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Find an article by course, topic or objective. Open the article or its current course goal to choose a lesson and student check, with the relevant scope notes.

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Shared Calculus articles retain their canonical AB owner and native BC reading view. BC-only content remains distinct. Unmatched Draft articles retain their editorial status.

AP Physics 1

1.1 · Scalars and Vectors in One Dimension

Learning goals and teaching choices
Learning goals in the current course
- 1.1.A: Describe a scalar or vector quantity using magnitude and direction, as appropriate.
  Open the goal for lessons, student checks and current scope notes.
- 1.1.B: Describe a vector sum in one dimension.
  Open the goal for lessons, student checks and current scope notes.
1.2 · Displacement, Velocity, and Acceleration

Learning goals and teaching choices
Learning goals in the current course
- 1.2.A: Describe a change in an object’s position.
  Open the goal for lessons, student checks and current scope notes.
- 1.2.B: Describe the average velocity and acceleration of an object.
  Open the goal for lessons, student checks and current scope notes.
1.3 · Representing Motion

Learning goals and teaching choices
Learning goals in the current course
- 1.3.A: Describe the position, velocity, and acceleration of an object using representations of that object’s motion.
  Open the goal for lessons, student checks and current scope notes.
1.4 · Reference Frames and Relative Motion

Learning goals and teaching choices
Learning goals in the current course
- 1.4.A: Describe the reference frame of a given observer.
  Open the goal for lessons, student checks and current scope notes.
- 1.4.B: Describe the motion of objects as measured by observers in different inertial reference frames.
  Open the goal for lessons, student checks and current scope notes.
1.5 · Vectors and Motion in Two Dimensions

Learning goals and teaching choices
Learning goals in the current course
- 1.5.A: Describe the perpendicular components of a vector.
  Open the goal for lessons, student checks and current scope notes.
- 1.5.B: Describe the motion of an object moving in two dimensions.
  Open the goal for lessons, student checks and current scope notes.
2.1 · Systems and Center of Mass

Learning goals and teaching choices
Learning goals in the current course
- 2.1.A: Describe the properties and interactions of a system.
  Open the goal for lessons, student checks and current scope notes.
- 2.1.B: Describe the location of a system’s center of mass with respect to the system’s constituent parts.
  Open the goal for lessons, student checks and current scope notes.
2.2 · Forces and Free-Body Diagrams

Learning goals and teaching choices
Learning goals in the current course
- 2.2.A: Describe a force as an interaction between two objects or systems.
  Open the goal for lessons, student checks and current scope notes.
- 2.2.B: Describe the forces exerted on an object or system using a free-body diagram.
  Open the goal for lessons, student checks and current scope notes.
2.3 · Newton’s Third Law

Learning goals and teaching choices
Learning goals in the current course
- 2.3.A: Describe the interaction of two objects using Newton’s third law and a representation of paired forces exerted on each object.
  Open the goal for lessons, student checks and current scope notes.
2.4 · Newton’s First Law

Learning goals and teaching choices
Learning goals in the current course
- 2.4.A: Describe the conditions under which a system’s velocity remains constant.
  Open the goal for lessons, student checks and current scope notes.
2.5 · Newton’s Second Law

Learning goals and teaching choices
Learning goals in the current course
- 2.5.A: Describe the conditions under which a system’s velocity changes.
  Open the goal for lessons, student checks and current scope notes.
2.6 · Gravitational Force

Learning goals and teaching choices
Learning goals in the current course
- 2.6.A: Describe the gravitational interaction between two objects or systems with mass.
  Open the goal for lessons, student checks and current scope notes.
- 2.6.B: Describe situations in which the gravitational force can be considered constant.
  Open the goal for lessons, student checks and current scope notes.
- 2.6.C: Describe the conditions under which the magnitude of a system’s apparent weight is different from the magnitude of the gravitational force exerted on that system.
  Open the goal for lessons, student checks and current scope notes.
- 2.6.D: Describe inertial and gravitational mass.
  Open the goal for lessons, student checks and current scope notes.
2.7 · Kinetic and Static Friction

Learning goals and teaching choices
Learning goals in the current course
- 2.7.A: Describe kinetic friction between two surfaces
  Open the goal for lessons, student checks and current scope notes.
- 2.7.B: Describe static friction between two surfaces.
  Open the goal for lessons, student checks and current scope notes.
2.8 · Spring Forces

Learning goals and teaching choices
Learning goals in the current course
- 2.8.A: Describe the force exerted on an object by an ideal spring
  Open the goal for lessons, student checks and current scope notes.
2.9 · Circular Motion

Learning goals and teaching choices
Learning goals in the current course
- 2.9.A: Describe the motion of an object traveling in a circular path.
  Open the goal for lessons, student checks and current scope notes.
- 2.9.B: Describe circular orbits using Kepler’s third law.
  Open the goal for lessons, student checks and current scope notes.
3.1 · Translational Kinetic Energy

Learning goals and teaching choices
Learning goals in the current course
- 3.1.A: Describe the translational kinetic energy of an object in terms of the object’s mass and velocity.
  Open the goal for lessons, student checks and current scope notes.
3.2 · Work

Learning goals and teaching choices
Learning goals in the current course
- 3.2.A: Describe the work done on an object or system by a given force or collection of forces.
  Open the goal for lessons, student checks and current scope notes.
3.3 · Potential Energy

Learning goals and teaching choices
Learning goals in the current course
- 3.3.A: Describe the potential energy of a system.
  Open the goal for lessons, student checks and current scope notes.
3.4 · Conservation of Energy

Learning goals and teaching choices
Learning goals in the current course
- 3.4.A: Describe the energies present in a system.
  Open the goal for lessons, student checks and current scope notes.
- 3.4.B: Describe the behavior of a system using conservation of mechanical energy principles.
  Open the goal for lessons, student checks and current scope notes.
- 3.4.C: Describe how the selection of a system determines whether the energy of that system changes.
  Open the goal for lessons, student checks and current scope notes.
3.5 · Power

Learning goals and teaching choices
Learning goals in the current course
- 3.5.A: Describe the transfer of energy into, out of, or within a system in terms of power.
  Open the goal for lessons, student checks and current scope notes.
4.1 · Linear Momentum

Learning goals and teaching choices
Learning goals in the current course
- 4.1.A: Describe the linear momentum of an object or system.
  Open the goal for lessons, student checks and current scope notes.
4.2 · Change in Momentum and Impulse

Learning goals and teaching choices
Learning goals in the current course
- 4.2.A: Describe the impulse delivered to an object or system.
  Open the goal for lessons, student checks and current scope notes.
- 4.2.B: Describe the relationship between the impulse exerted on an object or a system and the change in momentum of the object or system.
  Open the goal for lessons, student checks and current scope notes.
4.3 · Conservation of Linear Momentum

Learning goals and teaching choices
Learning goals in the current course
- 4.3.A: Describe the behavior of a system using conservation of linear momentum.
  Open the goal for lessons, student checks and current scope notes.
- 4.3.B: Describe how the selection of a system determines whether the momentum of that system changes.
  Open the goal for lessons, student checks and current scope notes.
4.4 · Elastic and Inelastic Collisions

Learning goals and teaching choices
Learning goals in the current course
- 4.4.A: Describe whether an interaction between objects is elastic or inelastic.
  Open the goal for lessons, student checks and current scope notes.
5.1 · Rotational Kinematics

Learning goals and teaching choices
Learning goals in the current course
- 5.1.A: Describe the rotation of a system with respect to time using angular displacement, angular velocity, and angular acceleration.
  Open the goal for lessons, student checks and current scope notes.
5.2 · Connecting Linear and Rotational Motion

Learning goals and teaching choices
Learning goals in the current course
- 5.2.A: Describe the linear motion of a point on a rotating rigid system that corresponds to the rotational motion of that point, and vice versa.
  Open the goal for lessons, student checks and current scope notes.
5.3 · Torque

Learning goals and teaching choices
Learning goals in the current course
- 5.3.A: Identify the torques exerted on a rigid system.
  Open the goal for lessons, student checks and current scope notes.
- 5.3.B: Describe the torques exerted on a rigid system.
  Open the goal for lessons, student checks and current scope notes.
5.4 · Rotational Inertia

Learning goals and teaching choices
Learning goals in the current course
- 5.4.A: Describe the rotational inertia of a rigid system relative to a given axis of rotation.
  Open the goal for lessons, student checks and current scope notes.
- 5.4.B: Describe the rotational inertia of a rigid system rotating about an axis that does not pass through the system’s center of mass.
  Open the goal for lessons, student checks and current scope notes.
5.5 · Rotational Equilibrium and Newton’s First Law in Rotational Form

Learning goals and teaching choices
Learning goals in the current course
- 5.5.A: Describe the conditions under which a system’s angular velocity remains constant.
  Open the goal for lessons, student checks and current scope notes.
5.6 · Newton’s Second Law in Rotational Form

Learning goals and teaching choices
Learning goals in the current course
- 5.6.A: Describe the conditions under which a system’s angular velocity changes.
  Open the goal for lessons, student checks and current scope notes.
6.1 · Rotational Kinetic Energy

Learning goals and teaching choices
Learning goals in the current course
- 6.1.A: Describe the rotational kinetic energy of a rigid system in terms of the rotational inertia and angular velocity of that rigid system.
  Open the goal for lessons, student checks and current scope notes.
6.2 · Torque and Work

Learning goals and teaching choices
Learning goals in the current course
- 6.2.A: Describe the work done on a rigid system by a given torque or collection of torques.
  Open the goal for lessons, student checks and current scope notes.
6.3 · Angular Momentum and Angular Impulse

Learning goals and teaching choices
Learning goals in the current course
- 6.3.A: Describe the angular momentum of an object or rigid system.
  Open the goal for lessons, student checks and current scope notes.
- 6.3.B: Describe the angular impulse delivered to an object or rigid system by a torque.
  Open the goal for lessons, student checks and current scope notes.
- 6.3.C: Relate the change in angular momentum of an object or rigid system to the angular impulse given to that object or rigid system.
  Open the goal for lessons, student checks and current scope notes.
6.4 · Conservation of Angular Momentum

Learning goals and teaching choices
Learning goals in the current course
- 6.4.A: Describe the behavior of a system using conservation of angular momentum.
  Open the goal for lessons, student checks and current scope notes.
- 6.4.B: Describe how the selection of a system determines whether the angular momentum of that system changes.
  Open the goal for lessons, student checks and current scope notes.
6.5 · Rolling

Learning goals and teaching choices
Learning goals in the current course
- 6.5.A: Describe the kinetic energy of a system that has translational and rotational motion.
  Open the goal for lessons, student checks and current scope notes.
- 6.5.B: Describe the motion of a system that is rolling without slipping.
  Open the goal for lessons, student checks and current scope notes.
- 6.5.C: Describe the motion of a system that is rolling while slipping.
  Open the goal for lessons, student checks and current scope notes.
6.6 · Motion of Orbiting Satellites

Learning goals and teaching choices
Learning goals in the current course
- 6.6.A: Describe the motions of a system consisting of two objects interacting only via gravitational forces.
  Open the goal for lessons, student checks and current scope notes.
7.1 · Defining Simple Harmonic Motion (SHM)

Learning goals and teaching choices
Learning goals in the current course
- 7.1.A: Describe simple harmonic motion.
  Open the goal for lessons, student checks and current scope notes.
7.2 · Frequency and Period of SHM

Learning goals and teaching choices
Learning goals in the current course
- 7.2.A: Describe the frequency and period of an object exhibiting SHM.
  Open the goal for lessons, student checks and current scope notes.
7.3 · Representing and Analyzing SHM

Learning goals and teaching choices
Learning goals in the current course
- 7.3.A: Describe the displacement, velocity, and acceleration of an object exhibiting SHM.
  Open the goal for lessons, student checks and current scope notes.
7.4 · Energy of Simple Harmonic Oscillators

Learning goals and teaching choices
Learning goals in the current course
- 7.4.A: Describe the mechanical energy of a system exhibiting SHM.
  Open the goal for lessons, student checks and current scope notes.
8.1 · Internal Structure and Density

Learning goals and teaching choices
Learning goals in the current course
- 8.1.A: Describe the properties of a fluid.
  Open the goal for lessons, student checks and current scope notes.
8.2 · Pressure

Learning goals and teaching choices
Learning goals in the current course
- 8.2.A: Describe the pressure exerted on a surface by a given force.
  Open the goal for lessons, student checks and current scope notes.
- 8.2.B: Describe the pressure exerted by a fluid.
  Open the goal for lessons, student checks and current scope notes.
8.3 · Fluids and Newton’s Laws

Learning goals and teaching choices
Learning goals in the current course
- 8.3.A: Describe the conditions under which a fluid’s velocity changes.
  Open the goal for lessons, student checks and current scope notes.
- 8.3.B: Describe the buoyant force exerted on an object interacting with a fluid.
  Open the goal for lessons, student checks and current scope notes.
8.4 · Fluids and Conservation Laws

Learning goals and teaching choices
Learning goals in the current course
- 8.4.A: Describe the flow of an incompressible fluid through a cross-sectional area by using mass conservation.
  Open the goal for lessons, student checks and current scope notes.
- 8.4.B: Describe the flow of a fluid as a result of a difference in energy between two locations within the fluid– Earth system.
  Open the goal for lessons, student checks and current scope notes.

AP Calculus AB

Fall 2020; edition 2026-27

1.1 · Introducing Calculus: Can Change Occur at an Instant?

