Course Title:
AP Calculus AB and AP Calculus BC
Grade:
11 or 12
Length of Course:
One Year (5 credits)
Prerequisites:
Precalculus
Description:
Each of the respective curricula for both AP Calculus AB and AP Calculus BC were designed to meet (and in many
cases) exceed the curricular expectations of the College Board. As such, each curriculum has undergone an AP
Course Audit (administered by the College Board) and has received certification from the College Board indicating
that our adopted curricula meets or exceeds the College Board’s requirements.
Given the similarity of the two courses, this document describes the curricula for both AP Calculus AB and AP
Calculus BC. The AP Calculus AB course, consisting of 7 units, is a subset of the AP Calculus BC course, which
consists of 9 units. Both courses are virtually identical through the first 5 units but do start to differ significantly
beyond unit 5. Detailed in this document are the key definitions, key theorems, key skills and key critical thinking
questions that are to be covered as part of each course. Those definitions, theorems, skills and critical thinking
questions that are germaine only to BC Calculus are denoted as “BC only” in the curriculum guide. Instructional
material associated with each unit learning objective, as well as other known web resources for student learning, are
included as well.
In addition to delineating the required topics for the two courses, this curriculum guide also includes examples of
student exploratory activities used to help students be more actively engaged in the discovery and reinforcement of the
major conceptual underpinnings of calculus (see Table 1: Example Student Exploratory Activities). Many of the
exploratory activities, by design, require the use of graphing calculators so that students can investigate key ideas
graphically and numerically as well as analytically. Students are required to have a graphing calculator for the class (a
TI-83 Plus is recommended).
Evaluation:
Grades are based on a combination of tests, quizzes, homework assignments and/or group projects. Homework
assignments, in particular, are considered an integral part of the learning process for this course. When homework
assignments are due, students take turns presenting and explaining their solutions to critical problems in class. This
approach not only reinforces their ability to communicate mathematics and their corresponding solutions effectively,
but also serves to help identify areas where students need extra help.
Scope and Sequence:
Pacing is a critical part of the curricular expectations for the course. Unit sequencing and pacing for both
AP Calculus AB and AP Calculus BC are summarized in the attached pacing guide (see Table 2: Unit
Sequencing and Pacing).
Text:
Calculus: Graphical, Numerical, Algebraic, Ross L. Finney, Franklin D. Demana, Bert K. Waits, Daniel Kennedy,
Prentice Hall 2003 [Finney]
Reference Texts and Online Resources:
Calculus: Concepts and Contexts 3th Edition, James Stewart, Brooks Cole [Stewart]
MIT Lecture Videos from David Jerison’s Single Variable Calculus Course
[http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures] [MIT-18.01]
Topic-specific Lecture Notes and Interactive Java Applets from MIT Compiled for High School Students Taking
Calculus [http://ocw.mit.edu/high-school/calculus] [MIT-HSCalc]
AP Calculus
Unit
Unit 1: Review of
Prerequisities
Unit 2: Limits and Continuity
Unit Learning Objectives:
Key Definitions, Theorems, Skills and Critical Thinking Questions
Instructional Materials and
Online Resources
Key skills that students will be able to do in this unit:

Write the equation of a line given a point and the slope.

Find the domain and range of a given function.

Recognize even and odd functions.

Graph piecewise-defined functions.

Change growth or decay factors in exponential expressions to base e.

Find the inverse of a function (including exponential and trigonometric functions).

Evaluate inverse epressions.

Solve exponential and log equations.

Change bases in log expressions.

Graph trigonometric functions.

Solve trigonometric equations.

Parametrize common curves like line segments, circles and ellipses (BC only).
AB and BC:
[Finney] Section 1.1 – 1.3; 1.5 –
1.6
Key definitions and theorems introduced in this unit: average speed, instantaneous speed, limit, one-sided limit, twosided limit, end-behavior model, continuity, Intermediate Value Theorem, average rate of change, instantaneous rate
of change, instantaneous slope, tangent line to a curve at a given point, normal line to a curve at a given point.
AB and BC:
[Finney] Sections 2.1 – 2.4
[MIT-18.01]
Lecture 1: Rate of Change,
Lecture 2: Limits
Key skills that students will be able to do in this unit:

Find limits from graphs.

