AP® Calculus BC - Wisconsin Virtual School document outlines the topics and subtopics that are covered in each ... Quiz, which is a computer ... Composite Functions, Composite Domains,

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AP® Calculus BC Course Syllabus

Course Description AP Calculus BC is a two-semester course in which students study functions, limits, derivatives, integrals, and infinite series. This document outlines the topics and subtopics that are covered in each chapter/unit.

Throughout the course, students write and work with functions represented by written descriptions, mathematical rules, graphs and tabular data. Students develop and practice skills using a graphing calculator to solve problems, experiment, interpret results, and support their conclusions. Students learn the meaning of the derivative and apply it to a variety of problems while developing a deeper understanding of the meaning of the solutions to those problems. Students study integrals and learn the relationship between the derivative and the definite integral, using written work and graphing technology to explore and interpret this relationship.

Students discover how calculus is used to model real-world phenomena by using functions, differential equations, integrals, and graphing technology to solve problems, support solutions, and interpret findings. Students communicate mathematics to the teacher through course participation and written work and to peers through a discussion forum monitored by the teacher.

Students communicate about mathematics through written work and discussion forums with peers that are monitored by the teacher. Asynchronous and synchronous discussion activities throughout the course provide multiple opportunities for students to interact with each other and share ideas about math problems and problem-solving strategies. Discussions include opportunities for students to work in small groups where they collaborate on specific assignments. The syllabus outline indicates where these discussions occur and what the topics are.

The teacher hosts and facilitates weekly synchronous sessions with students who are enrolled in this course. In these regularly scheduled sessions, students communicate with each other and with the teacher about course content and assignments. These synchronous sessions allow for timely verbal dialogue about AP Calculus BC content and course assignments. As needed, the teacher guides students through appropriate explanations of assigned problems and solution sets. Helpful guidelines for these sessions are provided to the teacher.

All students enrolled in this course are assigned to a “section” with a qualified teacher who is responsible for ensuring student success and addressing student questions, problems, and concerns. In addition, each student must have a mentor available at their school or at home to support the student and make sure assignments are completed in a timely manner.

The content and reference materials for this course align with College Board frameworks and College Board approved textbooks.

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Course Prerequisites Algebra II, Geometry, Pre-Calculus with Trigonometry

Course Materials This online course offers instructional content that incorporates required topics in a balanced and comprehensive sequence. Online digital instruction includes text, figures, graphic elements, carefully structured problem sets, exploration guides, and graphing calculator instructions to convey and highlight important information and provide students with specific applications of concepts they are studying.

The required virtual content for this course is covered in:

Thomas, Paul et al. (editors). AP Calculus BC, K12 digital edition. Herndon, VA: 2012.

In addition, students should have this required (printed) textbook: Larson, Ron, and Bruce H. Edwards. Calculus of a Single Variable, AP Edition (9th ed.), Belmont, CA: Brooks/Cole, Cengage Learning, 2010. [ISBN: 0547212909]

The following additional textbooks (optional) may be used to supplement the material presented in this course:

Finney, Ross L., Franklin Demana, Bert Waits, and Daniel Kennedy. Calculus: Graphical, Numerical, Algebraic (3rd ed.), Boston: Pearson Addison Wesley, 2007. [ISBN: 0132014084]

Stewart, James. Single Variable Calculus (7th ed.), Belmont, CA: Brooks/Cole, Cengage Learning, 2011. [ISBN: 0538497831]

Specific information for use of these texts with course content appear at the end of this document.

The student or the school must purchase a TI-84 Plus calculator (or similar calculator approved by the College Board) for the AP Calculus BC Exam.

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Types of Instructional Activities in This Course

Activity Type Learn Description

Video Lecture

Primary instructional content is presented online to introduce and teach new concepts through multimedia and interactive experiences.

Explore

Paper and pencil activities are included in Explore activities, as well as graphing calculator activities to show students key steps for using calculators to explore, experiment, interpret findings, and/or support their conclusions.

Discuss

Students discuss topics in an online threaded discussion board forum. Teachers participate in these discussions, and students receive credit for appropriate participation. Synchronous, teacher-led “Class Connect” sessions occur multiple times each week. In these sessions students communicate orally to demonstrate how their mathematical reasoning applies to key concepts.

Activity Type Practice Description

Try It

Students answer online, computer-scored (ungraded) questions to help them synthesize what they have learned in a lesson. This helps them think about the content before applying it in a problem set. Every lesson with Video Lectures includes six to ten Try It questions.

Problem Set

Every lesson with Video Lectures has a Problem Set in which students work offline to practice what they have learned. One Problem Set is provided as a PDF for each lesson. Each lesson also includes suggested assignments for each of the three recommended textbooks.

Activity Type Assessment Description

Quiz Most lessons include a Quiz, which is a computer-graded assessment.

Review Lesson

Review Lessons cover the material presented in a specific unit or semester. Calculator skills are also reviewed in these lessons to help prepare students to use them on tests and exams.

Unit Test

A Unit Test is an assessment of material covered in a given unit. Each test is modeled after the AP Exam. Students complete certain portions of the test using graphing calculators, but are prohibited from using them on other parts of the tests. Each test includes a computer-graded, multiple-choice section plus a free-response section that is teacher graded in accordance with a detailed rubric.

Semester Exam

A comprehensive Semester Exam is administered at the end of each semester. Students are required to use graphing calculators to solve problems, experiment, interpret results, support their conclusions, and verify hand-written work. The semester exam is modeled after the AP Exam; students complete certain parts of the exam using graphing calculators, but are prohibited from using them on other parts of the exam.

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Course Outline

Semester A

Unit 1: The Basics (~17 Days)

Students prepare to study calculus by reviewing basic pre-calculus concepts from algebra and trigonometry. They learn what calculus is, why it was invented, and what it is used for.

Pre-Calculus Review Introduction to Calculus • Video Lectures: The Study of Change, History of Calculus, Calculus Today, The Study of Calculus • Discussion: Introduction

Using a Graphing Calculator • Graphing Calculator: Finding Zeros of Functions

Combining Functions • Video Lectures: Sums, Differences, Products, Quotients

Composite and Inverse Functions • Video Lectures: Composite Functions, Composite Domains, Inverse Functions, Domains of Inverse

Functions • Graphing Calculator: Exploring Functions Graphically and Numerically

Graphical Symmetry • Video Lectures: Symmetry, Even and Odd Functions, Inverse Is Reflection of Original

Patterns in Graphs • Video Lectures: Function Families, Rules, Absolute Value • Graphing Calculator: Shifting and Exploring Function Graphs

Unit Review Unit Test

Unit 2: Limits and Continuity (~16 Days) This unit addresses Topic I: Functions, Graphs, and Limits of the College Board’s Calculus BC topic outline. Students learn two important concepts that underlie all of calculus: limits and continuity. Limits help students understand differentiation (the slope of a curve) and integration (the area inside a curved shape). Continuity is an important property of functions.