Learning goals and teaching choices
Learning goals in the current course
- CHA-1.A: Interpret the rate of change at an instant in terms of average rates of change over intervals containing that instant.
  Open the goal for lessons, student checks and current scope notes.
1.2 · Defining Limits and Using Limit Notation

Learning goals and teaching choices
Learning goals in the current course
- LIM-1.A: Represent limits analytically using correct notation.
  Open the goal for lessons, student checks and current scope notes.
- LIM-1.B: Interpret limits expressed in analytic notation.
  Open the goal for lessons, student checks and current scope notes.
1.3 · Estimating Limit Values from Graphs

Learning goals and teaching choices
Learning goals in the current course
- LIM-1.C: Estimate limits of functions.
  Open the goal for lessons, student checks and current scope notes.
1.4 · Estimating Limit Values from Tables

Learning goals and teaching choices
Learning goals in the current course
- LIM-1.C: Estimate limits of functions.
  Open the goal for lessons, student checks and current scope notes.
1.5 · Determining Limits Using Algebraic Properties of Limits

Learning goals and teaching choices
Learning goals in the current course
- LIM-1.D: Determine the limits of functions using limit theorems.
  Open the goal for lessons, student checks and current scope notes.
1.6 · Determining Limits Using Algebraic Manipulation

Learning goals and teaching choices
Learning goals in the current course
- LIM-1.E: Determine the limits of functions using equivalent expressions for the function or the squeeze theorem.
  Open the goal for lessons, student checks and current scope notes.
1.7 · Selecting Procedures for Determining Limits

Learning goals and teaching choices

Learning goals in the current course

This synthesis introduces no new objective. The current outline links the applicable earlier goals.
1.8 · Determining Limits Using the Squeeze Theorem

Learning goals and teaching choices
Learning goals in the current course
- LIM-1.E: Determine the limits of functions using equivalent expressions for the function or the squeeze theorem.
  Open the goal for lessons, student checks and current scope notes.
1.9 · Connecting Multiple Representations of Limits

Learning goals and teaching choices

Learning goals in the current course

This synthesis introduces no new objective. The current outline links the applicable earlier goals.
1.10 · Exploring Types of Discontinuities

Learning goals and teaching choices
Learning goals in the current course
- LIM-2.A: Justify conclusions about continuity at a point using the definition.
  Open the goal for lessons, student checks and current scope notes.
1.11 · Defining Continuity at a Point

Learning goals and teaching choices
Learning goals in the current course
- LIM-2.A: Justify conclusions about continuity at a point using the definition.
  Open the goal for lessons, student checks and current scope notes.
1.12 · Confirming Continuity over an Interval

Learning goals and teaching choices
Learning goals in the current course
- LIM-2.B: Determine intervals over which a function is continuous.
  Open the goal for lessons, student checks and current scope notes.
1.13 · Removing Discontinuities

Learning goals and teaching choices
Learning goals in the current course
- LIM-2.C: Determine values of x or solve for parameters that make discontinuous functions continuous, if possible.
  Open the goal for lessons, student checks and current scope notes.
1.14 · Connecting Infinite Limits and Vertical Asymptotes

Learning goals and teaching choices
Learning goals in the current course
- LIM-2.D: Interpret the behavior of functions using limits involving infinity.
  Open the goal for lessons, student checks and current scope notes.
1.15 · Connecting Limits at Infinity and Horizontal Asymptotes

Learning goals and teaching choices
Learning goals in the current course
- LIM-2.D: Interpret the behavior of functions using limits involving infinity.
  Open the goal for lessons, student checks and current scope notes.
1.16 · Working with the Intermediate Value Theorem (IVT)

Learning goals and teaching choices
Learning goals in the current course
- FUN-1.A: Explain the behavior of a function on an interval using the Intermediate Value Theorem.
  Open the goal for lessons, student checks and current scope notes.
2.1 · Defining Average and Instantaneous Rates of Change at a Point

Learning goals and teaching choices
Learning goals in the current course
- CHA-2.A: Determine average rates of change using difference quotients.
  Open the goal for lessons, student checks and current scope notes.
- CHA-2.B: Represent the derivative of a function as the limit of a difference quotient.
  Open the goal for lessons, student checks and current scope notes.
2.2 · Defining the Derivative of a Function and Using Derivative Notation

Learning goals and teaching choices
Learning goals in the current course
- CHA-2.B: Represent the derivative of a function as the limit of a difference quotient.
  Open the goal for lessons, student checks and current scope notes.
- CHA-2.C: Determine the equation of a line tangent to a curve at a given point.
  Open the goal for lessons, student checks and current scope notes.
2.3 · Estimating Derivatives of a Function at a Point

Learning goals and teaching choices
Learning goals in the current course
- CHA-2.D: Estimate derivatives.
  Open the goal for lessons, student checks and current scope notes.
2.4 · Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist

Learning goals and teaching choices
Learning goals in the current course
- FUN-2.A: Explain the relationship between differentiability and continuity.
  Open the goal for lessons, student checks and current scope notes.
2.5 · Applying the Power Rule

Learning goals and teaching choices
Learning goals in the current course
- FUN-3.A: Calculate derivatives of familiar functions.
  Open the goal for lessons, student checks and current scope notes.
2.6 · Derivative Rules: Constant, Sum, Difference, and Constant Multiple

Learning goals and teaching choices
Learning goals in the current course
- FUN-3.A: Calculate derivatives of familiar functions.
  Open the goal for lessons, student checks and current scope notes.
2.7 · Derivatives of cos x, sin x, e^x, and ln x

Learning goals and teaching choices
Learning goals in the current course
- FUN-3.A: Calculate derivatives of familiar functions.
  Open the goal for lessons, student checks and current scope notes.
- LIM-3.A: Interpret a limit as a definition of a derivative.
  Open the goal for lessons, student checks and current scope notes.
2.8 · The Product Rule

Learning goals and teaching choices
Learning goals in the current course
- FUN-3.B: Calculate derivatives of products and quotients of differentiable functions.
  Open the goal for lessons, student checks and current scope notes.
2.9 · The Quotient Rule

Learning goals and teaching choices
Learning goals in the current course
- FUN-3.B: Calculate derivatives of products and quotients of differentiable functions.
  Open the goal for lessons, student checks and current scope notes.
2.10 · Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

Learning goals and teaching choices
Learning goals in the current course
- FUN-3.B: Calculate derivatives of products and quotients of differentiable functions.
  Open the goal for lessons, student checks and current scope notes.
3.1 · The Chain Rule

Learning goals and teaching choices
Learning goals in the current course
- FUN-3.C: Calculate derivatives of compositions of differentiable functions.
  Open the goal for lessons, student checks and current scope notes.
3.2 · Implicit Differentiation

Learning goals and teaching choices
Learning goals in the current course
- FUN-3.D: Calculate derivatives of implicitly defined functions.
  Open the goal for lessons, student checks and current scope notes.
3.3 · Differentiating Inverse Functions

Learning goals and teaching choices
Learning goals in the current course
- FUN-3.E: Calculate derivatives of inverse and inverse trigonometric functions.
  Open the goal for lessons, student checks and current scope notes.
3.4 · Differentiating Inverse Trigonometric Functions

Learning goals and teaching choices
Learning goals in the current course
- FUN-3.E: Calculate derivatives of inverse and inverse trigonometric functions.
  Open the goal for lessons, student checks and current scope notes.
3.5 · Selecting Procedures for Calculating Derivatives

Learning goals and teaching choices

Learning goals in the current course

This synthesis introduces no new objective. The current outline links the applicable earlier goals.
3.6 · Calculating Higher-Order Derivatives

Learning goals and teaching choices
Learning goals in the current course
- FUN-3.F: Determine higher order derivatives of a function.
  Open the goal for lessons, student checks and current scope notes.
4.1 · Interpreting the Meaning of the Derivative in Context

Learning goals and teaching choices
Learning goals in the current course
- CHA-3.A: Interpret the meaning of a derivative in context.
  Open the goal for lessons, student checks and current scope notes.
4.2 · Straight-Line Motion: Connecting Position, Velocity, and Acceleration

Learning goals and teaching choices
Learning goals in the current course
- CHA-3.B: Calculate rates of change in applied contexts.
  Open the goal for lessons, student checks and current scope notes.
4.3 · Rates of Change in Applied Contexts Other Than Motion

Learning goals and teaching choices
Learning goals in the current course
- CHA-3.C: Interpret rates of change in applied contexts.
  Open the goal for lessons, student checks and current scope notes.
4.4 · Introduction to Related Rates

Learning goals and teaching choices
Learning goals in the current course
- CHA-3.D: Calculate related rates in applied contexts.
  Open the goal for lessons, student checks and current scope notes.
4.5 · Solving Related Rates Problems

Learning goals and teaching choices
Learning goals in the current course
- CHA-3.E: Interpret related rates in applied contexts.
  Open the goal for lessons, student checks and current scope notes.
4.6 · Approximating Values of a Function Using Local Linearity and Linearization

Learning goals and teaching choices
Learning goals in the current course
- CHA-3.F: Approximate a value on a curve using the equation of a tangent line.
  Open the goal for lessons, student checks and current scope notes.
4.7 · Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms

Learning goals and teaching choices
Learning goals in the current course
- LIM-4.A: Determine limits of functions that result in indeterminate forms.
  Open the goal for lessons, student checks and current scope notes.
5.1 · Using the Mean Value Theorem

Learning goals and teaching choices
Learning goals in the current course
- FUN-1.B: Justify conclusions about functions by applying the Mean Value Theorem over an interval.
  Open the goal for lessons, student checks and current scope notes.
5.2 · Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

Learning goals and teaching choices
Learning goals in the current course
- FUN-1.C: Justify conclusions about functions by applying the Extreme Value Theorem.
  Open the goal for lessons, student checks and current scope notes.
5.3 · Determining Intervals on Which a Function Is Increasing or Decreasing

Learning goals and teaching choices
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.4 · Using the First Derivative Test to Determine Relative (Local) Extrema

Learning goals and teaching choices
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.5 · Using the Candidates Test to Determine Absolute (Global) Extrema

Learning goals and teaching choices
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.6 · Determining Concavity of Functions over Their Domains

Learning goals and teaching choices
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.7 · Using the Second Derivative Test to Determine Extrema

Learning goals and teaching choices
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.8 · Sketching Graphs of Functions and Their Derivatives

Learning goals and teaching choices
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.9 · Connecting a Function, Its First Derivative, and Its Second Derivative

Learning goals and teaching choices
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.10 · Introduction to Optimization Problems

Learning goals and teaching choices
Learning goals in the current course
- FUN-4.B: Calculate minimum and maximum values in applied contexts or analysis of functions.
  Open the goal for lessons, student checks and current scope notes.
5.11 · Solving Optimization Problems

Learning goals and teaching choices
Learning goals in the current course
- FUN-4.C: Interpret minimum and maximum values calculated in applied contexts.
  Open the goal for lessons, student checks and current scope notes.
5.12 · Exploring Behaviors of Implicit Relations

Learning goals and teaching choices
Learning goals in the current course
- FUN-4.D: Determine critical points of implicit relations.
  Open the goal for lessons, student checks and current scope notes.
- FUN-4.E: Justify conclusions about the behavior of an implicitly defined function based on evidence from its derivatives.
  Open the goal for lessons, student checks and current scope notes.
6.1 · Exploring Accumulations of Change

Learning goals and teaching choices
Learning goals in the current course
- CHA-4.A: Interpret the meaning of areas associated with the graph of a rate of change in context.
  Open the goal for lessons, student checks and current scope notes.
6.2 · Approximating Areas with Riemann Sums

Learning goals and teaching choices
Learning goals in the current course
- LIM-5.A: Approximate a definite integral using geometric and numerical methods.
  Open the goal for lessons, student checks and current scope notes.
6.3 · Riemann Sums, Summation Notation, and Definite Integral Notation

Learning goals and teaching choices
Learning goals in the current course
- LIM-5.B: Interpret the limiting case of the Riemann sum as a definite integral.
  Open the goal for lessons, student checks and current scope notes.
- LIM-5.C: Represent the limiting case of the Riemann sum as a definite integral.
  Open the goal for lessons, student checks and current scope notes.
6.4 · The Fundamental Theorem of Calculus and Accumulation Functions

Learning goals and teaching choices
Learning goals in the current course
- FUN-5.A: Represent accumulation functions using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
6.5 · Interpreting the Behavior of Accumulation Functions Involving Area

Learning goals and teaching choices
Learning goals in the current course
- FUN-5.A: Represent accumulation functions using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
6.6 · Applying Properties of Definite Integrals

Learning goals and teaching choices
Learning goals in the current course
- FUN-6.A: Calculate a definite integral using areas and properties of definite integrals.
  Open the goal for lessons, student checks and current scope notes.
6.7 · The Fundamental Theorem of Calculus and Definite Integrals

Learning goals and teaching choices
Learning goals in the current course
- FUN-6.B: Evaluate definite integrals analytically using the Fundamental Theorem of Calculus.
  Open the goal for lessons, student checks and current scope notes.
6.8 · Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation

Learning goals and teaching choices
Learning goals in the current course
- FUN-6.C: Determine antiderivatives of functions and indefinite integrals, using knowledge of derivatives.
  Open the goal for lessons, student checks and current scope notes.
6.9 · Integrating Using Substitution

Learning goals and teaching choices
Learning goals in the current course
- FUN-6.D: For integrands requiring substitution or rearrangements into equivalent forms: (a) Determine indefinite integrals. (b) Evaluate definite integrals.
  Open the goal for lessons, student checks and current scope notes.
6.10 · Integrating Functions Using Long Division and Completing the Square

Learning goals and teaching choices
Learning goals in the current course
- FUN-6.D: For integrands requiring substitution or rearrangements into equivalent forms: (a) Determine indefinite integrals. (b) Evaluate definite integrals.
  Open the goal for lessons, student checks and current scope notes.
6.14 · Selecting Techniques for Antidifferentiation