Find limits by algebraic simplification and substitution.

Determine one- and two-sided limits.

Use the sandwich theorem to find limits.

Find average and instantaneous speeds.

Find finite limits as x approaches + and – infinity.

Find vertical asymptotes (infinite limits as x approaches a).

Find end behavior models.

Determine continuity at a point using the definition of continuity.

Use the Intermediate Value Theorem for Continuous Functions to determine the existence of a solution.

Find the slope of a curve at given point.

Find the tangent line at a given point.

Find the normal line at a given point.
Key critical thinking questions for this unit:

Does the existence of a limit as x approaches some value c require that the function be defined at c? Why
or why not?

How can a limit fail to exist?

How are we able to calculate slope at a single point when the formula for slope clearly calls for two
points?
AP Calculus, page 2
BC Only:
[Finney] Section 1.4
AP Calculus
Unit
Unit 3: Derivatives
Unit Learning Objectives:
Key Definitions, Theorems, Skills and Critical Thinking Questions
Key definitions and theorems introduced in this unit: derivative, derivative notation, one-sided derivatives,
differentiability, local linearity, Intermediate Value Theorem for Derivatives, second and higher order derivatives,
chain rule, implicit differentation.
Key skills that students will be able to do in this unit:

Use the definition of a derivative to find the derivative of a function.

Identify the graphical relationship between f and f’.

Determine when a function might fail to exist at a given point.

Use a calculator to find the derivative.

Determine the derivative of a constant, a positive/negative integer power of x, a constant multiple of a
function, sums and differences of functions, and products and quotients of functions.

Find the instantaneous rate of change of function.

Determine the speed, velocity and acceleration of an object (algebraically, numerically and graphically).

Find the derivative of any trigonometric function.

Find the derivative of a composite function using the chain rule.

Find the derivative of implicitly defined functions.

Find the derivative of inverse function (especially inverse trig function).

Compute the value of the derivative of a function given information about the derivative of its inverse.

Find the derivative of an exponential function.

Find the derivative of a logarithmic function.
Key critical thinking questions for this unit:

Why are the alternative definitions of the derivative equivalent?

Is the derivative of the product of two functions equal to the product of the derivative of each function?

What is the relationship between the graph of f and the graph of f’? What is the relationship between the
graph of f’ to the graph of f’’?

How is the chain rule related to implicit differentiation?

How can implicit differentiation be used to find the derivative of an inverse trigonometric function? How
can implicit differentiation be used to find the derivative of a log function?
AP Calculus, page 3
Instructional Materials and
Online Resources
AB and BC:
[Finney] Section 3.1 – 3.9
[MIT-18.01]
Lecture 3: Derivatives,
Lecture 4: Chain Rule,
Lecture 5 Implicit
Differentiation,
Lecture 6: Exponentials and
Logs
[MIT-HSCalc] Java Applet on
Derivatives & Tangent Lines
(plots the derivative of a function
and shows the relationship
between the derivative and the
tangent line)
AP Calculus
Unit
Unit 4: Applications of
Derivatives
Unit Learning Objectives:
Key Definitions, Theorems, Skills and Critical Thinking Questions
Key definitions and theorems introduced in this unit: absolute/global extreme values, local/relative extreme
values, Extreme Value Theorem, critical points, Mean Value Theorem, increasing/decreasing functions, first
derivative test for local extrema, concavity, points of inflection second derivative test for local extrema,
optimization, linearization, differentials, Newton’s Method, related rate equations.
Key skills that students will be able to do in this unit:

Determine the local and/or global extreme values of a function.

Find the function f (the anti-derivative) given its derivative.

Use derivatives to find critical points.

Use derivatives to find when the function is increasing or decreasing.

Use derivatives to find when the function is concave up or concave down.

Use the first and second derivative tests to determine the local extreme values of a function.

