Syllabus for AP Calculus BC Fall 2015

Size: px
Start display at page:

Download "Syllabus for AP Calculus BC Fall 2015"

Transcription

1 Syllabus for AP Calculus BC Fall 2015 Mr. Hadley Approach: I use a multirepresentational approach, The Rule of Five, to teach the concepts of calculus. I present topics graphically, numerically, analytically, verbally, and in writing, and emphasize the connections between them. The students learn to work with functions presented in each of the five ways and understand the connections between them. I emphasize learning the language of calculus and insist that my students communicate using the correct terminology in writing and orally when they ask questions and discuss their problem solving strategies. Technology: Each student has at least a TI83+ or TI84+. I use Geo-sketchpad, PowerPoint, Podcasts and applets from websites for teaching purposes. The students are taught four basic calculator capabilities and use technology regularly to solve problems, experiment, interpret results and support conclusions. Major Assignments and Assessments: Students have homework for each topic and must show their work. When we discuss the homework problems in class, the students write their Solutions on the board and explain their work. We discuss the concepts involved and alternate problemsolving methods. They have several quizzes and a test in each unit, and a final exam at the end of the semester. The exam and tests are made up of both multiple choice and free response questions from previous AP exams. AP problem sets are assigned as homework and as projects several times each semester. Students are allowed to work with a partner and also get help from me. Students are assigned weekly journal problems and or questions. They are required to write about concepts, procedures and their solutions. Textbook: Single Variable Calculus: Early Transcendentals Rogawkski, W.H Freeman and Company, 2008 Single Variable Calculus: Early Transcendentals 7E, Stewart, Brooks/Cole, 2012 Other Instructional Materials: Calculus, Graphical, Numerical, Algebraic, Finney, Demanna, Waits, Kennedy, Pearson Prentice Hall, 2007 Calculus Concepts and Applications Foerster, Key Curriculum Press, 2005 Calculus: Anton, Bivens, and Davis, Anton Textbooks, 2002 Concepts and Calculators in Calculus, Best, Carter, and Crabtree, Venture Publishing, 1997 Calculus of a Single Variable Larson, Edwards, and Hostetler, Houghton Mifflin 2006 AP Calculus AP Test Prep Series Finney, Demanna, Waits, Kennedy, Pearson Prentice Hall, 2007

2 AP Calculus BC Grading Categories Functions and Limits 15% Unit 1 AP Exam Prep 10% Derivatives 25% SLO 10% Units 2-3 Integrals 25% Final Exam 5% Units 4-5 Polynomial approximations and series/parametric, vector, and polar 10% Units 6-7 Expectations Be on time. Respect teachers, other students and their property. Follow the rules as stated in the SCHS Student Handbook. No grooming, food or drinks in the classroom - water is acceptable. The class room should remain clean. Unit 1 Functions, Graphs and Limits Review of functions Limits Continuity Intermediate Value Theorem Use the TI84 to graph functions in an arbitrary viewing windows and find zeros of functions Estimate limits from tables and graphs Find limits algebraically Find onesided limits Find nonexistent limits Apply properties of limits Describe a function s asymptotic behavior in terms of limits involving infinity Determine continuity at a point and on an interval Identify types of discontinuity Apply the Intermediate Value Theorem Text: Single Variable Calculus: Early Transcendentals Rogawkski: Chapter 1 and 2 Calculus: by Larson (Chapter 1)

3 Unit 2 Derivatives Concept of The Derivative Computing Derivatives Derivative at Point Derivative as Function Second Derivative Approximate average rate of change and instantaneous rate of change (including average velocity and instantaneous velocity) from graphs and tables Use a difference quotient to approximate a derivative at a point & Compute the value of a derivative at a point using the definition of f '(a), the limit of a difference quotient Estimate the derivative from graphs and tables Apply the rules for derivatives of polynomial, exponential and trigonometric functions Apply the rules for derivatives of sums, products, and quotients of functions Apply the Chain Rule Determine if a function is continuous and differentiable at a point, and the relationship between continuity and differentiability Solve particle motion problems involving position, velocity, acceleration, speed, and total distance traveled Use the TI84 to compute the derivative numerically Find a derivative of a function using the definition of f '(x) Find equations of tangent lines and normal lines Recognize graphs that have points at which there are vertical tangents or no tangents Find a linear approximation of f at a point and use it to approximate f at another value Interpret the meaning of a derivative as an instantaneous rate of change Translate equations involving derivatives into verbal descriptions (in sentence form) and vice versa Interpret the second derivative as a rate of change of a rate of change Compare relative magnitudes of functions and their rates of change Apply the relationships between differentiability and continuity Text: Single Variable Calculus: Early Transcendentals Rogawkski: Chapter 3 Supplementary Problems from Calculus by Anton Problems from Calculus by Best Demonstration of derivative at a point using technology such as Geo-Sketchpad Game Students work in groups to match graphs of f and f ' PowerPoint Graphs of functions are projected using PowerPoint. Students draw the graphs of the derivatives, and then the derivative graphs are projected for comparison. Calculus by Larson (2.3, 2.4, 5.1, 5.2, 5.4) Given graphs of functions, students calculate slopes at several points, then draw the graphs of the derivatives and predict the derivative formulas Demonstration for derivatives of exponential functions using technology such as TIinteractive or Geo-Sketchpad

