * Descriptive statistics regarding student performance on Examination 3:**

(n = 10, for both parts)

//Part 1//: (25 points)
 * Mean: 19.3
 * Median: 19.5
 * Mode:24
 * Standard Deviation: 4.5

//Part 2//: (75 points)
 * Mean: 51.2
 * Median: 54.5
 * Mode: N/A
 * Standard Deviation: 11.6