AP Calculus — Gradarius (2024)

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• 1. Defining Limits Using Limit Notation (LIM-1.A and LIM-1.B)

  2. Estimating Limit Values from Graphs and Tables (LIM-1.C)

  3. Determining Limits Using Algebraic Properties of Limits (LIM-1.D)

  4. Determining Limits Using Algebraic Manipulation and Squeeze Theorem (LIM-1.E)

  5. Exploring Types of Discontinuities Defining Continuity at a Point (LIM-2.A)

  6. Confirming Continuity over an Interval (LIM-2.B)

  7. Removing Discontinuities (LIM-2.C)

  8. Connecting Infinite Limits and Vertical & Horizontal Asymptotes (LIM-2.D)

  9. Explain the behavior of a function on an interval using the Intermediate Value Theorem (FUN-1.A)

• 1. Determining Average and Instantaneous Rates of Change at a Point (CHA-2.A and CHA-2.B)

  2. Defining the Derivative of a Function and Using Derivative Notation (CHA-2.B and CHA-2.C)

  3. Estimating Derivatives of a Function at a Point (CHA-2.D)

  4. Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist (FUN-2.A.)

  5. Applying the Power Rule and Derivative Rules: Constant, Sum, Difference, and Constant Multiple (FUN-3.A.)

  6. The Product and Quotient Rules (FUN-3.B)

  7. Derivatives of cos x, sin x, e^x, and ln x and Finding the Derivative of Tangent, Cotangent, Secant, and/or Cosecant Functions (FUN-3.A, LIM-3.A. and FUN-3.B)

• 1. The Chain Rule (FUN-3.C)

  2. Implicit Differentiation (FUN-3.D)

  3. Differentiating Inverse Functions (FUN-3.E)

  4. Calculating Higher-Order Derivatives (FUN-3.F)

• 1. 1. Interpreting the Meaning of the Derivative in Context (CHA-3.A)

     2. Straight-Line Motion: Connecting Position, Velocity, and Acceleration (CH-3.B)

     3. Rates of Change in Applied Contexts Other Than Motion (CHA-3.C)

     4. Introduction to Related Rates and Solving Related Rates Problems (CHA-3.D and CHA-3.E)

     5. Approximating Values of a Function Using Local Linearity and Linearization (CHA-3.F)

     6. Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms (LIM-4.A)

• 1. Using the Mean Value Theorem (FUN-1.B)

  2. Extreme Value Theorem, Global Versus Local Extrema, and Critical Points (FUN-1.C)

  3. Determining Intervals on Which a Function Is Increasing or Decreasing (FUN-4.A)

  4. Using the First Derivative Test to Determine Relative (Local) Extrema (FUN-4.A)

  5. Using the Candidates Test to Determine Absolute (Global) Extrema (FUN-4.A)

  6. Determining Concavity of Functions over Their Domains (FUN-4.A)

  7. Using the Second Derivative Test to Determine Extrema (FUN-4.A)

  8. Sketching Graphs of Functions and Their Derivatives and Connecting a Function, Its First Derivative, and Its Second Derivative (FUN-4.A)

  9. Introduction to Optimization Problems (FUN-4.B)

• 1. Exploring Accumulations of Change (CHA-4.A)

  2. Approximating Areas with Riemann Sums (LIM-5.A)

  3. Riemann Sums, Summation Notation, and Definite Integral Notation (LIM-5.B, LIM-5.C)

  4. The Fundamental Theorem of Calculus and Accumulation Functions (FUN-5.A)

  5. Interpreting the Behavior of Accumulation Functions Involving Area (FUN-5.A)

  6. Applying Properties of Definite Integrals (FUN-6.A)

  7. The Fundamental Theorem of Calculus and Definite Integrals (FUN-6.B)

  8. Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation (FUN-6.C)

  9. Integrating Using Substitution (FUN-6.D)

  10. Integrating Functions Using Long Division and Completing the Square (FUN-6.D)

• 1. Modeling Situations with Differential Equations (FUN-7.A)

  2. Verifying Solutions for Differential Equations (FUN-7.B)

  3. Sketching Slope Fields (FUN-7.C)

  4. Reasoning Using Slope Fields (FUN-7.C)

  5. Finding General Solutions Using Separation of Variables (FUN-7.D)

  6. Finding Particular Solutions Using Initial Conditions and Separation of Variables (FUN-7.E)

  7. Exponential Models with Differential Equations (FUN-7.F)

• 1. Find the Average Value of a Function on an Interval (CHA-4.B)

  2. Connecting Position, Velocity, and Acceleration Functions Using Integrals (CHA-4.C)

  3. Using Accumulation Functions and Definite Integrals in Applied Context (CHA-4.D)

  4. Finding the Area Between Curves Expressed as Functions of x (CHA-4.E)

  5. Find the Area Between Curves Expressed as Functions of y (CHA-5.)

  6. Finding the Area Between Curves That Intersect at More than Two Points

  7. Volumes with Cross Sections: Squares and Rectangles

  8. Volumes with Cross Sections: Triangles and Semicircles

  9. Volumes with Disc Method: Revolving Around the x- or y-axis

  10. Volumes with Washer Method: Revolving Around the x- or y-axis

  11. Volumes with Washer Method: Revolving Around Other Axes

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