Determine the concavity of a function and locate the points of inflection by analyzing the second
derivative.

Graph f using information about f’ and f’’.

Solve real-world problems that involve finding minimum or maximum values of functions.

Find the linearization of a function and use Newton’s method to approximate the zeros of a function.

Estimate the change in a function using differentials.

Recognize and solve related rates problems.
Key critical thinking questions for this unit:

How does f’ and f’’ determine the shape of f?

What factors determine the accuracy of a linearization? How can you make a linearization more
accurate?

What is the significance of the Mean Value Theorem? What is its geometric interpretation?

Is f’’’(0) sufficient to guarantee an inflection point? Why or why not?

How can one recognize a related rates problem?
AP Calculus, page 4
Instructional Materials and
Online Resources
AB and BC:
[Finney] Section 4.1 – 4.6
[MIT-18.01]
Lecture 9: Linear & Quadratic
Approximations,
Lecture 10: Curve Sketching,
Lecture 11: Max-Min,
Lecture 12: Related Rates,
Lecture 13: Newton’s Method,
Lecture 14: Mean Value
Theorem.
AP Calculus
Unit
Unit 5: The Definite Integral
Unit Learning Objectives:
Key Definitions, Theorems, Skills and Critical Thinking Questions
Key definitions and theorems introduced in this unit:Rectangular Approximation Method (RAM), Reimann Sums,
integral, integrand, upper and lower limit, variable of integration, integral notation, antiderivative, definite
integral, Mean Value Theorem for Definite Integrals, Fundamental Theorem of Calculus, Part 1 and Part 2,
Trapezoidal Rule.
Key skills that students will be able to do in this unit:

Approximate the area under the graph of a nonnegative continuous function by using rectangular
approximation methods.

Interpret the area under a graph as a net accumulation of a rate of change.

Express the area under a curve as a definite integral and as a limit of Riemann sums.

Compute the area under a curve using a numerical integration procedure.

Apply rules for definite integrals to evaluate definite integrals

Find the average value of a function over a closed interval.

Use the Fundamental Theorem of Calculus to find the derivative of an integral function.

Use the Fundamental Theorem of Calculus to evaluate a definite integral

Understand the relationship between the derivative and the definite integral as expressed in both parts of
the Fundamental Theorem of Calculus.

Approximate the definite integral by using the Trapezoidal Rule.
Key critical thinking questions for this unit:

Why is the change in y (i.e. delta y) not equal to the differential of y?

What determines the accuracy of a Reimann Sum? What determines whether a Reimann Sum is an
overestimate or an underestimate?

Explain how an integral is the limit of Reimann Sums.

What is the difference between a definite integral and an indefinite integral?

How can we approximate volumes of solids using Reimann Sums?

Why is the chain rule needed when taking the derivative of an integral function whose upper limit
and/or lower limit is more than a function of x?
AP Calculus, page 5
Instructional Materials and
Online Resources
AB and BC:
[Finney] Section 5.1 – 5.5
[MIT-18.06]
Lecture 18: Definite Integrals,
Lecture 19: First Fundamental
Theorem,
Lecture 20: Second Fundamental
Theorem
[MIT-HSCalc] Java Applet on
Numerical Integration (uses the
left hand rule, the right hand rule
and the trapezoidal rule to
approximate the area under a
specified curve).
AP Calculus
Unit
Unit 6: Differential Equations and
Mathematical Modeling
Unit Learning Objectives:
Key Definitions, Theorems, Skills and Critical Thinking Questions
Key definitions and theorems introduced in this unit: indefinite integral, slope field, differential equation, initial
value problem, integration by substitution, integration by parts, Law of Exponential Change, Newton’s Law of
Cooling, Logistic Growth Model, Euler’s Method.
Key skills that students will be able to do in this unit:

Evaluate indefinite integrals or antiderivatives.

Evaluate integrals by method of substitution.

Evaluate integrals by method of integration by parts (BC only).

Evaluate integrals by method of partial fractions (BC only).

Solve a differential equation with initial conditions algebraically by separation of variables.

Solve a differential equation with initial conditions graphically by constructing a slope field.

Solve a differential equation with initial conditions numerically by Euler’s method (BC only).

Model real-world unconstrainted exponential growth using the Law of Exponential Change and find the
solution of the Exponential Change Model algebraically, numerically, and graphically (BC only).

Model real-world constrained exponential growth problems using the logistic growth model and find the
solution of the logistic growth model algebraically, numerically and graphically (BC only).

Approximate the definite integral by using the Trapezoidal Rule.
Instructional Materials and
Online Resources
AB and BC:
[Finney] Section 6.1 – 6.2
[MIT-18.01]
Lecture 15 Antiderivatives,
Lecture 16 Differential
Equations
BC only:
[Finney] Section 6.3 – 6.6
[MIT-18.01]
Lecture 30 Integration by Parts
Key critical thinking questions for this unit:

How does one derive the rule for integration by parts? What derivative operation is rule for integration
by parts derived from?

What determines the accuracy of Euler’s Method?

How is constrained growth modeled by the logistic growth function?
Unit 7: Applications of Definite
Integrals
Key definitions and theorems introduced in this unit: Net Change, displacement, area between curves, NINT,
solid of revolution, cylindrical shell, arc length.
Key skills that students will be able to do in this unit:

Use definite integrals to calculate net change (e.g. net displacement) in functions expressed analytically
or in tabular form.

Use definite integrals to calculate the total area under a curve (e.g. total distance traveled).

Use definite integrals to calculate the area between curves, integrating with respect to x and integrating
with respect to y.

Use definite integrals to calculate the volume generated by known cross-sections (square, circular,
triangular0.

Use definite integrals to calculate the volume of solids of revolution (disc method, washer method, and
cylindrical shell method-BC only).

Use calculator programs such as NINT to evaluate definite integrals.

Use definite integrals to calculate the length of smooth curve (BC only).
Key critical thinking questions for this unit:

Why does the definite integral of a rate of change function produce a net change of that function?

Describe the general strategy for calculating volumes by integration?
AP Calculus, page 6
AB and BC:
[Finney] Section 7.1 – 7.3
[MIT-18.01] Lecture 22: Volumes
BC only:
[Finney] Section 7.4
AP Calculus
Unit
Unit 8: Infinite Series (BC only)
Unit Learning Objectives:
Key Definitions, Theorems, Skills and Critical Thinking Questions
Key definitions and theorems introduced in this unit: infinite series, geometric series, power series, convergence,
divergence, term-by-term differentiation/integration, harmonic series, Taylor series, MacLaurin series, Taylor’s
Theorem, Remainder Estimation Theorem, radius of convergence, nth term test, direct comparison test, ratio test,
integral test, limit comparison test, p-series test, alternating series test, Alternating Series Estimation Theorem.
Key skills that students will be able to do in this unit (BC only):

Recognize standard indeterminate forms and use L’Hopital’s Rule to evaluate them.

Evaluate integrals using the method of partial fractions.

Evaluate integrals using the method of trigonometric substitutions.

Evaluate improper integrals.

Determine whether improper integrals diverge or converge using direct comparison or limit comparison.

Find the nth term of a power series and express the power series in sigma notation.

Determine whether a geometric series diverges or converges, and if it converges what it converges to.

Generate the power series of a given function by applying transformations on a geometric series.

Generate the Taylor and MacLaurin series for a given function.

Estimate an upper bound for the truncation error of a Taylor series using the Remainder Estimation
Theorem.

Find the radius of convergence of a given power series.

Determine whether a given power series converges or diverges.

Finding the interval of convergence of a given power series by testing for convergence at the endpoints
of the convergence interval.

Use the Alternating Series Test to test an alternating series for convergence.

Estimate an upper bound for the truncation error of an alternating series using the Alternating Series
Estimation Theorem.
Key critical thinking questions for this unit:

What does it mean for a series to converge? What does it mean for a series to diverge?

How is the linearization of a function related to a Taylor series?

What factors determine the error of a given nth order Taylor polynomial?