Introduction • Video Lectures: Limits, Unequal Limits, Ways to Find Limits

Finding Limits Analytically • Video Lectures: Identities, Factoring and Rationalizing, Trigonometric

Asymptotes as Limits • Video Lectures: Asymptotes Revisited, Horizontal Asymptotes, Vertical Asymptotes, Drawing a

Graph with Asymptote Information,

Relative Magnitudes for Limits • Video Lectures: Comparing Algebraic Functions, Comparing Exponential Functions, Comparing

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Exponential Functions to Algebraic Polynomials and Power Functions • Discussion: Analyzing Examples of Infinities

When Limits Do and Don’t Exist • Video Lectures: Vertical Asymptotes, Left-and-Right Hand Limits Don’t Match, Oscillating Limits

Continuity • Video Lectures: What Is Continuity?, Discontinuity Types: Jump, Discontinuity Types: Infinite,

Discontinuity Types: Removable, All Together

Intermediate and Extreme Value Theorems • Video Lectures: The Intermediate Value Theorem, The Extreme Value Theorem • Discussion: Limits and the Predator/Prey Model


Unit 3: The Derivative (~25 Days) This unit addresses Topic II: Derivatives of the College Board’s Calculus BC topic outline. Students learn how to calculate a derivative, the slope of a curve at a specific point. They learn techniques for finding derivatives of algebraic functions (such as y = x2) and trigonometric functions (such as y = sin x). Students also interpret the derivative as a rate of change and move fluidly between multiple representations including graphs, tables, and equations.

Introduction: Slope and Change • Video Lectures: Slope, Instantaneous Rate of Change

Derivative at a Point • Video Lectures: Slope of Curve, Differentiable, Calculating the Derivative • Graphing Calculator: Computing the Derivative of a Function Numerically

The Derivative • Video Lectures: Finding and Using the Derivative Function, Units, Slope, Notation

The Power Rule • Video Lectures: The Derivative as a Function, The Power Rule, Trigonometric Derivatives • Discussion: Discovering Rules for Derivatives

Sums, Differences, Products, and Quotients • Video Lectures: Sums, Products, Quotients, Applying the Quotient Rule

Graphs of Functions and Derivatives • Video Lectures: Zeros, Extreme Values, Steepness, Graphical Differentiation, Non Differentiable

Continuity and Differentiability • Video Lectures: Review, Discontinuous, Continuous, Differentiable

Rolle’s and Mean Value Theorems • Video Lectures: Rolle’s, Mean Value

Higher-Order Derivatives

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• Graphing Calculator: Higher-Order Derivatives

Concavity • Video Lectures: The Second Derivative, Inflection Points

Chain Rule

• Video Lectures: Units, Chain Rule, Applying the Chain Rule, Derivatives of Complicated Functions

Implicit Differentiation • Video Lectures: Implicit Equations and Their Derivatives, Derivative of an Ellipse, Derivative of a

Circle and a Hyperbola, Tough Analytical Derivatives


Unit 4: Rates of Change (~17 Days)

This unit focuses on Second Derivatives and Applications of Derivatives within Topic II: Derivatives of the College Board’s Calculus BC topic outline. Students learn how to use calculus to model and analyze changing aspects of our world. In addition to the AB topics in this unit, BC students analyze polar and vector-valued functions.

Introduction • Exploration: Maximums

Extrema • Video Lectures: Extrema, First Derivative Test, Sketching with the Second Derivative, Second

Derivative Test

Optimization • Video Lectures: Minimizing, Maximizing, Sketching with the Second Derivative, Travel Time,

Travel Time 2 • Discussion: Applications of Optimization

Tangent and Normal Lines • Video Lectures: The Tangent Line to a Curve, Normal Line, Finding Lines • Discussion: Linear Approximations of sin x

Tangents to Polar Curves • Video Lectures: Polar Form of the Derivative, Tangents to Polar Curves, Horizontal and Vertical

Tangents to Polar Curves

Tangent Line Approximation • Video Lectures: Local Linearity, Approximation, Calculator,

Rates and Derivatives • Video Lectures: Rates of Change as Derivatives, Economics, Translating • Discussion: Uses of Rates in Real-World Applications

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Related Rates • Video Lectures: Related Rates are Applications of the Chain Rule, Related Rates Story Problems

Technique, Commonly Needed Formulas and Rules

Rectilinear Motion • Video Lectures: Rectilinear, Speed & Velocity • Graphing Calculator: Velocity and Acceleration

Motion with Vector Functions • Video Lectures: Magnitude and Direction, Decomposing into Components, Velocity and

Acceleration Vectors


Unit 5: The Integral, Part 1 (~16 Days)

This unit focuses on Topic III: Integrals in the College Board’s Calculus BC topic outline. Students learn numerical approximations to definite integrals, interpretations and properties of definite integrals, the Fundamental Theorem of Calculus, and techniques of anti-differentiation. They learn how to find areas of curved shapes.

Introduction • Graphing Calculator: Analyzing Velocity and Distance for a Car Trip

Riemann Sums • Video Lectures: Area, Approximating Area, Inscribed and Circumscribed Rectangles, Improving

the Estimate, Riemann Sums

Area Approximations • Video Lectures: Trapezoid Rule, From a Function with a Formula, From a Function Graph, From

Numerical Data, Error

The Definite Integral • Video Lectures: Many Intervals, Definite Integral, Evaluating Definite Integrals, Approximating

Numerically, Limit of Sums • Graphing Calculator: Taking More Intervals

Properties of Integrals • Video Lectures: Signed Area, Properties, Using Rules

Graphing Calculator: Integration • Graphing Calculator: Using fnint()

Applications of Accumulated Change • Video Lectures: Accumulation, Average Value, Velocity Curves, Exercises, Accumulated Change

Antiderivatives

• Video Lectures: Going Backwards, Antiderivatives, Some Rules, Differential Equations • Going Between Position, Velocity, and Acceleration

Composite Functions

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• Video Lectures: Chain Rule, Differential Form, Substitution, Another Substitution Example, Practice, Guess & Check, Guess & Check II


Semester B

Unit 1: The Integral, Part 2 (~10 Days)

This unit focuses on Topic III: Integrals in the College Board’s Calculus BC topic outline. Students learn the Fundamental Theorem of Calculus, and techniques of anti-differentiation. They learn how to find areas of curved shapes.

The Fundamental Theorems of Calculus • Video Lectures: Area Functions, The First Fundamental Theorem, The Second Fundamental

Theorem, Units, Names

Definite Integrals of Composite Functions • Video Lectures: Fundamental Theorems, Definite Integrals, Area, Upper Limits, Strange

Substitutions, When to Substitute

Analyzing Functions and Integrals • Video Lectures: Leibniz’s Rule, Leibniz’s Rule II, Area Functions, Analyzing Functions, One More

Analyzing Functions Example


Unit 2: Applications of Integrals (~13 Days)

This unit focuses on Topic III: Integrals in the College Board’s Calculus BC topic outline. Students learn to use integrals and antiderivatives to solve problems. In addition to the AB topics, BC students learn to calculate arc length for a smooth curve.

Introduction and Area between Curves • Video Lectures: Accumulation, Two Curves, Multiple Curves, Cutting Area Horizontally

More Areas and Averages • Video Lectures: Area Problems, No Formula?, Working Backwards

Volumes of Revolution • Video Lectures: Principles, A Calculus View of Volume, Solids of Revolution • Discussion: Hands-on Solids and Volumes

Cross Sections • Video Lectures: Cross Sections, Other Shapes for Cross-Sections, Finding Dimensions of Solids

Arc Length • Video Lectures: Determine the Arc Length Formula, Arc Length Example y = f(x), Arc Length

Example x=f(y)

More Rectilinear Motion • Video Lectures: Total vs. Net, Velocity vs. Speed, Putting It All Together, Other Accumulated

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Changes

Other Applications of the Definite Integral • Video Lectures: Geometry, Surface Area, Applications from Physics, Nifty Application,

Connections


Unit 3: Transcendental and Parametric Functions (~23 Days) This unit focuses on Topic II: Derivatives and Topic III: Integrals in the College Board’s Calculus BC topic outline. Students learn to calculate and use derivatives, antiderivatives, and integrals of exponential functions (such as y = 3x where the input variable is an exponent), logarithmic functions (the inverses of exponential functions), and trigonometric functions (such as y = secant x). In addition to the AB topics, BC students learn how to use L’Hôpital’s Rule and the methods of partial fractions and integration by parts. Also, students learn how to find improper integrals, and derivatives and integrals of parametric functions.

Introduction and Derivatives of Inverses • Video Lectures: Inverse Functions, Derivatives of Inverse Functions, The Graphical View, Inverse

Trig Functions

Inverse Trigonometric Functions • Video Lectures: Domain Restrictions, Derivatives of Arctan and Arccos, Complicated Examples,

Using Derivatives

Logarithmic and Exponential Review • Video Lectures: Exponential Growth and Decay Functions, Logarithms, Slope, Applications • Discussion: Challenges with Logarithms • Graphing Calculator: Derivatives of Exponential Functions

Transcendentals and 1/x • Graphing Calculator: Explore transcendentals and 1/x

Derivatives of Logarithms and Exponentials • Video Lectures: Definition, Laws, Logarithmic Differentiation, Exponential Function, Other Bases

L’Hôpital’s Rule • Video Lectures: Indeterminate Quotients and L’Hospital’s Rule, Indeterminate Products,

Indeterminate Differences, Indeterminate Powers

Analysis of Transcendental Curves • Video Lectures: Curve Analysis, Tangent and Normal Lines, Optimization, Rates of Change,

Related Rates

Integrating Transcendental Functions • Video Lectures: Recap Rules, Practice, Strategies, Applications

Partial Fractions

• Video Lectures: Partial Fractions I, Partial Fractions II

Integration by Parts

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• Video Lectures: Formula and Overall Approach, Repeated Use of Integration by Parts, Utilizing Constant Multiples of Original Integral, Definite Integrals with Integration by Parts

Improper Integrals • Video Lectures: Improper Integrals with Infinite Limits of Integration, Improper Integrals with

Infinite Discontinuities, Volume of an Infinite Solid

Applications of Transcendental Integrals • Video Lectures: Area and Averages, Volume, Motion, Accumulations

Derivatives of Parametric Functions • Video Lectures: Sketching Parametric Curves, Differentiating a Parametric Curve, Finding the

Slope of a Tangent Line to a Parametric Curve, Finding Horizontal and Vertical Tangents to a Parametric Curve

Integrating Parametric and Polar Functions • Video Lectures: Length of Parametric and Polar Curves, Area in Polar Coordinates, Surface Area

with a Parametric Curve


Unit 4: Separable Differential Equations and Slope Fields (~11 Days)

This unit focuses on Topic II: Derivatives of the College Board’s Calculus BC topic outline, specifically, on Equations Involving Derivatives. Students investigate differential equations and solve the equations using a technique called “separating the variables.” In addition to the topics covered in AB, BC students also learn to use Euler’s method to estimate the solution of differential equations and use logistic equations to model growth.

Slope Fields • Video Lectures: What is a Differential Equation?, Slope Fields, Conic Sections, Solving Some

Simple Differential Equations, Separating Isn’t Always the Answer

Differential Equations as Models • Video Lectures: A Field Guide to Differential Equations, English to Math, Separating the

Variables, Solving Separable Differential Equations

Euler’s Method • Video Lectures: Overall Approach, Approximating with Euler’s Method, Automating the Process

Exponential Growth and Decay • Video Lectures: A Family of Exponential Functions, Modeling Exponential Growth, Modeling

Exponential Decay, Modified Growth and Decay

Logistic Growth • Video Lectures: The Logistic Growth Equation, Modeling Logistic Growth

More Applications of Differential Equations [C4] • Video Lectures: Law of Cooling, Falling Bodies, Mixing Problems, Logistic Growth, Connections


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Unit 5: Sequences and Series (~13 Days)

This unit focuses on Topic IV: Polynomial Approximations and Series of the College Board’s Calculus BC topic outline, specifically, on Series of Constants and Taylor Series.

Sequences • Video Lectures: Sequences as Functions, Limit Laws and Squeeze Theorem, Bounded Monotonic

Sequences

Series • Video Lectures: Series and Sigma Notation, Partial Sums and Convergence, Telescoping Series,

Geometric Series and Formula

Convergence Tests • Video Lectures: Integral Test, P-Series, Alternating Series Test

More Convergence Tests • Video Lectures: Direct Comparison Test, Limit Comparison Test

Radius of Convergence • Video Lectures: Absolute Convergence, Ratio Test, Test for Divergence, Interval of Convergence

Functions Defined by Power Series • Video Lectures: Building a Library of Functions, Differentiating to Obtain Series Representations,

Integrating to Obtain Series Representations

Taylor and Maclaurin Series • Video Lectures: Taylor Polynomials, Taylor Series, Maclaurin Series

Taylor’s Theorem and Lagrange Error • Video Lectures: Error with Series, Taylor’s Theorem, Lagrange Form


Unit 6: AP Exam Prep (~6 Days)

Students review what they have learned and become more familiar with AP-type questions in preparation for the AP Exam. Students are also provided with access to previously released AP Exams for practice.

Exam Strategies • Video Lectures: T-Minus, One Day, Calculators, Multiple Choice, Free Response, Do’s and Don’ts

Review of Topics Practice Exams

• Video Lectures: How an AP Exam Score is Calculated, Rubrics, Strategies, Guesses About What Will Be on the Exam

Final Exam

Unit 7: Post-Exam Project (~15 Days)

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If there is sufficient time after the AP Exam, teachers may assign a special project. These projects provide an opportunity for students to apply Calculus tools and concepts in real-world problems.

Evidence of Required Scoring Components

Component 2a: The course provides opportunities for students to reason with definitions and theorems.

Component 2b: The course provides opportunities for students to connect concepts and processes.

Component 2c: The course provides opportunities for students to implement algebraic/computational processes.

Component 2d: The course provides opportunities for students to engage with graphical, numerical, analytical, and verbal representations and demonstrate connections among them.

Component 2e: The course provides opportunities for students to build notational fluency.

Component 2f: The course provides opportunities for students to communicate mathematical ideas in words, both orally and in writing.

Component 3b: Students have opportunities to use calculators to solve problems.

Component 3c: Students have opportunities to use a graphing calculator to explore and interpret calculus concepts.

Sample Activities

Semester A, Unit 1: The Basics

Explore Shifting and Distorting Graphs: Students use a graphing calculator to investigate families of functions (including trigonometric, power, and step functions) with the form f(x-a) and f(bx) to see how the parameters a and b affect the shape of the graph. [SC 2b, 2d, 2e, 3b, 3c]

Semester A, Unit 2: Limits and Continuity

Peer Interaction with Discussion Board: Students respond to a simplified predator-prey situation model, writing and talking about functions with limits that do not exist. [SC 2a, 2f]

Semester A, Unit 3: The Derivative

Explore: Compute the Derivative of a Function Numerically: Students use the nDeriv feature on their calculators to calculate derivatives numerically and explore the graphs of these derivatives. The problem set includes opportunities for students to demonstrate that they can use a graphing calculator to find a numerical derivative, as does the unit test. [SC 2c, 2d, 3b, 3c]

Learn, Try, Practice, and Explore the Derivative as a Function: Students watch a video lecture that covers the development of the derivative formula. Then students use the nDeriv feature on their calculators to graph the derivative of several functions and compare those graphs to hand-drawn graphs. In the problem set, students practice using the definition of derivative to fine derivatives. Students also practice working with prime and differential notation for derivatives. [SC 2a, 2b, 2c, 2d, 2e, 3b, 3c]

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Semester A, Unit 4: Rates of Change

Learn, Try, and Practice Extrema and Number Line Tests: Students connect concepts involving concavity and first and second derivatives to processes (including number line tests) for identifying maxima and minima. This is demonstrated through video lectures, practiced in problem sets, and assessed with a computer-scored quiz. [SC 2b, 2c, 2d]

Learn, Try, and Practice Rates and Derivatives: Students convert among verbal, graphical, and analytical representations of derivatives as rates. Concepts are demonstrated through video lectures, practiced in problem sets, and assessed with a computer-scored quiz. [SC 2a, 2b, 2c, 2d, 2e, 2f]

Explore Rectilinear Motion: Students gather real-world motion data and then use the data to explore the relationships between distance, velocity, and acceleration, and connect these to derivatives. [SC 2b, 2c, 2f, 3b]

Semester A, Unit 5: The Integral, Part 1

Explore Area Approximations: Students use the trapezoidal rule and Riemann sums, along with a calculator, to estimate areas under several curves. Concepts are demonstrated through video lectures, practiced in problem sets, and assessed with a computer-scored quiz. [SC 2b, 2c, 2d, 2f, 3b, 3c]

Explore the Definite Integral: Students use their calculators to calculate the sum of a sequence and apply this to calculating Riemann sums with smaller and smaller intervals. Students use the successive approximations to make conjectures about the effect of smaller intervals on the quality of the approximations. Later, students use the fnInt() function to calculate definite integrals. [SC 2b, 2c, 2d, 2f, 3b, 3c]

Semester B, Unit 1: The Integral, Part 2

Exploring the Fundamental Theorem of Calculus: Students use the fnInt() function on their calculators to discover the relationship between the definite integral and the antiderivative. They then make conjectures about how to calculate the definite integral of power functions. [SC 2a, 2b, 2d, 2e, 2f, 3c]

Learn, Try, and Practice Definite Integrals of Composite Functions: Students interpret interval and integral notation and use integral notation to show the steps to evaluate integrals. Concepts and skills are demonstrated through video lectures, practiced in problem sets, and assessed with a computer-scored quiz. [SC 2a, 2c, 2e]

Semester B, Unit 2: Applications of Integrals

Learn, Try, and Practice Volumes of Revolution: Students use disks and washers to set up integrals representing volumes of solids created by rotating a function about an axis. Then they use these integrals to calculate the volumes. Concepts and skills are demonstrated through video lectures, practiced in problem sets, and assessed with a computer-scored quiz. [SC 2b, 2d]

Peer Interaction: Volumes of Revolution: Students create a solid from cross sections made of cardboard and calculate the volume of the sum of the cross sections. Students then model the smoothed version of their solid and discuss how well the cross-sections estimate the volume of the smoothed version. [SC 2b, 2f]

Semester B, Unit 3: Transcendental and Parametric Functions

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Learn, Try, and Practice Partial Fractions: Students use the method of partial fractions to decompose and find integrals of rational functions. Concepts and skills are demonstrated through video lectures, practiced in problem sets, and assessed with a computer-scored quiz. [SC 2a, 2b, 2c, 3b]

Semester B, Unit 4: Simple ODEs

Learn, Try, and Practice Euler’s Method: Students use Euler’s method with various step sizes to approximate the solutions of various differential equations. Students also use concavity to determine whether an approximation yields an over- or under-estimate. Concepts and skills are demonstrated through video lectures, practiced in problem sets, and assessed with a computer-scored quiz. [SC 2b, 2c, 2d, 2e, 2f, 3b, 3c]

Semester B, Unit 5: Sequences and Series

Learn, Try, and Practice Radius of Convergence: For various power series, students determine the center of the series and determine its radius or interval of convergence. Students then use properties of convergence to determine whether certain power series converge or not for given parameter values. Concepts and skills are demonstrated through video lectures, practiced in problem sets, and assessed with a computer-scored quiz. [SC 2a, 2b, 2c]

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Textbook Resources Semester A If textbooks are updated with new editions, page number references may change.

Unit 1: The Basics

Topic Stewart text Finney text Larson text

Pre-Calculus Review

Practice: Diagnostic Tests pp. xxiv–xxv, #1–10 all; p. xxvi, #1–5 all; p. xxvii, #1–7 all; p. xxviii, #1–9 all

Practice: pp. 56–57, #1–43 odd, 53–61 odd

Practice: Review Exercises pp. 37–38, #1–49 odd; Problem Solving pp. 39–40, #1–15 odd

Introduction to Calculus

Read: pp. 1–8

Practice: p. 8, #1–9 all

Read: Calculus at Work on pp.181, 319, 376, 430, 529

Read: pp. 41–46


Function Basics

Read: pp. 10–15

Practice: pp.19–22, #1–13 all, 23, 31–45 odd, 63

Read: pp. 12–15, Examples 1–3

Practice: p. 19, #1–19 odd, 35–39 odd

Read: pp. 19–22

Practice: pp. 27–28, #1–8 all, 13–43 odd

Combining Functions

Read: pp. 39–40


Practice: p. 21, #71; p. 28, #47

Read: pp. 24–25

Practice: pp. 27–30, #9–12 all, 97; p. 38, #45

Composite and Inverse Functions

Read: pp. 40–41; pp.384–387

Practice: p. 43, #31–51 odd; p. 390, #1–31 odd

Read: pp. 17–18, Examples 7–8; pp. 37–40, Examples 1–2

Practice: p. 20, #51–53 all; p. 44, # 1–23 odd

Read: p. 25; pp. 343–347

Practice: p. 28, #59–65 all; p. 349, #1–35 odd

Graphical Symmetry

Read: pp. 17–19

Practice: pp. 22–23, #69–79 odd

Read: pp. 15–16, Example 4


Read: pp. 2–6; p. 26

Practice: p. 8, #29–57 odd; p. 29, #69–75 all

Patterns in Graphs

Read: pp. 36–39

Practice: p. 42, #1–23 odd

Read: p. 17, Example 7


Read: p. 23


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Unit 2: Limits and Continuity


Introduction

Read: pp. 50–52

Practice: pp. 59–60, #1–12 all


Practice: p. 66, #1–4

Read: pp. 48–49

Practice: pp. 54–55, #2–22 even

Finding Limits

Analytically

Read: pp. 62–67

Practice: pp. 69–71, #1–9 all, 11–33 odd, 47; Challenge: 58


Practice: pp. 66–67, #5–28 all; Challenge: 50–51

Read: pp. 59–64

Practice: pp. 67–68, #1–37 odd, 42–52 even, 65–69 odd

Asymptotes as Limits

Read: pp. 56–58; pp. 223–231

Practice: p. 61, #29–37 all; pp.234–235, #1–6 all, 7–29 odd, 33–37 odd


Practice: p. 76, #1–7 odd, 13–33 odd

Read: pp. 83–87; pp. 198–200

Practice: pp. 88–89, #1–12 all, 13–23 odd, 34–42 even; Challenge: 69; p. 205, #1–12 all

Relative Magnitudes

for Limits

Practice: pp. 234–235, #10, 12, 26, 34, 36


Practice: p. 76, #35–40 all, 39–51 odd

Read: p. 201


When Limits Do and Don’t Exist

Read: pp. 53–56

Practice: pp. 60–61, #13–26 all; Challenge: 43


Practice: pp. 66–68, #29–37 odd, 39–44 all; Challenge: 58

Read: pp. 50–51


Continuity

Read: pp. 81–83

Practice: pp. 90, #1–9 odd, 17–23 odd

Read: pp. 78–82


Read: pp. 70–73

Practice: pp. 78–81, #1–6 all, 7–13 odd, 17–23 odd, 27–43 odd, 52; Challenge: 98

Intermediate and Extreme Value Theorems

Read: pp. 89–90; pp. 198–200

Practice: p. 92, #51–58 all; pp. 204–205, #1–10 all, 11–27 odd

Read: p. 83; pp. 187–189

Practice: p. 85, #45, 46, 51; pp. 193–194, #1–10 all

Read: pp. 77–78; p. 164

Practice: pp. 80–81, #83–94 all; p. 164, #a, b

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Unit 3: The Derivative


Introduction:

Slope and Change

Read: pp. 104–106

Practice: pp. 110–111, #1–15 odd, 34–38 even, 42, 44

Read: pp. 87–88

Practice: p. 92, #1–6 all, 8; Challenge: 33

Read: pp. 96–97


Derivative at a Point

Read: pp. 107–110

Practice: pp. 111–112, #17–31 odd, 47, 51

Read: pp. 88–91

Practice: pp. 92–93, #7–15 odd, 19, 25, 27

Read: pp. 98–99


The Derivative

Read: pp. 114–120

Practice: pp. 122–124, #1–21 odd, 25–27 odd, 32–34 even

Read: pp. 99–104

Practice: pp. 105–107, #1–11 odd, 21, 24, 29

Read: pp. 99–103

Practice: pp. 104–105, #11–21 odd, 27, 37, 57; Challenge: 64

Power Rule

Read: pp. 126–130, 133–134; pp. 140–143

Practice: pp. 136–138, #1–5 odd, 9–13 odd, 21, 47–49 odd, 66; Challenge: 76-77; pp. 146, # 1–2, 26

Read: pp. 116–119, 121–122; pp. 141–142; pp. 161–162

Practice: pp. 124–125, #1–11 odd, 25, 30, 32; Challenge: 49; p. 146, #1, 3; p. 162, #31–34 all

Read: pp. 107–114

Practice: pp. 115–117, #1–2, 4–30 even, 31, 38, 39–45 odd, 55, 59, 63; Challenge: 87–92 all

Sum, Differences, Products, Quotients

Read: pp. 126–136; pp. 140–146

Practice: pp. 136–139, #2, 8, 12, 18, 22, 26, 36, 50, 68; Challenge: 80; pp. 146–147, #3–15 odd, 26, 28, 31, 34

Read: pp. 116–122; pp. 141–145

Practice: pp. 124–125, #13–23 odd, 27, 31, 38, 44; Challenge: 50; pp. 146, #5–9 odd, 27

Read: pp. 111–112; pp. 119–124

Practice: p. 115, #40–54 even; p. 126, #2–18 even, 25–37 odd, 40–54 even

Graphs of Functions

and Derivatives

Read: pp. 114–115

Practice: pp. 122–124, #2–14 even

Read: pp. 101–102

Practice: p. 105, #13–16 all, 22, 24, 26–27

Practice: pp. 104–105, #39–42 all, 45–52 all

Continuity and Differentiability

Read: pp. 114–120

Practice: pp. 124–125, #35–40 all, 49–53 all

Read: pp. 109–113

Practice: p. 114, #1–16 all, 35; p. 147, #37

Read: pp. 101–103

Practice: p. 106, #89–98 all, 102–104 all

Rolle’s and Mean Value Theorems

Read: pp. 208–212


Read: pp. 196–198

Practice: pp. 202–203, #1–5 all, 7–13 all; Challenge: 46

Read: pp. 172–175

Practice: pp. 176–177, #1–10 all, 12–30 every third problem, 31–35 all, 37, 41, 47, 49, 50; Challenge: 60

18

Unit 3: The Derivative (continued)


Higher-Order Derivatives

Read: pp. 120–122

Practice: p. 125, #45-48 all

Read: pp. 122–123

Practice: pp. 124–125, #33–36 all, 47

Read: p. 125

Practice: pp. 128–129, #93–107 odd, 111–116 all, 119, 135–136

Concavity

Read: pp. 213–220


Read: pp. 207–209


Read: pp. 190–194

Practice: p. 195, #5–11 odd, 17–21 odd, 27, 31

Identifying Functions

and Derivatives

Read: pp. 114–122

Practice: p. 125, #41–44 all; p. 137, #59–64 all

Practice: pp. 215–217, #30, 49–50

Practice: p. 138, #101–104 all; p. 187, #59–70 all; p. 196, #61–64 all

Chain Rule

Read: pp. 148–153

Practice: pp. 154–155, #1–6 all, 9–45 every third problem, 47, 57, 63; Challenge: 65

Read: pp. 148–152

Practice: pp. 153–154, #1–8 all, 9–39 every third problem, 63; Challenge: 56

Read: pp. 130–136

Practice: pp. 137–139, #1–6 all, 9–36 every third problem, 45–80 every fifth problem, 109; Challenge: 112

Implicit Differentiation

Read: pp. 157–161

Practice: pp. 161–163, #3–39 every third problem; Challenge: 57

Read: pp. 157–160

Practice: pp.162–163, #1–43 odd; Challenge: 54

Read: pp. 141–145

Practice: pp. 146–147, #1–15 odd, 18–27 every third problem, 33, 36, 45, 48, 53

Unit 4: Rates of Change


Introduction Practice: p. 220, #5–6 Practice: p. 215, #21–24 all Practice: p. 186, #2–8 even; p. 195, #2–4 even

Extrema

Read: pp. 198–204; pp. 213–220

Practice: pp. 204–205, #1–6 all, 7, 9, 12–60 every fourth problem; pp. 221–222, #10–18 even, 21–35 odd; Challenge: 49

Read: pp. 187–192; pp. 198–201; pp. 205–214

Practice: pp. 193–194, #1–10 all, 12–28 even, 37–41 odd; pp. 202–203, #15–28 all; p. 215, #1–6 all, 25–29 odd, 34–42 even

Read: pp. 164–168; pp. 179–185; pp. 190–194

Practice: pp. 169–170, #3–45 every third problem, 55–59 odd; pp. 186–187, #1–7 odd, 12–48 every fourth problem; pp. 195–197, #1–3 odd, 8–52 every fourth problem; Challenge: 82

20

Unit 4: Rates of Change (continued)


Optimization

Read: pp. 250–256

Practice: p. 256, 1–13 odd, 21, 23, 35, 38, 48; Challenge: 55

Read: pp. 219–225

Practice: pp. 226–229, #1–11 odd, 12–27 every third problem, 30; Challenge: 38

Read: pp. 218–222

Practice: pp. 223–225, #1–27 odd; Challenge: 38

Tangent and Normal

Lines




Practice: pp. 105–106, #17–20 all; p. 146, #21–23 all, 29


BC—Tangents to Polar Curves

Read: pp. 683–685

Practice: p. 688, # 55–63 all



Read: pp. 735–736


Tangent Line

Approximation

Read: pp. 183–185

Practice: pp. 187–188, #1–10 all, 24–28 even; Challenge: 42

Read: pp. 233–235

Practice: pp. 242–244, #1–3 all, 5–14 all; Challenge: 45

Read: p. 235

Practice: pp. 240–241, #1–6 all, 47–48; Challenge: 52

Rates and Derivatives

Read: pp. 164–173

Practice: pp. 173–175, #11–23 odd, 29, 31; Challenge: 25

Read: pp. 127–134

Practice: pp. 135–138, #1–5 all, 25–29 all, 34

Practice: pp. 118, #107– 108, 110; pp. 127–128, #83–87 all; Challenge: 91

Related Rates

Read: pp. 176–180

Practice: pp. 180–182, #3–36 every third problem

Read: pp. 246–250

Practice: pp. 251–253, #3–30 every third problem

Read: pp. 149–153

Practice: 154–157, #1–9 odd, 12–33 every third problem, 43; Challenge: 52

Rectilinear Motion

Read: pp. 164–166

Practice: p. 173, # 1–10 all

Read: pp. 128–133

Practice: pp. 136–137, #9–23 odd, 24; Challenge: 18

Read: pp. 113–114; p. 125

Practice: pp. 117–118, #97–104; Challenge:105; p. 129, #117–119 all; p. 189, #89–93 odd

BC—Motion with Vector

Functions

Not Available Read: pp. 538–543

Practice: 545–546, #27–36 all, 45; Challenge: 49

Read: pp. 764–771

Practice: p. 774, #91, 93, 94

21

Unit 5: The Integral, Part 1


Introduction and Foundations

Read: pp. 291–292

Practice: p. 294, #14

Read: pp. 263–265



Riemann Sums

Read: pp. 284–293

Practice: pp. 293–294, #1–8 all, 13, 16–18 all

Read: pp. 263–269

Practice: pp. 270–271, #1–6 all, 9, 11, 15, 17, 23

Read: pp. 259–264

Practice: pp. 267–268, #1–9 odd, 18–20 all, 27–35 odd, 41–43 all

Area Approximations

Read: pp. 530–533

Practice: pp. 540–541, #3a, 7a, 9a, 15a, 29a

Read: pp. 306–308

Practice: p. 312, #1(a, b)–6(a, b), 7–9 all, 12

Read: pp. 311–312

Practice: pp. 316–317, #1–9 odd (only apply Trapezoid Rule), 46a, 52–53

The Definite Integral

Read: pp. 295–303

Practice: pp. 306–307, #1–11 odd, 17–20 all, 26, 29–30, 33, 36, 40

Read: pp. 274–282

Practice: pp. 282–283, #1–31 odd, 47, 49

Read: pp. 271–275


Properties of Integrals

Read: pp. 303–306

Practice: p. 308, #42–64 even

Read: pp. 285–286

Practice: pp. 290–291, #1–7 all

Read: pp. 276–278

Practice: pp. 279–280, #34–48 even, 65–70 all; Challenge: 52

Graphing Calculator:

Integration

Practice: p. 307, #14–15 Read: p. 281

Practice: p. 283, #33, 36; p. 291, #11, 14

Practice: p. 281, #61, 64

Applications of

Accumulated Change

Read: pp. 373–375

Practice: pp. 375–376, #15–16

Read: pp. 286–287


Read: p. 286


Antiderivatives

Read: pp. 269–273

Practice: pp. 273–275, #1–19 odd, 24–40 every fourth problem, 43, 45, 51–57 odd; Challenge: 70

Read: pp. 200–201

Practice: p. 203, #29–38 all, 43–44

Read: pp. 248–255

Practice: pp. 255–257, #1–14 all, 16–48 every fourth problem, 60, 64–65, 71–75 odd

Composite Functions

Read: pp. 330–333


Read: pp. 331–337

Practice: pp. 337–339, #1–12 all, 16–64 every fourth problem

Read: pp. 297–302

Practice: pp. 306–307, #1–6 all, 8–40 every fourth problem, 48–72 every fourth problem

22

Textbook Resources Semester B

Unit 1: The Integral, Part 2


Fundamental Theorem of Calculus

Practice: pp. 309–310, Discover Project: #1–4 all

Practice: p. 289, Exploration 2: #1–4 all, 6–8 all

Practice: p. 296, Section Project: a–d all

More of the

Fundamental Theorem

Read: pp. 310–317; pp. 321–326

Practice: pp. 318–319, #1–6 all, 8–54 every fourth problem; pp. 327–328, #43–63 odd

Read: pp. 294–302

Practice: pp. 302–303, #1–19 odd, 21, 25, 27–47 odd, 58; Challenge: 64

Read: pp. 282–292

Practice: pp. 293–295, #3–33 every third problem, 35, 41, 46, 55, 57, 63, 65, 75–87 odd; Challenge: 66

Definite Integrals of

Composite Functions

Read: pp. 330–334

Practice: pp. 335–336, #1–6 all, 8–32 every fourth problem, 35, 39, 43, 56; Challenge: 60

Read: pp. 331–337

Practice: pp. 337–338, #1–15 odd, 18–24 even, 27–63 every third problem

Read: pp. 297–304

Practice: pp. 306–307, #8–36 every fourth problem, 48–72 every fourth problem, 91–101 odd, 115, 118

Analyzing Functions

and Integrals

Read: pp. 334–335

Practice: pp. 336, #41, 46, 55

Read: pp. 288–290


Read: p. 305

Practice: p. 308, #103–110 all, 112

Unit 2: Applications of Integrals


Read: pp. 344–348 Read: pp. 390–394 Read: pp. 448–453

Introduction & Area Between Curves

Practice: p. 349, #1–11 odd, 15–39 every third problem; Challenge: 42

Practice: pp. 395–397, #1–13 odd. 16–40 every fourth problem;

Practice: pp. 454–457, #1–17 odd, 21–36 every third problem, 38, 42,

Challenge: 48 46–47, 49, 53, 60; Challenge: 97

More Areas Practice: p. 350, #48–54 all Practice: pp. 396–397,

#41, 43, 49 Practice: pp. 455–456, #61–70 all; Challenge: 93; p. 517, #3

23

Unit 2: Applications of Integrals (continued)


Volumes of Revolution

Read: pp. 352–358; pp. 363–366

Practice: pp. 360–361, #3–42 every third problem; Challenge: 45–46; pp. 366–367, #1–7 odd, 3–27 every third problem, 33, 37, 39; Challenge: 36

Read: pp. 399–403

Practice: pp. 406–409, #1–9 odd, 12–36 every fourth problem; Challenge: 53

Read: pp. 458–463; pp. 469–473

Practice: pp. 465–467, #2–10 all, 11–25 odd, 32, 34, 40, 57, 59, 65; Challenge: 68; pp. 474–476, #2–14 even, 15–33 every third problem, 37, 46, 59

Cross Sections

Read: pp. 358–360


Read: pp. 403–404


Read: pp. 463–464

Practice: p. 468, #71–76 all; Challenge: 79

BC—Arc Length

Read: pp. 562–567

Practice: pp. 567–568, #1–7 odd, 8–10 all, 19–23 odd, 31; Challenge: 32

Read: pp. 412–415

Practice: pp. 416–417, #1–17 odd, 22, 25, 27

Read: pp. 478–481

Practice: pp. 485–488, #1–10 all, 15, 18–22 even, 27, 34, 36; Challenge: 65

More Rectilinear Motion

Read: pp. 346–347, Example 4

Practice: pp 349–350, #43–47 all; p. 376, #16

Read: pp. 379–383

Practice: p. 386, #1–6 all, 9, 11, 12–17 all, 19


Other Applications of Definite Integrals

Read: pp. 369–371; pp. 373–375; pp. 569– 574; pp. 576–578; pp. 587–590; pp. 592–597

Practice: pp. 371–372, #3–27 odd; pp. 375–376, #1–17 odd; pp. 574–575, #1–2, 5–11 odd, 15, 18, 33; Challenge: 28; pp. 584–585, #1–17 odd; pp. 590–591, #2–12 even; Challenge: 19; pp. 597–598, #1–15 odd

Read: pp. 383–385; p. 405; pp. 419–424

Practice: pp. 386–387, #21–22, 25, 29; Challenge: 27; p. 409, #55–62 all; pp. 425–427, #3–27 every third problem; Challenge: 31

Read: pp. 482–484; pp. 489–494; pp. 509–512

Practice: pp. 486–488, #37–47 odd, 55, 59, 65; pp. 495–496, #1–29 odd; pp. 513–514, #2–26 even, 29

Unit 3: Inverse and Transcendental Functions


Read: pp. 384–389 Read: pp. 37–40; Read: pp. 343–348

Introduction and Derivatives of Inverses

Practice: pp. 390–391, #1–16 all, 17–33 odd, 36–42 even

pp. 49–51; pp. 165–166

Practice: p. 44, #1–10 all, 16–24 even; Challenge: 45;

Practice: pp. 349–350, #1–7 odd, 9–12 all, 15–39 every third problem,

p. 53, #25–42 all; 41, 43, 49, 51, 63, 66, 71, p. 170, #28 75, 81, 83; Challenge: 100

24

Unit 3: Inverse and Transcendental Functions (continued)


Inverse Trig Functions

Read: pp. 453–459

Practice: pp. 459–461, #1–10 all, 12–16 even, 23–27 odd, 31, 33, 39–40, 49, 59–69 odd; Challenge: 48

Read: pp. 166–169

Practice: p. 170, #1–29 odd; Challenge: 33

Read: pp. 373–378

Practice: pp. 379–381, #3–33 every third problem, 43, 45, 51, 53, 57, 62–63, 65, 73, 75, 81, 97, 99; Challenge: 102

Logarithmic and Exponential Review

Read: pp. 446–448

Practice: p. 428, #1–14 all; p. 434, #1–26 all; p. 456, #1–5 all, 8–10 all

Read: pp. 22–25; pp. 40–43

Practice: pp. 26–28, #2–12 even, 13–18 all, 19–25 odd, 29, 31, 38; Challenge: 39; p. 44, #11–12, 33–42 all, 46–48 all; Challenge: 49

Read: pp. 352–353; p. 363

Practice: p. 331, #7–10 all, 11–37 odd; p. 358, #4–24 every fourth problem, 25–31 all; p. 368, #4, 8, 12, 15–18 all, 21–25 odd, 31

Transcendentals and 1/x Practice: p. 429: #85 Not Available Practice: p. 331, #1–2

Derivatives of Logs and Exponents

Read: pp. 421–425; pp. 429–433; pp. 437–443

Practice: p. 428, #17–45 odd, 49–50, 61–64 all; p. 435, #33–51 odd; p. 444, #25–41 odd

Read: pp. 172–178

Practice: pp. 178–179, #2–28 even, 33–41 odd, 43–48 all

Read: pp. 324–330; pp. 354–355; pp. 362–367

Practice: pp. 331–333, #48–76 even, 83–85 all, 102–106 even, 111–114 all; p. 359, #39–59 odd, 69, 73; p. 368, #41–61 odd, 67, 70

BC—L’Hôpital’s Rule

Read: pp. 469–477

Practice: pp. 477–478, #1–5 odd, 8–64 every fourth problem, 75, 79; Challenge: 81

Read: pp. 444–450

Practice: pp. 450–451, #1–29 odd, 33–51 every third problem

Read: pp.569–575

Practice: pp.576–578, #1–9 odd, 12–64 every fourth problem, 72, 74, 79, 89; Challenge: 94

Analysis of Transcendental Curves

Practice: p. 428, #47–48, 55–60 all; p. 435, #53–54, 56, 67–75 all; p. 445, #43; Challenge: 62

Read: pp. 87–91

Practice: p. 92, #3–4; p. 96, #37–38; pp. 178– 179, #29–32 all, 49–53 all; p. 194, #11–14 all; pp. 215–216, #4, 12–13, 37–38; p. 228, #26; Challenge: 28

Practice: pp. 331–333, #43–46 all, 77–81 odd, 87–88, 91–95 odd, 115; Challenge: 119; pp. 358– 360, #37, 62–68 even, 71, 79–85 odd; Challenge: 90, 93; pp. 368–369, #63, 66, 71, 73

Integrating Transcendental

Functions

Read: pp. 426–427; p. 434; p. 440, Example 3

Practice: p. 429, #65–74 all; p. 436, #81–92 all; p. 445, #45–50 all; p. 461, #60–70 all

Practice: p.291, #21, 29; p. 303, #53; p. 312, #4; pp. 337–338, #9–10, 29, 33, 39–45 odd

Read: pp. 334–339; pp. 356–357; p. 365, Example 4

Practice: pp. 340–341, #3–24 every third problem, 27–39 odd, 54–60 even; p. 360, #99–115 odd; p. 369, #75–85 odd

25

Unit 3: Inverse and Transcendental Functions (continued)


BC—Partial Fractions

Read: pp. 508–516

Practice: pp. 516–517, #1–6 all, 7–29 odd, 39–40; Challenge 53

Read: pp. 362–364

Practice: pp. 369–371, #1–18 all, 47

Read: pp. 554–560

Practice: pp. 561–562, #1–6 all, 7–21 odd, 25, 29; Challenge: 51

BC—Integration by Parts

Read: pp. 488–492

Practice: pp. 492–493, #2–3, 6–8 all, 13, 23, 28, 37, 39, 45–47 all

Read: pp. 341–344

Practice: pp. 346–347, #1, 4, 5, 8, 11–15 odd, 25–26, 33

Read: pp. 527–532

Practice: pp. 533–535, #5–6, 9–10, 25–31 odd, 51, 60, 67, 69, 84; Challenge: 113

BC—Improper Integrals

Read: pp. 543–550

Practice: pp. 551–552, #1 (a, b, d), 2 (a–c), 3, 5, 11, 15, 27, 29, 31, 33, 45, 63

Read: pp. 459–467

Practice: pp. 467–468, #2–4 all, 5–15 odd, 25, 27, 32–38 even

Read: pp. 580–586

Practice: pp. 587–588, #1–3 all, 6–12 all, 19, 21, 35–39 odd, 43, 49, 55–56

Applications of Transcendental Integrals

Practice: p. 429, #76–79 all; p. 436, #93–96 all, 99–100; p. 445, #51–52

Read: pp. 350–356; pp. 379–385

Practice: pp. 357–358, #15–28 all; p. 386, #7, 21; p. 397, #47, 54–55; p. 409, #65, 68; p. 416, #10; p. 425, #4

