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AP Calculus BC
Study AP Calculus BC
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- 1Limits and Continuity
- 2Differentiation: Definition and Fundamental Properties
- 3Differentiation: Composite, Implicit, and Inverse Functions
- 4Contextual Applications of Differentiation
- 5Analytical Applications of Differentiation
- 6Integration and Accumulation of Change
- 7Differential Equations
- 8Applications of Integration
- 9Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- 10Infinite Sequences and Series
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- AP Calculus BC — Question index
- 1.15 Connecting Limits at Infinity and Horizontal Asymptotes
- 1.16 Working with the Intermediate Value Theorem (IVT)
- 2.1 Defining Average and Instantaneous Rates of Change at a Point
- 2.3 Estimating Derivatives of a Function at a Point
- 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
- 2.7 Derivatives of cos x, sin x, e^x, and ln x
- 2.8 The Product Rule
- 2.9 The Quotient Rule
- 3.1 The Chain Rule
- 3.2 Implicit Differentiation
- 3.6 Calculating Higher-Order Derivatives
- 4.1 Interpreting the Meaning of the Derivative in Context
- 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
- 4.4 Introduction to Related Rates
- 4.5 Solving Related Rates Problems
- 4.6 Approximating Values of a Function Using Local Linearity and Linearization
- 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
- 5.1 Using the Mean Value Theorem
- 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
- 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing
- 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
- 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
- 5.6 Determining Concavity of Functions over Their Domains
- 5.7 Using the Second Derivative Test to Determine Extrema
- 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative
- 5.10 Introduction to Optimization Problems
- 5.12 Exploring Behaviors of Implicit Relations
- 6.1 Exploring Accumulations of Change
- 6.2 Approximating Areas with Riemann Sums
- 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
- 6.4 The Fundamental Theorem of Calculus and Accumulation Functions
- 6.5 Interpreting the Behavior of Accumulation Functions Involving Area
- 6.6 Applying Properties of Definite Integrals
- 6.7 The Fundamental Theorem of Calculus and Definite Integrals
- 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
- 6.11 Integrating Using Integration by Parts
- 6.12 Integrating Using Linear Partial Fractions
- 6.13 Evaluating Improper Integrals
- 7.2 Verifying Solutions for Differential Equations
- 7.3 Sketching Slope Fields
- 7.4 Reasoning Using Slope Fields
- 7.5 Approximating Solutions Using Euler's Method
- 7.6 Finding General Solutions Using Separation of Variables
- 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables
- 8.1 Finding the Average Value of a Function on an Interval
- 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
- 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
- 8.4 Finding the Area Between Curves Expressed as Functions of x
- 8.7 Volumes with Cross Sections: Squares and Rectangles
- 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
- 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis
- 8.12 Volume with Washer Method: Revolving Around Other Axes
- 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled
- 9.1 Defining and Differentiating Parametric Equations
- 9.3 Finding Arc Lengths of Curves Given by Parametric Equations
- 9.4 Defining and Differentiating Vector-Valued Functions
- 9.5 Integrating Vector-Valued Functions
- 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions
- 9.7 Defining Polar Coordinates and Differentiating in Polar Form
- 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
- 9.9 Finding the Area of the Region Bounded by Two Polar Curves
- 10.2 Working with Geometric Series
- 10.4 Integral Test for Convergence
- 10.6 Comparison Tests for Convergence
- 10.7 Alternating Series Test for Convergence
- 10.8 Ratio Test for Convergence
- 10.9 Determining Absolute or Conditional Convergence
- 10.10 Alternating Series Error Bound
- 10.11 Finding Taylor Polynomial Approximations of Functions
- 10.12 Lagrange Error Bound
- 10.13 Radius and Interval of Convergence of Power Series
- 10.14 Finding Taylor or Maclaurin Series for a Function
- 10.15 Representing Functions as Power Series
- 1. Limits and Continuity
- 2. Differentiation: Definition and Fundamental Properties
- 3. Differentiation: Composite, Implicit, and Inverse Functions
- 4. Contextual Applications of Differentiation
- 5. Analytical Applications of Differentiation
- 6. Integration and Accumulation of Change
- 7. Differential Equations
- 8. Applications of Integration
- 9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- 10. Infinite Sequences and Series
- 1.1 Introducing Calculus: Can Change Occur at an Instant?
