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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
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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
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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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