Describe a general strategy for efficiently determining whether a given series converges or diverges.
AP Calculus, page 7
Instructional Materials and
Online Resources
BC only:
[Finney] Section 8.1, 8.3 – 8.4
[Finney] Section 9.1 – 9.5
[MIT-18.01]
Lecture 35: Indeterminate
Forms,
Lecture 36: Improper Integrals,
Lecture 37: Infinite Series,
Lecture 38: Taylor Series
AP Calculus
Learning Objectives
The student will …
Unit 9: Parametric, Vector and
Polar Functions (BC only)
Unit Learning Objectives:
Key Definitions, Theorems, Skills and Critical Thinking Questions
Key definitions and theorems introduced in this unit: first and second derivatives of a parametric function, arc length
of a parametrized curve, component form of vectors, standard unit vectors, derivatives of vector-valued functions,
integrals of vector-valued functions, projectile motion, polar coordinates, polar graphs, slope of polar graphs, area
enclosed by polar graphs.
Key skills that students will be able to do in this unit (BC Only):

Find the derivative at a point of a parametrized curve.

Find the second derivative of a parametrized curve.

Find the length of smooth parametrized curve.

Express vectors in component form.

Perform vector operations (addition, subtraction and scalar multiplication).

Find the dot product of two vectors and the angle between two vectors using the dot product.

Find vectors tangent to and normal to a parametrized curve.

Find the derivative of a vector function.

Find the velocity, speed, acceleration and direction of motion of an object given the object’s position
vector function.

Find the definite and indefinite integral of a vector-valued function.

Model projectile-motion using vector-valued functions.

Graph polar curves.

Convert equations from cartesian coordinates to polar coordinates and vice-versa.

Find the slope of a polar curve.

Find horizontal and vertical tangents and apply L’Hopital’s Rule for indeterminate cases.

Find the area of the region between a polar curve and the origin and the area of the region between two
polar curves.

Find the length of polar curve.
Key critical thinking questions for this unit:

How is the chain rule used in finding the derivative of a parametrized curve?

What is the difference, mathematically, between speed and velocity? How are they related to each other
mathematically?

How is the chain rule used in finding the derivative of a polar curve?

When and why do you need to use L’Hopital’s Rule when it comes to polar curves?