4 Unit 3 Applications of Derivatives Extreme Values Graphing Second Derivatives Optimization Related Rates Linearization Use the sign of f ' to determine the increasing, decreasing behavior of f and to determine if f is monotonic Use the sign of f " to determine the concavity of f Find derivatives of logarithmic and inverse trigonometric functions Use implicit differentiation to find and apply rates of change of implicitly defined functions Use implicit differentiation to find the derivative of an inverse function Solve related rates problems and explain the solution using a sentence and units Determine if a function satisfies the conditions of the Extreme Value Theorem Find critical points of a function Find extreme values of functions (local and global) and where they occur Apply First and Second Derivative Tests to determine local extrema Analyze graphs of f ' and f " as aids in sketching a graph of f Use a graph or sign chart of f ' as an aid in determining increasing and decreasing behavior of f. Use a graph or sign chart of f " as aids in determining concavity of f and inflection points Relate inflection points of f, the local extrema of f ', and the change in sign of f " Apply Rolle's Theorem and the Mean Value Theorem Apply L'Hospital's Rule Use derivatives to analyze families of functions Solve optimization problems Find a linear approximation of f at a point and use it to approximate f at another value Text: Single Variable Calculus: Early Transcendentals Rogawkski: Chapter 4 Calculus by Larson (5.1, 5.2, 5.8, 2.5, 2.6) Given graphs of functions, students calculate slopes at several points, then draw the graphs of the derivatives and predict the derivative formulas Student Presentations Each homework problem on related rates is presented by one student who writes his solution on a transparency and explains it to the class. The other students then ask questions and offer alternative strategies. Calculus by Larson (Chapter 3, 7.7) Game students work in groups matching graphs of f, f ' and f "

5 Unit 4 Definite Integrals Interpretations of Definite Integrals Properties of Definite Integrals Numeric Approximations to Definite Integrals The Fundamental Theorem of Calculus Techniques for finding antiderivatives Compute Riemann sums using left, right, and midpoint evaluation points Use Riemann sums and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically and by tables of values. Given a table or graph of the rate of change of a quantity, approximate the change in the quantity Approximate distance traveled using velocity tables and graphs Solve application problems by setting up an approximating Riemann sum and representing its limit as a definite integral Define the definite integral as a limit of Riemann sums Identify the relationship between graphs of f and f ' and sketch the graph of f given f ' Use the FTC to compute values of f, given f ' Find antiderivatives that follow directly from derivatives of basic functions Determine Antiderivatives by substitution of variables (including change of limits definite integrals), parts, and simple partial fractions (nonrepeating linear factors only). Calculate Improper integrals (as limits of definite integrals). Apply the properties of antiderivatives Use the Fundamental Theorem of Calculus to evaluate definite integrals and to find area Find specific antiderivatives using initial conditions Find distance and velocity from acceleration with initial conditions Use the FTC to represent a particular antiderivative and analytically and graphically analyze the functions so defined Apply the Second Fundamental Theorem of Calculus Use the definite integral to compute area Use the TI84 to compute definite integrals numerically Use the definite integral of the rate of change of a quantity over an interval to find the change in the quantity over the interval Use sentences to explain the meaning of a definite integral and give units Use the definite integral to compute distance traveled by a particle along a line Find the average value of a function using the definite integral Text: Variable Calculus: Early Transcendentals Rogawkski: Chapter 5 Calculus by Larson Supplementary problems from Calculus by Anton Students use a program on the Nspire (TI84) to find Reimann sums and the trapezoidal sums and the corresponding graphs for large values of n to help them visualize and understand the limit definition of the definite integral Students fill a region below a function s graph with dried beans, then smooth out the beans to form a rectangle whose height approximates the average value of the function Supplementary problems from Calculus by Best

6 Unit 5 Applications of Integrals Techniques for finding Antiderivatives Initial Condition Problems Differential Equations Integral as net change over time Areas of regions between curves Volumes of solids with known cross-sections Volumes of solids of revolution including disc and washer method Use integrals to calculate net change and total accumulation Find areas of regions between curves using horizontal or vertical representative rectangles Use definite integrals to find volumes of solids with known cross sections Use definite integrals to find volumes of solids of revolution using discs and washers Use Riemann sums to approximate volume given a table of values Find antiderivatives by Chain Rule for Integration and by u substitution of variables Find integrals that lead to inverse trig functions Find definite integrals by substitution including change of limits Write a differential equations that model a given statement Solve logistic differential equations and use them in modeling. Use slope fields to interpret differential equations geometrically and relate slope fields and solution curves for differential equations Find Numerical solution of differential equations using Euler s method. Apply L Hospital s Rule, including its use in determining limits and convergence of improper integrals Text: Variable Calculus: Early Transcendentals Rogawkski: Chapter 6, 7, 8 and 9 Calculus, Graphical, Numerical, Algebraic, Finney: Chapter 6 Problems from Calculus by Best Slope Fields Lab TI 84 programs Calculus by Larson Slopefields handout from College Board Students practice drawing slope fields, matching slope fields to differential equations, and matching slope fields to solutions of differential equations. Game Students work in groups to match slope field graphs with their equations and a written description of the solution. Calculus by Larson ( ) CD "Tools for Enriching Calculus" by Stewart to help students visualize the solids Applet on volumes of solids at and at Students build solids with a given cross section and base from materials such as clay

7 Unit 6 Polynomial Approximations and Series Concept of Series Series of Constants Taylor Series Application and Skills: Manipulate Taylor series to create new series Determine Convergence and divergence of series Utilize Taylor polynomial approximation with graphical demonstration of convergence Solve problems for Maclaurin series and the general Taylor series centered at x = a. Understand Maclaurin series for the functions ex, sin x, cos x, and 1/(1-x). Manipulate Taylor series and shortcuts to compute Taylor series, including substitution, differentiation, antidifferentiation and the formation of new series from known series. Utilize Functions defined by power series. Calculate the Radius and interval of convergence of power series. Understand Lagrange error bound for Taylor polynomials. Use Technology to explore convergence and divergence. Understand decimal expansion using series Understand Geometric series with applications. Understand The harmonic series. Understand Alternating series with error bound. Understand that Terms of series as areas of rectangles and their relationship to improper integrals, including the integral test and its use in testing the convergence of p-series. Understand the ratio test for convergence and divergence. Compare series to test for convergence or divergence. Apply L Hospital s Rule, including its use in determining limits and convergence of improper integrals Text: Variable Calculus: Early Transcendentals Rogawkski: Chapter 8.4 and 10 Resouces:

