AP Calculus AB Practice Test
- How limits help us to handle change at an instant (20)
- Definition and properties of limits in various representations (20)
- Definitions of continuity of a function at a point and over a domain (20)
- Asymptotes and limits at infinity (20)
- Reasoning using the Squeeze theorem and the Intermediate Value Theorem (20)
- Defining the derivative of a function at a point and as a function (20)
- Connecting differentiability and continuity (20)
- Determining derivatives for elementary functions (20)
- Applying differentiation rules (20)
- The chain rule for differentiating composite functions (20)
- Implicit differentiation (20)
- Differentiation of general and particular inverse functions (20)
- Determining higher-order derivatives of functions (20)
- Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change (20)
- Applying understandings of differentiation to problems involving motion (20)
- Generalizing understandings of motion problems to other situations involving rates of change (20)
- Solving related rates problems (20)
- Local linearity and approximation (20)
- L’Hospital’s rule (20)
- Mean Value Theorem and Extreme Value Theorem (20)
- Derivatives and properties of functions (20)
- How to use the first derivative test; second derivative test and candidates test (20)
- Sketching graphs of functions and their derivatives (20)
- How to solve optimization problems (20)
- Behaviors of Implicit relations (20)
- Using definite integrals to determine accumulated change over an interval (0)
- Approximating integrals using Riemann Sums (10)
- Accumulation functions; the Fundamental Theorem of Calculus and definite integrals (0)
- Antiderivatives and indefinite integrals (0)
- Properties of integrals and integration techniques; extended (20)
- Interpreting verbal descriptions of change as separable differential equations (20)
- Sketching slope fields and families of solution curves (20)
- Solving separable differential equations to find general and particular solutions (20)
- Deriving and applying a model for exponential growth and decay (10)
- Determining the average value of a function using definite integrals (20)
- Modeling particle motion (20)
- Solving accumulation problems (20)
- Finding the area between curves (20)
- Determining volume with cross-sections; the disc method and the washer method (20)
Exam Format & Components
Section 1 : Multiple Choice
45 Questions | 1hr 45mins | 50% of Score
The multiple-choice section of the AP Calculus AB exam is divided into two parts, testing a comprehensive range of calculus concepts through different types of functions and representations:
Part A (No Calculator):
Questions: 30 (33.3% of score)
Focus: Tests your ability to solve calculus problems manually, involving algebraic, exponential, logarithmic, trigonometric, and other general function types.
Representations: Includes analytical, graphical, tabular, and verbal forms to assess your understanding from multiple perspectives.
Part B (Calculator Permitted):
Questions: 15 (16.7% of score)
Focus: Requires the use of a graphing calculator to solve some questions, emphasizing your ability to integrate technology effectively in solving complex calculus problems.
Types of Questions: Continues to explore a broad spectrum of functions and representations, similar to Part A, but with the added complexity that calculators can help manage.
Section 2 : Free Response
6 Questions | 1hr 30mins | 50% of Score
Components:
Part A (Calculator Required):
Problems: 2 (16.7% of score)
Focus: Challenges you to apply graphing calculators in solving intricate calculus problems, testing both procedural and conceptual understanding.
Context: At least one problem will likely incorporate a real-world scenario, linking theoretical calculus concepts to practical applications.
Part B (No Calculator):
Problems: 4 (33.3% of score)
Focus: Tests your ability to solve calculus problems without the aid of a calculator, focusing on a clear understanding of fundamental calculus principles and techniques.
Content: Includes a mix of procedural and conceptual tasks, with at least one problem set in a real-world context to evaluate how you apply calculus concepts to analyze and solve real-life problems.
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