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

Here are links to the Exam Questions, Detailed Sample Solutions, and Comments from the Graders.

(Calculus Exam home page.)

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