AP Calculus BC Syllabus s1

AP Calculus BC Syllabus

COURSE OVERVIEW

The goal of this course – About 75% of the AP Calculus BC curriculum is a repeat of AP Calculus AB. However, many concepts will be intertwined with other concepts and will challenge your ability to solve equations and simplify expressions from every topic you have learned throughout your lifetime of studying mathematics. Therefore, the goal is to become experts in every area of mathematics- from basic algebra to geometry to trigonometry to calculus.

The major topics of study will include but not limited to the following: - Functions, Graphs, and Limits as delineated in the Calculus BC Topic Outline in the AP Calculus Course Description - Derivatives as delineated in the Calculus BC Topic Outline in the AP Calculus Course Description - Integrals as delineated in the Calculus BC Topic Outline in the AP Calculus Course Description - Polynomial Approximations and Infinite Series as delineated in the Calculus BC Topic Outline in the AP Calculus Course Description

The Rule of Four will be emphasized throughout the course. Our textbook embodies this philosophy where each major topic is presented four ways: 1) Graphically (using graphs to make inferences and supporting ideas and conclusions) 2) Numerically (using and analyzing tables) 3) Analytically (performing and understanding the algebra and the symbols behind the concepts) 4) Verbally (explaining and discussing concepts both orally and in writing)

CONTACT INFORMATION (541)386– 4500 ext.4651 or [email protected] Tactay’s cell number (541)399-1024 (note the last four digits is 210 )

HOW TO GET HELP You may receive help from Mr. Tactay before school starting from approximately 8:00 am, or during his Prep Per iods, 4 and 8, during lunch (arrange with Mr. Tactay first), or after school. The school website currently contains my syllabus and assignment sheets. I will also try to include all handouts and grades on the website.

REQUIRED MATERIALS

It is your responsibility to come to class prepared. It is highly recommended that you have a 3-inch BINDER and develop a system TO FILE YOUR HOMEWORK, QUIZZES, AND TESTS. TEXTBOOK and RESOURCE MATERIALS Calculus. Deborah Hughes-Hallett, Andrew M. Gleason, et al. John Wiley & Sons, Inc. 2005. Fourth Edition. Amsco’s AP* Calculus AB/BC: Preparing for the Advanced Placement Examinations. Maxine Lifshitz. Amsco School Publications. 2004. Master the AP* Calculus AB & BC Tests. W. Michael Kelly and Contributing Author, Mark Wilding. Peterson’s, a division of Thomson Learning, Inc. 2002. * AP is a registered trademark of the College Entrance Examination Board, which does not endorse these books.

ACTIVITIES and WRITING ASSIGNMENTS The use of calculators to solve problems and verify answers will be ongoing throughout the course. However, separate activities will be given to help conceptualize major ideas. Each activity below can be found in the course outline, denoted by *.

Group/Calculator Activity 1: Domain, Range, and Asymptotes You will work in groups to predict the domain, range, and asymptotes of various functions, then verify using the calculator.

Group/Calculator Activity 2: Limits You will work in groups to graphically and numerically evaluate limits using the calculator.

Calculator Activity 3: Zooming in to find the Derivative You will zoom in at a point to find the derivative using a Difference Quotient. You will then verify using Math 8.

Writing Assignment 1: The Derivative You will explain the meaning of the derivative, relating the graphical meaning of slope to the formal definition of the derivative.

Group Activity 4: Tangent Line Approximations You will work in groups to find equations of tangent lines numerically (from a table of values) and algebraically (using the short-cuts) and use them to predict values.

Group/Calculator Activity 5: Optimization - Maximizing and Minimizing You will work in groups to solve classic optimization problems. You will solve the problem first without the use of calculus by creating a table, and then verify using the graph. You will then solve the problem using calculus.

Group Activity 6: The Definite Integral and Distance Traveled You will work in groups to find the distance between two locations in town. You will record data of your velocities for three different cases – every two minutes, every minute, and then every 10 seconds. The definite integral using the trapezoid rule for the three different cases will estimate the distance traveled.

Writing Assignment 2: The Definite Integral You will explain the meaning of the definite integral, relating the graphical meaning of area to the notation of the definite integral. Group Activity 7: Find the Volume You will work in groups to find the volume of an irregular shaped figure by slicing the figure and numerically evaluating the volume using a Trapezoidal Approximation. And if possible, create an equation to create an integral expression to find the volume.

GRADING Classwork: Homework and Quizzes - These daily assignments are worth 15% of your overall grade. Each Homework is worth 8 points. Points for Quizzes will vary. Tests - Tests are worth 100 points each and will be 45% of your overall grade. They are curved according to your potential to pass the AP Exam. That is, a 90 average on tests would correlate to a potential of passing the AP Exam with a 3 score. An average in the upper 90’s would correlate to a 4. An average of over a 100 would correlate to a 5. They will be taken on scheduled dates. If you miss a test, you must make it up the day you return to class. NO EXCEPTIONS. You must make prior arrangements (before the test, not on test day) with Mr. Tactay in order to take the test on a later date. Final Exam – This makes up 40% of your overall Semester Grade.

There is NO RETESTING in this course.

Academic Honesty – Any cheating in any form, despite how small, will result in an automatic zero points.

LETTER GRADES

A 90% and above C 70% - 79.94% F less than 60% B 80% - 89.94% D 60% - 69.94%

TEST TAKING & QUIZ BEHAVIOR

Nothing is allowed on the desks during tests or quizzes except for a calculator (when allowed) and a writing utensil. Notes are not allowed. There will be absolutely NO FORM OF INTERACTION OR COMMUNICATION – VERBAL OR NONVERBAL - UNTIL EVERYONE HAS COMPLETED THE TEST. This includes talking, eye contact, passing notes, asking for pencil, paper, etc. If you need anything, raise your hand and ask Mr. Tactay. Leave your seats only to sharpen you pencil or to hand in your tests. CONSEQUENCES: Inappropriate behavior during tests will result in lunch time detention or an automatic ZERO on the test. TEST TIME LIMIT: You are to complete your tests or quizzes in the allotted time. You will be given the entire class period to complete your tests. YOU WILL NOT BE ALLOWED TO TURN IN AN UNFINISHED TEST AND COME BACK LATER TO FINISH IT.

CHAPTER TESTS & FINAL EXAM Every question on the chapter tests will be an AP style question. The first semester is devoted to mastering the multiple choice portion of the AP Exam, while the second semester will be devoted to mastering the free response portion. Each chapter test will include material from previous tests. The Final Exam will be equivalent to the entire multiple choice portion of the AP Exam. Similarly, the last chapter test in the second semester before the actual AP Exam will be comparable to the free response portion. There will be about a month remaining after the AP Exam. An additional chapter will be covered at that time. That chapter test will only have material from that chapter and will take the place of the final exam.

THE AP CALCULUS EXAM The AP Calculus Exam is on Tuesday, May 15, 2018. This is an A-Day. All topics, problems, and examples ill represent the type of knowledge, skill, and understanding you will need to be successful on the AP Calculus Exam. This exam, as well as all other AP Exams, will give you a score ranging from 1 to 5. A score of at least a 3 is considered passing by most colleges.

AP Exam 2018 Approximate costs and deadline dates.

Regular Registration: $94 per exam, ($55 per exam if on free/reduced lunch): Deadline March 9, 2018 Late Registration: $149/exam, ($55 per exam if on free/reduced lunch): Deadline March 16, 2018

AP Pre-Administration Sessions: Must attend one of the two sessions usually scheduled in late April.

Students who have school related conflicts may choose to test late (sports contests) or if a student registers for two exams on the same day and time. ($139/exam)

If you have any questions, then contact Ms. Bentley, guidance counselor.

TARDY POLICY This policy is for the entire semester and will start over for the second semester. First four tardies: no consequence. Fifth and every tardy thereafter: a discipline referral will be given for each tardy.

LEAVING CLASS It is a school policy that you use the pass (color coded lanyard) to leave class. Only one person may leave. CELL PHONES, and OTHER ELECTRONIC DEVICES IN CLASS When you arrive to class, it is school policy to place your cell phone in the appropriate pocket in the cell phone organizer. It will remain there for the entire class period or when I say that it is free time. Not following this policy will result in a REFERRAL.

All other electronic devise must be put away, OUT OF SIGHT, and TURNED OFF completely.

USING YOUR CELL PHONE OR OTHER ELECTRONIS IN CLASS AT INAPPROPRIATE TIMES WILL RESULT INA REFERRAL.

AP Calculus BC Learning Goals and Course Outline * denotes Group/Calculator activity This outline for Calculus BC includes all Calculus AB Topics.

Unit 1: Review - Functions and Graphs (2 weeks) A. Simplify, Graph, and Analyze Basic Functions and their Graphs 1. Slope and Equation of lines 2. Exponential, Logarithmic Functions, and Polynomials B. Understand the Properties and Language of Functions and Inverses * 1. Domain, Range, and Asymptotes - Group/Calculator Activity 1 2. Graphs of Inverse Functions C. Graph a Function from a Family of Functions - Translations, Reflections, and Amplitudes D. Graph, Solve, and Apply Trigonometric Functions 1. Unit Circle and Graphing 2. Solving and Applications E. Understand Properties of Limits and Evaluating Limits 1. The Concept of Limits for Finding Horizontal or Vertical Asymptotes 2. Left and Right Hand Limits 3. The Limit Definition for Continuity/Discontinuity * 4. Analyzing Limits Approaching a Finite Number and Infinity Graphically and Numerically - Group/Calculator Activity 2 F. Evaluate Limits using Algebraic Techniques 1. Limits Approaching a Finite Number 2. Limits Approaching Infinity 3. Limits of Piecewise Functions 4. Limits of Trigonometric Functions G. Understand Removable and Jump (Essential) Discontinuity 1. Graphical Analysis of Discontinuity – show on the calculator how to recognize 2. The Algebraic Relationship of the Function and the Discontinuity

