Specification points
College Board AP Calculus BC calculus-bc
202 points in 10 topics, with College Board's codes and titles.
Codes and titles are read by a script from College Board's published specification and have not been checked by a person. What each point covers is in the specification itself: College Board’s specification.
1 Limits and Continuity
- 1.1 Introducing Calculus: Can Change Occur at an Instant?
- CHA-1.A Instantaneous rate of change from average rates
- 1.2 Defining Limits and Using Limit Notation
- LIM-1.A Limit notation
- LIM-1.B Interpreting limits
- 1.3 Estimating Limit Values from Graphs
- LIM-1.C Estimating limits
- 1.4 Estimating Limit Values from Tables
- 1.5 Determining Limits Using Algebraic Properties of Limits
- LIM-1.D Limit theorems
- 1.6 Determining Limits Using Algebraic Manipulation
- LIM-1.E Limits by equivalent expressions and the squeeze theorem
- 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
- LIM-2.A Continuity at a point
- 1.11 Defining Continuity at a Point
- 1.12 Confirming Continuity over an Interval
- LIM-2.B Intervals of continuity
- 1.13 Removing Discontinuities
- LIM-2.C Removing discontinuities
- 1.14 Connecting Infinite Limits and Vertical Asymptotes
- LIM-2.D Limits involving infinity
- 1.15 Connecting Limits at Infinity and Horizontal Asymptotes
- 1.16 Working with the Intermediate Value Theorem (IVT)
- FUN-1.A The Intermediate Value Theorem
2 Differentiation: Definition and Fundamental Properties
- 2.1 Defining Average and Instantaneous Rates of Change at a Point
- CHA-2.A Average rates of change
- CHA-2.B The derivative as a limit of difference quotients
- 2.2 Defining the Derivative of a Function and Using Derivative Notation
- CHA-2.C Tangent lines
- 2.3 Estimating Derivatives of a Function at a Point
- CHA-2.D Estimating derivatives
- 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
- FUN-2.A Differentiability and continuity
- 2.5 Applying the Power Rule
- FUN-3.A Derivatives of familiar functions
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
- 2.7 Derivatives of cos x, sin x, eˣ, and ln x
- LIM-3.A The limit definition of the derivative
- 2.8 The Product Rule
- FUN-3.B The product and quotient rules
- 2.9 The Quotient Rule
- 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
3 Differentiation: Composite, Implicit, and Inverse Functions
- 3.1 The Chain Rule
- FUN-3.C The chain rule
- 3.2 Implicit Differentiation
- FUN-3.D Implicit differentiation
- 3.3 Differentiating Inverse Functions
- FUN-3.E Derivatives of inverse and inverse trigonometric functions
- 3.4 Differentiating Inverse Trigonometric Functions
- 3.5 Selecting Procedures for Calculating Derivatives
- 3.6 Calculating Higher-Order Derivatives
- FUN-3.F Higher-order derivatives
4 Contextual Applications of Differentiation
- 4.1 Interpreting the Meaning of the Derivative in Context
- CHA-3.A The derivative in context
- 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
- CHA-3.B Calculating rates of change in context
- 4.3 Rates of Change in Applied Contexts Other Than Motion
- CHA-3.C Interpreting rates of change in context
- 4.4 Introduction to Related Rates
- CHA-3.D Calculating related rates
- 4.5 Solving Related Rates Problems
- CHA-3.E Interpreting related rates
- 4.6 Approximating Values of a Function Using Local Linearity and Linearization
- CHA-3.F Local linear approximation
- 4.7 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms
- LIM-4.A L’Hospital’s rule and indeterminate forms
5 Analytical Applications of Differentiation
- 5.1 Using the Mean Value Theorem
- FUN-1.B The Mean Value Theorem
- 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
- FUN-1.C The Extreme Value Theorem
- 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing
- FUN-4.A Function behaviour from its derivatives
- 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
- FUN-4.B Optimisation
- 5.11 Solving Optimization Problems
- FUN-4.C Interpreting optimised values
- 5.12 Exploring Behaviors of Implicit Relations
- FUN-4.D Critical points of implicit relations
- FUN-4.E Behaviour of implicitly defined functions
6 Integration and Accumulation of Change
- 6.1 Exploring Accumulations of Change
- CHA-4.A Area under a rate-of-change graph in context
- 6.2 Approximating Areas with Riemann Sums
- LIM-5.A Approximating definite integrals
- 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
