# AP Calculus AB Practice Test

*(100)*

- 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)*

*(80)*

- 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)*

*(80)*

- 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)*

*(120)*

- 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)*

*(120)*

- 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)*

*(90)*

- Using definite integrals to determine accumulated change over an interval
*(20)* - Approximating integrals using Riemann Sums
*(10)* - Accumulation functions; the Fundamental Theorem of Calculus and definite integrals
*(20)* - Antiderivatives and indefinite integrals
*(20)* - Properties of integrals and integration techniques; extended
*(20)*

*(70)*

- 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)*

*(100)*

- 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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