Course at a Glance UNIT Limits and Continuity 1 AP EXAM WEIGHTING CLASS PERIODS Plan CHA 1.1 2 LIM ~22–23 AB ~13–14 BC CLASS PERIODS Introducing Calculus: Can Change Occur at an Instant? 1.3 Estimating Limit Values from Graphs 4 1.4 Estimating Limit 1.5 Determining Limits Properties of Limits 1.6 1.7 Selecting Procedures for Determining Limits 1.8 Determining Limits Using the Squeeze Theorem 1 LIM Teach 3 MATHEMATICAL PRACTICES LIM Mathematical practices spiral throughout 1.9 2 1 2 Implementing Mathematical Processes 3 4 LIM Communication and Notation Connecting Representations LIM LIM Discontinuities Change LIM Limits FUN Analysis of Functions LIM BC ONLY LIM 3 and Continuity: Determining When Derivatives Do and 2.5 Applying the Power Rule FUN 2.6 Derivative Rules: Constant, Sum, 1 Constant Multiple 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 over an Interval FUN 1.13 Removing Discontinuities 1.14 1 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions Limits and Vertical Asymptotes 1.15 2 FUN Connecting 1 1.12 3 Assess 2.4 1 FUN 1 LIM Estimating Derivatives of a Function at a Point 1 1.11 1 2.3 1 3 BIG IDEAS CHA Connecting Multiple Representations 1.10 3 of a Function and Using Derivative Notation 3 FUN ~9–10 BC 2.2 Determining Limits Manipulation ~13–14 AB 4–7% BC Instantaneous Rates of Change at a Point 1 FUN 1 LIM CHA 10–12% AB 2.1 2 1 1 LIM CHA CHA 2 LIM Basic Derivative Rules AP EXAM WEIGHTING Using Limit Notation 2 LIM 2 4–7% BC 1.2 2 LIM 10–12% AB UNIT Connecting Limits at Asymptotes 1.16 Working with the Intermediate Value Theorem (IVT) Personal Progress Check 1 Personal Progress Check 2 Multiple-choice: ~45 questions Multiple-choice: ~30 questions Free-response: 3 questions (partial) Free-response: 3 questions (partial) NOTE: Composite, Implicit, and Inverse Functions UNIT 3 AP EXAM WEIGHTING CLASS PERIODS FUN 3.1 9–13% AB ~10–11 AB 4 4–7% BC ~8–9 BC The Chain Rule 1 FUN UNIT AP EXAM WEIGHTING CLASS PERIODS CHA 4.1 1 CHA 3.2 4.2 1 1 FUN 3.3 Functions 3 FUN Inverse Trigonometric Functions FUN 3.5 1 Selecting Procedures for Calculating Derivatives ~10–11 AB 6–9% BC ~6–7 BC Interpreting the Meaning of the Straight-Line Motion: Connecting Position, Velocity, and Acceleration Rates of Change in 1 3.6 Order Derivatives AP EXAM WEIGHTING 15–18% AB 8–11% BC CLASS PERIODS ~15–16 AB ~10–11 BC FUN FUN 4.4 1 CHA 4.5 Introduction to Related Rates Solving Related Rates CHA 3 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing 5.4 Using the First Derivative Test to Determine Relative 5.5 Using the Candidates Test to Determine 5.6 Determining Concavity of Functions over Their Domains 5.7 Using the Second Derivative Test to 5.8 Sketching Graphs of Functions and Their Derivatives 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative 3 1 4.6 of a Function Using Local Linearity and Linearization 1 LIM Points 2 FUN Using the Mean Value Theorem 5.2 3 FUN CHA 5.1 3 Than Motion 3 FUN 5 FUN 4.3 2 3.4 1 CHA 10–15% AB Analytical Applications of UNIT Applications of 4.7 FUN 2 FUN for Determining Limits of Indeterminate Forms 3 FUN 2 FUN 2 FUN 5.10 Introduction to 5.11 Solving Optimization 2 FUN 3 FUN 1 5.12 Implicit Relations 3 Personal Progress Check 3 Personal Progress Check 4 Personal Progress Check 5 Multiple-choice: ~15 questions Free-response: 3 questions (partial/full) Multiple-choice: ~15 questions Free-response: 3 questions Multiple-choice: ~35 questions Free-response: 3 questions Integration and Accumulation UNIT AP EXAM WEIGHTING 17–20 % AB 17–20 % BC AP EXAM WEIGHTING CLASS PERIODS ~18–20 