# AP Calculus BC 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)*

*(40)*

- Using definite integrals to determine accumulated change over an interval
*(0)* - Approximating integrals with 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)* - Determining improper integrals
*(10)*

*(70)*

- Interpreting verbal descriptions of change as separable differential equations
*(20)* - Sketching slope fields and families of solution curves
*(20)* - Using Euler’s method to approximate values on a particular solution curve
*(0)* - Solving separable differential equations to find general and particular solutions
*(20)* - Deriving and applying exponential and logistic models
*(10)*

*(110)*

- 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)* - Determining the length of a planar curve using a definite integral
*(10)*

*(60)*

- Finding derivatives of parametric functions and vector-valued functions
*(10)* - Calculating the accumulation of change in length over an interval using a definite integral
*(10)* - Determining the position of a particle moving in a plane
*(10)* - Calculating velocity; speed and acceleration of a particle moving along a curve
*(10)* - Finding derivatives of functions written in polar coordinates
*(10)* - Finding the area of regions bounded by polar curves
*(10)*

*(50)*

- Applying limits to understand convergence of infinite series
*(10)* - Types of series: Geometric; harmonic and p-series
*(10)* - A test for divergence and several tests for convergence
*(0)* - Approximating sums of convergent infinite series and associated error bounds
*(10)* - Determining the radius and interval of convergence for a series
*(10)* - Representing a function as a Taylor series or a Maclaurin series on an appropriate interval
*(10)*

## Exam Format & Components

**Section 1 : Multiple Choice**

45 Questions | 1hr 45mins | 50% of Score

**Detailed Breakdown**:

**Part A**: No graphing calculator permitted. This section includes 30 questions (33.3% of the score), focusing on your ability to manually solve problems involving algebraic, exponential, logarithmic, trigonometric, and other types of functions.**Part B**: Graphing calculator required. Comprises 15 questions (16.7% of the score), where you’re expected to solve more complex problems that may involve higher-level calculations and interpretations using graphical, tabular, and verbal forms of data.

**Section 2 : Free Response**

6 Questions | 1hr 30mins | 50% of Score

**Detailed Breakdown**:

**Part A**: Graphing calculator required. Consists of 2 problems (16.7% of the score) that typically require computational solutions with graphical representations, often integrating real-world applications to assess both procedural and conceptual understanding.**Part B**: No graphing calculator permitted. Includes 4 problems (33.3% of the score), focusing on a variety of functions and function representations. This part emphasizes a balance between procedural tasks and conceptual questions, including at least two scenarios that involve real-world contexts to demonstrate practical applications of calculus concepts.

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