8 Unit 7 Parametric, polar and vector functions. Compute of derivatives of Parametric, polar and vector functions Analyzing planar curves Applications of derivatives in parametric form, polar form and vector form, including velocity and acceleration Applications and skills Calculate derivatives of parametric, polar and vector functions Find arc length of parametric curves Differentiate and integrate vector valued functions Calculate slopes, lengths and areas inside polar curves Text: Variable Calculus: Early Transcendentals Rogawkski: Chapter 11 Vectors: AP Curriculum Module Unit 8 Review for AP Exam

Syllabus for AP Calculus AB Spring 2015

Syllabus for AP Calculus AB Spring 2015 Syllabus for AP Calculus AB Spring 2015 Mr. Hadley michael.hadley@cobbk12.org Approach: I use a multirepresentational approach, The Rule of Five, to teach the concepts of calculus. I present topics graphically,

More information

Correlation with College Board Advanced Placement Course Descriptions

Correlation with College Board Advanced Placement Course Descriptions Correlation with College Board Advanced Placement Course Descriptions The following tables show which sections of Calculus: Concepts and Applications cover each of the topics listed in the 2004 2005 Course

More information

B L U E V A L L E Y D I S T R I C T C U R R I C U L U M & I N S T R U C T I O N Mathematics AP Calculus BC

B L U E V A L L E Y D I S T R I C T C U R R I C U L U M & I N S T R U C T I O N Mathematics AP Calculus BC B L U E V A L L E Y D I S T R I C T C U R R I C U L U M & I N S T R U C T I O N Mathematics AP Calculus BC Weeks ORGANIZING THEME/TOPIC CONTENT CHAPTER REFERENCE FOCUS STANDARDS & SKILLS Analysis of graphs.

More information

AP Calculus BC. Functions, Graphs, and Limits

AP Calculus BC. Functions, Graphs, and Limits AP Calculus BC The Calculus courses are the Advanced Placement topical outlines and prepare students for a successful performance on both the Advanced Placement Calculus exam and their college calculus

More information

I. AP Calculus AB Major Topic: Functions, Graphs, and Limits

I. AP Calculus AB Major Topic: Functions, Graphs, and Limits A.P. Calculus AB Course Description: AP Calculus AB is an extension of advanced mathematical concepts studied in Precalculus. Topics include continuity and limits, composite functions, and graphing. An

More information

AP Calculus BC Scope & Sequence

AP Calculus BC Scope & Sequence AP Calculus BC Scope & Sequence Grading Period Unit Title Learning Targets Throughout the School Year First Grading Period *Apply mathematics to problems in everyday life *Use a problem-solving model that

More information

Advanced Placement Calculus II- What Your Child Will Learn

Advanced Placement Calculus II- What Your Child Will Learn Advanced Placement Calculus II- What Your Child Will Learn Upon completion of AP Calculus II, students will be able to: I. Functions, Graphs, and Limits A. Analysis of graphs With the aid of technology,

More information

Radnor High School Course Syllabus Advanced Placement Calculus BC 0460

Radnor High School Course Syllabus Advanced Placement Calculus BC 0460 Radnor High School Modified April 24, 2012 Course Syllabus Advanced Placement Calculus BC 0460 Credits: 1 Grades: 11, 12 Weighted: Yes Prerequisite: Recommended by Department Length: Year Format: Meets

More information

Topics Covered in Calculus BC

Topics Covered in Calculus BC Topics Covered in Calculus BC Calculus BC Correlation 5 A Functions, Graphs, and Limits 1. Analysis of graphs 2. Limits or functions (including one sides limits) a. An intuitive understanding of the limiting

More information

CHINO VALLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL GUIDE CALCULUS BC ADVANCED PLACEMENT

CHINO VALLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL GUIDE CALCULUS BC ADVANCED PLACEMENT CHINO VALLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL GUIDE CALCULUS BC ADVANCED PLACEMENT Course Number 5125 Department Mathematics Prerequisites Successful completion of Honors Pre-Calculus or Trigonometry

More information

AP Calculus B C Syllabus

AP Calculus B C Syllabus AP Calculus B C Syllabus Course Textbook Finney, Ross L., et al. Calculus: Graphical, Numerical, Algebraic. Boston: Addison Wesley, 1999. Additional Texts & Resources Best, George, Stephen Carter, and

More information

AP Calculus AB Syllabus

AP Calculus AB Syllabus AP Calculus AB Syllabus Overview AP Calculus AB is comparable to a calculus course in a college or university. Students are expected to seek college credit and/or college placement from colleges or universities

More information

Prentice Hall. Calculus: Graphical, Numerical, Algebraic National Advanced Placement Course Descriptions for Calculus BC.

Prentice Hall. Calculus: Graphical, Numerical, Algebraic National Advanced Placement Course Descriptions for Calculus BC. Prentice Hall Grades 9-12 Calculus: Graphical, Numerical, Algebraic 2007 C O R R E L A T E D T O National Advanced Placement Course Descriptions for Calculus BC Grades 9-12 I Functions, Graphs, and Limits

More information

Notes about changes to Approved Syllabus # 43080v2

Notes about changes to Approved Syllabus # 43080v2 Notes about changes to Approved Syllabus # 43080v2 1. An update to the syllabus was necessary because of a county wide adoption of new textbooks for AP Calculus. 2. No changes were made to the Course Outline

More information

AP Calculus BC Syllabus

AP Calculus BC Syllabus AP Calculus BC Syllabus Course Overview AP Calculus BC is the study of the topics covered in college-level Calculus I and Calculus II. This course includes instruction and student assignments on all of

More information

Calculus Graphical, Numerical, Algebraic 2012

Calculus Graphical, Numerical, Algebraic 2012 A Correlation of Graphical, Numerical, Algebraic 2012 To the Advanced Placement (AP)* AB/BC Standards Grades 9 12 *Advanced Placement, Advanced Placement Program, AP, and Pre-AP are registered trademarks

More information

*AP Calculus BC (#9550)

*AP Calculus BC (#9550) AASD MATHEMATICS CURRICULUM *AP Calculus BC (#9550) Description This course is an in-depth development and extension of the concepts of calculus that were introduced to the students in Introduction to

More information

Calculus Graphical, Numerical, Algebraic AP Edition, Demana 2012

Calculus Graphical, Numerical, Algebraic AP Edition, Demana 2012 A Correlation of Graphical, Numerical, Algebraic AP Edition, Demana 2012 To the Advanced Placement AB/BC Standards Bid Category 13-100-40 AP is a trademark registered and/or owned by the College Board,

More information

Academic Content Standard MATHEMATICS. MA 51 Advanced Placement Calculus BC

Academic Content Standard MATHEMATICS. MA 51 Advanced Placement Calculus BC Academic Content Standard MATHEMATICS MA 51 Advanced Placement Calculus BC Course #: MA 51 Grade Level: High School Course Name: Advanced Placement Calculus BC Level of Difficulty: High Prerequisites:

More information

MIDLAND ISD ADVANCED PLACEMENT CURRICULUM STANDARDS AP CALCULUS BC

MIDLAND ISD ADVANCED PLACEMENT CURRICULUM STANDARDS AP CALCULUS BC Curricular Requirement 1: The course teaches all topics associated with Functions, Graphs, and Limits; Derivatives; Integrals; and Polynomial Approximations and Series as delineated in the Calculus BC

More information

Calculus: Graphical, Numerical, Algebraic 2012

Calculus: Graphical, Numerical, Algebraic 2012 A Correlation of Graphical, Numerical, Algebraic 2012 To the Advanced Placement (AP) Calculus AB/BC Standards Introduction The following correlation demonstrates the alignment of content between Graphical,

More information

AP Calculus BC. Course Overview. Course Outline and Pacing Guide

AP Calculus BC. Course Overview. Course Outline and Pacing Guide AP Calculus BC Course Overview AP Calculus BC is designed to follow the topic outline in the AP Calculus Course Description provided by the College Board. The primary objective of this course is to provide

More information

Topic Outline for Calculus BC

Topic Outline for Calculus BC Techniques of antidifferentiation Antiderivatives following directly from derivatives of basic functions. Antiderivatives by substitution of variables (including change of limits for definite integrals).

More information

PETERS TOWNSHIP HIGH SCHOOL

PETERS TOWNSHIP HIGH SCHOOL PETERS TOWNSHIP HIGH SCHOOL COURSE SYLLABUS: AP CALCULUS BC Course Overview and Essential Skills AP Calculus BC is a challenging class which will prepare students to take the AP Calculus BC Exam in May

More information

AP Calculus BC: Syllabus 3

AP Calculus BC: Syllabus 3 AP Calculus BC: Syllabus 3 Scoring Components SC1 SC2 SC3 SC4 The course teaches Functions, Graphs, and Limits as delineated in the Calculus BC Topic The course teaches Derivatives as delineated The course

More information

Syllabus for AP Calculus BC

Syllabus for AP Calculus BC Syllabus for AP Calculus BC Underlying Focus: The emphasis in AP Calculus is on an intuitive understanding of all concepts and the interplay between the geometric and analytic information and on the use

More information

AP Calculus BC Syllabus

AP Calculus BC Syllabus AP Calculus BC Syllabus Course Overview and Philosophy This course is designed to be the equivalent of a college-level course in single variable calculus. The primary textbook is Calculus, 7 th edition,

More information

Standards for AP Calculus AB

Standards for AP Calculus AB I. Functions, Graphs and Limits Standards for AP Calculus AB A. Analysis of graphs. With the aid of technology, graphs of functions are often easy to produce. The emphasis is on the interplay between the

More information

AP Calculus BC. Course Description:

AP Calculus BC. Course Description: AP Calculus BC Course Description: The two fundamental problems of Calculus include: 1) finding the slope of the tangent to a curve, determined by the derivative, and 2) finding the area of a region under

More information

Grading System 50% Tests and Projects, 50% Homework and Class Participation

Grading System 50% Tests and Projects, 50% Homework and Class Participation AP Calculus (AB) Grades Recommended: 11, 12 Course Code: MA 590, Ma 591 Prerequisites: MA321, MA521 Length of course: one year Description The student will study all of the topics required for the Advanced

More information

BC Calculus Syllabus. Assessment Students are assessed in the following ways:

BC Calculus Syllabus. Assessment Students are assessed in the following ways: BC Calculus Syllabus Assessment Students are assessed in the following ways: Unit tests Project Problem Sessions Weekly assignments done outside of class that consist of problems from released Quizzes

More information

MATHEMATICS AP Calculus (BC) Standard: Number, Number Sense and Operations

MATHEMATICS AP Calculus (BC) Standard: Number, Number Sense and Operations Standard: Number, Number Sense and Operations Computation and A. Develop an understanding of limits and continuity. 1. Recognize the types of nonexistence of limits and why they Estimation are nonexistent.

