# AP Calculus BC Exam: 2021 Results

The following data reflect the 124,335 students worldwide who took either the paper or the digital AP Calculus BC Exam prior to June 12.

## AP Calculus BC score distributions, 2019 vs. 2021

The following table enables comparisons of student performance in 2021 to student performance on the comparable full-length exam prior to the covid-19 pandemic.

AP Score | 2019 | 2021 |
---|---|---|

5 | 43% | 38% |

4 | 18% | 17% |

3 | 20% | 20% |

2 | 14% | 18% |

1 | 5% | 7% |

It’s important to honor the work of students who did not qualify for a score of 3+, but who nonetheless developed basic understandings and skills in the course. As a reminder, the most recent research on students who achieve a score of 2 in AP Calculus BC found that they proceed to earn significantly higher grades when taking the course in college than students with the same high school GPA, SAT score, race, and gender. And these outcomes are stronger for AP Calculus BC students who receive a 2 than they are for students receiving 2s in most other AP subjects.

## The May 4 In-School Paper Exam

The largest exam date for AP Calculus BC was May 4, so the following information is specific to the exam version administered on that date.

As usual, students scored significantly higher on the multiple-choice section than on the free-response questions.

**Multiple-Choice Section**

- Course Units:
- AP Calculus BC students generally performed well across units but found Unit 10 (Infinite Sequences and Series) the most challenging, followed by Unit 9 and Unit 6.

**Free-Response Section:**- The strongest results were typically on Question 4, the graphical analysis. 35% of students earned 7–9 points out of 9 possible.
- By far the most challenging questions on this year’s exam were:
- Question 2, about parametric particle motion; 5% of students earned 7–9 points out of 9 possible; 28% of students earned 0 points.
- Question 6, integral test-limit; 5% of students earned 7–9 points out of 9 possible; 27% of students earned 0 points.
- Differences in the testing mode (paper or digital). For sections of the exam that proved easier to take digitally, the digital versions require more points for each AP score. For sections of the exam that proved easier to take on paper, the paper exam requires more points for each AP score.
- Differences in the difficulty of specific questions. When exam questions prove easier, more points are required for each AP score, and when exam questions prove more difficult, fewer points are required on one version than another.
- The net result for this year’s AP Calculus BC Exams is that out of 108 points possible, some of the digital versions were equivalent in difficulty to the paper versions, and some of the digital versions were slightly more difficult. Accordingly, students taking one of the more difficult digital versions needed to earn 1–6 fewer points, depending on their version, than students who took the paper exam on May 4.

## The Digital Exams

To support student access, different testing modes—paper and digital—were essential. To protect exam security, many different exam versions were necessary. Accordingly, to provide students with similar opportunities for success regardless of which version they took, each version of the exam had to be analyzed separately by psychometricians to identify its unique difficulty level so that standards for scores of 3, 4, and 5 could then be separately identified for each exam version. Analyses focused on: