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

Save this PDF as:

Size: px
Start display at page:

Transcription

1 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. 2. Explain why lim f ( x) = f ( a) defines continuity and vice versa. x a 3. Apply the theorem "differentiability implies continuity" properly when analyzing a function. 4. Rewrite the limit of a Riemann Sum as a definite integral. 5. Analyze the convergence of sequences of real numbers. 6. Determine whether the convergence of a series is absolute or conditional. 7. Recognize the types of nonexistence of limits and why they are nonexistent. * Pertains only to the BC Curriculum

2 Standard: Measurement Measurement Units A. Explain differences among accuracy, precision and error, and describe how each of those can affect solutions in measurement 1. Use differentials for error approximation. 2. Ensure that all decimal answers remain accurate to 3 places throughout the solution of a multi-step problem. Measurement Unit, Use Measurement Techniques and Tools B. Estimate and compute length, area, and volume in increasingly complex problem 1. Find the area under a curve on an interval using the definite integral. 2. Find the area between two curves on an interval using the definite integral. 3. Evaluate an antiderivative as the accumulation of area under a given function. F( x) = x 0 f ( t) dt 4. Find the volume of a solid of revolution about the x-axis, the y-axis, or line parallel to either axis. 5. Find the volume of a solid with known cross sections. *6. Find the area bounded by polar curves. Use Measurement Techniques and Tools *7. Find the length of a path (including parametrically-defined curves). C. Demonstrate fluency in alternative coordinate systems. *1. Convert between polar and rectangular coordinates. *2. Manipulate/graph vector functions *3. Manipulate/graph parametric equations. *4. Manipulate/graph polar equations.

3 Standard: Measurement Measurement Units D. Solve problem situations involving derived measurements. 1. Record the correct units of measure on each application problem (e.g. ft/min, gal/sec 2 ).

4 Standard: Patterns, Algebra Analyze Change A. Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior. 1. Evaluate functions whose limit at certain x- values is k. 2. Analyze the roots of the derivative to find the critical numbers of f(x). 3. Analyze f '(x) to find the slope of a curve and the equation of the tangent to the curve at a point. 4. Analyze the zeros and values of f '(x) on intervals to find the absolute and relative maximums and minimums of f(x). 5. Analyze the values of f '(x) to find where f(x) is increasing or decreasing. 6. Analyze the zeros and values of f ''(x) to find the points of inflection and concavity of f(x). 7. Analyze the first and second derivatives of the position function to find the velocity and acceleration functions, respectively. 8. Evaluate f (c) to find the instantaneous rate of change of f(x) at x = c. 9. Evaluate antiderivatives to find distance and velocity from acceleration with initial conditions. 10. Analyze the definite integral to find the average value of a function on an interval.

5 Standard: Patterns, Algebra Analyze Change 11. Find solutions to growth and decay problems by solving ky dx Algebraic Representations B. Apply methods to represent, generalize and solve problem 1. Evaluate a limit in indeterminate form by rewriting the function using algebraic manipulation to create an equivalent function. 2. Evaluate a limit at infinity by dividing every term by the highest-powered term in the denominator. 3. Identify and solve for the equation(s) of any asymptotes of the graph of a function. 4. Solve optimization problems by analyzing the derivative. 5. Apply the method of finding a derivative using implicit differentiation. 6. Solve related rates problems using implicit differentiation. 7. Apply the technique of integration by substitution (change of variables) to find the integral. 8. Find the integral using the technique of separable differential equations. *9. Find motion on a plane curve using velocity and acceleration vectors.

6 Standard: Patterns, Algebra Algebraic Representations B. Apply methods to represent, generalize and solve problem *10. Find the tangent line to parametrically defined curves. *11. Find the work required with either force or displacement as a variable. *12. Solve and apply logistic differential equations. *13. Find the integral using the technique of trig substitution. *14. Find the integral using the technique of integration by parts. *15. Find the integral using the technique of integration by partial fractions (only linear factors in the denominator). *16. Evaluate geometric, alternating, and p-series types of special series. *17. Manipulate power series by addition, substitution, termby-term differentiation and integration. *18. Find the radius of and interval of convergence of a power series.

7 Standard: Patterns, Algebra Algebraic Representations C. Apply formulas and theorems appropriately to problem 1. Apply formulas developed via the Squeeze Theorem where applicable to find limits. 2. Apply the Intermediate Value Theorem to find a zero. 3. Apply the Power Rule to solve for the derivative of a polynomial. 4. Apply formulas for the derivatives of the six trigonometric ratios. 5. Apply the Product Rule to find the derivative of the product of two or more functions. 6. Apply the Quotient Rule to find the derivative of the quotient of two functions. 7. Apply the Chain Rule to find the derivative of composite functions. 8. Solve for the value at which the instantaneous rate of change is the same as the average rate of change on an interval using the Mean Value Theorem. 9. Employ established rules and techniques to find the derivatives of inverse functions (including logarithmic, exponential, and trigonometric functions). 10. Approximate the value of the definite integral using rectangles (Riemann Sum) and trapezoids (Trapezoidal Rule).

8 Standard: Patterns, Algebra Algebraic Representations C. Apply formulas and theorems appropriately to problem 11. Evaluate a definite integral using the Fundamental Theorem of Calculus. 12. Evaluate the derivative using the Second Fundamental Theorem of Calculus. 13. Employ basic integration formulas to find the antiderivative. 14. Find the volume of a solid of revolution using the Disc/Washer Method. 15. Find the volume of a solid of revolution using the Shell Method. 16. Find the volume of a solid using the method of Known Cross Sections. *17. Find the numerical solution of differential equations using Euler's Method. *18. Determine the convergence of improper integrals using l'hopital's Rule. *19. Find the convergence of a series by employing the comparison test, ratio test, root test, l'hopital's Rule and/or the integral test. *20. Use Maclaurin series expansion to represent and e x. 1, sin(x), 1 x *21 Represent a function using a Taylor series.

9 Standard: Patterns, Algebra Algebraic Representations C. Apply formulas and theorems appropriately to problem Algebraic Representations, Analyze Change *22 Represent functions using Taylor polynomials with remainder and Lagrange error approximation. D. Analyze and compare functions and their graphs. 1. Evaluate limits by inspecting the graph of the function. 2. Evaluate limits at infinity as the value of a horizontal asymptote. 3. Demonstrate the understanding of the derivative as the slope of a curve at a point. 4. Describe the characteristics of a function based on the analysis of its first and second derivatives. 5. Sketch a precise graph of f(x) by inspecting the graphs of f '(x) and f ''(x). 6. Estimate the instantaneous rate of change of f(x) at a point on the graph of f(x). 7. Evaluate differential equations by looking at their Slope Fields and vice versa. *8. Sketch the graph of a parametrically defined curve. *9. Sketch the graph of a curve defined in polar coordinates. *10.Sketch the graph of a vector function.

10 Standard: Data Analysis and Probability Data Collection E. Demonstrate expertise with the graphing calculator. 1. Visually compare the graphs of f(x), f '(x), and f ''(x) to describe the impact of each upon the other. 2. Find roots, intersection, extremes, slope at a point, and area under the curve for any function. 3. Explore the direction, extremes, concavity, and inflection points of a function. Data Collection, Statistical Methods A. Create and analyze tabular and graphical displays of data using appropriate tools, including spreadsheets and graphing calculators. *4. Explore the convergence or divergence of a graph of f(x). 1. Construct a scatter plot to analyze and interpret a table of data. 2. Estimate the limit of a function by analyzing a table of values of f(x). 3. Estimate the instantaneous rate by analyzing a table of values of f(x). 4. Estimate the area under a curve by analyzing a table of values of f(x).

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.

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

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

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

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,

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

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

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

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

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

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:

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

*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

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

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

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

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

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

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

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

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,

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,

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

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

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

AP Calculus BC Lesson Outlines Third Quarter: January 5 March 11, 2016

Jan. 6 The Calculus of Integration CH 4.3 (Review from before the break) Riemann Sums, Definite Integrals CH 4.4 (Review from before the break) First Fundamental Theorem CH 4.4 Mean Value Theorem for Integrals

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

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

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

Syllabus for AP Calculus BC Fall 2015

Syllabus for AP Calculus BC Fall 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,

Due Date: Thursday, March 22, 2018

The Notebook Project AP Calculus AB This project is designed to improve study skills and organizational skills for a successful career in mathematics. You are to turn a composition notebook into a Go To

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

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,

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.