More information

Prentice Hall Calculus: Graphical, Numerical, and Algebraic AP* Student Edition 2007

Prentice Hall Calculus: Graphical, Numerical, and Algebraic AP* Student Edition 2007 Prentice Hall Calculus: Graphical, Numerical, and Algebraic AP* Student Edition 2007 C O R R E L A T E D T O AP Calculus AB Standards I Functions, Graphs, and Limits Analysis of graphs. With the aid of

More information

Advanced Placement AB Calculus

Advanced Placement AB Calculus Advanced Placement AB Calculus Performance Objectives and Time Table Text: Calculus, 8 th edition, by Howard Anton, Irl Bivens, Stephen Davis. John Wiley & Sons, Inc. 005 FIRST NINE WEEKS SECOND NINE WEEKS

More information

Mathematics Scope & Sequence Calculus AB

Mathematics Scope & Sequence Calculus AB Mathematics Scope & Sequence 2015-16 Calculus AB Revised: March 2015 First Six Weeks (29 ) Limits and Continuity Limits of (including onesided limits) An intuitive understanding of the limiting process

More information

Region 16 Board of Education AP Calculus Curriculum 2008

Region 16 Board of Education AP Calculus Curriculum 2008 Region 16 Board of Education AP Calculus Curriculum 2008 Course Description This course develops students understanding of the concepts of calculus and provides experience with its methods and applications.

More information

General Calculus II. Course Text. Course Description. Course Objectives. Course Prerequisites. Important Terms

General Calculus II. Course Text. Course Description. Course Objectives. Course Prerequisites. Important Terms Course Text General Calculus II Students may select any one of these texts aligned to this course: Larson, R., Hostetler, R. P., and Edwards, B. Calculus Early Transcendental Functions, 3rd edition. Houghton

More information

AP Calculus AB. Course Overview. Course Outline and Pacing Guide

AP Calculus AB. Course Overview. Course Outline and Pacing Guide AP Calculus AB Course Overview AP Calculus AB is designed to follow the topic outline in the AP Calculus Course Description provided by the College Board. The primary objective of this course is to provide

More information

Advanced Placement Calculus I - What Your Child Will Learn

Advanced Placement Calculus I - What Your Child Will Learn Advanced Placement Calculus I - What Your Child Will Learn I. Functions, Graphs, and Limits A. Analysis of graphs With the aid of technology, graphs of functions are often easy to produce. The emphasis

More information

AP Calculus BC Syllabus Course Overview

AP Calculus BC Syllabus Course Overview AP Calculus BC Syllabus Course Overview Textbook Anton, Bivens, and Davis. Calculus: Early Transcendentals, Combined version with Wiley PLUS. 9 th edition. Hoboken, NJ: John Wiley & Sons, Inc. 2009. Course

More information

AP Calculus BC Syllabus

AP Calculus BC Syllabus Instructor: Jennifer Manzano-Tackett jennifer-manzano@scusd.edu (916) 395-5090 Ext. 506308 www.mt-jfk.com AP Calculus BC Syllabus Textbook: Calculus, 6th edition, by Larson, Hostetler and Edwards: Houghton

More information

AP Calculus AB Course Outline

AP Calculus AB Course Outline AP Calculus AB Course Outline Prerequisite: Satisfactory completion of: Geometry, Algebra II, and Pre-calculus Advanced Placement Calculus AB is designed as college-level Calculus I. Students are required

More information

2007 ~ 2008 AP CALCULUS AB SYLLABUS

2007 ~ 2008 AP CALCULUS AB SYLLABUS 2007 ~ 2008 AP CALCULUS AB SYLLABUS Teacher: Mr. Leckie Room: 201 Course: AP Calculus AB Textbook: Calculus: Graphical, Numerical, Algebraic, 3 rd edition COURSE CONTENT: Calculus is the mathematics of

More information

AP Calculus AB Syllabus

AP Calculus AB Syllabus AP Calculus AB Syllabus Course Overview and Philosophy This course is designed to be the equivalent of a college-level course in single variable calculus. The primary textbook is Calculus of a Single Variable,

More information

AP Calculus AB Syllabus

AP Calculus AB Syllabus Introduction AP Calculus AB Syllabus Our study of calculus, the mathematics of motion and change, is divided into two major branches differential and integral calculus. Differential calculus allows us

More information

AP Calculus AB - Course Outline

AP Calculus AB - Course Outline By successfully completing this course, you will be able to: a. Work with functions represented in a variety of ways and understand the connections among these representations. b. Understand the meaning

More information

Unit 1: Pre-Calculus Review (2 weeks) A. Lines 1. Slope as rate of change 2. Parallel and perpendicular lines 3. Equations of lines

Unit 1: Pre-Calculus Review (2 weeks) A. Lines 1. Slope as rate of change 2. Parallel and perpendicular lines 3. Equations of lines Calculus AB Syllabus AB Course Outline The following is an outline of the topics we will cover and a typical sequence in which those topics will be covered. The time spent is only an estimate of the average

More information

COURSE OBJECTIVES LIST: CALCULUS

COURSE OBJECTIVES LIST: CALCULUS COURSE OBJECTIVES LIST: CALCULUS Calculus Honors and/or AP Calculus AB are offered. Both courses have the same prerequisites, and cover the same material. Girls enrolled in AP Calculus AB have the following

More information

HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK

HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK COURSE / SUBJECT A P C a l c u l u s ( B C ) KEY COURSE OBJECTIVES/ENDURING UNDERSTANDINGS OVERARCHING/ESSENTIAL SKILLS OR QUESTIONS Limits and Continuity Derivatives

More information

Course Syllabus BHS Room 309 (360)

Course Syllabus BHS Room 309 (360) AP Calculus Mrs. Stansbery Course Syllabus BHS Room 309 (360) 473-0875 sandra.stansbery@bremertonschools.org Classroom Expectations 1. Come to class on time and prepared to learn. Take care of locker visits,

More information

Curriculum and Pacing Guide Mr. White AP Calculus AB Revised May 2015

Curriculum and Pacing Guide Mr. White AP Calculus AB Revised May 2015 Curriculum and Pacing Guide Mr. White AP Calculus AB Revised May 2015 Students who successfully complete this course will receive one credit AP Calculus AB and will take the AP Calculus AB Exam. 1. The

More information

Instructional Unit: A. Approximate limits, derivatives, and definite integrals using numeric methods