- 1.2 Defining Limits and Using Limit Notation
- 1.3 Estimating Limit Values from Graphs
- 1.4 Estimating Limit Values from Tables
- 1.5 Determining Limits Using Algebraic Properties of Limits
- 1.6 Determining Limits Using Algebraic Manipulation
- 1.7 Selecting Procedures for Determining Limits
- 1.8 Determining Limits Using the Squeeze Theorem
- 1.9 Connecting Multiple Representations of Limits
- 1.10 Exploring Types of Discontinuities
- 1.11 Defining Continuity at a Point
- 1.12 Confirming Continuity over an Interval
- 1.13 Removing Discontinuities
- 1.14 Connecting Infinite Limits and Vertical Asymptotes
- 1.15 Connecting Limits at Infinity and Horizontal Asymptotes
- 1.16 Working with the Intermediate Value Theorem (IVT)
- 2.1 Defining Average and Instantaneous Rates of Change at a Point
- 2.2 Defining the Derivative of a Function and Using Derivative Notation
- 2.3 Estimating Derivatives of a Function at a Point
- 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
- 2.5 Applying the Power Rule
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
- 2.7 Derivatives of cos x, sin x, e^x, and ln x
- 2.8 The Product Rule
- 2.9 The Quotient Rule
- 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
- 3.1 The Chain Rule
- 3.2 Implicit Differentiation
- 3.3 Differentiating Inverse Functions
- 3.4 Differentiating Inverse Trigonometric Functions
- 3.5 Selecting Procedures for Calculating Derivatives
- 3.6 Calculating Higher-Order Derivatives
- 4.1 Interpreting the Meaning of the Derivative in Context
- 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
- 4.3 Rates of Change in Applied Contexts Other Than Motion
- 4.4 Introduction to Related Rates
- 4.5 Solving Related Rates Problems
- 4.6 Approximating Values of a Function Using Local Linearity and Linearization
- 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
- 5.1 Using the Mean Value Theorem
- 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
- 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing
- 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
- 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
- 5.6 Determining Concavity of Functions over Their Domains
- 5.7 Using the Second Derivative Test to Determine Extrema
- 5.8 Sketching Graphs of Functions and Their Derivatives
- 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative
- 5.10 Introduction to Optimization Problems
- 5.11 Solving Optimization Problems
- 5.12 Exploring Behaviors of Implicit Relations
- 6.1 Exploring Accumulations of Change
- 6.2 Approximating Areas with Riemann Sums
- 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
- 6.4 The Fundamental Theorem of Calculus and Accumulation Functions
- 6.5 Interpreting the Behavior of Accumulation Functions Involving Area
- 6.6 Applying Properties of Definite Integrals
- 6.7 The Fundamental Theorem of Calculus and Definite Integrals
- 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
- 6.9 Integrating Using Substitution
- 6.10 Integrating Functions Using Long Division and Completing the Square
- 6.11 Integrating Using Integration by Parts
- 6.12 Integrating Using Linear Partial Fractions
- 6.13 Evaluating Improper Integrals
- 6.14 Selecting Techniques for Antidifferentiation
- 7.1 Modeling Situations with Differential Equations
- 7.2 Verifying Solutions for Differential Equations
- 7.3 Sketching Slope Fields
- 7.4 Reasoning Using Slope Fields
- 7.5 Approximating Solutions Using Euler's Method
- 7.6 Finding General Solutions Using Separation of Variables
- 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables
- 7.8 Exponential Models with Differential Equations
- 7.9 Logistic Models with Differential Equations
- 8.1 Finding the Average Value of a Function on an Interval
- 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
- 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
- 8.4 Finding the Area Between Curves Expressed as Functions of x
- 8.5 Finding the Area Between Curves Expressed as Functions of y
- 8.6 Finding the Area Between Curves That Intersect at More Than Two Points
- 8.7 Volumes with Cross Sections: Squares and Rectangles
- 8.8 Volumes with Cross Sections: Triangles and Semicircles
