AP Calculus BC 2024 Questions And Answers

AP Calculus AB is designed to be the equivalent of a first semester college calculus course devoted to topics in differential and integral calculus. AP Calculus BC is designed to be the equivalent to both first and second semester college calculus courses. AP Calculus BC applies the content and skills learned in AP Calculus AB to parametrically defined curves, polar curves, and vector-valued functions; develops additional integration techniques and applications; and introduces the topics of sequences and series.

Questions And Worked Solutions For AP Calculus BC 2024

Click on the following image to get the complete paper of AP Calculus BC 2024 Free Response Questions. Scroll down the page for step-by-step solutions.

 
AP Calculus BC 2024 Free Response Questions - Complete Paper (pdf)

• AP Calculus BC 2024 Free Response Question 1

• AP Calculus BC 2024 Free Response Question 2

• AP Calculus BC 2024 Free Response Question 3

• AP Calculus BC 2024 Free Response Question 4

• AP Calculus BC 2024 Free Response Question 5

• AP Calculus BC 2024 Free Response Question 6

1. The temperature of coffee in a cup at time t minutes is modeled by a decreasing differentiable function C, where C(t) is measured in degrees Celsius. For 0 ≤ t ≤ 12, selected values of C(t) are given in the table shown.
2. A particle moving along a curve in the xy-plane has position (x(t),y(t)) at time t seconds, where x(t) and y(t) are measured in centimeters.
3. The depth of seawater at a location can be modeled by the function H that satisfies the differential equation
4. The graph of the differentiable function f , shown for −6 ≤ x ≤ 7, has a horizontal tangent at x = −2 and is linear for 0 ≤ x ≤ 7. Let R be the region in the second quadrant bounded by the graph of f , the vertical line x = −6, and the x- and y-axes. Region R has area 12.
5. The function f is twice differentiable for all x with f(0) = 0. Values of f’, the derivative of f , are given in the table for selected values of x.
6. The Maclaurin series for a function f 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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