Instructional Unit: A. Approximate limits, derivatives, and definite integrals using numeric methods Curriculum: AP Calculus AB-I Curricular Unit: Limits, Derivatives, and Integrals Instructional Unit: A. Approximate limits, derivatives, and definite integrals using numeric methods Description Section

More information

Ms. York s AP Calculus AB Class Room #: Phone #: Conferences: 11:30 1:35 (A day) 8:00 9:45 (B day)

Ms. York s AP Calculus AB Class Room #: Phone #: Conferences: 11:30 1:35 (A day) 8:00 9:45 (B day) Ms. York s AP Calculus AB Class Room #: 303 E-mail: hyork3@houstonisd.org Phone #: 937-239-3836 Conferences: 11:30 1:35 (A day) 8:00 9:45 (B day) Course Outline By successfully completing this course,

More information

CHINO VALLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL GUIDE ADVANCED PLACEMENT CALCULUS AB

CHINO VALLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL GUIDE ADVANCED PLACEMENT CALCULUS AB CHINO VALLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL GUIDE ADVANCED PLACEMENT CALCULUS AB Course Number 5124 Department Mathematics Prerequisites Successful completion of Integrated Math 3 Honors (Honors

More information

AP Calculus Curriculum Guide Dunmore School District Dunmore, PA

AP Calculus Curriculum Guide Dunmore School District Dunmore, PA AP Calculus Dunmore School District Dunmore, PA AP Calculus Prerequisite: Successful completion of Trigonometry/Pre-Calculus Honors Advanced Placement Calculus is the highest level mathematics course offered

More information

AP Calculus AB Course Description and Syllabus

AP Calculus AB Course Description and Syllabus AP Calculus AB Course Description and Syllabus Course Objective: This course is designed to prepare the students for the AP Exam in May. Students will learn to use graphical, numerical, verbal and analytical

More information

School District of Marshfield Course Syllabus

School District of Marshfield Course Syllabus School District of Marshfield Course Syllabus Course Name: AP Calculus AB Honors Length of Course: 1 Year Credit: 1 Program Goal(s): The School District of Marshfield Mathematics Program will prepare students

More information

AP Calculus AB Syllabus

AP Calculus AB Syllabus AP Calculus AB Syllabus Course Description: This is a college level course covering derivatives, integrals, limits, applications and modeling of these topics. Course Objectives: The objectives of this

More information

Houston Independent School District AP CALCULUS AB COURSE SYLLABUS

Houston Independent School District AP CALCULUS AB COURSE SYLLABUS AP Course Design and Philosophy In one high school year-long course, AP Calculus AB provides a semester or more of university-level calculus. As students of a university-level course, calculus students

More information

COURSE: AP Calculus BC GRADE: 12 PA ACADEMIC STANDARDS FOR MATHEMATICS:

COURSE: AP Calculus BC GRADE: 12 PA ACADEMIC STANDARDS FOR MATHEMATICS: COURSE: AP Calculus BC GRADE: 12 UNIT 1: Functions and Graphs TIME FRAME: 7 Days PA ACADEMIC STANDARDS FOR MATHEMATICS: M11.A.1 M11.A.1.1 M11.A.1.1.1 M11.A.1.1.2 M11.A.1.1.3 M11.A.2 M11.A.2.1 M11.A.2.1.1

More information

K-12 MATHEMATICS STANDARDS

K-12 MATHEMATICS STANDARDS MATHEMATICS To the reader: This document presents our mathematics standards through the lens of Understanding by Design. We began by identifying the important broad understandings and the essential questions

More information

NJCCCS AREA: Mathematics. North Brunswick Township Public Schools AP CALCULUS BC. Acknowledgements. Anna Goncharova, Mathematics Teacher

NJCCCS AREA: Mathematics. North Brunswick Township Public Schools AP CALCULUS BC. Acknowledgements. Anna Goncharova, Mathematics Teacher NJCCCS AREA: Mathematics North Brunswick Township Public Schools AP CALCULUS BC Acknowledgements Anna Goncharova, Mathematics Teacher Diane M. Galella, Supervisor of Mathematics Date: New Revision May

More information

Greenwich Public Schools Mathematics Curriculum Objectives. Calculus

Greenwich Public Schools Mathematics Curriculum Objectives. Calculus Mathematics Curriculum Objectives Calculus June 30, 2006 NUMERICAL AND PROPORTIONAL REASONING Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify

More information

AP Calculus BC. Course: AP Calculus BC

AP Calculus BC. Course: AP Calculus BC AP Calculus BC Course: AP Calculus BC Course Overview: This course is taught over a school year (2 semesters). During the first semester on a 90 minute mod, students cover everything in the Calculus AP

More information

Calculus. reparation for Calculus, Limits and Their Properties, and Differentiation. Gorman Learning Center (052344) Basic Course Information

Calculus. reparation for Calculus, Limits and Their Properties, and Differentiation. Gorman Learning Center (052344) Basic Course Information Calculus Gorman Learning Center (052344) Basic Course Information Title: Calculus Transcript abbreviations: calcag / calc Length of course: Full Year Subject area: Mathematics ("c") / Calculus UC honors

More information

Burlington County Institute of Technology Curriculum Document

Burlington County Institute of Technology Curriculum Document Burlington County Institute of Technology Curriculum Document Course Title: Calculus Curriculum Area: Mathematics Credits: 5 Credits per course Board Approved: June 2017 Prepared by: Jessica Rista, John

More information

Harbor Creek School District

Harbor Creek School District Unit 1 Days 1-9 Evaluate one-sided two-sided limits, given the graph of a function. Limits, Evaluate limits using tables calculators. Continuity Evaluate limits using direct substitution. Differentiability

More information

MEDFORD HIGH SCHOOL COURSE SYLLABUS. Advanced Placement Calculus AB

MEDFORD HIGH SCHOOL COURSE SYLLABUS. Advanced Placement Calculus AB MEDFORD HIGH SCHOOL COURSE SYLLABUS Department: Course Title: Mathematics Advanced Placement Calculus AB Level and/or Grade: AP; Grade 11/12 Prerequisite: B+ or better in Honors Pre-Calculus or teacher