AB ~15–16 BC CLASS PERIODS UNIT 6 CHA Accumulations of Change 4 LIM with Riemann Sums LIM 6.3 FUN 6.4 FUN Notation FUN 1 FUN 6.5 2 FUN The Fundamental Theorem of Calculus and Accumulation Functions Interpreting the Behavior of Accumulation Functions Involving Area 6.6 Applying Properties of 6.7 The Fundamental Theorem of Calculus 7.1 FUN 6.8 ~9–10 BC CLASS PERIODS Modeling Situations Verifying Solutions for 7.3 Sketching Slope Fields CHA 7.4 4 7.6 FUN Finding General Solutions Using Integrals: Basic Rules and Notation 3 6.9 Integrating Using Finding Particular Solutions Using Initial Conditions and 6.11 1 FUN Equations 7.9 Logistic Models with BC ONLY 6.12 CHA Integrals in Applied 8.4 8.5 6.14 Selecting Techniques Finding the Area Between Curves 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 3 3 CHA 8.10 Volume with Disc Method: Revolving 8.11 Volume with Washer Method: Revolving Around the x- or y 8.12 Volume with Washer Method: Revolving 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled 2 CHA 4 CHA Using Linear Partial Fractions BC ONLY Evaluating Improper Integrals BC ONLY Finding the Area Between Curves Functions of x 2 CHA Integrating Using 6.13 1 FUN Integrating Functions Using Long Division and Completing the Square BC ONLY 1 LIM Using Accumulation 3 6.10 1 FUN 8.3 1 CHA 7.8 1 FUN Connecting Position, Velocity, and Acceleration of Functions Using Integrals Functions of y 7.7 3 FUN 8.2 4 CHA ~19–20 AB ~13–14 BC Finding the Average Value of a Function on an Interval 3 CHA Solutions Using Euler’s Method BC ONLY 1 FUN Reasoning Using Slope Fields 7.5 1 FUN CHA 10–15% AB 6–9% BC 8.1 1 1 2 FUN CHA CHA 4 FUN Finding Antiderivatives AP EXAM WEIGHTING 7.2 1 3 ~8–9 AB 6–9% BC Equations 3 FUN 6–12% AB 3 Riemann Sums, Summation Notation, 2 8 Equations 2 FUN 6.2 1 7 FUN 6.1 Applications of Integration UNIT 2 CHA 3 1 BC ONLY Personal Progress Check 6 Personal Progress Check 7 Personal Progress Check 8 Multiple-choice: Multiple-choice: Multiple-choice: ~30 questions Free-response: 3 questions Free-response: 3 questions Free-response: 3 questions Parametric Equations, Polar Coordinates, and Vector-Valued Functions BC ONLY UNIT 9 AP EXAM WEIGHTING N/A AB CLASS PERIODS N/A AB CHA CHA 1 CHA ~10–11 BC Second Derivatives of Parametric Equations Finding Arc Lengths of Curves Given 1 9.4 1 FUN 9.5 Integrating VectorValued Functions 9.6 Solving Motion 1 FUN N/A AB LIM Parametric and VectorValued Functions 9.7 Coordinates and 2 10.2 Working with Geometric Series 10.3 The th Term Test for Divergence 10.4 Integral Test for Convergence 3 3 10.5 -Series 3 10.6 Comparison Tests for Convergence 10.7 Alternating Series Test for Convergence 10.8 Ratio Test for Convergence 3 LIM 3 LIM 3 LIM 10.9 or Conditional Convergence 3 Polar Form CHA 9.8 Find the Area of a Polar Region or the Area 3 Polar Curve CHA 3 9.9 Finding the Area of the Two Polar Curves LIM ~17–18 BC Series 3 LIM 17–18% BC 10.1 3 LIM Valued Functions 1 FUN CLASS PERIODS LIM Equations CHA N/A AB LIM 9.3 Sequences and Series BC ONLY AP EXAM WEIGHTING LIM Parametric Equations 9.2 10 11–12% BC 9.1 2 UNIT 10.10 Alternating Series Error Bound 10.11 3 Finding Taylor Polynomial 2 of Functions 1 LIM LIM 10.12 Lagrange Error Bound 10.13 Radius and Interval of Convergence of Power Series 10.14 Finding Taylor or Maclaurin Series for a Function 10.15 Representing Functions as Power Series 1 LIM 2 LIM 2 LIM 3 Personal Progress Check 9 Personal Progress Check 10 Multiple-choice: ~25 questions Free-response: 3 questions Multiple-choice: ~45 questions Free-response: 3 questions