- LIM-5.B Riemann sums and definite integrals
- LIM-5.C Definite integrals as limits of Riemann sums
- 6.4 The Fundamental Theorem of Calculus and Accumulation Functions
- FUN-5.A Accumulation functions
- 6.5 Interpreting the Behavior of Accumulation Functions Involving Area
- 6.6 Applying Properties of Definite Integrals
- FUN-6.A Definite integrals from areas and properties
- 6.7 The Fundamental Theorem of Calculus and Definite Integrals
- FUN-6.B The Fundamental Theorem of Calculus
- 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
- FUN-6.C Antiderivatives and indefinite integrals
- 6.9 Integrating Using Substitution
- FUN-6.D Integration by substitution
- 6.10 Integrating Functions Using Long Division and Completing the Square
- 6.11 Integrating Using Integration by Parts
- FUN-6.E Integration by parts
- 6.12 Integrating Using Linear Partial Fractions
- FUN-6.F Integration by partial fractions
- 6.13 Evaluating Improper Integrals
- LIM-6.A Improper integrals
- 6.14 Selecting Techniques for Antidifferentiation
7 Differential Equations
- 7.1 Modeling Situations with Differential Equations
- FUN-7.A Modelling with differential equations
- 7.2 Verifying Solutions for Differential Equations
- FUN-7.B Verifying solutions of differential equations
- 7.3 Sketching Slope Fields
- FUN-7.C Estimating solutions with slope fields and Euler’s method
- 7.4 Reasoning Using Slope Fields
- 7.5 Approximating Solutions Using Euler’s Method
- 7.6 Finding General Solutions Using Separation of Variables
- FUN-7.D General solutions of differential equations
- 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables
- FUN-7.E Particular solutions of differential equations
- 7.8 Exponential Models with Differential Equations
- FUN-7.F Differential equations in context
- FUN-7.G Solving differential equations in context
- 7.9 Logistic Models with Differential Equations
- FUN-7.H The logistic growth model
8 Applications of Integration
- 8.1 Finding the Average Value of a Function on an Interval
- CHA-4.B Average value of a function
- 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
- CHA-4.C Rectilinear motion with integrals
- 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
- CHA-4.D Definite integrals in accumulation problems
- CHA-4.E Net change with definite integrals
- 8.4 Finding the Area Between Curves Expressed as Functions of x
- CHA-5.A Area between curves
- 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
- CHA-5.B Volumes with known cross sections
- 8.8 Volumes with Cross Sections: Triangles and Semicircles
- 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
- CHA-5.C Volumes of revolution
- 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
- CHA-6.A Arc length of a function
9 Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- 9.1 Defining and Differentiating Parametric Equations
- CHA-3.G Derivatives of parametric functions
- 9.2 Second Derivatives of Parametric Equations
- 9.3 Finding Arc Lengths of Curves Given by Parametric Equations
- CHA-6.B Arc length of a parametric curve
- 9.4 Defining and Differentiating Vector-Valued Functions
- CHA-3.H Derivatives of vector-valued functions
- 9.5 Integrating Vector-Valued Functions
- FUN-8.A Position from a rate vector and initial conditions
- 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions
- FUN-8.B Planar motion
- 9.7 Defining Polar Coordinates and Differentiating in Polar Form
- FUN-3.G Derivatives in polar coordinates
- 9.8 Area of a polar region
- CHA-5.D Areas bounded by polar curves
- 9.9 Finding the Area of the Region Bounded by Two Polar Curves
10 Infinite Sequences and Series
- 10.1 Defining Convergent and Divergent Infinite Series
- LIM-7.A Convergence and divergence of 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
- LIM-7.B Approximating the sum of a series
- 10.11 Finding Taylor Polynomial Approximations of Functions
- LIM-8.A Taylor polynomials
- LIM-8.B Approximating with Taylor polynomials
- 10.12 Lagrange Error Bound
- LIM-8.C Error bounds for Taylor polynomials
- 10.13 Radius and Interval of Convergence of Power Series
- LIM-8.D Radius and interval of convergence
- 10.14 Finding Taylor or Maclaurin Series for a Function
- LIM-8.E Taylor and Maclaurin series
- LIM-8.F Interpreting Taylor and Maclaurin series
- 10.15 Representing Functions as Power Series
- LIM-8.G Representing functions as power series