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

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

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

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

CHAPTER 1 Prerequisites for Calculus 2. CHAPTER 2 Limits and Continuity 58

CHAPTER 1 Prerequisites for Calculus 2 1.1 Lines 3 Increments Slope of a Line Parallel and Perpendicular Lines Equations of Lines Applications 1.2 Functions and Graphs 12 Functions Domains and Ranges Viewing

AP CALCULUS AB Study Guide for Midterm Exam 2017

AP CALCULUS AB Study Guide for Midterm Exam 2017 CHAPTER 1: PRECALCULUS REVIEW 1.1 Real Numbers, Functions and Graphs - Write absolute value as a piece-wise function - Write and interpret open and closed

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

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

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

Curriculum Map: Mathematics

Curriculum Map: Mathematics Course: Calculus Grade(s): 11/12 Unit 1: Prerequisites for Calculus This initial chapter, A Prerequisites for Calculus, is just that-a review chapter. This chapter will provide

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

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

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

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).

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.

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

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,

Review for Final. The final will be about 20% from chapter 2, 30% from chapter 3, and 50% from chapter 4. Below are the topics to study:

Review for Final The final will be about 20% from chapter 2, 30% from chapter 3, and 50% from chapter 4. Below are the topics to study: Chapter 2 Find the exact answer to a limit question by using the

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

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

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

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

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

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

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

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

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

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

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,

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

Learning Objectives for Math 166

Learning Objectives for Math 166 Chapter 6 Applications of Definite Integrals Section 6.1: Volumes Using Cross-Sections Draw and label both 2-dimensional perspectives and 3-dimensional sketches of the

MATH 100 and MATH 180 Learning Objectives Session 2010W Term 1 (Sep Dec 2010)

Course Prerequisites MATH 100 and MATH 180 Learning Objectives Session 2010W Term 1 (Sep Dec 2010) As a prerequisite to this course, students are required to have a reasonable mastery of precalculus mathematics

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.

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

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,

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

Index. Excerpt from "Calculus" 2013 AoPS Inc. Copyrighted Material INDEX

Index #, 2 \, 5, 4 [, 4 - definition, 38 ;, 2 indeterminate form, 2 22, 24 indeterminate form, 22 23, see Euler s Constant 2, 2, see infinity, 33 \, 6, 3, 2 3-6-9 triangle, 2 4-dimensional sphere, 85 45-45-9

AP* Calculus Free-response Question Type Analysis and Notes Revised to include the 2013 Exam By Lin McMullin

AP* Calculus Free-response Question Type Analysis and Notes Revised to include the 2013 Exam By Lin McMullin General note: AP Questions often test several diverse ideas or concepts in the same question.

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...

Learning Objectives for Math 165

Learning Objectives for Math 165 Chapter 2 Limits Section 2.1: Average Rate of Change. State the definition of average rate of change Describe what the rate of change does and does not tell us in a given

Varberg 8e-9e-ET Version Table of Contents Comparisons 8th Edition 9th Edition Early Transcendentals 9 Ch Sec Title Ch Sec Title Ch Sec Title 1 PRELIMINARIES 0 PRELIMINARIES 0 PRELIMINARIES 1.1 The Real

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

Calculus Early Transcendentals

Calculus Early Transcendentals 978-1-63545-101-6 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Gilbert Strang, Massachusetts

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

Quick Review Sheet for A.P. Calculus Exam

Quick Review Sheet for A.P. Calculus Exam Name AP Calculus AB/BC Limits Date Period 1. Definition: 2. Steps in Evaluating Limits: - Substitute, Factor, and Simplify 3. Limits as x approaches infinity If

CW High School. Calculus/AP Calculus A

1. Algebra Essentials (25.00%) 1.1 I can apply the point-slope, slope-intercept, and general equations of lines to graph and write equations for linear functions. 4 Pro cient I can apply the point-slope,

Fairfield Public Schools

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

Math 121 Calculus 1 Fall 2009 Outcomes List for Final Exam

Math 121 Calculus 1 Fall 2009 Outcomes List for Final Exam This outcomes list summarizes what skills and knowledge you should have reviewed and/or acquired during this entire quarter in Math 121, and what

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

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

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

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

How do limits demonstrate the dynamic nature of Calculus? How will the three processes confirm the uniqueness of a limit?

WDHS Curriculum Map: created by Andrea Kappre Course: Honors Calculus March 2012 Time Interval/ Content Standards/ Strands Essential Questions Skills Assessment Unit 1: Limits Sections 2-1 -2-5 F-IF.7.

Calculus Early Transcendentals

Calculus Early Transcendentals 978-1-63545-101-6 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Gilbert Strang, Massachusetts

Calculus Early Transcendentals

Calculus Early Transcendentals 978-1-63545-101-6 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Gilbert Strang, Massachusetts

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,

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

Review Guideline for Final

Review Guideline for Final Here is the outline of the required skills for the final exam. Please read it carefully and find some corresponding homework problems in the corresponding sections to practice.