Learning goals and teaching choices

Learning goals in the current course

This synthesis introduces no new objective. The current outline links the applicable earlier goals.
7.1 · Modeling Situations with Differential Equations

Learning goals and teaching choices
Learning goals in the current course
- FUN-7.A: Interpret verbal statements of problems as differential equations involving a derivative expression.
  Open the goal for lessons, student checks and current scope notes.
7.2 · Verifying Solutions for Differential Equations

Learning goals and teaching choices
Learning goals in the current course
- FUN-7.B: Verify solutions to differential equations.
  Open the goal for lessons, student checks and current scope notes.
7.3 · Sketching Slope Fields

Learning goals and teaching choices
Learning goals in the current course
- FUN-7.C: Estimate solutions to differential equations.
  Open the goal for lessons, student checks and current scope notes.
7.4 · Reasoning Using Slope Fields

Learning goals and teaching choices
Learning goals in the current course
- FUN-7.C: Estimate solutions to differential equations.
  Open the goal for lessons, student checks and current scope notes.
7.6 · Finding General Solutions Using Separation of Variables

Learning goals and teaching choices
Learning goals in the current course
- FUN-7.D: Determine general solutions to differential equations.
  Open the goal for lessons, student checks and current scope notes.
7.7 · Finding Particular Solutions Using Initial Conditions and Separation of Variables

Learning goals and teaching choices
Learning goals in the current course
- FUN-7.E: Determine particular solutions to differential equations.
  Open the goal for lessons, student checks and current scope notes.
7.8 · Exponential Models with Differential Equations

Learning goals and teaching choices
Learning goals in the current course
- FUN-7.F: Interpret the meaning of a differential equation and its variables in context.
  Open the goal for lessons, student checks and current scope notes.
- FUN-7.G: Determine general and particular solutions for problems involving differential equations in context.
  Open the goal for lessons, student checks and current scope notes.
8.1 · Finding the Average Value of a Function on an Interval

Learning goals and teaching choices
Learning goals in the current course
- CHA-4.B: Determine the average value of a function using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.2 · Connecting Position, Velocity, and Acceleration of Functions Using Integrals

Learning goals and teaching choices
Learning goals in the current course
- CHA-4.C: Determine values for positions and rates of change using definite integrals in problems involving rectilinear motion.
  Open the goal for lessons, student checks and current scope notes.
8.3 · Using Accumulation Functions and Definite Integrals in Applied Contexts

Learning goals and teaching choices
Learning goals in the current course
- CHA-4.D: Interpret the meaning of a definite integral in accumulation problems.
  Open the goal for lessons, student checks and current scope notes.
- CHA-4.E: Determine net change using definite integrals in applied contexts.
  Open the goal for lessons, student checks and current scope notes.
8.4 · Finding the Area Between Curves Expressed as Functions of x

Learning goals and teaching choices
Learning goals in the current course
- CHA-5.A: Calculate areas in the plane using the definite integral.
  Open the goal for lessons, student checks and current scope notes.
8.5 · Finding the Area Between Curves Expressed as Functions of y

Learning goals and teaching choices
Learning goals in the current course
- CHA-5.A: Calculate areas in the plane using the definite integral.
  Open the goal for lessons, student checks and current scope notes.
8.6 · Finding the Area Between Curves That Intersect at More Than Two Points

Learning goals and teaching choices
Learning goals in the current course
- CHA-5.A: Calculate areas in the plane using the definite integral.
  Open the goal for lessons, student checks and current scope notes.
8.7 · Volumes with Cross Sections: Squares and Rectangles

Learning goals and teaching choices
Learning goals in the current course
- CHA-5.B: Calculate volumes of solids with known cross sections using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.8 · Volumes with Cross Sections: Triangles and Semicircles

Learning goals and teaching choices
Learning goals in the current course
- CHA-5.B: Calculate volumes of solids with known cross sections using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.9 · Volume with Disc Method: Revolving Around the x- or y-Axis

Learning goals and teaching choices
Learning goals in the current course
- CHA-5.C: Calculate volumes of solids of revolution using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.10 · Volume with Disc Method: Revolving Around Other Axes

Learning goals and teaching choices
Learning goals in the current course
- CHA-5.C: Calculate volumes of solids of revolution using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.11 · Volume with Washer Method: Revolving Around the x- or y-Axis

Learning goals and teaching choices
Learning goals in the current course
- CHA-5.C: Calculate volumes of solids of revolution using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.12 · Volume with Washer Method: Revolving Around Other Axes

Learning goals and teaching choices
Learning goals in the current course
- CHA-5.C: Calculate volumes of solids of revolution using definite integrals.
  Open the goal for lessons, student checks and current scope notes.

AP Calculus BC

Fall 2020; edition 2026-27

1.1 · Introducing Calculus: Can Change Occur at an Instant?

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-1.A: Interpret the rate of change at an instant in terms of average rates of change over intervals containing that instant.
  Open the goal for lessons, student checks and current scope notes.
1.2 · Defining Limits and Using Limit Notation

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-1.A: Represent limits analytically using correct notation.
  Open the goal for lessons, student checks and current scope notes.
- LIM-1.B: Interpret limits expressed in analytic notation.
  Open the goal for lessons, student checks and current scope notes.
1.3 · Estimating Limit Values from Graphs

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-1.C: Estimate limits of functions.
  Open the goal for lessons, student checks and current scope notes.
1.4 · Estimating Limit Values from Tables

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-1.C: Estimate limits of functions.
  Open the goal for lessons, student checks and current scope notes.
1.5 · Determining Limits Using Algebraic Properties of Limits

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-1.D: Determine the limits of functions using limit theorems.
  Open the goal for lessons, student checks and current scope notes.
1.6 · Determining Limits Using Algebraic Manipulation

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-1.E: Determine the limits of functions using equivalent expressions for the function or the squeeze theorem.
  Open the goal for lessons, student checks and current scope notes.
1.7 · Selecting Procedures for Determining Limits

Learning goals and teaching choices · Canonical shared AB article

Learning goals in the current course

This synthesis introduces no new objective. The current outline links the applicable earlier goals.
1.8 · Determining Limits Using the Squeeze Theorem

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-1.E: Determine the limits of functions using equivalent expressions for the function or the squeeze theorem.
  Open the goal for lessons, student checks and current scope notes.
1.9 · Connecting Multiple Representations of Limits

Learning goals and teaching choices · Canonical shared AB article

Learning goals in the current course

This synthesis introduces no new objective. The current outline links the applicable earlier goals.
1.10 · Exploring Types of Discontinuities

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-2.A: Justify conclusions about continuity at a point using the definition.
  Open the goal for lessons, student checks and current scope notes.
1.11 · Defining Continuity at a Point

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-2.A: Justify conclusions about continuity at a point using the definition.
  Open the goal for lessons, student checks and current scope notes.
1.12 · Confirming Continuity over an Interval

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-2.B: Determine intervals over which a function is continuous.
  Open the goal for lessons, student checks and current scope notes.
1.13 · Removing Discontinuities

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-2.C: Determine values of x or solve for parameters that make discontinuous functions continuous, if possible.
  Open the goal for lessons, student checks and current scope notes.
1.14 · Connecting Infinite Limits and Vertical Asymptotes

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-2.D: Interpret the behavior of functions using limits involving infinity.
  Open the goal for lessons, student checks and current scope notes.
1.15 · Connecting Limits at Infinity and Horizontal Asymptotes

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-2.D: Interpret the behavior of functions using limits involving infinity.
  Open the goal for lessons, student checks and current scope notes.
1.16 · Working with the Intermediate Value Theorem (IVT)

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-1.A: Explain the behavior of a function on an interval using the Intermediate Value Theorem.
  Open the goal for lessons, student checks and current scope notes.
2.1 · Defining Average and Instantaneous Rates of Change at a Point

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-2.A: Determine average rates of change using difference quotients.
  Open the goal for lessons, student checks and current scope notes.
- CHA-2.B: Represent the derivative of a function as the limit of a difference quotient.
  Open the goal for lessons, student checks and current scope notes.
2.2 · Defining the Derivative of a Function and Using Derivative Notation

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-2.B: Represent the derivative of a function as the limit of a difference quotient.
  Open the goal for lessons, student checks and current scope notes.
- CHA-2.C: Determine the equation of a line tangent to a curve at a given point.
  Open the goal for lessons, student checks and current scope notes.
2.3 · Estimating Derivatives of a Function at a Point

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-2.D: Estimate derivatives.
  Open the goal for lessons, student checks and current scope notes.
2.4 · Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-2.A: Explain the relationship between differentiability and continuity.
  Open the goal for lessons, student checks and current scope notes.
2.5 · Applying the Power Rule

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-3.A: Calculate derivatives of familiar functions.
  Open the goal for lessons, student checks and current scope notes.
2.6 · Derivative Rules: Constant, Sum, Difference, and Constant Multiple

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-3.A: Calculate derivatives of familiar functions.
  Open the goal for lessons, student checks and current scope notes.
2.7 · Derivatives of cos x, sin x, e^x, and ln x

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-3.A: Calculate derivatives of familiar functions.
  Open the goal for lessons, student checks and current scope notes.
- LIM-3.A: Interpret a limit as a definition of a derivative.
  Open the goal for lessons, student checks and current scope notes.
2.8 · The Product Rule

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-3.B: Calculate derivatives of products and quotients of differentiable functions.
  Open the goal for lessons, student checks and current scope notes.
2.9 · The Quotient Rule

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-3.B: Calculate derivatives of products and quotients of differentiable functions.
  Open the goal for lessons, student checks and current scope notes.
2.10 · Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-3.B: Calculate derivatives of products and quotients of differentiable functions.
  Open the goal for lessons, student checks and current scope notes.
3.1 · The Chain Rule

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-3.C: Calculate derivatives of compositions of differentiable functions.
  Open the goal for lessons, student checks and current scope notes.
3.2 · Implicit Differentiation

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-3.D: Calculate derivatives of implicitly defined functions.
  Open the goal for lessons, student checks and current scope notes.
3.3 · Differentiating Inverse Functions

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-3.E: Calculate derivatives of inverse and inverse trigonometric functions.
  Open the goal for lessons, student checks and current scope notes.
3.4 · Differentiating Inverse Trigonometric Functions

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-3.E: Calculate derivatives of inverse and inverse trigonometric functions.
  Open the goal for lessons, student checks and current scope notes.
3.5 · Selecting Procedures for Calculating Derivatives

Learning goals and teaching choices · Canonical shared AB article

Learning goals in the current course

This synthesis introduces no new objective. The current outline links the applicable earlier goals.
3.6 · Calculating Higher-Order Derivatives

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-3.F: Determine higher order derivatives of a function.
  Open the goal for lessons, student checks and current scope notes.
4.1 · Interpreting the Meaning of the Derivative in Context

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-3.A: Interpret the meaning of a derivative in context.
  Open the goal for lessons, student checks and current scope notes.
4.2 · Straight-Line Motion: Connecting Position, Velocity, and Acceleration

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-3.B: Calculate rates of change in applied contexts.
  Open the goal for lessons, student checks and current scope notes.
4.3 · Rates of Change in Applied Contexts Other Than Motion

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-3.C: Interpret rates of change in applied contexts.
  Open the goal for lessons, student checks and current scope notes.
4.4 · Introduction to Related Rates

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-3.D: Calculate related rates in applied contexts.
  Open the goal for lessons, student checks and current scope notes.
4.5 · Solving Related Rates Problems

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-3.E: Interpret related rates in applied contexts.
  Open the goal for lessons, student checks and current scope notes.
4.6 · Approximating Values of a Function Using Local Linearity and Linearization

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-3.F: Approximate a value on a curve using the equation of a tangent line.
  Open the goal for lessons, student checks and current scope notes.
4.7 · Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-4.A: Determine limits of functions that result in indeterminate forms.
  Open the goal for lessons, student checks and current scope notes.
5.1 · Using the Mean Value Theorem

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-1.B: Justify conclusions about functions by applying the Mean Value Theorem over an interval.
  Open the goal for lessons, student checks and current scope notes.
5.2 · Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-1.C: Justify conclusions about functions by applying the Extreme Value Theorem.
  Open the goal for lessons, student checks and current scope notes.
5.3 · Determining Intervals on Which a Function Is Increasing or Decreasing

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.4 · Using the First Derivative Test to Determine Relative (Local) Extrema

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.5 · Using the Candidates Test to Determine Absolute (Global) Extrema

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.6 · Determining Concavity of Functions over Their Domains

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.7 · Using the Second Derivative Test to Determine Extrema

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.8 · Sketching Graphs of Functions and Their Derivatives

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.9 · Connecting a Function, Its First Derivative, and Its Second Derivative

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  Open the goal for lessons, student checks and current scope notes.
5.10 · Introduction to Optimization Problems

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-4.B: Calculate minimum and maximum values in applied contexts or analysis of functions.
  Open the goal for lessons, student checks and current scope notes.
5.11 · Solving Optimization Problems

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-4.C: Interpret minimum and maximum values calculated in applied contexts.
  Open the goal for lessons, student checks and current scope notes.
5.12 · Exploring Behaviors of Implicit Relations

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-4.D: Determine critical points of implicit relations.
  Open the goal for lessons, student checks and current scope notes.
- FUN-4.E: Justify conclusions about the behavior of an implicitly defined function based on evidence from its derivatives.
  Open the goal for lessons, student checks and current scope notes.
6.1 · Exploring Accumulations of Change

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-4.A: Interpret the meaning of areas associated with the graph of a rate of change in context.
  Open the goal for lessons, student checks and current scope notes.
6.2 · Approximating Areas with Riemann Sums

