AP Calculus BC 2025 Scoring Guidelines

AP Calculus BC 2025 Scoring Guidelines

The AP Calculus BC 2025 Scoring Guidelines provide detailed information on how to evaluate student responses for the AP Calculus BC exam. It outlines the scoring criteria for various types of questions, including free-response sections that assess students' understanding of calculus concepts. Educators and students can utilize these guidelines to prepare effectively for the exam, ensuring they understand the expectations for scoring. The guidelines include examples of model solutions and scoring notes that clarify how points are awarded for specific answers. This resource is essential for AP Calculus BC students aiming to maximize their performance on the exam.

Key Points

  • Details scoring criteria for AP Calculus BC free-response questions
  • Includes model solutions and scoring notes for clarity
  • Helps educators evaluate student performance effectively
  • Essential for students preparing for the AP Calculus BC exam
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2025
AP
®
Calculus BC
Scoring Guidelines
© 2025 College Board. College Board, Advanced Placement, AP, AP Central, and the acorn logo are registered
trademarks of College Board. Visit College Board on the web: collegeboard.org.
AP Central is the official online home for the AP Program: apcentral.collegeboard.org.
AP® Calculus AB/BC 2025 Scoring Guidelines
© 2025 College Board
Part A (AB or BC): Graphing calculator required
Question 1 9 points
General Scoring Notes
• The model solution is presented using standard mathematical notation.
• Answers (numeric or algebraic) need not be simplified. Answers given as a decimal approximation should
be accurate to three places after the decimal point. Within each individual free-response question, at most
one point is not earned for inappropriate rounding.
An invasive species of plant appears in a fruit grove at time
t = 0
and begins to spread. The function C
defined by
C
(
t
)
= 7.6arctan
(
0.2t
)
models the number of acres in the fruit grove affected by the species t
weeks after the species appears. It can be shown that
38
Ct
′
( )
=
.
25 + t
2
(Note: Your calculator should be in radian mode.)
Model Solution Scoring
A
Find the average number of acres affected by the invasive species from time
t = 0
to time
t = 4
weeks.
Show the setup for your calculations.
1
4
C
(
t
)
dt
40−
∫
0
Average value
formula
Point 1 (P1)
1
=
(
11.112896
)
= 2.778224
4
From time
t = 0
to
t = 4
weeks, the average number of acres
affected by the invasive species was 2.778 acres.
Answer Point 2 (P2)
AP® Calculus AB/BC 2025 Scoring Guidelines
© 2025 College Board
Scoring Notes for Part A
• P1 is earned for the correct integral, with or without the differential, along with evidence of division
by 4. In the presence of the correct integral, the correct answer will suffice as evidence of division
by 4. These may appear all in one step, as in the model solution, or in multiple steps.
• P2 is earned for the correct answer, with or without supporting work. A reported answer should be
accu
rate to three places after the decimal point, rounded or truncated. An inappropriately rounded
answer does not earn the point.
• Incorrect or unclear communication between the correct integral and the correct answer is treated as
s
cratch work and is not considered in scoring. For example:
o
∫
4
C
(
t
)
dt = 11.112896
0
so the average velocity is 2.778224.
Note: This response earns P1 for the correct integral with the correct answer as evidence of
di
vision by 4. It also earns P2 for the correct answer.
o
∫
4
11.112896
C
(
t
)
dt = = 2.778 42 2
0
4
Note: This response earns P1 for the correct integral with the correct answer as evidence of
division by 4. It also earns P2 for the correct answer. (In this instance, incorrect linkage is not
considered in scoring.)
o
∫
4
C
(
t
)
dt = 2.778224
0
Note: This response earns P1 for the correct integral with the correct answer as evidence of
division by 4. It also earns P2 for the correct answer. (In this instance, incorrect linkage is not
considered in scoring.)
• Note that the values
1
(
11.112
)
4
and
1
(
11.113
)
4
are accurate to three digits after the decimal and
therefore earn P2.
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Faqs of AP Calculus BC 2025 Scoring Guidelines
What types of questions are included in the AP Calculus BC scoring guidelines?
The AP Calculus BC scoring guidelines cover various types of questions, including multiple-choice and free-response sections. The free-response questions assess students' ability to apply calculus concepts to solve problems, while the multiple-choice questions test their understanding of calculus principles. Each question type has specific scoring criteria that are clearly outlined in the guidelines, helping educators and students understand how to approach the exam.
How are points awarded for free-response questions in AP Calculus BC?
Points for free-response questions in AP Calculus BC are awarded based on specific criteria outlined in the scoring guidelines. Each question typically has a model solution that demonstrates the expected approach and reasoning. Educators evaluate student responses against these model solutions, awarding points for correct answers, appropriate methods, and clear communication of mathematical reasoning. The guidelines emphasize the importance of showing work and justifying answers to maximize scoring.
What is the significance of the model solutions provided in the scoring guidelines?
Model solutions in the AP Calculus BC scoring guidelines serve as benchmarks for what is expected in student responses. They illustrate the correct methods and reasoning needed to achieve full credit on free-response questions. By studying these model solutions, students can gain insights into effective problem-solving strategies and the level of detail required in their answers. This understanding is crucial for performing well on the exam.
How can students use the scoring guidelines to prepare for the AP Calculus BC exam?
Students can use the AP Calculus BC scoring guidelines to familiarize themselves with the exam format and expectations. By reviewing the scoring criteria and model solutions, they can identify key concepts and problem-solving techniques that are frequently tested. Practicing with past exam questions and comparing their responses to the scoring guidelines can help students improve their performance and confidence on test day.
What role do scoring notes play in the evaluation process?
Scoring notes in the AP Calculus BC scoring guidelines provide additional context and clarification for how points are awarded. They explain common student errors, acceptable variations in solutions, and the rationale behind scoring decisions. These notes are valuable for educators as they evaluate responses and ensure consistency in scoring across different student submissions. Understanding these notes can also help students refine their answers to align better with scoring expectations.