More information

LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING AND COMPUTER SCIENCE

LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING AND COMPUTER SCIENCE LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING AND COMPUTER SCIENCE MAT 201 - CALCULUS I PRE-REQUISITES: MAT 200 (PRECALCULUS) OR ITS EQUIVALENT BY WAIVER

More information

Syllabus for BC Calculus

Syllabus for BC Calculus Syllabus for BC Calculus Course Overview My students enter BC Calculus form an Honors Precalculus course which is extremely rigorous and we have 90 minutes per day for 180 days, so our calculus course

More information

MIDLAND ISD ADVANCED PLACEMENT CURRICULUM STANDARDS AP CALCULUS AB

MIDLAND ISD ADVANCED PLACEMENT CURRICULUM STANDARDS AP CALCULUS AB Curricular Requirement 1: The course teaches all topics associated with Functions, Graphs, and Limits; Derivatives; and Integrals as delineated in the Calculus AB Topic Outline in the AP Calculus Course

More information

Calculus Graphical, Numerical, Algebraic 5e AP Edition, 2016

Calculus Graphical, Numerical, Algebraic 5e AP Edition, 2016 A Correlation of Graphical, Numerical, Algebraic 5e AP Edition, 2016 Finney, Demana, Waits, Kennedy, & Bressoud to the Florida Advanced Placement AB/BC Standards (#1202310 & #1202320) AP is a trademark

More information

AP Calculus Overview

AP Calculus Overview AP Calculus Overview 2009-2010 Month Content Skills Assessment AUG.-SEPT. PreCalc Review - Reduce Rational Expressions - edhelper worksheet - Factor and solve Quadratic equations. - TM Algebra review Graph

More information

Saxon Calculus Scope and Sequence

Saxon Calculus Scope and Sequence hmhco.com Saxon Calculus Scope and Sequence Foundations Real Numbers Identify the subsets of the real numbers Identify the order properties of the real numbers Identify the properties of the real number

More information

2013 ~ 2014 AP CALCULUS AB SYLLABUS

2013 ~ 2014 AP CALCULUS AB SYLLABUS 2013 ~ 2014 AP CALCULUS AB SYLLABUS Teacher: Mr. Leckie Room 508 Course: AP Calculus AB Textbook: Calculus: Graphical, Numerical, Algebraic, 3 rd edition COURSE CONTENT: Calculus is the mathematics of

More information

Calculus Honors Curriculum Guide Dunmore School District Dunmore, PA

Calculus Honors Curriculum Guide Dunmore School District Dunmore, PA Calculus Honors Dunmore School District Dunmore, PA Calculus Honors Prerequisite: Successful completion of Trigonometry/Pre-Calculus Honors Major topics include: limits, derivatives, integrals. Instruction

More information

AP Calculus AB UNIT 1: PRECALCULUS REVIEW UNIT 2: BRIDGE TO CALCULUS LESSON 1: INTRO TO CALCULUS LESSON 2: FUNCTIONS

AP Calculus AB UNIT 1: PRECALCULUS REVIEW UNIT 2: BRIDGE TO CALCULUS LESSON 1: INTRO TO CALCULUS LESSON 2: FUNCTIONS Advanced Placement AP Calculus AB In AP* Calculus AB, students learn to understand change geometrically and visually (by studying graphs of curves), analytically (by studying and working with mathematical

More information

Calculus BC

Calculus BC Brief Description of Course Calculus BC 2007-2008 This course covers the topics limits, continuity, differentiation, antidifferentiation, definite integrals, techniques of integration, series and sequences,

More information

Advanced Placement Calculus Syllabus- BC

Advanced Placement Calculus Syllabus- BC Advanced Placement Calculus Syllabus- BC Prerequisites All students should have completed four years of secondary mathematics designed for accelerated students. These should consist of the accelerated

More information

Honors Calculus Curriculum Maps

Honors Calculus Curriculum Maps Honors Calculus Curriculum Maps Unit of Study: Prerequisites for Calculus Unit of Study: Limits and Continuity Unit of Study: Differentiation Unit of Study: Applications of Derivatives Unit of Study: The

More information

Curriculum Catalog

Curriculum Catalog 2017-2018 Curriculum Catalog - for use with AP courses 2017 Glynlyon, Inc. Table of Contents CALCULUS COURSE OVERVIEW... 1 UNIT 1: GRAPHS AND LIMITS... 1 UNIT 2: DERIVATIVES... 2 UNIT 3: RELATED RATES...

More information

AP Calculus AB Syllabus

AP Calculus AB Syllabus AP Calculus AB Syllabus Course Overview: All topics that are listed on the AP Central website for Calculus AB will be covered in this class and are listed below in the AP Calculus AB Course Outline. The

More information

CALCULUS SEVENTH EDITION. Indiana Academic Standards for Calculus. correlated to the CC2

CALCULUS SEVENTH EDITION. Indiana Academic Standards for Calculus. correlated to the CC2 CALCULUS SEVENTH EDITION correlated to the Indiana Academic Standards for Calculus CC2 6/2003 2002 Introduction to Calculus, 7 th Edition 2002 by Roland E. Larson, Robert P. Hostetler, Bruce H. Edwards

More information

Topic Subtopics Essential Knowledge (EK)

Topic Subtopics Essential Knowledge (EK) Unit/ Unit 1 Limits [BEAN] 1.1 Limits Graphically Define a limit (y value a function approaches) One sided limits. Easy if it s continuous. Tricky if there s a discontinuity. EK 1.1A1: Given a function,

