AP Calculus

Notes/HW Keys

AB Calculus

Parent/Student Syllabus

AP Calculus AB College Board Approved Syllabus

BC Calculus

Parent/Student Syllabus

AP Calculus BC College Board Approved Syllabus

Unit 2 - Differentiation: Definition and Fundamental Properties

• 2.1 Defining Average and Instantaneous Rate of Change at a Point

• 2.2 Defining the Derivative of a Function and Using Derivative Notation (2.2 includes equation of the tangent line)

• 2.3 Estimating Derivatives of a Function at a Point

• 2.4 Connecting Differentiability and Continuity

• 2.5 Applying the Power Rule

• 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple (2.6 includes horizontal tangent lines, equation of the normal line, and differentiability of piecewise)

• 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 Derivatives of tan(x), cot(x), sec(x), and csc(x)

• Review - Unit 2

Unit 3 - Differentiation: Composite, Implicit, and Inverse 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

• Review - Unit 3

Unit 4 - Contextual Applications of Differentiation

• 4.1 Interpreting the Meaning of the Derivative in Context

• 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration

• 4.3 Rates of Change in Applied Contexts Other Than Motion

• 4.4 Introduction to Related Rates

• 4.5 Solving Related Rates Problems

• 4.6 Approximating Values of a Function Using Local Linearity and Linearization

• 4.7 Using L'Hopital's Rule for Determining Limits of Indeterminate Forms

• Review - Unit 4

Unit 5 - Analytical Applications of Differentiation

• 5.1 Using the Mean Value Theorem

• 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

• 5.3 Determining Intervals on Which a Function is Increasing or Decreasing

• 5.4 Using the First Derivative Test to Determine Relative Local Extrema

• 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema

• 5.6 Determining Concavity of Functions over Their Domains

• 5.7 Using the Second Derivative Test to Determine Extrema

• Mid-Unit Review - Unit 5

• 5.8 Sketching Graphs of Functions and Their Derivatives

• 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative (5.9 includes a revisit of particle motion and determining if a particle is speeding up/down.)

• 5.10 Introduction to Optimization Problems

• 5.11 Solving Optimization Problems

• 5.12 Exploring Behaviors of Implicit Relations

• Review - Unit 5

Unit 6 - Integration and Accumulation of Change

• 6.1 Exploring Accumulation of Change

• 6.2 Approximating Areas with Riemann Sums

• 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation (EXTRA CREDIT)

• 6.4 The Fundamental Theorem of Calculus and Accumulation Functions (EXTRA CREDIT)

• 6.5 Interpreting the Behavior of Accumulation Functions Involving Area

• Mid-Unit Review - Unit 6

• 6.6 Applying Properties of Definite Integrals

• 6.7 The Fundamental Theorem of Calculus and Definite Integrals

• 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation

• 6.9 Integrating Using Substitution

• 6.10 Integrating Functions Using Long Division and Completing the Square

• 6.11 Integrating Using Integration by Parts (BC topic)

• 6.12 Integrating Using Linear Partial Fractions (BC topic)

• 6.13 Evaluating Improper Integrals (BC topic)

• 6.14 Selecting Techniques for Antidifferentiation

• Review - Unit 6

Unit 7 - Differential Equations

• 7.1 Modeling Situations with Differential Equations

• 7.2 Verifying Solutions for Differential Equations

• 7.3 Sketching Slope Fields

• 7.4 Reasoning Using Slope Fields

• 7.5 Euler's Method (BC topic)

• 7.6 General Solutions Using Separation of Variables

• 7.7 Particular Solutions using Initial Conditions and Separation of Variables

• 7.8 Exponential Models with Differential Equations

• 7.9 Logistic Models with Differential Equations (BC topic)

• Review - Unit 7

Unit 8 - Applications of Integration

• 8.1 Average Value of a Function on an Interval

• 8.2 Position, Velocity, and Acceleration Using Integrals

• 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts

• 8.4 Area Between Curves (with respect to x)

• 8.5 Area Between Curves (with respect to y)

• 8.6 Area Between Curves - More than Two Intersections

• Mid-Unit Review - Unit 8

• 8.7 Cross Sections: Squares and Rectangles

• 8.8 Cross Sections: Triangles and Semicircles

• 8.9 Disc Method: Revolving Around the x- or y- Axis

• 8.10 Disc Method: Revolving Around Other Axes

• 8.11 Washer Method: Revolving Around the x- or y-Axis

• 8.12 Washer Method: Revolving Around Other Axes

• 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC topic)

• Review - Unit 8

Unit 9 - Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC topics)

• 9.1 Defining and Differentiating Parametric Equations

• 9.2 Second Derivatives of Parametric Equations

• 9.3 Arc Lengths of Curves (Parametric Equations)

• 9.4 Defining and Differentiating Vector-Valued Functions

• 9.5 Integrating Vector-Valued Functions

• 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions

• 9.7 Defining Polar Coordinates and Differentiating in Polar Form

• 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

• 9.9 Finding the Area of the Region Bounded by Two Polar Curves

• Review - Unit 9

Unit 10 - Infinite Sequences and Series (BC topics)

• 10.1 Defining Convergent and Divergent Infinite Series

• 10.2 Working with Geometric Series

• 10.3 The nth Term Test for Divergence

• 10.4 Integral Test for Convergence

• 10.5 Harmonic Series and p-Series

• 10.6 Comparison Tests for Convergence

• 10.7 Alternating Series Test for Convergence

• 10.8 Ratio Test for Convergence

• 10.9 Determining Absolute or Conditional Convergence

• Mid-Unit Review - Unit 10

• 10.10 Alternating Series Error Bound

• 10.11 Finding Taylor Polynomial Approximations of Functions

• 10.12 Lagrange Error Bound

• 10.13 Radius and Interval of Convergence of Power Series

• 10.14 Finding Taylor Maclaurin Series for a Function

• 10.15 Representing Functions as a Power Series

• Review - Unit 10