| Full AP Calculus BC Notes (WIP) Formula Sheet |
| Unit 1 - Limits and Continuity |
Can Change Occur at an Instant? Defining Limits and Using Limit Notation Estimating Limit Values from Graphs Estimating Limit Values from Tables Determining Limits Using Algebraic Properties Determining Limits Using Algebraic Manipulation Selecting Procedures for Determining Limits Determining Limits Using the Squeeze Theorem Connecting Multiple Representations of Limits Exploring Types of Discontinuities Defining Continuity at a Point Confirming Continuity Over an Interval Removing Discontinuities Infinite Limits and Vertical Asymptotes Limits at Infinity and Horizontal Asymptotes Intermediate Value Theorem (IVT) |
Notes (WIP) |
| Unit 2 - Differentiation: Definition and Fundamental Properties |
Defining Average and Instantaneous Rate of Change at a Point Defining the Derivative of a Function and Using Derivative Notation Estimating Derivatives of a Function at a Point Connecting Differentiability and Continuity Applying the Power Rule Derivative Rules: COnstant, Sum, Difference, and Constant Multiple Derivatives of cos(x), sin(x), e^x, and ln(x) The Product Rule The Quotient Rule Derivatives of tan(x), cot(x), sec(x), and csc(x) |
Notes (WIP) |
| Unit 3 - Differentiation: Composite, Implicit, and Inverse Functions |
The Chain Rule Implicit Differentiation Differentiating Inverse Functions Differentiating Inverse Trigonometric Functions Selecting Procedures for Calculating Derivatives Calculating Higher-Order Derivatives |
Notes (WIP) |
| Unit 4 - Contextual Applications of Differentiation |
Interpreting the Meaning of the Derivative in Context Straight-Line Motion: Connecting Position, Velocity, and Acceleration Rates of Change in Applied Contexts Other Than Motion Introduction to Related Rates Solving Related Rates Problems Approximating Values of a Function Using Local Linearity and Linearization Using L'Hopital's Rule for Determining Limits of Indeterminate Forms |
Notes (WIP) |
| Unit 5 - Analytical Applications of Differentiation |
Using the Mean Value Theorem Extreme Value Theorem, Global Versus Local Extrema, and Critical Points Determining Intervals on Which a Function is Increasing or Decreasing Using the First Derivative Test to Determine Relative Local Extrema Using the Candidates Test to Determine Absolute (Global) Extrema Determining Concavity of Functions over Their Domains Using the Second Derivative Test to Determine Extrema Sketching Graphs of Functions and Their Derivatives Connecting a Function, Its First Derivative, and Its Second Derivative Introduction to Optimization Problems Solving Optimization Problems Exploring Behaviors of Implicit Relations |
Notes (WIP) |
| Unit 6 - Integration and Accumulation of Change |
Exploring Accumulation of Change Approximating Areas with Riemann Sums Riemann Sums, Summation Notation, and Definite Integral Notation The Fundamental Theorem of Calculus and Accumulation Functions Interpreting the Behavior of Accumulation Functions Involving Area Applying Properties of Definite Integrals The Fundamental Theorem of Calculus and Definite Integrals Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation Integrating Using Substitution Integrating Functions Using Long Division and Completing the Square Integrating Using Integration by Parts Integrating Using Linear Partial Fractions Evaluating Improper Integrals Selecting Techniques for Antidifferentiation |
Notes (WIP) |
| Unit 7 - Differential Equations |
Modeling Situations with Differential Equations Verifying Solutions for Differential Equations Sketching Slope Fields Reasoning Using Slope Fields Euler's Method General Solutions Using Separation of Variables Particular Solutions using Initial Conditions and Separation of Variables Exponential Models with Differential Equations Logistic Models with Differential Equations |
Notes (WIP) |
| Unit 8 - Applications of Integration |
Average Value of a Function on an Interval Position, Velocity, and Acceleration Using Integrals Using Accumulation Functions and Definite Integrals in Applied Contexts Area Between Curves (with respect to x) Area Between Curves (with respect to y) Area Between Curves - More than Two Intersections Cross Sections: Squares and Rectangles Cross Sections: Triangles and Semicircles Disc Method: Revolving Around the x or y axis Disc Method: Revolving Around Other Axes Washer Method: Revolving Around the x or y axis Washer Method: Revolving Around Other Axes THe Arc Length of a Smooth, Planar Curve and Distance Traveled |
Notes (WIP) |
| Unit 9 - Parametric Equations, Polar Coordinates, and Vector-Valued Functions |
Defining and Differentiating Parametric Equations Second Derivatives of Parametric Equations Arc Lengths of Curves (Parametric Equations) Defining and Differentiating Vector-Valued Functions Integrating Vector-Valued Functions Solving Motion Problems Using Parametric and Vector-Valued Functions Defining Polar Coordinates and Differentiating in Polar Form Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve Finding the Area of the Region Bounded by Two Polar Curves |
Notes (WIP) |
| Unit 10 - Infinite Sequences and Series |
Defining Convergent and Divergent Infinite Series Working with Geometric Series The nth Term Test for Divergence Integral Test for Convergence Harmonic Series and p-Series Comparison Tests for Convergence Alternating Series Test for Convergence Ratio Test for Convergence Determining Absolute or Conditional Convergence Alternating Series Error Bound Finding Taylor Polynomial Approximations of Functions Lagrange Error Bound Radius and Interval of Convergence of Power Series Finding Taylor Maclaurin Series for a Function Representing Functions as a Power Series |
Notes (WIP) |