AP Calculus AB FRQ 2024 Questions And Answers

AP Calculus AB 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 AB FRQ 2024

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

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

FRQ 1 concerns the temperature of coffee and a table of values
FRQ 2 concerns a particle moving along the x-axis
FRQ 3 concerns the depth of seawater and a differential equation
FRQ 4 concerns a graph and integrals for areas
FRQ 5 concerns an implicitly defined curve, implicit differentiation, and tangents
FRQ 6 concerns volumes of solids and areas.

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 moves along the x-axis so that its velocity at time t ≥ 0 is given by v(t) = ln (t² - 4t + 5) - 0.2t.
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. Consider the curve defined by the equation x² + 3y + 2y² = 48
6. The functions f and g are defined by f(x) = x² + 2 and g(x) = x² - 2x, as shown in the graph.

Key Topics in AP Calculus AB:
The course content is organized into eight commonly taught units, which have been arranged in the following suggested, logical sequence:
■ Unit 1: Limits and Continuity
■ Unit 2: Differentiation: Definition and Fundamental Properties
■ Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
■ Unit 4: Contextual Applications of Differentiation
■ Unit 5: Analytical Applications of Differentiation
■ Unit 6: Integration and Accumulation of Change
■ Unit 7: Differential Equations
■ Unit 8: Applications of Integration

AP Calculus AB Exam Structure
The AP Calculus AB exam is divided into two sections: Multiple Choice and Free Response.

Section I: Multiple Choice
45 Questions | 1 Hour 45 minutes | 50% of Exam Score
Part A: 30 questions; 60 minutes (calculator not permitted).
Part B: 15 questions; 45 minutes (graphing calculator required).
Questions include algebraic, exponential, logarithmic, trigonometric, and general types of functions.
Questions include analytical, graphical, tabular, and verbal types of representations.

Section II: Free Response
6 Questions | 1 Hour 30 Minutes | 50% of Exam Score
Part A: 2 questions; 30 minutes (graphing calculator required).
Part B: 4 questions; 60 minutes (calculator not permitted).
Questions include various types of functions and function representations and a roughly equal mix of procedural and conceptual tasks.
Questions include at least 2 questions that incorporate a real-world context or scenario into the question.

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