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-5.A: Approximate a definite integral using geometric and numerical methods.
  Open the goal for lessons, student checks and current scope notes.
6.3 · Riemann Sums, Summation Notation, and Definite Integral Notation

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- LIM-5.B: Interpret the limiting case of the Riemann sum as a definite integral.
  Open the goal for lessons, student checks and current scope notes.
- LIM-5.C: Represent the limiting case of the Riemann sum as a definite integral.
  Open the goal for lessons, student checks and current scope notes.
6.4 · The Fundamental Theorem of Calculus and Accumulation Functions

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-5.A: Represent accumulation functions using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
6.5 · Interpreting the Behavior of Accumulation Functions Involving Area

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-5.A: Represent accumulation functions using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
6.6 · Applying Properties of Definite Integrals

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-6.A: Calculate a definite integral using areas and properties of definite integrals.
  Open the goal for lessons, student checks and current scope notes.
6.7 · The Fundamental Theorem of Calculus and Definite Integrals

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-6.B: Evaluate definite integrals analytically using the Fundamental Theorem of Calculus.
  Open the goal for lessons, student checks and current scope notes.
6.8 · Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-6.C: Determine antiderivatives of functions and indefinite integrals, using knowledge of derivatives.
  Open the goal for lessons, student checks and current scope notes.
6.9 · Integrating Using Substitution

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-6.D: For integrands requiring substitution or rearrangements into equivalent forms: (a) Determine indefinite integrals. (b) Evaluate definite integrals.
  Open the goal for lessons, student checks and current scope notes.
6.10 · Integrating Functions Using Long Division and Completing the Square

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-6.D: For integrands requiring substitution or rearrangements into equivalent forms: (a) Determine indefinite integrals. (b) Evaluate definite integrals.
  Open the goal for lessons, student checks and current scope notes.
6.11 · Integrating Using Integration by Parts

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- FUN-6.E: For integrands requiring integration by parts: (a) Determine indefinite integrals. (b) Evaluate definite integrals.
  Open the goal for lessons, student checks and current scope notes.
6.12 · Integrating Using Linear Partial Fractions

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- FUN-6.F: For integrands requiring integration by linear partial fractions: (a) Determine indefinite integrals. (b) Evaluate definite integrals.
  Open the goal for lessons, student checks and current scope notes.
6.13 · Evaluating Improper Integrals

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-6.A: Evaluate an improper integral or determine that the integral diverges.
  Open the goal for lessons, student checks and current scope notes.
6.14 · Selecting Techniques for Antidifferentiation

Learning goals and teaching choices · Canonical shared AB article

Learning goals in the current course

This synthesis introduces no new objective. The current outline links the applicable earlier goals.
7.1 · Modeling Situations with Differential Equations

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-7.A: Interpret verbal statements of problems as differential equations involving a derivative expression.
  Open the goal for lessons, student checks and current scope notes.
7.2 · Verifying Solutions for Differential Equations

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-7.B: Verify solutions to differential equations.
  Open the goal for lessons, student checks and current scope notes.
7.3 · Sketching Slope Fields

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-7.C: Estimate solutions to differential equations.
  Open the goal for lessons, student checks and current scope notes.
7.4 · Reasoning Using Slope Fields

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-7.C: Estimate solutions to differential equations.
  Open the goal for lessons, student checks and current scope notes.
7.5 · Approximating Solutions Using Euler’s Method

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- FUN-7.C: Estimate solutions to differential equations.
  Open the goal for lessons, student checks and current scope notes.
7.6 · Finding General Solutions Using Separation of Variables

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-7.D: Determine general solutions to differential equations.
  Open the goal for lessons, student checks and current scope notes.
7.7 · Finding Particular Solutions Using Initial Conditions and Separation of Variables

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-7.E: Determine particular solutions to differential equations.
  Open the goal for lessons, student checks and current scope notes.
7.8 · Exponential Models with Differential Equations

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- FUN-7.F: Interpret the meaning of a differential equation and its variables in context.
  Open the goal for lessons, student checks and current scope notes.
- FUN-7.G: Determine general and particular solutions for problems involving differential equations in context.
  Open the goal for lessons, student checks and current scope notes.
7.9 · Logistic Models with Differential Equations

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- FUN-7.H: Interpret the meaning of the logistic growth model in context.
  Open the goal for lessons, student checks and current scope notes.
8.1 · Finding the Average Value of a Function on an Interval

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-4.B: Determine the average value of a function using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.2 · Connecting Position, Velocity, and Acceleration of Functions Using Integrals

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-4.C: Determine values for positions and rates of change using definite integrals in problems involving rectilinear motion.
  Open the goal for lessons, student checks and current scope notes.
8.3 · Using Accumulation Functions and Definite Integrals in Applied Contexts

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-4.D: Interpret the meaning of a definite integral in accumulation problems.
  Open the goal for lessons, student checks and current scope notes.
- CHA-4.E: Determine net change using definite integrals in applied contexts.
  Open the goal for lessons, student checks and current scope notes.
8.4 · Finding the Area Between Curves Expressed as Functions of x

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-5.A: Calculate areas in the plane using the definite integral.
  Open the goal for lessons, student checks and current scope notes.
8.5 · Finding the Area Between Curves Expressed as Functions of y

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-5.A: Calculate areas in the plane using the definite integral.
  Open the goal for lessons, student checks and current scope notes.
8.6 · Finding the Area Between Curves That Intersect at More Than Two Points

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-5.A: Calculate areas in the plane using the definite integral.
  Open the goal for lessons, student checks and current scope notes.
8.7 · Volumes with Cross Sections: Squares and Rectangles

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-5.B: Calculate volumes of solids with known cross sections using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.8 · Volumes with Cross Sections: Triangles and Semicircles

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-5.B: Calculate volumes of solids with known cross sections using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.9 · Volume with Disc Method: Revolving Around the x- or y-Axis

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-5.C: Calculate volumes of solids of revolution using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.10 · Volume with Disc Method: Revolving Around Other Axes

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-5.C: Calculate volumes of solids of revolution using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.11 · Volume with Washer Method: Revolving Around the x- or y-Axis

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-5.C: Calculate volumes of solids of revolution using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.12 · Volume with Washer Method: Revolving Around Other Axes

Learning goals and teaching choices · Canonical shared AB article
Learning goals in the current course
- CHA-5.C: Calculate volumes of solids of revolution using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
8.13 · The Arc Length of a Smooth, Planar Curve and Distance Traveled

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- CHA-6.A: Determine the length of a curve in the plane defined by a function, using a definite integral.
  Open the goal for lessons, student checks and current scope notes.
9.1 · Defining and Differentiating Parametric Equations

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- CHA-3.G: Calculate derivatives of parametric functions.
  Open the goal for lessons, student checks and current scope notes.
9.2 · Second Derivatives of Parametric Equations

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- CHA-3.G: Calculate derivatives of parametric functions.
  Open the goal for lessons, student checks and current scope notes.
9.3 · Finding Arc Lengths of Curves Given by Parametric Equations

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- CHA-6.B: Determine the length of a curve in the plane defined by parametric functions, using a definite integral.
  Open the goal for lessons, student checks and current scope notes.
9.4 · Defining and Differentiating Vector-Valued Functions

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- CHA-3.H: Calculate derivatives of vector-valued functions.
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9.5 · Integrating Vector-Valued Functions

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- FUN-8.A: Determine a particular solution given a rate vector and initial conditions.
  Open the goal for lessons, student checks and current scope notes.
9.6 · Solving Motion Problems Using Parametric and Vector-Valued Functions

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- FUN-8.B: Determine values for positions and rates of change in problems involving planar motion.
  Open the goal for lessons, student checks and current scope notes.
9.7 · Defining Polar Coordinates and Differentiating in Polar Form

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- FUN-3.G: Calculate derivatives of functions written in polar coordinates.
  Open the goal for lessons, student checks and current scope notes.
9.8 · Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- CHA-5.D: Calculate areas of regions defined by polar curves using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
9.9 · Finding the Area of the Region Bounded by Two Polar Curves

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- CHA-5.D: Calculate areas of regions defined by polar curves using definite integrals.
  Open the goal for lessons, student checks and current scope notes.
10.1 · Defining Convergent and Divergent Infinite Series

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-7.A: Determine whether a series converges or diverges.
  Open the goal for lessons, student checks and current scope notes.
10.2 · Working with Geometric Series

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-7.A: Determine whether a series converges or diverges.
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10.3 · The nth Term Test for Divergence

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-7.A: Determine whether a series converges or diverges.
  Open the goal for lessons, student checks and current scope notes.
10.4 · Integral Test for Convergence

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-7.A: Determine whether a series converges or diverges.
  Open the goal for lessons, student checks and current scope notes.
10.5 · Harmonic Series and p-Series

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-7.A: Determine whether a series converges or diverges.
  Open the goal for lessons, student checks and current scope notes.
10.6 · Comparison Tests for Convergence

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-7.A: Determine whether a series converges or diverges.
  Open the goal for lessons, student checks and current scope notes.
10.7 · Alternating Series Test for Convergence

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-7.A: Determine whether a series converges or diverges.
  Open the goal for lessons, student checks and current scope notes.
10.8 · Ratio Test for Convergence

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-7.A: Determine whether a series converges or diverges.
  Open the goal for lessons, student checks and current scope notes.
10.9 · Determining Absolute or Conditional Convergence

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-7.A: Determine whether a series converges or diverges.
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10.10 · Alternating Series Error Bound

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-7.B: Approximate the sum of a series.
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10.11 · Finding Taylor Polynomial Approximations of Functions

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-8.A: Represent a function at a point as a Taylor polynomial.
  Open the goal for lessons, student checks and current scope notes.
- LIM-8.B: Approximate function values using a Taylor polynomial.
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10.12 · Lagrange Error Bound

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-8.C: Determine the error bound associated with a Taylor polynomial approximation.
  Open the goal for lessons, student checks and current scope notes.
10.13 · Radius and Interval of Convergence of Power Series

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-8.D: Determine the radius of convergence and interval of convergence for a power series.
  Open the goal for lessons, student checks and current scope notes.
10.14 · Finding Taylor or Maclaurin Series for a Function

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-8.E: Represent a function as a Taylor series or a Maclaurin series.
  Open the goal for lessons, student checks and current scope notes.
- LIM-8.F: Interpret Taylor series and Maclaurin series.
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10.15 · Representing Functions as Power Series

Learning goals and teaching choices · BC-only content
Learning goals in the current course
- LIM-8.G: Represent a given function as a power series.
  Open the goal for lessons, student checks and current scope notes.

AP Chemistry

Fall 2024

1.1 · Moles and Molar Mass

Learning goals and teaching choices
Learning goals in the current course
- 1.1.A: Calculate quantities of a substance or its relative number of particles using dimensional analysis and the mole concept.
  Open the goal for lessons, student checks and current scope notes.
1.2 · Mass Spectra of Elements

Learning goals and teaching choices
Learning goals in the current course
- 1.2.A: Explain the quantitative relationship between the mass spectrum of an element and the masses of the element’s isotopes.
  Open the goal for lessons, student checks and current scope notes.
1.3 · Elemental Composition of Pure Substances

Learning goals and teaching choices
Learning goals in the current course
- 1.3.A: Explain the quantitative relationship between the elemental composition by mass and the empirical formula of a pure substance.
  Open the goal for lessons, student checks and current scope notes.
1.4 · Composition of Mixtures

Learning goals and teaching choices
Learning goals in the current course
- 1.4.A: Explain the quantitative relationship between the elemental composition by mass and the composition of substances in a mixture.
  Open the goal for lessons, student checks and current scope notes.
1.5 · Atomic Structure and Electron Configuration

Learning goals and teaching choices
Learning goals in the current course
- 1.5.A: Represent the ground-state electron configuration of an atom of an element or its ions using the Aufbau principle.
  Open the goal for lessons, student checks and current scope notes.
1.6 · Photoelectron Spectroscopy

Learning goals and teaching choices
Learning goals in the current course
- 1.6.A: Explain the relationship between the photoelectron spectrum of an atom or ion and: i. The ground-state electron configuration of the species. ii. The interactions between the electrons and the nucleus.
  Open the goal for lessons, student checks and current scope notes.
1.7 · Periodic Trends

Learning goals and teaching choices
Learning goals in the current course
- 1.7.A: Explain the relationship between trends in atomic properties of elements and electronic structure and periodicity.
  Open the goal for lessons, student checks and current scope notes.
1.8 · Valence Electrons and Ionic Compounds

Learning goals and teaching choices
Learning goals in the current course
- 1.8.A: Explain the relationship between trends in the reactivity of elements and periodicity.
  Open the goal for lessons, student checks and current scope notes.
2.1 · Types of Chemical Bonds

Learning goals and teaching choices
Learning goals in the current course
- 2.1.A: Explain the relationship between the type of bonding and the properties of the elements participating in the bond.
  Open the goal for lessons, student checks and current scope notes.
2.2 · Intramolecular Force and Potential Energy

Learning goals and teaching choices
Learning goals in the current course
- 2.2.A: Represent the relationship between potential energy and distance between atoms, based on factors that influence the interaction strength.
  Open the goal for lessons, student checks and current scope notes.
2.3 · Structure of Ionic Solids

Learning goals and teaching choices
Learning goals in the current course
- 2.3.A: Represent an ionic solid with a particulate model that is consistent with Coulomb’s law and the properties of the constituent ions.
  Open the goal for lessons, student checks and current scope notes.
2.4 · Structure of Metals and Alloys

Learning goals and teaching choices
Learning goals in the current course
- 2.4.A: Represent a metallic solid and/or alloy using a model to show essential characteristics of the structure and interactions present in the substance.
  Open the goal for lessons, student checks and current scope notes.
2.5 · Lewis Diagrams

