AP Calculus BC FRQ 2025 Questions And Answers

AP Calculus BC is a college-level calculus course designed to introduce students to the concepts and techniques of differential and integral calculus. It covers topics typically found in a first-semester college calculus course.

Questions And Worked Solutions For AP Calculus BC FRQ 2025

Click on the following image to get the complete paper of AP Calculus BC 2025 Free Response Questions. Scroll down the page for step-by-step solutions.

 
AP Calculus BC 2025 Free Response Questions - Complete Paper (pdf)

• AP Calculus BC 2025 Free Response Question 1

1. 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. …

• AP Calculus BC 2025 Free Response Question 2

2. Curve C is defined by the polar equation r(θ) = 2sin²θ for 0 ≤ θ ≤ π …

• AP Calculus BC 2025 Free Response Question 3

3. A student starts reading a book at time t = 0 minutes and continues reading for the next 10 minutes. The rate at which the student reads is modeled by the differentiable function R, where R(t) is measured in words per minute.

• AP Calculus BC 2025 Free Response Question 4

4. The continuous function f is defined on the closed interval -6 ≤ x ≤ 12. The graph of f,consisting of two semicircles and one line segment, is shown in the figure.

• AP Calculus BC 2025 Free Response Question 5

5. Let y = f(x) be the particular solution to the differential equation …

• AP Calculus BC 2022 Free Response Question 6

6. The Taylor series for a function f about x = 4 is given by …

Key Topics in AP Calculus BC:

1. All AP Calculus AB Topics:
   Limits and Continuity
   Derivatives (including all rules)
   Applications of Derivatives
   Integrals (including u-substitution)
   Fundamental Theorem of Calculus
   Applications of Integrals
   

2. Additional BC Topics:
   a) Advanced Integration Techniques:
   Integration by parts.
   Partial fractions.
   Improper integrals.
   b) Parametric Equations, Polar Coordinates, and Vector-Valued Functions:
   Derivatives and integrals of parametric equations.
   Derivatives and integrals in polar coordinates.
   Vector-valued functions and their derivatives and integrals.
   c) Infinite Series:
   Convergence and divergence of series.
   Taylor series and Maclaurin series.
   Power series.
   Lagrange error bound.
   d) Differential Equations:
   Euler’s method.
   Logistic differential equations.
   

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