- 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
- 8.10 Volume with Disc Method: Revolving Around Other Axes
- 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis
- 8.12 Volume with Washer Method: Revolving Around Other Axes
- 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled
- 9.1 Defining and Differentiating Parametric Equations
- 9.2 Second Derivatives of Parametric Equations
- 9.3 Finding Arc Lengths of Curves Given by Parametric Equations
- 9.4 Defining and Differentiating Vector-Valued Functions
- 9.5 Integrating Vector-Valued Functions
- 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions
- 9.7 Defining Polar Coordinates and Differentiating in Polar Form
- 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
- 9.9 Finding the Area of the Region Bounded by Two Polar Curves
- 10.1 Defining Convergent and Divergent Infinite Series
- 10.2 Working with Geometric Series
- 10.3 The nth Term Test for Divergence
- 10.4 Integral Test for Convergence
- 10.5 Harmonic Series and p-Series
- 10.6 Comparison Tests for Convergence
- 10.7 Alternating Series Test for Convergence
- 10.8 Ratio Test for Convergence
- 10.9 Determining Absolute or Conditional Convergence
- 10.10 Alternating Series Error Bound
- 10.11 Finding Taylor Polynomial Approximations of Functions
- 10.12 Lagrange Error Bound
- 10.13 Radius and Interval of Convergence of Power Series
- 10.14 Finding Taylor or Maclaurin Series for a Function
- 10.15 Representing Functions as Power Series
- 1. Limits and Continuity
- 2. Differentiation: Definition and Fundamental Properties
- 3. Differentiation: Composite, Implicit, and Inverse Functions
- 4. Contextual Applications of Differentiation
- 5. Analytical Applications of Differentiation
- 6. Integration and Accumulation of Change
- 7. Differential Equations
- 8. Applications of Integration
- 9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- 10. Infinite Sequences and Series
- 1. Limits and Continuity
- 2. Differentiation: Definition and Fundamental Properties
- 3. Differentiation: Composite, Implicit, and Inverse Functions
- 4. Contextual Applications of Differentiation
- 5. Analytical Applications of Differentiation
- 6. Integration and Accumulation of Change
- 7. Differential Equations
- 8. Applications of Integration
- 9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- 10. Infinite Sequences and Series
- Complete pack — exercise sheets + past papers
- 1 Limits and Continuity — Part 1
- 1 Limits and Continuity — Part 2
- 2 Differentiation: Definition and Fundamental Properties — Part 1
- 2 Differentiation: Definition and Fundamental Properties — Part 2
- 3 Differentiation: Composite, Implicit, and Inverse Functions — Part 1
- 3 Differentiation: Composite, Implicit, and Inverse Functions — Part 2
- 4 Contextual Applications of Differentiation — Part 1
- 4 Contextual Applications of Differentiation — Part 2
- 5 Analytical Applications of Differentiation — Part 1
- 5 Analytical Applications of Differentiation — Part 2
- 6 Integration and Accumulation of Change — Part 1
- 6 Integration and Accumulation of Change — Part 2
- 7 Differential Equations — Part 1
- 7 Differential Equations — Part 2
- 8 Applications of Integration — Part 1
- 8 Applications of Integration — Part 2
- 9 Parametric Equations, Polar Coordinates, and Vector-Valued Functions — Part 1
- 9 Parametric Equations, Polar Coordinates, and Vector-Valued Functions — Part 2
- 10 Infinite Sequences and Series — Part 1
- 10 Infinite Sequences and Series — Part 2
How to use these papers
Separate the BC-only questions — series, parametric, polar — and work those first. They are where the score is decided, and they are also the parts where released questions are most directly reusable year to year.
For series, the practice that pays is choosing the test, not applying it. Take twenty series from released papers and only decide which test you would use, without working any of them through; that trains the step that actually costs time in the exam.
Check whether you justified convergence rather than asserting it, and whether you gave the interval AND tested the endpoints. Endpoints are the single most commonly dropped mark in this part of the course.