Learning goals and teaching choices
Learning goals in the current course
- 2.5.A: Represent a molecule with a Lewis diagram.
  Open the goal for lessons, student checks and current scope notes.
2.6 · Resonance and Formal Charge

Learning goals and teaching choices
Learning goals in the current course
- 2.6.A: Represent a molecule with a Lewis diagram that accounts for resonance between equivalent structures or that uses formal charge to select between nonequivalent structures.
  Open the goal for lessons, student checks and current scope notes.
2.7 · VSEPR and Hybridization

Learning goals and teaching choices
Learning goals in the current course
- 2.7.A: Based on the relationship between Lewis diagrams, VSEPR theory, bond orders, and bond polarities: i. Explain structural properties of molecules. ii. Explain electron properties of molecules.
  Open the goal for lessons, student checks and current scope notes.
3.1 · Intermolecular and Interparticle Forces

Learning goals and teaching choices
Learning goals in the current course
- 3.1.A: Explain the relationship between the chemical structures of molecules and the relative strength of their intermolecular forces when: i. The molecules are of the same chemical species. ii. The molecules are of two different chemical species.
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3.2 · Properties of Solids

Learning goals and teaching choices
Learning goals in the current course
- 3.2.A: Explain the relationship among the macroscopic properties of a substance, the particulate-level structure of the substance, and the interactions between these particles.
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3.3 · Solids, Liquids, and Gases

Learning goals and teaching choices
Learning goals in the current course
- 3.3.A: Represent the differences between solid, liquid, and gas phases using a particulate-level model.
  Open the goal for lessons, student checks and current scope notes.
3.4 · Ideal Gas Law

Learning goals and teaching choices
Learning goals in the current course
- 3.4.A: Explain the relationship between the macroscopic properties of a sample of gas or mixture of gases using the ideal gas law.
  Open the goal for lessons, student checks and current scope notes.
3.5 · Kinetic Molecular Theory

Learning goals and teaching choices
Learning goals in the current course
- 3.5.A: Explain the relationship between the motion of particles and the macroscopic properties of gases with: i. The kinetic molecular theory (KMT). ii. A particulate model. iii. A graphical representation.
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3.6 · Deviation from Ideal Gas Law

Learning goals and teaching choices
Learning goals in the current course
- 3.6.A: Explain the relationship among non-ideal behaviors of gases, interparticle forces, and/or volumes.
  Open the goal for lessons, student checks and current scope notes.
3.7 · Solutions and Mixtures

Learning goals and teaching choices
Learning goals in the current course
- 3.7.A: Calculate the number of solute particles, volume, or molarity of solutions.
  Open the goal for lessons, student checks and current scope notes.
3.8 · Representations of Solutions

Learning goals and teaching choices
Learning goals in the current course
- 3.8.A: Using particulate models for mixtures: i. Represent interactions between components. ii. Represent concentrations of components.
  Open the goal for lessons, student checks and current scope notes.
3.9 · Separation of Solutions and Mixtures

Learning goals and teaching choices
Learning goals in the current course
- 3.9.A: Explain the results of a separation experiment based on intermolecular interactions.
  Open the goal for lessons, student checks and current scope notes.
3.10 · Solubility

Learning goals and teaching choices
Learning goals in the current course
- 3.10.A: Explain the relationship between the solubility of ionic and molecular compounds in aqueous and nonaqueous solvents, and the intermolecular interactions between particles.
  Open the goal for lessons, student checks and current scope notes.
3.11 · Spectroscopy and the Electromagnetic Spectrum

Learning goals and teaching choices
Learning goals in the current course
- 3.11.A: Explain the relationship between a region of the electromagnetic spectrum and the types of molecular or electronic transitions associated with that region.
  Open the goal for lessons, student checks and current scope notes.
3.12 · Properties of Photons

Learning goals and teaching choices
Learning goals in the current course
- 3.12.A: Explain the properties of an absorbed or emitted photon in relationship to an electronic transition in an atom or molecule.
  Open the goal for lessons, student checks and current scope notes.
3.13 · Beer-Lambert Law

Learning goals and teaching choices
Learning goals in the current course
- 3.13.A: Explain the amount of light absorbed by a solution of molecules or ions in relationship to the concentration, path length, and molar absorptivity.
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4.1 · Introduction for Reactions

Learning goals and teaching choices
Learning goals in the current course
- 4.1.A: Identify evidence of chemical and physical changes in matter.
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4.2 · Net Ionic Equations

Learning goals and teaching choices
Learning goals in the current course
- 4.2.A: Represent changes in matter with a balanced chemical or net ionic equation: i. For physical changes. ii. For given information about the identity of the reactants and/or product. iii. For ions in a given chemical reaction.
  Open the goal for lessons, student checks and current scope notes.
4.3 · Representations of Reactions

Learning goals and teaching choices
Learning goals in the current course
- 4.3.A: Represent a given chemical reaction or physical process with a consistent particulate model.
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4.4 · Physical and Chemical Changes

Learning goals and teaching choices
Learning goals in the current course
- 4.4.A: Explain the relationship between macroscopic characteristics and bond interactions for: i. Chemical processes. ii. Physical processes.
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4.5 · Stoichiometry

Learning goals and teaching choices
Learning goals in the current course
- 4.5.A: Explain changes in the amounts of reactants and products based on the balanced reaction equation for a chemical process.
  Open the goal for lessons, student checks and current scope notes.
4.6 · Introduction to Titration

Learning goals and teaching choices
Learning goals in the current course
- 4.6.A: Identify the equivalence point in a titration based on the amounts of the titrant and analyte, assuming the titration reaction goes to completion.
  Open the goal for lessons, student checks and current scope notes.
4.7 · Types of Chemical Reactions

Learning goals and teaching choices
Learning goals in the current course
- 4.7.A: Identify a reaction as acid-base, oxidation-reduction, or precipitation.
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4.8 · Introduction to Acid-Base Reactions

Learning goals and teaching choices
Learning goals in the current course
- 4.8.A: Identify species as Brønsted-Lowry acids, bases, and/or conjugate acid-base pairs, based on proton-transfer involving those species.
  Open the goal for lessons, student checks and current scope notes.
4.9 · Oxidation-Reduction (Redox) Reactions

Learning goals and teaching choices
Learning goals in the current course
- 4.9.A: Represent a balanced redox reaction equation using half-reactions.
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5.1 · Reaction Rates

Learning goals and teaching choices
Learning goals in the current course
- 5.1.A: Explain the relationship between the rate of a chemical reaction and experimental parameters.
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5.2 · Introduction to Rate Law

Learning goals and teaching choices
Learning goals in the current course
- 5.2.A: Represent experimental data with a consistent rate law expression.
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5.3 · Concentration Changes Over Time

Learning goals and teaching choices
Learning goals in the current course
- 5.3.A: Identify the rate law expression of a chemical reaction using data that show how the concentrations of reaction species change over time.
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5.4 · Elementary Reactions

Learning goals and teaching choices
Learning goals in the current course
- 5.4.A: Represent an elementary reaction as a rate law expression using stoichiometry.
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5.5 · Collision Model

Learning goals and teaching choices
Learning goals in the current course
- 5.5.A: Explain the relationship between the rate of an elementary reaction and the frequency, energy, and orientation of particle collisions.
  Open the goal for lessons, student checks and current scope notes.
5.6 · Reaction Energy Profile

Learning goals and teaching choices
Learning goals in the current course
- 5.6.A: Represent the activation energy and overall energy change in an elementary reaction using a reaction energy profile.
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5.7 · Introduction to Reaction Mechanisms

Learning goals and teaching choices
Learning goals in the current course
- 5.7.A: Identify the components of a reaction mechanism.
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5.8 · Reaction Mechanism and Rate Law

Learning goals and teaching choices
Learning goals in the current course
- 5.8.A: Identify the rate law for a reaction from a mechanism in which the first step is rate limiting.
  Open the goal for lessons, student checks and current scope notes.
5.9 · Pre-Equilibrium Approximation

Learning goals and teaching choices
Learning goals in the current course
- 5.9.A: Identify the rate law for a reaction from a mechanism in which the first step is not rate limiting.
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5.10 · Multistep Reaction Energy Profile

Learning goals and teaching choices
Learning goals in the current course
- 5.10.A: Represent the activation energy and overall energy change in a multistep reaction with a reaction energy profile.
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5.11 · Catalysis

Learning goals and teaching choices
Learning goals in the current course
- 5.11.A: Explain the relationship between the effect of a catalyst on a reaction and changes in the reaction mechanism.
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6.1 · Endothermic and Exothermic Processes

Learning goals and teaching choices
Learning goals in the current course
- 6.1.A: Explain the relationship between experimental observations and energy changes associated with a chemical or physical transformation.
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6.2 · Energy Diagrams

Learning goals and teaching choices
Learning goals in the current course
- 6.2.A: Represent a chemical or physical transformation with an energy diagram.
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6.3 · Heat Transfer and Thermal Equilibrium

Learning goals and teaching choices
Learning goals in the current course
- 6.3.A: Explain the relationship between the transfer of thermal energy and molecular collisions.
  Open the goal for lessons, student checks and current scope notes.
6.4 · Heat Capacity and Calorimetry

Learning goals and teaching choices
Learning goals in the current course
- 6.4.A: Calculate the heat q absorbed or released by a system undergoing heating/cooling based on the amount of the substance, the heat capacity, and the change in temperature.
  Open the goal for lessons, student checks and current scope notes.
6.5 · Energy of Phase Changes

Learning goals and teaching choices
Learning goals in the current course
- 6.5.A: Explain changes in the heat q absorbed or released by a system undergoing a phase transition based on the amount of the substance in moles and the molar enthalpy of the phase transition.
  Open the goal for lessons, student checks and current scope notes.
6.6 · Introduction to Enthalpy of Reaction

Learning goals and teaching choices
Learning goals in the current course
- 6.6.A: Calculate the heat q absorbed or released by a system undergoing a chemical reaction in relationship to the amount of the reacting substance in moles and the molar enthalpy of reaction.
  Open the goal for lessons, student checks and current scope notes.
6.7 · Bond Enthalpies

Learning goals and teaching choices
Learning goals in the current course
- 6.7.A: Calculate the enthalpy change of a reaction based on the average bond energies of bonds broken and formed in the reaction.
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6.8 · Enthalpy of Formation

Learning goals and teaching choices
Learning goals in the current course
- 6.8.A: Calculate the enthalpy change for a chemical or physical process based on the standard enthalpies of formation.
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6.9 · Hess’s Law

Learning goals and teaching choices
Learning goals in the current course
- 6.9.A: Represent a chemical or physical process as a sequence of steps.
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- 6.9.B: Explain the relationship between the enthalpy of a chemical or physical process and the sum of the enthalpies of the individual steps.
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7.1 · Introduction to Equilibrium

Learning goals and teaching choices
Learning goals in the current course
- 7.1.A: Explain the relationship between the occurrence of a reversible chemical or physical process, and the establishment of equilibrium, to experimental observations.
  Open the goal for lessons, student checks and current scope notes.
7.2 · Direction of Reversible Reactions

Learning goals and teaching choices
Learning goals in the current course
- 7.2.A: Explain the relationship between the direction in which a reversible reaction proceeds and the relative rates of the forward and reverse reactions.
  Open the goal for lessons, student checks and current scope notes.
7.3 · Reaction Quotient and Equilibrium Constant

Learning goals and teaching choices
Learning goals in the current course
- 7.3.A: Represent the reaction quotient Q_c or Q_p, for a reversible reaction, and the corresponding equilibrium expressions K_c = Q_c or K_p = Q_p.
  Open the goal for lessons, student checks and current scope notes.
7.4 · Calculating the Equilibrium Constant

Learning goals and teaching choices
Learning goals in the current course
- 7.4.A: Calculate K_c or K_p based on experimental observations of concentrations or pressures at equilibrium.
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7.5 · Magnitude of the Equilibrium Constant

Learning goals and teaching choices
Learning goals in the current course
- 7.5.A: Explain the relationship between very large or very small values of K and the relative concentrations of chemical species at equilibrium.
  Open the goal for lessons, student checks and current scope notes.
7.6 · Properties of the Equilibrium Constant

Learning goals and teaching choices
Learning goals in the current course
- 7.6.A: Represent a multistep process with an overall equilibrium expression, using the constituent K expressions for each individual reaction.
  Open the goal for lessons, student checks and current scope notes.
7.7 · Calculating Equilibrium Concentrations

Learning goals and teaching choices
Learning goals in the current course
- 7.7.A: Identify the concentrations or partial pressures of chemical species at equilibrium based on the initial conditions and the equilibrium constant.
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7.8 · Representations of Equilibrium

Learning goals and teaching choices
Learning goals in the current course
- 7.8.A: Represent a system undergoing a reversible reaction with a particulate model.
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7.9 · Introduction to Le Châtelier’s Principle

Learning goals and teaching choices
Learning goals in the current course
- 7.9.A: Identify the response of a system at equilibrium to an external stress, using Le Châtelier's principle.
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7.10 · Reaction Quotient and Le Châtelier’s Principle

Learning goals and teaching choices
Learning goals in the current course
- 7.10.A: Explain the relationships between Q, K, and the direction in which a reversible reaction will proceed to reach equilibrium.
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7.11 · Introduction to Solubility Equilibria

Learning goals and teaching choices
Learning goals in the current course
- 7.11.A: Calculate the solubility of a salt based on the value of K_sp for the salt.
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7.12 · Common-Ion Effect