Show how one derives the formula for the area between the origin and a polar curve.
AP Calculus, page 8
Instructional Materials and
Online Resources
BC only:
[Finney] Section 10.1 – 10.6
[MIT-18.01]
Lecture 31: Parametric
Equations,
Lecture 32: Polar Coordinates
[MIT-HSCalc] Java Applet: Polar
Plotter (shows the graph of a
function defined in polar
coordinates)
AP Calculus
Table 1: Example Student Exploratory Activities
Unit
Student Activities
Unit 3: Derivatives
Discovering the derivative of y = sin (x) graphically, algebraically and numerically. Students are asked to graph the function y = sin(x) in a
standard trigonometric window in a graphing calculator and on graph paper. Students are then asked to estimate the slope of the tangent line at
various x-values and plot the slope values as a function of x on graph paper. Students should focus on finding the x-values where the slope of y =
sin(x) is equal to: 0, -1, +1, +0.5, -0.5, +0.866 and -.0.866. After finding these points, they should see that the slope curve follows the path of the
cosine function. To validate this discovery, students should graph the numerical derivative of y = sin(x) in the same window and show that it is the
same graph as y = cos(x). Finally, the students can then proceed to prove that d/dx(sin x) = cos x using the definition of the derivative.
Unit 4:
Applications
of
Derivatives
Discovering the usefulness of Local Linearity in approximating functions. Students are asked to graph a variety of functions and then asked to
use the zoom feature of the calculator on that function. After a few repeated zooms, the discover that almost all curves “straighten out” around a
point when increasingly magnified. Students are asked to write and graph a linear equation that approximates the zoomed-in graph. Upon
zooming out they discover that the linear equation they graphed will closely approximate the tangent line. Next students are asked to graph a
function and then determine and graph its actual tangent line at a given point (a, f(a)). Using repeated zooms around the point, (a, f(a)), the
students are then asked find an approximation for f(a+h) where h is a very small number. At this point, various discussions ensue regarding why
the approximation is good or not good and what determines whether the approximation will be good or will not be good. This exercise helps
reinforce the underlying concept behind Linearization.
Optimization Project. Students work in small groups to determine the optimum (i.e. least cost of material) dimensions of a can for a given
volume. Students are at first asked to do this study using the simplifying assumption that the cost of producing a can is strictly related to the
surface area of the can. With this assumption, students should find that their optimum dimensions are as follows: that the height of the can should
equal the diameter of the can. However, upon comparing these results to the measurements of actual cans found on grocery shelves, they will find
that their results are somewhat off. Students are then asked to refine their assumptions and see how those refinements can affect their findings. A
typical refinement might be to now assume that the circular tops of the cans would have to be cut out of squares and that the total cost of producing
the can would have to take into account waste material as well. Students will find that the accuracy of their solutions will depend largely on the
validity of their assumptions. This project allows us to discuss the real-world tradeoff between model simplicity and model accuracy.
Unit 5: The
Definite
Integral
Estimating how far you drove without your odometer: approximating accumulation using definite integrals and reimann sums. This
activity is used to reinforce the notion of a definite integral as a way of calculating net change and/or accumulation. Students are asked to drive
with a friend or parent for 20 minutes. Students must record the starting odometer reading, the car’s speed at one-minute intervals, and the ending
odometer reading. Student’s then graph speed versus time and use integration techniques to approximate the distance traveled over the 20 minute
interval. They then compare this distance with the actual mileage determined by the odometer. As a further test, I provide them with my own
speed versus time readings and have them estimate how far I drove using integration techniques.
AP Calculus, page 9
AP Calculus
Unit
Student Activities
Unit 6:
Differential
Equations
Constructing Slope Fields. Using a 3x3 grid generated by Apple’s Grapher program projected onto a whiteboard, students will construct slope
fields for a given differential equation. Students are each assigned a coordinate point (i.e. [1,1], [1,2], etc.) in the projected grid. For a given
differential equation, each student computes the slope at his or her coordinate position and then goes to the board to draw a short line segment with
the calculated slope and the coordinate point as the midpoint of the segment. Continuing in this manner, the class would complete the slope field.
From this point, several discussions can ensue. In particular students can be asked to draw a particular solution to the differential equation by being
given a particular initial condition. Students can then see how different initial conditions can affect the solution to the differential equation.
Unit 7:
Applications
of Definite
Integrals
Visualizing volume calculations with winplot and play-doh. Students have a difficult time with calculating the volume of solids because they
have a hard time visualizing the solid. I use winplot to draw a function in 3D and use it to generate the solid of revolution as well as show crosssectional slices of the volume. As an additional aid in visualizing the procedure for calculating volumes, I use play-doh. Students build the solids
using play-doh and then use plastic knives or dental floss to cut through the solid and obtain the required cross sections. Students are asked to
describe the integral as they are cutting through the play-doh; that is, they point to where dx (or dy when appropriate) is on the cross-sectional slice,
the formula that they use to find the area of the cross-sectional play-doh slice and finally the rational for the upper and lower limits of integration.
Unit 8:
Infinite
Series
Constructing a Taylor/MacLaurin Series for y = sin(x) and exploring the convergence/divergence properties of an nth order Taylor
polynomial using a graphing calculator. Students are first asked to construct the eleventh order Taylor polynomial and the Taylor series for y =
sin(x) at x = 0. Once the power series has been constructed, the students graph each of the Taylor polynomials (P1, P3, P5, …, P11) and compare
them to the graph of y = sin(x). Students should discover that as the order of the Taylor polynomial increases, the Taylor polynomial starts to look
more and more like the entire sin curve. Students then graph the error of approximation (the difference between the actual value of the function and
the value of the Taylor polynomial) and see that the error of approximation is small near zero and gets larger as you move away from zero. This
exercise gives the students an appreciation for how the Taylor polynomial can converge to the function and how it eventually gets unbounded
beyond a certain interval. This exercise can be repeated to show how a Taylor series may not always converge – for example with y = ln (1 + x)
where the Taylor series fails to converge outside the interval from –1 to 1, no matter how many terms we add.
AP Calculus, page 10
AP Calculus
Table 2: Unit Sequencing and Pacing
Timeframe
Quarter 1
BC Unit Sequencing and Pacing
AB Unit Sequencing and Pacing
Unit 1: Review of Prerequisites (1 week or done as needed throughout the
year)
Unit 1: Review of Prerequisites (1 week or done as
needed throughout the year)
Unit 2: Limits and Continuity (2 weeks)

