## Calculus Examination Report—June 2011

Participation: The exam was written by 78 students, although 82 had registered and paid the non-refundable fee.

Summary: Of the 78 students who submitted a paper, 52 earned a score of 50% or better. In other words, 67% of the participants passed the test and are eligible to claim credit at a sponsoring university. The median grade was 66%. (These scores reflect a modest upward scaling.)

Scores of 90% or higher were earned by 10 students; scores below 30% were recorded by 8 students. There was a two-way tie for the top score of 95%.

 Summary Statistics Maximum 95.0 Minimum 4.0 Mean 61.7 Median 66.0 Standard deviation 22.2

Details: For each question, the following table shows the scores that separate the participants into four equally-sized groups. The median score divides the group in half; 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 ([anti-]derivatives) 10 60 80 90 Q2 (limits) 9 56 67 67 Q3 (implicit diff) 10 40 70 90 Q4 (linear approx) 5 40 40 100 Q5 (exp decay) 5 0 100 100 Q6 (tangent lines) 8 13 25 63 Q7 (def of deriv) 8 50 63 75 Q8 (combo) 6 0 17 17 Q9 (given accel) 6 50 100 100 Q10 (related rates) 8 13 63 63 Q11 (optimization) 9 22 44 100 Q12 (curve sketching) 9 33 56 89 Q13 (2-part area) 7 57 100 100 TOTAL 100 47 66 81