Read: pp. 362, 366–367, Examples 1, 6–7

Practice: pp. 341–342, #72, 74, 77, 83, 99; p. 361, #140, 142; pp. 369–371, #87, 95–97 all, 101, 106–107; Challenge: 111; pp. 454–455, #35, 51–52; p. 466, #25, 27–28, 35–38 all, 49; pp. 474–475, #13, 28, 36; pp. 485–486, #11–14 all, 23–24, 32

BC—Derivatives of Parametric Functions

Read: pp. 660–665; pp. 669–671

Practice: pp. 665–666, #3–30 every third problem; p. 675, #1–5 odd, 9–11 odd, 15–17 odd, 24, 29

Read: p. 151; pp. 531–532

Practice: pp. 153–154, #41–50 all; p. 535, #1–15 odd, 23, 25

Read: pp. 711–716; pp. 721–723

Practice: p. 718, #1, 3–42 every third problem; p. 727, #1–3 all, 6–39 every third problem

BC—Integrating Parametric and Polar

Functions

Read: pp. 669–674; pp. 689–692

Practice: pp. 675–676, #1–19 odd, 21–33 every third problem, 37–45 odd, 51, 57–63 odd; pp. 692–693, #1–21 odd, 24–48 every third problem; Challenge: 44

Read: pp. 531–535; pp. 552–554

Practice: pp. 535–536, #7–25 odd, 28–34 even; Challenge: 36; p. 558, #39–42 all, 45–57 every third problem; Challenge: 60a

Read: pp. 721–726; pp. 741–746

Practice: pp. 727–729, #1–17 odd, 19, 23, 27, 32–60 every fourth problem, 67–75 odd; Challenge: 61; pp. 747– 748, #1–15 odd, 20–48 every fourth problem, 55–61 odd, 67, 69, 77; Challenge: 79

26

Unit 4: Simple ODEs


Introduction and Slope

Fields

Read: pp. 604–608; pp. 609–613

Practice: pp. 608–609, #1–8 all, 11–13 all; pp. 616–617, #1–14 all, 18

Read: pp. 321–325

Practice: pp. 327–329, #1–10 all, 11–17 odd, 25–28 all, 29, 33, 35–40 all, 49–52 all

Read: pp. 406–409

Practice: pp. 411–412, #3–27 every third problem, 30, 32, 42–51 every third problem, 53–61 all, 63

Differential Equations

as Models

Read: pp. 618–621

Practice: p. 624, #1–18 all, 19–23 odd

Read: p. 350


Read: p. 415; pp. 423–424

Practice: p. 420, #1–23 odd; p. 431, #3–27 every third problem

BC—Euler’s Method

Read: pp. 613–615


Read: pp. 325–327

Practice: pp. 328–329, #41–48 all, 53–54

Read: p. 410


Exponential Growth

and Decay

Read: pp. 446–449; pp. 450–451

Practice: p. 452, #1–5 all, 8–11 all; p. 453, #18–20 all

Read: pp. 351–354

Practice: pp. 357–359, #15–18 all, 19–27 odd; Challenge: 36

Read: pp. 416–419

Practice: pp. 420–422, #25–55 odd, 64, 71

BC—Logistic Growth

Read: pp. 629–636

Practice: pp. 637–639, #1–9 odd, 15, 17; Challenge: 13

Read: pp. 362–368


Read: pp. 429–430


More Applications of Differential Equations

Read: pp. 449–450; pp. 622–627

Practice: pp. 452–453, #13–16 all; pp. 625–626, #43–48 all

Read: pp. 354–356

Practice: pp. 358–359, #30–33 all

Read: p. 419; pp. 434–437

Practice: p. 422, #73–74; pp. 440–441, #3–33 every third problem, 37–38

Unit 5: Sequences and Series


BC—Sequences

Read: pp. 714–723

Practice: pp. 724–725, #1–2, 3–81 every third problem

Read: pp. 435–440

Practice: pp. 441–442, #1–43 odd, 45–48 all

Read: pp. 596–603

Practice: pp. 604–606, #1–13 odd, 15–22 all, 25–115 every fifth problem

BC—Series

Read: pp. 727–734

Practice: pp. 735–736, #1–13 odd, 15–63 every third problem, 69

Read: pp. 473–476


Read: pp. 608–613

Practice: pp. 614–616, #1–17 odd, 19–24 all, 25–105 every fifth problem

27

Unit 5: Sequences and Series (continued)


BC—Convergence Tests

Read: pp. 738–744; pp. 746–750;

Practice: pp. 744–745, #3–27 every third problem, 29, 31, 36; p. 750, #1–35 odd

Read: pp. 504–506; pp. 513–516


Read: pp. 619–622; pp. 626–629

Practice: pp. 622–624, #5–95 every fifth problem; pp. 630–631, #1, 3–48 every third problem

BC—More Convergence Tests

Read: pp. 746-750; pp. 751-755; 756-761; pp. 763-764

Practice: p. 750, #1-2, 3-30 every third; p. 755, #1-29 odd, 32, 34; pp.761–762, #1–35 odd; pp. 764-765, #3–36 every third problem

Read: pp. 506-508; pp. 515-519, 521


Read: pp. 628–629; pp. 633-638; pp. 641-646

Practice: pp. 630-631, #15–28 all, 37; pp. 638– 639, #7-67 every third problem; pp. 647–649, #1, 3, 5–10 all, 15-105 every fifth problem

BC—Radius of Convergence

Read: pp. 767–769

Practice: pp. 769–770, #1–2, 3–33 odd

Read: pp. 503–510

Practice: p. 511, #1–2, 3–51 every third problem

Read: pp. 661–667

Practice: pp. 668–669, #5–9 odd, 12–45 every third problem, 49–52 all, 65

BC—Functions Defined by Power Series

Read: pp. 765–767, Examples 1–3; pp. 770–775

Practice: pp. 775–776, #1–2, 3–31 odd, 34

Read: pp. 476–480

Practice: pp. 481–483, #27–35 all, 55–63 odd, 64

Read: pp. 661–662, Example 1; pp. 671–675

Practice: p. 668, #1–4 all; pp. 676–677, #1–23 odd, 29, 31–34 all 35, 39, 45

BC—Taylor and Maclaurin

Series

Read: pp. 777–788

Practice: pp. 789–790, #1–4 all, 3–69 every third problem

Read: pp. 484–491


Read: pp. 650–655; pp. 678–686

Practice: pp. 658–659, #1–4 all, 5–29 odd, 33,37,41; pp. 687–688, #4–48 every fourth problem, 53–56 all, 57–75 every third problem

BC—Taylor’s Theorem

and Lagrange Error

Read: pp. 792–795

Practice: pp. 798–799, #1–9 odd, 13–29 odd

Read: pp. 495–499

Practice: pp. 500–501, #1–10 all, 13–23 odd, 27, 29, 34

Read: pp. 656–657

Practice: pp. 659–660, #45–59 odd

AP® Calculus BC - Wisconsin Virtual School document outlines the topics and subtopics that are covered in each ... Quiz, which is a computer ... Composite Functions, Composite Domains,

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