Rates of Change and Limits

Limits Involving Infinity

Continuity

Rates of Change and Tangent Lines
Unit 2: Limits and Continuity (3 weeks)

Rates of Change and Limits

Limits Involving Infinity

Continuity

Rates of Change and Tangent Lines
Unit 3: Derivatives (4 weeks)

Derivative of a Function

Differentiability

Rules of Differentiation

Velocity and Other Rates of Change

Chain Rule

Implicit Differentiation

Derivatives of Inverse Trigonometric Functions

Derivatives of Exponential and Logarithmic Functions
Unit 3: Derivatives (5 weeks)

Derivative of a Function

Differentiability

Rules of Differentiation

Velocity and Other Rates of Change

Chain Rule

Implicit Differentiation

Derivatives of Inverse Trigonometric
Functions

Derivatives of Exponential and Logarithmic
Functions
Unit 4: Applications of Derivatives (2 weeks)

Extreme Values of Functions

Mean Value Theorem

Connecting f’ and f’’’ with the Graph of f
Quarter 2
Unit 4: Applications of Derivatives (2 weeks - continued from Quarter 1)

Modeling and Optimization

Linearization and Newton’s Method

Related Rates
Unit 5: The Definite Integral (3 weeks)

Estimating with Finite Sums

Definite Integrals

Definite Integrals and Antiderivatives

Fundamental Theorem of Calculus

Trapezoidal Rule
Unit 6: Differential Equations and Mathematical Modeling (3 weeks)

Antiderivatives and Slope Fields

Integration by Substitution

Integration by Parts

Exponential Growth and Decay

Population Growth

Numerical Methods
AP Calculus, page 11
Unit 4: Applications of Derivatives (4 weeks)

Extreme Values of Functions

Mean Value Theorem

Connecting f’ and f’’’ with the Graph of f

Modeling and Optimization

Linearization and Newton’s Method

Related Rates
Unit 5: The Definite Integral (4 weeks)

Estimating with Finite Sums

Definite Integrals

Definite Integrals and Antiderivatives

Fundamental Theorem of Calculus

Trapezoidal Rule
Review for Midterm
AP Calculus
Timeframe
BC Unit Sequencing and Pacing
AB Unit Sequencing and Pacing
Review for Midterm
Quarter 3
Midterm
Midterm
Unit 7: Applications of Definite Integrals (3 weeks)

Integral as Net Change

Areas in the Plane

Volumes

Lengths of Curves
Unit 6: Differential Equations and Mathematical
Modeling (4 weeks)

Estimating with Finite Sums

Definite Integrals

Definite Integrals and Antiderivatives

Fundamental Theorem of Calculus

Trapezoidal Rule
Unit 8: Infinite Series (6 weeks)

L’Hopitals Rule

Partial Fractions

Improper Integrals

Power Series

Taylor Series

Taylor’s Theorem

Radius of Convergence

Testing Convergence at Endpoints
Quarter 4
Unit 7: Applications of Definite Integrals (4 weeks)

Integral as Net Change

Areas in the Plane

Volumes
Unit 9: Parametric, Vector and Polar Functions (2 weeks)

Parametric Functions

Vectors in the Plane

Vector-Valued Functions

Modeling Projectile Motion

Polar Coordinates and Polar Graphs

Calculus of Polar Curves
Review for AP Exam (4 weeks)
Review for AP Exam (2 weeks)
Final
Final
AP Calculus, page 12