AP Calculus AB and BC Course at a Glance, Effective Fall 2019 Course at a Glance Limits and Continuity UNIT 1 Personal Progress Check 1 Multiple choice ~45 questions Free response 3 questions (partial[.]
Course at a Glance UNIT AP EXAM WEIGHTING CLASS PERIODS Plan The Course at a Glance provides a useful visual organization of the AP Calculus AB and AP Calculus BC curricular components, including: §§ Sequence of units, along with approximate weighting and suggested pacing Please note, pacing is based on 45-minute class periods, meeting five days each week for a full academic year §§ Progression of topics within each unit § Spiraling of the big ideas and mathematical practices across units Teach Mathematical practices spiral throughout the course Implementing Mathematical Processes Justification Communication and Notation Connecting Representations LIM Limits LIM 1.2 LIM LIM LIM CHA 1.6 Determining Limits Using Algebraic Manipulation FUN 1.7 Selecting Procedures for Determining Limits 1.8 Determining Limits Using the Squeeze Theorem 1.9 1.10 Connecting Multiple Representations of Limits Exploring Types of Discontinuities FUN Analysis of Functions BC ONLY The purple shading represents BC only content Assess Assign the Personal Progress Checks—either as homework or in class—for each unit Each Personal Progress Check contains formative multiplechoice and free-response questions The feedback from the Personal Progress Checks shows students the areas where they need to focus Confirming Continuity over an Interval 1.13 Removing Discontinuities LIM LIM 2.3 Estimating Derivatives of a Function at a Point 2.5 Applying the Power Rule FUN 2.7 Derivatives of cos x, sin x, ex, and ln x 2.8 The Product Rule 2.9 The Quotient Rule LIM FUN FUN 1.12 Defining the Derivative of a Function and Using Derivative Notation FUN ~9–10 BC 2.2 FUN ~13–14 AB 4–7% BC Defining Average and Instantaneous Rates of Change at a Point Determining Limits Using Algebraic Properties of Limits LIM Defining Limits and Using Limit Notation 10–12% AB 2.1 1.5 LIM CHA CHA LIM Introducing Calculus: Can Change Occur at an Instant? Estimating Limit Values from Tables LIM CLASS PERIODS 1.4 LIM AP EXAM WEIGHTING Estimating Limit Values from Graphs LIM 1.3 LIM Big ideas spiral across topics and units Change ~22–23 AB ~13–14 BC Differentiation: Definition and Basic Derivative Rules UNIT 10–12% AB 4–7% BC BIG IDEAS CHA 1.1 MATHEMATICAL PRACTICES CHA Limits and Continuity FUN LIM FUN 1.16 Working with the Intermediate Value Theorem (IVT) Personal Progress Check Personal Progress Check Multiple-choice: ~45 questions Multiple-choice: ~30 questions Free-response: questions (partial) Free-response: questions (partial) NOTE: Partial versions of the free-response questions are provided to prepare students for more complex, full questions that they will encounter on the AP Exam 00762-114-CED-Calculus-AB/BC_Introduction.indd 20 3/13/19 2:45 PM Differentiation: Composite, Implicit, and Inverse Functions UNIT AP EXAM WEIGHTING CLASS PERIODS FUN 3.1 ~8–9 BC The Chain Rule FUN 9–13% AB 4–7% BC ~10–11 AB AP EXAM WEIGHTING CLASS PERIODS CHA 4.1 3.2 Implicit Differentiation CHA 4.2 1 FUN 3.3 FUN 3.4 FUN 3.5 Differentiating Inverse Functions Differentiating Inverse Trigonometric Functions Selecting Procedures for Calculating Derivatives CHA 3.6 Calculating HigherOrder Derivatives CHA Straight-Line Motion: Connecting Position, Velocity, and Acceleration Introduction to Related Rates 4.5 Solving Related Rates Problems 4.6 Approximating Values of a Function Using Local Linearity and Linearization AP EXAM WEIGHTING 15–18% AB 8–11% BC CLASS PERIODS ~15–16 AB ~10–11 BC FUN 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 5.8 Sketching Graphs of Functions and Their Derivatives 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative FUN FUN FUN FUN 1 LIM Interpreting the Meaning of the Derivative in Context 4.4 CHA ~10–11 AB ~6–7 BC 4.7 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms Analytical Applications of Differentiation UNIT 6–9% BC Rates of Change in Applied Contexts Other Than Motion CHA 10–15% AB 4.3 FUN Contextual Applications of Differentiation UNIT FUN FUN FUN FUN FUN FUN FUN 5.12 Exploring Behaviors of Implicit Relations Personal Progress Check Personal Progress Check Personal Progress Check Multiple-choice: ~15 questions Free-response: questions (partial/full) Multiple-choice: ~15 questions Free-response: questions Multiple-choice: ~35 questions Free-response: questions 00762-114-CED-Calculus-AB/BC_Introduction.indd 21 3/13/19 2:45 PM UNIT AP EXAM WEIGHTING CLASS PERIODS CHA 6.1 LIM 6.2 LIM 6.3 FUN 6.4 FUN 6.5 FUN Integration and Accumulation of Change AP EXAM WEIGHTING CLASS PERIODS Exploring Accumulations of Change FUN Approximating Areas with Riemann Sums FUN Riemann Sums, Summation Notation, and Definite Integral Notation FUN The Fundamental Theorem of Calculus and Accumulation Functions Interpreting the Behavior of Accumulation Functions Involving Area 6.6 Applying Properties of Definite Integrals 6.7 The Fundamental Theorem of Calculus and Definite Integrals 17–20% BC ~15–16 BC 7.1 FUN 6.8 FUN 6.9 Integrating Using Substitution 6.10 Integrating Functions Using Long Division and Completing the Square FUN FUN 6.11 FUN ~8–9 AB ~9–10 BC Modeling Situations with Differential Equations Verifying Solutions for Differential Equations 7.3 Sketching Slope Fields 7.4 Reasoning Using Slope Fields 7.5 Approximating Solutions Using Euler’s Method bc only FUN FUN FUN 7.6 FUN FUN Using Linear Partial Fractions bc only 6.13 Evaluating Improper Integrals bc only 6.14 AP EXAM WEIGHTING 7.7 7.8 Finding General Solutions Using Separation of Variables Finding Particular Solutions Using Initial Conditions and Separation of Variables Exponential Models with Differential Equations CHA 7.9 Logistic Models with Differential Equations bc only 8.1 Finding the Average Value of a Function on an Interval 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts 8.4 Finding the Area Between Curves Expressed as Functions of x 8.5 Finding the Area Between Curves Expressed as Functions of y 8.6 Finding the Area Between Curves That Intersect at More Than Two Points 8.7 Volumes with Cross Sections: Squares and Rectangles 8.8 Volumes with Cross Sections: Triangles and Semicircles 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis CHA CHA CHA CHA CHA CHA FUN 10–15% AB 6–9% BC CLASS PERIODS CHA Applications of Integration UNIT 6–9% BC CHA CHA Integrating Using Integration by Parts 6.12 FUN 6–12% AB CHA 8.11 bc only LIM Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation 7.2 FUN Differential Equations UNIT CHA Volume with Washer Method: Revolving Around the x- or y-Axis CHA Selecting Techniques for Antidifferentiation 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled bc only Personal Progress Check Personal Progress Check Personal Progress Check Multiple-choice: §§ §§ Free-response: questions Multiple-choice: § ~15 questions (AB) §§ Free-response: questions Multiple-choice: ~30 questions Free-response: questions 00762-114-CED-Calculus-AB/BC_Introduction.indd 22 3/13/19 2:45 PM UNIT Parametric Equations, Polar Coordinates, and Vector-Valued Functions bc only AP EXAM WEIGHTING CLASS PERIODS CHA 9.1 CHA 9.2 CHA 9.3 CHA 9.4 FUN FUN FUN ~10–11 BC Second Derivatives of Parametric Equations LIM Defining and Differentiating VectorValued Functions 9.6 Solving Motion Problems Using Parametric and VectorValued Functions CHA 17–18% BC ~17–18 BC 10.2 LIM Working with Geometric Series LIM LIM LIM LIM LIM 10.8 LIM Ratio Test for Convergence 9.8 CHA CLASS PERIODS LIM Finding Arc Lengths of Curves Given by Parametric Equations Infinite Sequences and Series bc only AP EXAM WEIGHTING Defining and Differentiating Parametric Equations Integrating VectorValued Functions 10 11–12% BC 9.5 UNIT 9.9 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 LIM LIM LIM LIM LIM LIM 10.14 Finding Taylor or Maclaurin Series for a Function Personal Progress Check Personal Progress Check 10 Multiple-choice: ~25 questions Free-response: questions Multiple-choice: ~45 questions Free-response: questions 00762-114-CED-Calculus-AB/BC_Introduction.indd 23 3/13/19 2:45 PM ... Approximating Areas with Riemann Sums FUN Riemann Sums, Summation Notation, and Definite Integral Notation FUN The Fundamental Theorem of Calculus and Accumulation Functions Interpreting the Behavior... BC CHA CHA Integrating Using Integration by Parts 6.12 FUN 6–12% AB CHA 8.11 bc only LIM Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation 7.2 FUN Differential Equations... HigherOrder Derivatives CHA Straight-Line Motion: Connecting Position, Velocity, and Acceleration Introduction to Related Rates 4.5 Solving Related Rates Problems 4.6 Approximating Values of a Function