Learning goals and teaching choices
Learning goals in the current course
- 7.12.A: Identify the solubility of a salt, and/or the value of K_sp for the salt, based on the concentration of a common ion already present in solution.
  Open the goal for lessons, student checks and current scope notes.
8.1 · Introduction to Acids and Bases

Learning goals and teaching choices
Learning goals in the current course
- 8.1.A: Calculate the values of pH and pOH, based on K_w and the concentration of all species present in a neutral solution of water.
  Open the goal for lessons, student checks and current scope notes.
8.2 · pH and pOH of Strong Acids and Bases

Learning goals and teaching choices
Learning goals in the current course
- 8.2.A: Calculate pH and pOH based on concentrations of all species in a solution of a strong acid or a strong base.
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8.3 · Weak Acid and Base Equilibria

Learning goals and teaching choices
Learning goals in the current course
- 8.3.A: Explain the relationship among pH, pOH, and concentrations of all species in a solution of a monoprotic weak acid or weak base.
  Open the goal for lessons, student checks and current scope notes.
8.4 · Acid-Base Reactions and Buffers

Learning goals and teaching choices
Learning goals in the current course
- 8.4.A: Explain the relationship among the concentrations of major species in a mixture of weak and strong acids and bases.
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8.5 · Acid-Base Titrations

Learning goals and teaching choices
Learning goals in the current course
- 8.5.A: Explain results from the titration of a mono- or polyprotic acid or base solution, in relation to the properties of the solution and its components.
  Open the goal for lessons, student checks and current scope notes.
8.6 · Molecular Structure of Acids and Bases

Learning goals and teaching choices
Learning goals in the current course
- 8.6.A: Explain the relationship between the strength of an acid or base and the structure of the molecule or ion.
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8.7 · pH and pKa

Learning goals and teaching choices
Learning goals in the current course
- 8.7.A: Explain the relationship between the predominant form of a weak acid or base in solution at a given pH and the pK_a of the conjugate acid or the pK_b of the conjugate base.
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8.8 · Properties of Buffers

Learning goals and teaching choices
Learning goals in the current course
- 8.8.A: Explain the relationship between the ability of a buffer to stabilize pH and the reactions that occur when an acid or a base is added to a buffered solution.
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8.9 · Henderson-Hasselbalch Equation

Learning goals and teaching choices
Learning goals in the current course
- 8.9.A: Identify the pH of a buffer solution based on the identity and concentrations of the conjugate acid-base pair used to create the buffer.
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8.10 · Buffer Capacity

Learning goals and teaching choices
Learning goals in the current course
- 8.10.A: Explain the relationship between the buffer capacity of a solution and the relative concentrations of the conjugate acid and conjugate base components of the solution.
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8.11 · pH and Solubility

Learning goals and teaching choices
Learning goals in the current course
- 8.11.A: Identify the qualitative effect of changes in pH on the solubility of a salt.
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9.1 · Introduction to Entropy

Learning goals and teaching choices
Learning goals in the current course
- 9.1.A: Identify the sign and relative magnitude of the entropy change associated with chemical or physical processes.
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9.2 · Absolute Entropy and Entropy Change

Learning goals and teaching choices
Learning goals in the current course
- 9.2.A: Calculate the standard entropy change for a chemical or physical process based on the absolute entropies (standard molar entropies) of the species involved in the process.
  Open the goal for lessons, student checks and current scope notes.
9.3 · Gibbs Free Energy and Thermodynamic Favorability

Learning goals and teaching choices
Learning goals in the current course
- 9.3.A: Explain whether a physical or chemical process is thermodynamically favored based on an evaluation of ΔG°.
  Open the goal for lessons, student checks and current scope notes.
9.4 · Thermodynamic and Kinetic Control

Learning goals and teaching choices
Learning goals in the current course
- 9.4.A: Explain, in terms of kinetics, why a thermodynamically favored reaction might not occur at a measurable rate.
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9.5 · Free Energy and Equilibrium

Learning goals and teaching choices
Learning goals in the current course
- 9.5.A: Explain whether a process is thermodynamically favored using the relationships between K, ΔG°, and T.
  Open the goal for lessons, student checks and current scope notes.
9.6 · Free Energy of Dissolution

Learning goals and teaching choices
Learning goals in the current course
- 9.6.A: Explain the relationship between the solubility of a salt and changes in the enthalpy and entropy that occur in the dissolution process.
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9.7 · Coupled Reactions

Learning goals and teaching choices
Learning goals in the current course
- 9.7.A: Explain the relationship between external sources of energy or coupled reactions and their ability to drive thermodynamically unfavorable processes.
  Open the goal for lessons, student checks and current scope notes.
9.8 · Galvanic (Voltaic) and Electrolytic Cells

Learning goals and teaching choices
Learning goals in the current course
- 9.8.A: Explain the relationship between the physical components of an electrochemical cell and the overall operational principles of the cell.
  Open the goal for lessons, student checks and current scope notes.
9.9 · Cell Potential and Free Energy

Learning goals and teaching choices
Learning goals in the current course
- 9.9.A: Explain whether an electrochemical cell is thermodynamically favored, based on its standard cell potential and the constituent half-reactions within the cell.
  Open the goal for lessons, student checks and current scope notes.
9.10 · Cell Potential Under Nonstandard Conditions

Learning goals and teaching choices
Learning goals in the current course
- 9.10.A: Explain the relationship between deviations from standard cell conditions and changes in the cell potential.
  Open the goal for lessons, student checks and current scope notes.
9.11 · Electrolysis and Faraday’s Law

Learning goals and teaching choices
Learning goals in the current course
- 9.11.A: Calculate the amount of charge flow based on changes in the amounts of reactants and products in an electrochemical cell.
  Open the goal for lessons, student checks and current scope notes.

AP Physics 2

Fall 2024; current 2026–27 updates

9.1 · Kinetic Theory of Temperature and Pressure

Learning goals and teaching choices
Learning goals in the current course
- 9.1.A: Describe the pressure a gas exerts on its container in terms of atomic motion within that gas.
  Open the goal for lessons, student checks and current scope notes.
- 9.1.B: Describe the temperature of a system in terms of the atomic motion within that system.
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9.2 · The Ideal Gas Law

Learning goals and teaching choices
Learning goals in the current course
- 9.2.A: Describe the properties of an ideal gas.
  Open the goal for lessons, student checks and current scope notes.
9.3 · Thermal Energy Transfer and Equilibrium

Learning goals and teaching choices
Learning goals in the current course
- 9.3.A: Describe the transfer of energy between two systems in thermal contact due to temperature differences of those two systems.
  Open the goal for lessons, student checks and current scope notes.
9.4 · The First Law of Thermodynamics

Learning goals and teaching choices
Learning goals in the current course
- 9.4.A: Describe the internal energy of a system.
  Open the goal for lessons, student checks and current scope notes.
- 9.4.B: Describe the behavior of a system using thermodynamic processes.
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9.5 · Specific Heat and Thermal Conductivity

Learning goals and teaching choices
Learning goals in the current course
- 9.5.A: Describe the energy required to change the temperature of an object by a certain amount.
  Open the goal for lessons, student checks and current scope notes.
- 9.5.B: Describe the rate at which energy is transferred by conduction through a given material.
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9.6 · Entropy and the Second Law of Thermodynamics

Learning goals and teaching choices
Learning goals in the current course
- 9.6.A: Describe the change in entropy for a given system over time.
  Open the goal for lessons, student checks and current scope notes.
10.1 · Electric Charge and Electric Force

Learning goals and teaching choices
Learning goals in the current course
- 10.1.A: Describe the electric force that results from the interactions between charged objects or systems.
  Open the goal for lessons, student checks and current scope notes.
- 10.1.B: Describe the electric and gravitational forces that result from interactions between charged objects with mass.
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- 10.1.C: Describe the electric permittivity of a material or medium.
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10.2 · Conservation of Electric Charge and the Process of Charging

Learning goals and teaching choices
Learning goals in the current course
- 10.2.A: Describe the behavior of a system using conservation of charge.
  Open the goal for lessons, student checks and current scope notes.
10.3 · Electric Fields

Learning goals and teaching choices
Learning goals in the current course
- 10.3.A: Describe the electric field produced by a charged object or configuration of point charges.
  Open the goal for lessons, student checks and current scope notes.
- 10.3.B: Describe the electric field generated by charged conductors or insulators.
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10.4 · Electric Potential Energy

Learning goals and teaching choices
Learning goals in the current course
- 10.4.A: Describe the electric potential energy of a system.
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10.5 · Electric Potential

Learning goals and teaching choices
Learning goals in the current course
- 10.5.A: Describe the electric potential due to a configuration of charged objects.
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- 10.5.B: Describe the relationship between electric potential and electric field.
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10.6 · Capacitors

Learning goals and teaching choices
Learning goals in the current course
- 10.6.A: Describe the physical properties of a parallel-plate capacitor.
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10.7 · Conservation of Electric Energy

Learning goals and teaching choices
Learning goals in the current course
- 10.7.A: Describe changes in energy in a system due to a difference in electric potential between two locations.
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11.1 · Electric Current

Learning goals and teaching choices
Learning goals in the current course
- 11.1.A: Describe the movement of electric charges through a medium.
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11.2 · Simple Circuits

Learning goals and teaching choices
Learning goals in the current course
- 11.2.A: Describe the behavior of a circuit.
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11.3 · Resistance, Resistivity, and Ohm’s Law

Learning goals and teaching choices
Learning goals in the current course
- 11.3.A: Describe the resistance of an object using physical properties of that object.
  Open the goal for lessons, student checks and current scope notes.
- 11.3.B: Describe the electrical characteristics of elements of a circuit.
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11.4 · Electric Power

Learning goals and teaching choices
Learning goals in the current course
- 11.4.A: Describe the transfer of energy into, out of, or within an electric circuit, in terms of power.
  Open the goal for lessons, student checks and current scope notes.
11.5 · Compound Direct Current (DC) Circuits

Learning goals and teaching choices
Learning goals in the current course
- 11.5.A: Describe the equivalent resistance of multiple resistors connected in a circuit.
  Open the goal for lessons, student checks and current scope notes.
- 11.5.B: Describe a circuit with resistive wires and a battery with internal resistance.
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- 11.5.C: Describe the measurement of current and potential difference in a circuit.
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11.6 · Kirchhoff’s Loop Rule

Learning goals and teaching choices
Learning goals in the current course
- 11.6.A: Describe a circuit or elements of a circuit by applying Kirchhoff’s loop rule.
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11.7 · Kirchhoff’s Junction Rule

Learning goals and teaching choices
Learning goals in the current course
- 11.7.A: Describe a circuit or elements of a circuit by applying Kirchhoff’s junction rule.
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11.8 · Resistor-Capacitor (RC) Circuits

Learning goals and teaching choices
Learning goals in the current course
- 11.8.A: Describe the equivalent capacitance of multiple capacitors.
  Open the goal for lessons, student checks and current scope notes.
- 11.8.B: Describe the behavior of a circuit containing combinations of resistors and capacitors.
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12.1 · Magnetic Fields

Learning goals and teaching choices
Learning goals in the current course
- 12.1.A: Describe the properties of a magnetic field.
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- 12.1.B: Describe the magnetic behavior of a material as a result of the configuration of magnetic dipoles in the material.
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- 12.1.C: Describe the magnetic permeability of a material.
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12.2 · Magnetism and Moving Charges

Learning goals and teaching choices
Learning goals in the current course
- 12.2.A: Describe the magnetic field produced by moving charged objects.
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- 12.2.B: Describe the force exerted on moving charged objects by a magnetic field.
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12.3 · Magnetism and Current-Carrying Wires

Learning goals and teaching choices
Learning goals in the current course
- 12.3.A: Describe the magnetic field produced by a current- carrying wire.
  Open the goal for lessons, student checks and current scope notes.
- 12.3.B: Describe the force exerted on a current-carrying wire by a magnetic field.
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12.4 · Electromagnetic Induction and Faraday’s Law

Learning goals and teaching choices
Learning goals in the current course
- 12.4.A: Describe the induced electric potential difference resulting from a change in magnetic flux.
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13.1 · Reflection

Learning goals and teaching choices
Learning goals in the current course
- 13.1.A: Describe light as a ray.
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- 13.1.B: Describe the reflection of light from a surface.
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13.2 · Images Formed by Mirrors

Learning goals and teaching choices
Learning goals in the current course
- 13.2.A: Describe the image formed by a mirror.
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13.3 · Refraction

Learning goals and teaching choices
Learning goals in the current course
- 13.3.A: Describe the refraction of light between two media.
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13.4 · Images Formed by Lenses

Learning goals and teaching choices
Learning goals in the current course
- 13.4.A: Describe the image formed by a lens.
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14.1 · Properties of Wave Pulses and Waves

Learning goals and teaching choices
Learning goals in the current course
- 14.1.A: Describe the physical properties of waves and wave pulses.
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14.2 · Periodic Waves

Learning goals and teaching choices
Learning goals in the current course
- 14.2.A: Describe the physical properties of a periodic wave.
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14.3 · Boundary Behavior of Waves and Polarization

Learning goals and teaching choices
Learning goals in the current course
- 14.3.A: Describe the interaction between a wave and a boundary.
  Open the goal for lessons, student checks and current scope notes.
14.4 · Electromagnetic Waves

Learning goals and teaching choices
Learning goals in the current course
- 14.4.A: Describe the properties of an electromagnetic wave.
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14.5 · The Doppler Effect

Learning goals and teaching choices
Learning goals in the current course
- 14.5.A: Describe the properties of a wave based on the relative motion between the source of the wave and the observer of the wave.
  Open the goal for lessons, student checks and current scope notes.
14.6 · Wave Interference and Standing Waves

