## AP Calculus

### Introduction

The AP Calculus test has two different versions: AB and BC. Both tests consist of two sections; Section I is multiple choice, and Section II is free response. Both sections contain questions that require a graphing calculator, as well as questions on which a graphing calculated is not permitted. The total exam is 3 hours and 15 minutes.

An AP Calculus AB course is typically equivalent to one semester of college calculus, whereas an AP Calculus BC course is typically equivalent to a full-year college calculus course. Thus, at most universities, an AP Calculus AB score of 4 or 5 would allow a student to skip out of one semester of Calculus, whereas an AP Calculus BC score of 4 or 5 would allow a student to skip out of a year-long calculus course.

- Analysis of graphs
- Limits of functions
- Asymptotic and unbounded behavior
- Continuity as a property of functions
- Parametric, polar, and vector functions

**Functions, graphs, and limits**

- Concepts of a derivative
- Derivative at a point
- Derivative as a function
- Second derivatives
- Applications of derivatives
- Computation of derivatives

**Derivatives**

- Interpretations and properties of definite integrals
- Applications of integrals
- Fundamental Theorem of Calculus
- Techniques of antidifferentiation
- Applications of antidifferentiation
- Numerical approximations to indefinite integrals

**Integrals**

- Concept of series
- Series of constants
- Taylor series

**The AP Calculus BC exam tests all of the above**

*as well*as the following:The format for both the AB and BC exams is as follows:

Section |
Number of Questions |
Time |
Calculator Allowed |
---|---|---|---|

Multiple choice Part A |
28 |
55 minutes |
No |

Multiple choice Part B |
17 |
50 minutes |
Yes |

Free-response Part A |
2 |
30 minutes |
Yes (and necessary) |

Free-response Part B |
4 |
60 minutes |
No |

**Important idiosyncrasies**

Multiple-Choice:

In the multiple-choice section, points are awarded according to the number of questions answered correctly, and no points are deducted for incorrect answers. Thus, students should always answer every question.

Free-response:

During the second time portion in the free-response (part B) students are allowed to continue to work on part A, but they are no longer allowed to use a calculator.

Multiple-choice questions can receive a maximum of 1 point, with no partial credit possible. Each free-response question is scored out of 9 points, with partial credit given according the written work of the student. Scores on the free response questions, which are scored by graders, are weighted and combined with the machine-scored multiple-choice questions to produce a score between 1 and 5. The total correct answers in the multiple choice section are multiplied by 1.2, and then added to the raw free response score to determine the composite score. This score is compared to the composite-score scale of that year’s exam to determine an AP score of 1 – 5. Section I and Section II both have equal weight.

A score of 5 is called “extremely well qualified” and a score of 4 is called “well qualified”, which is why these scores are honored by universities that give credit for AP exams. A grade of 3 is called “qualified”, and is unlikely to be counted for college credit or placement. A grade of 2, “possibly qualified”, or a grade of 1, “no recommendation” are extremely unlikely to earn any kind of credit from a university.

The table below breaks down the 2010 scores on both the AB and BC exams:

Grade |
Calculus AB |
Calculus BC |
---|---|---|

5 |
21.2% |
49.4% |

4 |
16.4% |
15.4% |

3 |
18% |
18% |

2 |
11.2% |
5.8% |

1 |
33.1% |
11.4% |

3 or higher |
55.7% |
82.8% |

Clearly, a large percentage of students score highly (4 or 5) on both the AB and BC versions of the exam. Thus, exam score is highly correlated to preparation during the corresponding course in the academic year, rather than highly specialized additionally studying, such as on the SAT.

- Plot the graph of a function within an arbitrary viewing window
- Find the zeros of functions
- Numerically calculate the derivate of a function
- Numerically calculate the value of a definite integral

Across the exam, outside of just calculator-involved questions, students must show their work to receive credit. Answers that include explanations or justifications should use complete sentences. Methods, reasoning, and conclusions must be clearly presented if the student wishes to receive full credit.