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AP Calculus BC Subject Group Overview - Semester 1 Unit Unit 1: Limits & Unit 2: Differentiation: Unit 3: Differentiation: Unit 4: Contextual Unit 5: Analytical Unit 6: Integration & Unit 7: Differential Name Continuity Definition and Basic Composite, Implicit, Applications of Applications of Accumulation of Equations Derivative Rules and Inverse Function Differentiation Differentiation Change Time Frame 3 Weeks 2 Weeks 2 Weeks 2 Weeks 3 Weeks 3 Weeks 3 Weeks Standards AP Calc BC 1.1-1.16 AP Calc BC 2.1-2.10 AP Calc BC 3.1-3.6 AP Calc BC 4.1-4.7 AP Calc BC 5.1-5.12 AP Calc BC 6.1-5.114 AP Calc BC 7.1-7.9 1.1 Introducing Calculus: 2.1 Defining average and 3.1 The chain rule 4.1 Interpreting the 5.1 Using the mean value 6.1 Exploring accumulations 7.1 Modeling situations with Can change occur at an instantaneous rates of 3.2 Implicit meaning of the derivative in theorem of chang differential equations instant? change differentiation context 5.2 Extreme value theorem, 6.2 Approximating areas 7.2 Verifying solutions for 1.2 Defining limits and using 2.2 Defining the derivative 3.3 Differentiation 4.2 Straight-line motion: global versus local extrema, with Reimann sums differential equations limit notation of a function and using inverse functions Connecting position, and critical points 6.3 Riemann sums, 7.3 Sketching slope fields 1.3 Estimating limit values derivative notation 3.4 Differentiation velocity, and acceleration 5.3 Determining intervals on summation notation, and 7.4 Reasoning using slope from graphs 2.3 Estimating inverse trigonometric 4.3 Rates of change in which a function is definite integral notation fields 1.4 Estimating limit values derivatives of a function at a applied contexts other than increasing or decreasing 6.4 The fundamental 7.5 Approximating solutions from tables point functions motion 5.4 Using the first derivative theorem of calculus and using Euler’s method 1.5 Determining limits using 2.4 Connecting 3.5 Selecting procedures 4.4 Introduction to related test to determine relative accumulation functions 7.6 Finding general algebraic properties of differentiability with for calculating rates (local) extrema 6.5 Interpreting the solutions using separation limits continuity derivatives 4.5 Solving related rates 5.5 Using the candidates behavior of accumulation of variables 1.6 Determining 2.5 Applying the power rule 3.6 Calculative higher problems test to determine absolute functions involving area 7.7 FInding particular limits using algebraic 2.6 Derivative rules: order derivatives 4.6 Approximating values of (global) extrema 6.6 Applying properties of solutions using initial manipulation constant, sum, difference, a function using local 5.6 Determining concavity definite integrals conditions and separation 1.7 Selecting procedures for and constant multiple linearity and linearization of functions over their 6.7 The fundamental of variables determining limits 2.7 Derivative of cos(x), 4.7 Using L’Hospital’s rule domains theorem of calculus and 7.8 Exponential models with x Content 1.8 Determining limits using sin(x), e , and ln(x) for determining limits of 5.7 Using the second definite integrals differential equations Specific the Squeeze Theorem 2.8 The product rule indeterminate forms derivative test to determine 6.8 Finding antiderivatives 7.9 Logistic models with Information 1.9 Connecting multiple 2.9 The quotient rule extrema and indefinite integrals: differential equations representations of limits 2.10 Finding the derivatives 5.8 Sketching graphs of basic rules and notation 1.10 Exploring types of of tangent, cotangent, functions and their 6.9 Integrating using discontinuities secant, and/or cosecant derivatives substitution 1.11 Defining continuity at a functions 5.9 Connecting a function, 6.10 Integrating functions point its first derivative, and its using long division and 1.12 Confirming continuity second derivative completing the square over an interval 6.11 Integrating 1.13 Removing using integration by parts discontinuities 6.12 Using linear partial 1.14 Connecting infinite fractions limits and vertical 6.13 Evaluating improper asymptotes integrals 1.15 Connecting limits at 6.14 Selecting techniques infinity and horizontal for antidifferentiation asymptotes 1.16 Working with the Intermediate Value Theorem (IVT) MCS Subject Group Overview. AP Calculus BC Last Revised: August, 2022 AP Calculus BC Subject Group Overview - Semester 1 Unit Unit 1: Limits & Unit 2: Differentiation: Unit 3: Differentiation: Unit 4: Contextual Unit 5: Analytical Unit 6: Integration & Unit 7: Differential Name Continuity Definition and Basic Composite, Implicit, Applications of Applications of Accumulation of Equations Derivative Rules and Inverse Function Differentiation Differentiation Change Homework Quizzes Homework Quizzes Homework Quizzes Homework Quizzes Homework Quizzes Homework Quizzes Homework Quizzes Common Formative Formative Formative Formative Formative Formative Formative Assessments Assessments Assessments Assessments Assessments Assessments Assessments Assessments / Major Summative Summative Summative Summative Summative Summative Summative Projects Assessment Assessment Assessment Assessment Assessment Assessment Assessment AP Classroom (within AP Classroom (within AP Classroom (within AP Classroom (within AP Classroom (within AP Classroom (within AP Classroom (within AP Central, AP Central, AP Central, AP Central, AP Central, AP Central, AP Central, collegeboard.org) collegeboard.org) collegeboard.org) collegeboard.org) collegeboard.org) collegeboard.org) collegeboard.org) Calculus textbook: Calculus textbook: Calculus textbook: Calculus textbook: Calculus textbook: Calculus textbook: Calculus textbook: Calculus, 11e, Larson Calculus, 11e, Larson Calculus, 11e, Larson Calculus, 11e, Larson Calculus, 11e, Larson Calculus, 11e, Larson Calculus, 11e, Larson & Edwards & Edwards & Edwards & Edwards & Edwards & Edwards & Edwards Tony Record (Avon Tony Record (Avon Tony Record (Avon Tony Record (Avon Tony Record (Avon Tony Record (Avon Tony Record (Avon HS) created HS) created HS) created HS) created HS) created HS) created HS) created resources resources resources resources resources resources resources Resources www.flippedmath.co www.flippedmath.co www.flippedmath.co www.flippedmath.co www.flippedmath.co www.flippedmath.co www.flippedmath.co m m m m m m m Khan Academy Khan Academy Khan Academy Khan Academy Khan Academy Khan Academy Khan Academy Delta Math Delta Math Delta Math Delta Math Delta Math Delta Math Delta Math Master Math Master Math Master Math Mentor Master Math Mentor Master Math Mentor Master Math Mentor Master Math Mentor Mentor (pdf files and Mentor (pdf files and (pdf files and videos) (pdf files and videos) (pdf files and videos) (pdf files and videos) (pdf files and videos) videos) videos) Teacher created Teacher created Teacher created Teacher created Teacher created Teacher created Teacher created resources resources resources resources resources resources resources MCS Subject Group Overview. AP Calculus BC Last Revised: August, 2022 AP Calculus BC Subject Group Overview - Semester 2 Unit Unit 9: Parametric Equations, Polar Name Unit 8: Applications of Integration Coordinates, and Vector-valued Unit 10: Infinite Sequences & Series AP Exam review Functions Time Frame 3 Weeks 4 weeks 5 Weeks 4 Weeks Standards AP Calc BC 8.1-8.13 AP Calc BC 9.1-9.9 AP Calc BC 10.1-10.15 All AP Calc BC standards 1.1-10.15 8.1 Finding the average value of a function 9.1 Defining and differentiating parametric 10.1 Defining convergent and divergent 1.1-10.15 on an interval equations infinite series 8.2 Connecting position, velocity, and 9.2 Second derivatives of parametric 10.2 Working with geometric series acceleration of functions using integrals equations 10.3 The nth term test for divergence 8.3 Using accumulation functions and 9.3 Finding arc lengths of curves given 10.4 Integral test for convergence definite integrals in applied contexts parametric equations 10.5 Harmonic series and p-series 8.4 Finding the area between curves 9.4 Defining and differentiating vector- 10.6 Comparison tests for convergence expressed as functions of y valued functions 10.7 Alternating series test for convergence 8.5 Finding the area between curves 9.5 Integrating vector-valued functions 10.8 Ratio test for convergence expressed as functions of y 9.6 Solving motion problems using 10.9 Determining absolute or conditional 8.6 Finding the area between curves that parametric and vector-valued functions convergence Content intersect at more than two points 9.7 Defining polar coordinates and 10.10 Alternating series error bound Specific 8.7 Volumes with cross sections: squares differentiating in polar form 10.11 Finding taylor polynomial Information and rectangles 9.8 Find the area of a polar region or the approximations of functions 8.8 Volumes with cross sections: triangles area bounded by a single polar curve 10.12 Lagrange error bound and semicircles 9.9 Find the area of the region bounded by 10.13 Radius and interval of convergence of 8.9 Volume with disc method: revolving two polar curves power series around the x- or y-axis 10.14 Finding Taylor or Maclaurin series for 8.10 Volume with disc method: revolving a function around other axes 10.15 Representing functions as power 8.11 Volume with washer method: series Revolving around the x- or y-axis 8.12 Volume with washer method: revolving around other axes 8.13 The arc length of a smooth, planar curve and distance traveled Common Common Homework Quizzes Common Homework Quizzes Common Homework Quizzes Mock AP Exam Assessments Common Formative Assessments Common Formative Assessments Common Formative Assessments / Major Common Summative Assessment Common Summative Assessment Common Summative Assessment Projects MCS Subject Group Overview. AP Calculus BC Last Revised: August, 2022 AP Calculus BC Subject Group Overview - Semester 2 Unit Unit 9: Parametric Equations, Polar Name Unit 8: Applications of Integration Coordinates, and Vector-valued Unit 10: Infinite Sequences & Series AP Exam review Functions AP Classroom (within AP Central, AP Classroom (within AP Central, AP Classroom (within AP Central, Past AP exams (released and secure collegeboard.org) collegeboard.org) collegeboard.org) questions) Calculus textbook: Calculus textbook: Calculus textbook: AP Classroom (within AP Central, Calculus, 11e, Larson & Edwards Calculus, 11e, Larson & Edwards Calculus, 11e, Larson & Edwards collegeboard.org) Tony Record (Avon HS) created Tony Record (Avon HS) created Tony Record (Avon HS) created Tony Record (Avon HS) created resources resources resources resources www.flippedmath.com www.flippedmath.com www.flippedmath.com Calculus textbook: Calculus, 11e, Larson & Edwards Resources Khan Academy Khan Academy Khan Academy www.flippedmath.com Delta Math Delta Math Delta Math Khan Academy Master Math Mentor (pdf files and Master Math Mentor (pdf files and Master Math Mentor (pdf files and videos) videos) videos) Delta Math Teacher created resources Teacher created resources Teacher created resources Master Math Mentor (pdf files and videos) Teacher created resources MCS Subject Group Overview. AP Calculus BC Last Revised: August, 2022
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