# Calculus Exam Report--June 2001

Overview: The exam was written by 257 students, although 264 had registered and paid the non-refundable fee. A score of 86% or better earned a position in the Top Ten; there were ten students scoring 14% or less.

Question-by-question results are shown in the following table. To illustrate the meaning of its entries, consider Question 4. The question was worth 4% of the examination score. About 93% of all candidates earned at least some part marks on this question, while 76% of all candidates got 3/4 or 4/4. Within the group of students who attempted this question (i.e., those scoring one mark or more), the average score was 80%.

 Question Value (%) % earningScore > 0 % earningScore > 74% Average Score (%) (using only score>0) Q1 12 100 77 80 Q2 6 95 70 80 Q3 6 93 72 84 Q4 4 93 76 83 Q5 8 90 33 51 Q6 8 95 55 70 Q7 8 76 63 84 Q8 6 24 11 66 Q9 6 95 51 74 Q10 8 84 39 64 Q11 10 43 17 51 Q12 9 93 72 86 Q13 9 79 4 24 TOTAL 100 100 19 57

Remarks: Most students had difficulty with the conceptual questions 8 and 13, and with the optimization problem 11; many lost points on 5(b) and 10. Basic calculus activities like calculating derivatives from well-known rules and translating derivative information into a reasonable sketch were generally well done. Standard application-oriented questions (related rates, velocity and acceleration, exponential growth and decay) fell in the middle. These patterns are typical.

Scaling: The official scores are slightly higher than the raw scores summarized above. Marks were raised slightly by adjusting the percentage values of the questions to increase the influence of the standard-skills questions (all but 8 and 13). This produced an overall average score of 62%, with 28% of the candidates earning a score of 75% or higher, and 28% failing. The remaining 44% of all candidates passed with percentage scores between 50% and 74%. These percentages match the results of previous years very closely.

After scaling, the Top Ten scores ranged from 93% to 99%; the candidate 10th from the bottom earned just 16%.