Learning goals and teaching choices
Learning goals in the current course
- 14.6.A: Describe the net disturbance that occurs when two or more wave pulses or waves overlap.
  Open the goal for lessons, student checks and current scope notes.
- 14.6.B: Describe the properties of a standing wave.
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14.7 · Diffraction

Learning goals and teaching choices
Learning goals in the current course
- 14.7.A: Describe the behavior of a wave and the diffraction pattern resulting from a wave passing through a single opening.
  Open the goal for lessons, student checks and current scope notes.
14.8 · Double-Slit Interference and Diffraction Gratings

Learning goals and teaching choices
Learning goals in the current course
- 14.8.A: Describe the behavior of a wave and the diffraction pattern resulting from the wave passing through multiple openings.
  Open the goal for lessons, student checks and current scope notes.
14.9 · Thin-Film Interference

Learning goals and teaching choices
Learning goals in the current course
- 14.9.A: Describe the behavior of light that interacts with a thin film.
  Open the goal for lessons, student checks and current scope notes.
15.1 · Quantum Theory and Wave-Particle Duality

Learning goals and teaching choices
Learning goals in the current course
- 15.1.A: Describe the properties and behavior of an object that exhibits both particle-like and wave-like behavior.
  Open the goal for lessons, student checks and current scope notes.
15.2 · The Bohr Model of Atomic Structure

Learning goals and teaching choices
Learning goals in the current course
- 15.2.A: Describe the properties of an atom.
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15.3 · Emission and Absorption Spectra

Learning goals and teaching choices
Learning goals in the current course
- 15.3.A: Describe the emission or absorption of photons by atoms.
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15.4 · Blackbody Radiation

Learning goals and teaching choices
Learning goals in the current course
- 15.4.A: Describe the electromagnetic radiation emitted by an object due to its temperature.
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15.5 · The Photoelectric Effect

Learning goals and teaching choices
Learning goals in the current course
- 15.5.A: Describe an interaction between photons and matter using the photoelectric effect.
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15.6 · Compton Scattering

Learning goals and teaching choices
Learning goals in the current course
- 15.6.A: Describe the interaction between photons and matter using Compton scattering.
  Open the goal for lessons, student checks and current scope notes.
15.7 · Fission, Fusion, and Nuclear Decay

Learning goals and teaching choices
Learning goals in the current course
- 15.7.A: Describe the physical properties that constrain the behavior of interacting nuclei, subatomic particles, and nucleons.
  Open the goal for lessons, student checks and current scope notes.
- 15.7.B: Describe the radioactive decay of a given sample of material consisting of a finite number of nuclei.
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15.8 · Types of Radioactive Decay

Learning goals and teaching choices
Learning goals in the current course
- 15.8.A: Describe the processes by which individual nuclei decay.
  Open the goal for lessons, student checks and current scope notes.

AP Statistics

Effective Fall 2026; 2026–27 course and May 2027 exam

1.1 · Introducing Statistics: What Can We Learn from Data?

Learning goals and teaching choices
Learning goals in the current course
- 1.1.A: Identify components within a statistical study.
  Open the goal for lessons, student checks and current scope notes.
- 1.1.B: Determine an investigative question within a statistical study.
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1.2 · Variables

Learning goals and teaching choices
Learning goals in the current course
- 1.2.A: Identify observational units, variables, parameters, and statistics from a statistical study or data set.
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- 1.2.B: Identify types of variables.
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- 1.2.C: Identify types of quantitative variables.
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1.3 · Tabular Representation and Summary Statistics for One Categorical Variable

Learning goals and teaching choices
Learning goals in the current course
- 1.3.A: Construct categorical one-variable tabular representations.
  Open the goal for lessons, student checks and current scope notes.
- 1.3.B: Describe categorical one-variable tabular representations with summary statistics.
  Open the goal for lessons, student checks and current scope notes.
1.4 · Graphical Representations for One Categorical Variable

Learning goals and teaching choices
Learning goals in the current course
- 1.4.A: Construct categorical one-variable graphical representations.
  Open the goal for lessons, student checks and current scope notes.
- 1.4.B: Justify a claim using categorical one-variable graphical representations.
  Open the goal for lessons, student checks and current scope notes.
- 1.4.C: Compare multiple categorical one-variable tabular and graphical representations.
  Open the goal for lessons, student checks and current scope notes.
1.5 · Graphical Representations for One Quantitative Variable

Learning goals and teaching choices
Learning goals in the current course
- 1.5.A: Construct quantitative one-variable graphical representations.
  Open the goal for lessons, student checks and current scope notes.
1.6 · Descriptions for One Quantitative Variable Distributions

Learning goals and teaching choices
Learning goals in the current course
- 1.6.A: Describe distributions of quantitative one-variable graphical representations.
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- 1.6.B: Justify a claim using distributions of quantitative one-variable graphical representations.
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1.7 · Summary Statistics for One Quantitative Variable

Learning goals and teaching choices
Learning goals in the current course
- 1.7.A: Calculate measures of center and position for quantitative data.
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- 1.7.B: Calculate measures of variability for quantitative data.
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- 1.7.C: Calculate different units of measurement for summary statistics.
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- 1.7.D: Calculate outliers for quantitative data.
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- 1.7.E: Compare multiple quantitative one-variable summary statistics.
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- 1.7.F: Justify the selection of a summary statistic for describing quantitative data.
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1.8 · Graphical Representations of Summary Statistics for One Quantitative Variable

Learning goals and teaching choices
Learning goals in the current course
- 1.8.A: Construct quantitative one-variable graphical representations of summary statistics.
  Open the goal for lessons, student checks and current scope notes.
- 1.8.B: Describe quantitative one-variable graphical representations of summary statistics based on the relationship of the mean and the median.
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1.9 · Comparisons of the Distributions for One Quantitative Variable

Learning goals and teaching choices
Learning goals in the current course
- 1.9.A: Compare multiple quantitative one-variable graphical representations.
  Open the goal for lessons, student checks and current scope notes.
- 1.9.B: Compare multiple quantitative one-variable graphical representations of summary statistics.
  Open the goal for lessons, student checks and current scope notes.
- 1.9.C: Justify a claim using multiple quantitative one-variable graphical representations.
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- 1.9.D: Calculate z-scores with population parameters.
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- 1.9.E: Compare z-scores as measures of relative position for distributions.
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1.10 · The Investigative Question Revisited and Data Collection

Learning goals and teaching choices
Learning goals in the current course
- 1.10.A: Determine the components of an investigative question within a statistical study.
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- 1.10.B: Identify a census.
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- 1.10.C: Identify an experiment.
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- 1.10.D: Identify an observational study.
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- 1.10.E: Justify the appropriateness of generalizations for a statistical study.
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1.11 · Random Sampling

Learning goals and teaching choices
Learning goals in the current course
- 1.11.A: Identify a sampling method given a description of a study.
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- 1.11.B: Justify the appropriateness of a sampling method.
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1.12 · Potential Problems with Sampling

Learning goals and teaching choices
Learning goals in the current course
- 1.12.A: Identify potential sources of bias in sampling methods.
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1.13 · Experimental Design

Learning goals and teaching choices
Learning goals in the current course
- 1.13.A: Identify elements of a well-designed experiment.
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- 1.13.B: Identify experimental designs.
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- 1.13.C: Justify the appropriateness of a particular experimental design.
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- 1.13.D: Justify the appropriateness of the conclusions based on a well-designed experiment.
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2.1 · Tabular and Graphical Representations for the Distributions of Two Categorical Variables

Learning goals and teaching choices
Learning goals in the current course
- 2.1.A: Compare tabular and graphical representations for the relationship between two categorical variables.
  Open the goal for lessons, student checks and current scope notes.
- 2.1.B: Justify a claim using tabular and graphical representations for the distributions of two categorical variables.
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2.2 · Summary Statistics for Two Categorical Variables

Learning goals and teaching choices
Learning goals in the current course
- 2.2.A: Calculate summary statistics from two-way tables.
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- 2.2.B: Compare summary statistics for two categorical variables.
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- 2.2.C: Justify a claim using summary statistics for two categorical variables.
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2.3 · Estimating Probabilities Using Simulation

Learning goals and teaching choices
Learning goals in the current course
- 2.3.A: Estimate probabilities using simulations.
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2.4 · Introduction to Probability

Learning goals and teaching choices
Learning goals in the current course
- 2.4.A: Calculate probabilities for events and their complements.
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2.5 · Mutually Exclusive Events

Learning goals and teaching choices
Learning goals in the current course
- 2.5.A: Justify why two events are mutually exclusive (or disjoint) using joint probability.
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2.6 · Conditional Probability

Learning goals and teaching choices
Learning goals in the current course
- 2.6.A: Calculate conditional probabilities.
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2.7 · Independent Events and Unions of Events

Learning goals and teaching choices
Learning goals in the current course
- 2.7.A: Calculate probabilities for independent events and for the union of two events.
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2.8 · Introduction to Random Variables and Probability Distributions

Learning goals and teaching choices
Learning goals in the current course
- 2.8.A: Construct a probability distribution for a discrete random variable.
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2.9 · Parameters of Random Variables

Learning goals and teaching choices
Learning goals in the current course
- 2.9.A: Calculate the mean and standard deviation for a discrete random variable.
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- 2.9.B: Interpret the mean and standard deviation for a discrete random variable.
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2.10 · The Binomial Distribution

Learning goals and teaching choices
Learning goals in the current course
- 2.10.A: Justify why a random variable is or is not a binomial random variable.
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- 2.10.B: Calculate the mean and standard deviation for a binomial distribution.
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- 2.10.C: Interpret the mean, standard deviation, and probabilities for a binomial distribution.
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- 2.10.D: Estimate probabilities of binomial random variables using data from a simulation.
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- 2.10.E: Calculate probabilities for a binomial distribution.
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2.11 · The Normal Distribution

Learning goals and teaching choices
Learning goals in the current course
- 2.11.A: Describe a normal distribution.
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- 2.11.B: Calculate the mean and standard deviation for a normal distribution.
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- 2.11.C: Calculate percentages from a normal distribution using the empirical rule.
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- 2.11.D: Calculate the probability that a particular value lies within a given interval of a normal distribution.
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- 2.11.E: Calculate the associated intervals and areas of a normal distribution.
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- 2.11.F: Compare measures of relative position for distributions.
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2.12 · Sampling Distributions and the Central Limit Theorem

Learning goals and teaching choices
Learning goals in the current course
- 2.12.A: Describe sampling distributions with simulations.
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3.1 · Estimators

Learning goals and teaching choices
Learning goals in the current course
- 3.1.A: Justify why an estimator is or is not unbiased.
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- 3.1.B: Calculate estimates for a population parameter.
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3.2 · Sampling Distributions for Sample Proportions

Learning goals and teaching choices
Learning goals in the current course
- 3.2.A: Calculate the mean and standard deviation of a sampling distribution for a sample proportion.
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- 3.2.B: Justify the appropriateness of conditions for the sampling distribution of a sample proportion.
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- 3.2.C: Interpret the mean, standard deviation, and probabilities for a sampling distribution of a sample proportion.
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3.3 · Constructing a Confidence Interval for a Population Proportion

Learning goals and teaching choices
Learning goals in the current course
- 3.3.A: Identify an appropriate confidence interval procedure including the parameter for a population proportion.
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- 3.3.B: Justify the appropriateness of constructing a confidence interval for a population proportion by verifying conditions.
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- 3.3.C: Calculate an appropriate confidence interval for a population proportion.
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- 3.3.D: Calculate the standard error and margin of error of a sample statistic for a confidence interval for a population proportion, and estimate a given sample size from the margin of error.
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3.4 · Justifying a Claim Based on a Confidence Interval for a Population Proportion

Learning goals and teaching choices
Learning goals in the current course
- 3.4.A: Interpret a confidence interval in context for a population proportion.
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- 3.4.B: Justify a claim based on a confidence interval for a population proportion.
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- 3.4.C: Identify the relationships among sample size, confidence interval width, confidence level, and margin of error for a population proportion.
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3.5 · Setting Up a Test for a Population Proportion

Learning goals and teaching choices
Learning goals in the current course
- 3.5.A: Identify an appropriate testing method for a population proportion including the parameter for the population proportion.
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- 3.5.B: Identify the null and alternative hypotheses for a population proportion.
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- 3.5.C: Justify the appropriateness of a hypothesis test for a population proportion by verifying conditions.
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3.6 · p-Values

Learning goals and teaching choices
Learning goals in the current course
- 3.6.A: Interpret the p-value of a hypothesis test for a population proportion.
  Open the goal for lessons, student checks and current scope notes.
3.7 · Carrying Out a Test for a Population Proportion

Learning goals and teaching choices
Learning goals in the current course
- 3.7.A: Calculate an appropriate test statistic and p-value for testing a hypothesis about a population proportion.
  Open the goal for lessons, student checks and current scope notes.
- 3.7.B: Justify a claim about the population based on the results of a hypothesis test for a population proportion.
  Open the goal for lessons, student checks and current scope notes.
3.8 · Potential Errors When Performing Tests

Learning goals and teaching choices
Learning goals in the current course
- 3.8.A: Identify Type I and Type II errors.
  Open the goal for lessons, student checks and current scope notes.
- 3.8.B: Calculate the probability of Type I and Type II errors.
  Open the goal for lessons, student checks and current scope notes.
- 3.8.C: Identify the factors that affect the probability of errors in hypothesis testing.
  Open the goal for lessons, student checks and current scope notes.
- 3.8.D: Interpret Type I and Type II errors.
  Open the goal for lessons, student checks and current scope notes.
3.9 · Sampling Distributions for the Difference Between Sample Proportions