More information

HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK

HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK COURSE / SUBJECT A P C a l c u l u s ( A B ) KEY COURSE OBJECTIVES/ENDURING UNDERSTANDINGS OVERARCHING/ESSENTIAL SKILLS OR QUESTIONS Limits and Continuity Derivatives

More information

GOVERNOR LIVINGSTON HIGH SCHOOL MATHEMATICS DEPARTMENT CALCULUS, AP CALCULUS AB/BC #MAY1212/MAY1130/MAY1131

GOVERNOR LIVINGSTON HIGH SCHOOL MATHEMATICS DEPARTMENT CALCULUS, AP CALCULUS AB/BC #MAY1212/MAY1130/MAY1131 BERKELEY HEIGHTS PUBLIC SCHOOLS BERKELEY HEIGHTS, NEW JERSEY GOVERNOR LIVINGSTON HIGH SCHOOL MATHEMATICS DEPARTMENT CALCULUS, AP CALCULUS AB/BC #MAY1212/MAY1130/MAY1131 Curriculum Guide November 2011 Mrs.

More information

Calculus I Curriculum Guide Scranton School District Scranton, PA

Calculus I Curriculum Guide Scranton School District Scranton, PA Scranton School District Scranton, PA Prerequisites: Successful completion of Elementary Analysis or Honors Elementary Analysis is a high level mathematics course offered by the Scranton School District.

More information

Single Variable Calculus, Early Transcendentals

Single Variable Calculus, Early Transcendentals Single Variable Calculus, Early Transcendentals 978-1-63545-100-9 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax

More information

Wellston City Schools Calculus Curriculum Calendar

Wellston City Schools Calculus Curriculum Calendar Wellston City Schools Calculus 2006-2007 Curriculum Calendar Grading Period 1:Week 1: Review 11 th grade standards Learn to represent functions using: *Words *Tables of values *Graphs *Formulas Present

More information

AP Calculus AB. Syllabus. Course Overview and Philosophy. Course Planner:

AP Calculus AB. Syllabus. Course Overview and Philosophy. Course Planner: AP Calculus AB Syllabus Course Overview and Philosophy We cover all topics in the Calculus AB topic outline in the AP Calculus Course Description, and we also include integration by parts, shell method,

More information

TEXTBOOK: Calculus With Analytic Geometry by Roland Larson, Robert Hostetler, and Bruce Edwards; 6 th edition, 1998, Houghton ;Mifflin Company.

TEXTBOOK: Calculus With Analytic Geometry by Roland Larson, Robert Hostetler, and Bruce Edwards; 6 th edition, 1998, Houghton ;Mifflin Company. AP Calculus AB Syllabus. Kelli Gamez Warble 2009 Course Overiew COURSE FOCUS: the study of functions in a variety of representations (numerical, graphical, analytical, and verbal); the investigation of

More information

Advanced Placement Calculus AB. South Texas ISD. Scope and Sequence with Learning Objectives

Advanced Placement Calculus AB. South Texas ISD. Scope and Sequence with Learning Objectives Advanced Placement Calculus AB South Texas ISD Scope and Sequence with Learning Objectives Advanced Placement Calculus AB Scope and Sequence - Year at a Glance AP Calculus AB - First Semester Three Weeks

More information

West Windsor-Plainsboro Regional School District AP Calculus BC Grades 9-12

West Windsor-Plainsboro Regional School District AP Calculus BC Grades 9-12 West Windsor-Plainsboro Regional School District AP Calculus BC Grades 9-12 Unit 1: Limits and Continuity What is a limit? Definition of limit, continuous, Sandwich Theorem, Intermediate Value Theorem

More information

AP Calculus BC Course Syllabus. Lyn Davies. Denver School of the Arts

AP Calculus BC Course Syllabus. Lyn Davies. Denver School of the Arts AP Calculus BC 2016-17 Course Syllabus Lyn Davies Denver School of the Arts This syllabus was developed according to scoring guidelines offered by the AP Course Audit rubric for AP Calculus AB with BC

More information

Topic Outline AP CALCULUS AB:

Topic Outline AP CALCULUS AB: Topic Outline AP CALCULUS AB: Unit 1: Basic tools and introduction to the derivative A. Limits and properties of limits Importance and novelty of limits Traditional definitions of the limit Graphical and

More information

Fairfield Public Schools

Fairfield Public Schools Mathematics Fairfield Public Schools AP Calculus BC AP Calculus BC BOE Approved 04/08/2014 1 AP CALCULUS BC Critical Areas of Focus Advanced Placement Calculus BC consists of a full year of college calculus.

More information

Calculus I

Calculus I Calculus I 978-1-63545-038-5 To learn more about all our offerings Visit Knewton.com/highered Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Gilbert Strang, Massachusetts Institute

More information

Milford Public Schools Curriculum. Department: Mathematics Course Name: Calculus Course Description:

Milford Public Schools Curriculum. Department: Mathematics Course Name: Calculus Course Description: Milford Public Schools Curriculum Department: Mathematics Course Name: Calculus Course Description: UNIT # 1 Unit Title: Limits, Continuity, and Definition of the Derivative The idea of limits is important

More information

AP Calculus AB and AP. Calculus BC Exam. ApTutorGroup.com. ApTutorGroup.com SAMPLE QUESTIONS

AP Calculus AB and AP. Calculus BC Exam. ApTutorGroup.com. ApTutorGroup.com SAMPLE QUESTIONS SAMPLE QUESTIONS AP Calculus AB and AP Calculus BC Exam Originally published in the Fall 2014 AP Calculus AB and AP Calculus BC Curriculum Framework The College Board The College Board is a mission-driven

More information

Mr. Olson AP Calculus (BC) 2014 Syllabus Course Overview

Mr. Olson AP Calculus (BC) 2014 Syllabus Course Overview Mr. Olson AP Calculus (BC) 2014 Syllabus Course Overview The objective of this course is to enable students to understand and apply the concepts of calculus in a variety of situations. All students should

More information