## Calculus Examination Report--June 2007

Participation: The exam was written by 199 students, although 209 had registered and paid the non-refundable fee. Among the 199 students who wrote, 195 earned a raw score of 10% or higher. All statistics that follow refer to this group of 195.

Summary: Of the 195 students discussed below, 128 earned a score of 50% or better. In other words, 66% of the participants passed the test and are eligible to claim credit at a sponsoring university. The median grade was 59%. (These scores reflect a modest upward scaling.)

Scores of 85% or higher were earned by 20 students; scores below 30% were recorded by 17 students. There were three raw scores above 90%: scaling boosted these to 97%, 98%, and 99%.

Details: For each question, the following table shows the scores that separate the participants into four equally-sized cohorts: the median score has half the group above and the other half below; quartiles 1 and 3 bisect the lower and upper halves again. Scores are reported using percentages instead of individual points to make comparisons easier.

 Question Point Value Quartile 1 (%) Median (%) Quartile 3 (%) Q1 (tan line) 4 75 100 100 Q2 (implicit diff) 6 67 100 100 Q3 (derivative rules) 6 67 83 100 Q4 (limits) 6 33 50 50 Q5 (derivative def) 6 50 100 100 Q6 (linear approx) 6 0 17 33 Q7 (related rates) 8 0 37.5 62.5 Q8 (moving point) 7 29 71 86 Q9 (logarithmic diff & limits) 5 0 20 40 Q10 (exponential growth & decay) 8 0 25 75 Q11 (curve-sketching) 10 30 60 80 Q12 (linearization/Newton's Method) 6 0 17 50 Q13 (optimization) 8 0 0 0 Q14 (concavity) 8 37.5 62.5 87.5 Q15 (integrals) 6 33 50 100

Commentary: Students did extremely well on questions 1, 2, 3, and 5, and reasonably well on 8, 10, 11, 14, and 15. Questions 13, 6, and 9 were devastating for these students. Here are links to the Exam Questions, the Detailed Solutions, and Graders' Comments.

Scaling: Modest upward scaling was applied.

(Click a graphic to recheck.)