Learning goals and teaching choices
Learning goals in the current course
- 3.9.A: Calculate the mean and standard deviation of the sampling distribution for the difference between two sample proportions.
  Open the goal for lessons, student checks and current scope notes.
- 3.9.B: Justify the appropriateness of conditions for the sampling distribution for the difference between two sample proportions.
  Open the goal for lessons, student checks and current scope notes.
- 3.9.C: Interpret the mean, standard deviation, and probabilities for the sampling distribution for the difference between two sample proportions.
  Open the goal for lessons, student checks and current scope notes.
3.10 · Constructing a Confidence Interval for the Difference Between Two Population Proportions

Learning goals and teaching choices
Learning goals in the current course
- 3.10.A: Identify an appropriate confidence interval procedure including the parameters for the difference between two population proportions.
  Open the goal for lessons, student checks and current scope notes.
- 3.10.B: Justify the appropriateness of constructing a confidence interval for the difference between two population proportions by verifying conditions.
  Open the goal for lessons, student checks and current scope notes.
- 3.10.C: Calculate an appropriate confidence interval for the difference between two population proportions.
  Open the goal for lessons, student checks and current scope notes.
- 3.10.D: Calculate the standard error and margin of error for estimating the difference between two population proportions.
  Open the goal for lessons, student checks and current scope notes.
3.11 · Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Proportions

Learning goals and teaching choices
Learning goals in the current course
- 3.11.A: Interpret a confidence interval in context for the difference between two population proportions.
  Open the goal for lessons, student checks and current scope notes.
- 3.11.B: Justify a claim based on a confidence interval for the difference between two population proportions.
  Open the goal for lessons, student checks and current scope notes.
3.12 · Setting Up a Test for the Difference Between Two Population Proportions

Learning goals and teaching choices
Learning goals in the current course
- 3.12.A: Identify an appropriate testing method for the difference between population proportions including the parameters.
  Open the goal for lessons, student checks and current scope notes.
- 3.12.B: Identify the null and alternative hypotheses for the difference between population proportions.
  Open the goal for lessons, student checks and current scope notes.
- 3.12.C: Justify the appropriateness of a hypothesis test for the difference between two population proportions by verifying conditions.
  Open the goal for lessons, student checks and current scope notes.
3.13 · Carrying Out a Test for the Difference Between Two Population Proportions

Learning goals and teaching choices
Learning goals in the current course
- 3.13.A: Calculate an appropriate test statistic and p-value for testing a hypothesis for the difference between two population proportions.
  Open the goal for lessons, student checks and current scope notes.
- 3.13.B: Interpret the p-value of a hypothesis test for the difference between two population proportions.
  Open the goal for lessons, student checks and current scope notes.
- 3.13.C: Justify a claim about the populations based on the results of a hypothesis test for the difference between two population proportions.
  Open the goal for lessons, student checks and current scope notes.
3.14 · Setting Up a Chi-Square Test for Homogeneity or Independence

Learning goals and teaching choices
Learning goals in the current course
- 3.14.A: Describe chi-square distributions.
  Open the goal for lessons, student checks and current scope notes.
- 3.14.B: Identify an appropriate testing method for comparing distributions in two-way tables of categorical data including the populations and variables.
  Open the goal for lessons, student checks and current scope notes.
- 3.14.C: Identify the null and alternative hypotheses for a chi-square test for homogeneity or independence.
  Open the goal for lessons, student checks and current scope notes.
- 3.14.D: Justify the appropriateness of a chi-square test for independence or homogeneity by verifying conditions.
  Open the goal for lessons, student checks and current scope notes.
3.15 · Carrying Out a Chi-Square Test for Homogeneity or Independence

Learning goals and teaching choices
Learning goals in the current course
- 3.15.A: Calculate expected counts for two-way tables of categorical data.
  Open the goal for lessons, student checks and current scope notes.
- 3.15.B: Calculate the appropriate test statistic and p-value for a chi-square test for homogeneity or independence.
  Open the goal for lessons, student checks and current scope notes.
- 3.15.C: Interpret the p-value for the chi-square test for homogeneity or independence.
  Open the goal for lessons, student checks and current scope notes.
- 3.15.D: Justify a claim about the population(s) based on the results of a chi-square test for homogeneity or independence.
  Open the goal for lessons, student checks and current scope notes.
4.1 · Sampling Distributions for Sample Means

Learning goals and teaching choices
Learning goals in the current course
- 4.1.A: Calculate the mean and standard deviation of a sampling distribution of a sample mean.
  Open the goal for lessons, student checks and current scope notes.
- 4.1.B: Justify the appropriateness of conditions for the sampling distribution of a sample mean.
  Open the goal for lessons, student checks and current scope notes.
- 4.1.C: Interpret the mean, standard deviation, and probabilities for the sampling distribution of a sample mean.
  Open the goal for lessons, student checks and current scope notes.
4.2 · Constructing a Confidence Interval for a Population Mean or Population Mean Difference

Learning goals and teaching choices
Learning goals in the current course
- 4.2.A: Describe t-distributions.
  Open the goal for lessons, student checks and current scope notes.
- 4.2.B: Identify an appropriate confidence interval procedure including the parameter for a population mean or population mean difference.
  Open the goal for lessons, student checks and current scope notes.
- 4.2.C: Justify the appropriateness of constructing a confidence interval for a population mean or population mean difference by verifying conditions.
  Open the goal for lessons, student checks and current scope notes.
- 4.2.D: Calculate an appropriate confidence interval for a population mean or population mean difference.
  Open the goal for lessons, student checks and current scope notes.
- 4.2.E: Calculate the standard error and margin of error for a sample size for a one-sample t-interval.
  Open the goal for lessons, student checks and current scope notes.
4.3 · Justifying a Claim Based on a Confidence Interval for a Population Mean or Population Mean Difference

Learning goals and teaching choices
Learning goals in the current course
- 4.3.A: Interpret a confidence interval in context for a population mean or population mean difference.
  Open the goal for lessons, student checks and current scope notes.
- 4.3.B: Justify a claim based on a confidence interval for a population mean or population mean difference.
  Open the goal for lessons, student checks and current scope notes.
- 4.3.C: Identify the relationships among sample size, confidence interval width, confidence level, and margin of error for a population mean or population mean difference.
  Open the goal for lessons, student checks and current scope notes.
4.4 · Setting Up a Test for a Population Mean or Population Mean Difference

Learning goals and teaching choices
Learning goals in the current course
- 4.4.A: Identify an appropriate testing method and parameter for a population mean or population mean difference with unknown \(\sigma\).
  Open the goal for lessons, student checks and current scope notes.
- 4.4.B: Identify the null and alternative hypotheses for a population mean or population mean difference with unknown \(\sigma\).
  Open the goal for lessons, student checks and current scope notes.
- 4.4.C: Justify the appropriateness of a hypothesis test for a population mean or population mean difference by verifying conditions.
  Open the goal for lessons, student checks and current scope notes.
4.5 · Carrying Out a Test for a Population Mean or Population Mean Difference

Learning goals and teaching choices
Learning goals in the current course
- 4.5.A: Calculate an appropriate test statistic and p-value for testing a hypothesis about a population mean or population mean difference.
  Open the goal for lessons, student checks and current scope notes.
- 4.5.B: Interpret the p-value of a hypothesis test for a population mean or population mean difference.
  Open the goal for lessons, student checks and current scope notes.
- 4.5.C: Justify a claim about the population based on the results of a hypothesis test for a population mean or population mean difference.
  Open the goal for lessons, student checks and current scope notes.
4.6 · Sampling Distributions for the Difference Between Two Sample Means

Learning goals and teaching choices
Learning goals in the current course
- 4.6.A: Calculate the mean and standard deviation of a sampling distribution for the difference between two sample means.
  Open the goal for lessons, student checks and current scope notes.
- 4.6.B: Justify the appropriateness of conditions for the sampling distribution of the difference between two sample means.
  Open the goal for lessons, student checks and current scope notes.
- 4.6.C: Interpret the mean, standard deviation, and probabilities for a sampling distribution for the difference between sample means.
  Open the goal for lessons, student checks and current scope notes.
4.7 · Constructing a Confidence Interval for the Difference Between Two Population Means

Learning goals and teaching choices
Learning goals in the current course
- 4.7.A: Identify an appropriate confidence interval procedure including the parameter for the difference between two population means.
  Open the goal for lessons, student checks and current scope notes.
- 4.7.B: Justify the appropriateness of constructing a confidence interval for the difference between two population means by verifying conditions.
  Open the goal for lessons, student checks and current scope notes.
- 4.7.C: Calculate an appropriate confidence interval for the difference between two population means.
  Open the goal for lessons, student checks and current scope notes.
- 4.7.D: Calculate the standard error and margin of error for estimating the difference between two population means.
  Open the goal for lessons, student checks and current scope notes.
4.8 · Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Means

Learning goals and teaching choices
Learning goals in the current course
- 4.8.A: Interpret a confidence interval in context for the difference between two population means.
  Open the goal for lessons, student checks and current scope notes.
- 4.8.B: Justify a claim based on a confidence interval for the difference between two population means.
  Open the goal for lessons, student checks and current scope notes.
4.9 · Setting Up a Test for the Difference Between Two Population Means

Learning goals and teaching choices
Learning goals in the current course
- 4.9.A: Identify an appropriate testing method for the difference between two population means including the parameters for the difference between the two population means.
  Open the goal for lessons, student checks and current scope notes.
- 4.9.B: Identify the null and alternative hypotheses for the difference between two population means.
  Open the goal for lessons, student checks and current scope notes.
- 4.9.C: Justify the appropriateness of a hypothesis test for the difference between two population means by verifying conditions.
  Open the goal for lessons, student checks and current scope notes.
4.10 · Carrying Out a Test for the Difference Between Two Population Means

Learning goals and teaching choices
Learning goals in the current course
- 4.10.A: Calculate an appropriate test statistic and p-value for testing a hypothesis for the difference between two population means.
  Open the goal for lessons, student checks and current scope notes.
- 4.10.B: Interpret the p-value of a hypothesis test for the difference between two population means.
  Open the goal for lessons, student checks and current scope notes.
- 4.10.C: Justify a claim about the populations based on the results of a hypothesis test for the difference between two population means.
  Open the goal for lessons, student checks and current scope notes.
5.1 · Graphical Representations Between Two Quantitative Variables

Learning goals and teaching choices
Learning goals in the current course
- 5.1.A: Construct scatterplots depicting the relationship between two quantitative variables.
  Open the goal for lessons, student checks and current scope notes.
- 5.1.B: Describe the characteristics of a scatterplot.
  Open the goal for lessons, student checks and current scope notes.
- 5.1.C: Justify a claim using scatterplots depicting the relationship between two quantitative variables.
  Open the goal for lessons, student checks and current scope notes.
5.2 · Correlation

Learning goals and teaching choices
Learning goals in the current course
- 5.2.A: Interpret the correlation for a linear relationship.
  Open the goal for lessons, student checks and current scope notes.
5.3 · Linear Regression Models

Learning goals and teaching choices
Learning goals in the current course
- 5.3.A: Calculate a predicted response value using a linear regression model.
  Open the goal for lessons, student checks and current scope notes.
5.4 · Residuals

Learning goals and teaching choices
Learning goals in the current course
- 5.4.A: Calculate the differences between the observed and predicted values.
  Open the goal for lessons, student checks and current scope notes.
- 5.4.B: Interpret the differences between the observed and predicted values.
  Open the goal for lessons, student checks and current scope notes.
- 5.4.C: Describe the form of association of bivariate data using residual plots.
  Open the goal for lessons, student checks and current scope notes.
5.5 · Least-Squares Regression

Learning goals and teaching choices
Learning goals in the current course
- 5.5.A: Calculate the coefficients for the least-squares regression line model.
  Open the goal for lessons, student checks and current scope notes.
- 5.5.B: Interpret coefficients for the least-squares regression line model.
  Open the goal for lessons, student checks and current scope notes.

Reusable building blocks

AP Physics 1

1.1 · Scalars and Vectors in One Dimension

1.2 · Displacement, Velocity, and Acceleration

1.3 · Representing Motion

1.4 · Reference Frames and Relative Motion

1.5 · Vectors and Motion in Two Dimensions

2.1 · Systems and Center of Mass

2.2 · Forces and Free-Body Diagrams

2.3 · Newton’s Third Law

2.4 · Newton’s First Law

2.5 · Newton’s Second Law

2.6 · Gravitational Force

2.7 · Kinetic and Static Friction

2.8 · Spring Forces

2.9 · Circular Motion

3.1 · Translational Kinetic Energy

3.2 · Work

3.3 · Potential Energy

3.4 · Conservation of Energy

3.5 · Power

4.1 · Linear Momentum

4.2 · Change in Momentum and Impulse

4.3 · Conservation of Linear Momentum

4.4 · Elastic and Inelastic Collisions

5.1 · Rotational Kinematics

5.2 · Connecting Linear and Rotational Motion

5.3 · Torque

5.4 · Rotational Inertia

5.5 · Rotational Equilibrium and Newton’s First Law in Rotational Form

5.6 · Newton’s Second Law in Rotational Form

6.1 · Rotational Kinetic Energy

6.2 · Torque and Work

6.3 · Angular Momentum and Angular Impulse

6.4 · Conservation of Angular Momentum

6.5 · Rolling

6.6 · Motion of Orbiting Satellites

7.1 · Defining Simple Harmonic Motion (SHM)

7.2 · Frequency and Period of SHM

7.3 · Representing and Analyzing SHM

7.4 · Energy of Simple Harmonic Oscillators

8.1 · Internal Structure and Density

8.2 · Pressure

8.3 · Fluids and Newton’s Laws

8.4 · Fluids and Conservation Laws

AP Calculus AB

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