Unit 2: Introduction to The Derivative (2 weeks) A. Understand the Graphical Definition of The Derivative - Slope of the Tangent Line 1. Relationship between the Derivative and its Function 2. The Derivative as the Average Rate of Change 3. Difference Quotient B. Using the Formal Definition of the Derivative 1. Recognize the Definition * 2. Find the Derivative at a Point Using the Definition - Calculator Activity 3 C. Understand, Interpret, and Apply the Derivative 1. Instantaneous and Average Velocity 2. The Meaning Behind the Units and Notations of the Derivative 3. Estimate the Derivative from a Tables of x, y Values D. Graph the Derivative of a Function E. Find the Equation of a Tangent Line 1. Use the Calculator to Find Slope at a Point 2. Estimate the Equation of a Tangent Line from a Tables of x, y Values

F. Analyze the Graph of a Function to Determine Values of the First and Second Derivatives 1. Find Critical Points from the Graph of the Function 2. Understand the Relationship between the Intervals of Increase or Decrease of the Function and the Values of the First Derivative 3. Understand the Relationship between the Intervals of Concave Up or Down of the Function and the Values of the Second Derivative 4. Sketch the First Derivative from the Behavior of the Function G. Estimate the Second Derivative from Tables of Values *H. Writing Assignment 1: The Derivative

Unit 3: Rules and Shortcuts of The Derivative (2 weeks) A. Derivatives of Powers, Polynomials, and Exponents B. Derivatives of Trigonometric Functions C. Derivatives of Natural Logs D. Derivatives of Inverse Trigonometric Functions E. Derivative using the Chain Rule F. Derivative using the Product and Quotient Rules *G. Find the Equation of a Tangent Line Using the Rules and Shortcuts for Derivatives - Group/Calculator Activity 4 H. Derivatives of an Implicit Functions

Unit 4: Application of Derivatives (3 weeks) A. Find the Critical Points of a Function Using the Short-Cuts of the Derivative 1. Use the First Derivative Test to find Local (relative) extrema 2. Classify Critical Points and Endpoints as Global (absolute) extrema B. Analyze the Graphs and Values of the First and Second Derivatives 1. Finding Intervals of Increase or Decrease of the Parent Function 2. Finding Intervals of Concave Up or Down of the Parent Function 3. Use the Second Derivative Test to Find Extrema 4. Sketch the First Derivative from the Behavior of the Function *C. Optimization - Use the Derivative and Critical Points to Solve Problems that Maximize or Minimize Physical Measurements - Group/Calculator Activity 5 D. Related Rates - Use Implicit Differentiation to Solve Problems Involving Rates of Change Over Time E. Use the Derivative to Solve Problems Involving Position, Velocity, and Acceleration of a Particle in Motion or Projectiles F. Understand Basic Derivative Theorems 1. The Extreme Value Theorem 2. Rolle’s Theorem 3. The Mean Value Theorem G. Evaluate Limits using L’Hôpital’s Rule (BC topic) H. Slope Fields (BC topic) I. Numerical solution of differential equations using Euler's Method (BC topic)

Unit 5: The Definite Integral (2 weeks) A. Understand the Graphical Definition of the Definite Integral 1. Approximate the Area Under a Curve Using Riemann Sums a. Left- and Right-Hand Sums b. Midpoint Rule 2. Approximate the Area Under Using the Trapezoid Rule *B.Group Activity 6

C. Use the Short-Cuts to Find the Antiderivatives or Indefinite Integrals of Power Functions D. Apply The Fundamental Theorem of Calculus 1. Calculate the Definite Integral 2. Interpret the Meaning of the Definite Integral of Rates (eg. Velocity, Gallons per minute, Population per year, etc.) 3. Find the Area Under the Curve of a Function a. Interpret that Area as the Total Change of its Antiderivative b. Use that Area to Graph the Antiderivative 4. Given a Rate, find the accumulated change in the Antiderivative E. Use the Definite Integral to Find the Average Value of a Function (BC topic) *F. Writing Assignment 2: The Definite Integral

Unit 6: More on The Definite Integral (2 weeks) A. Integrate Exponential, Natural Logarithmic, and Trigonometric Functions B. Integrate by u-Substitution (BC topic) C. Solve Differential Equations by Separation of Variables D. Integration by Parts (BC topic) E. Partial Fractions (BC topic) F. Trigonometric Substitution for powers of sine and cosine G. Improper Integrals (BC topic)

Unit 7: Applications The Definite Integral (2 weeks) A. Common Applications 1. Income Stream 2. Density 3. Work B. Find the Area Between Two Functions (BC topic) C. Find the Volumes of Solids of Revolution 1. Disk Method 2. Washer Method D. Find the Volumes of Solids with Known Cross Sections Perpendicular to the x-axis or y-axis E. Solving logistic differential equations and using them in modeling (BC topic) *F. Group Activity 7

Unit 8: Parametric and Polar Functions (3 Weeks) all BC Topics A. Graphing Parametric and Polar Functions B. Analysis of planar curves given in parametric and polar forms C. Analysis of velocity and acceleration vectors D. Derivatives of parametric, polar, and vector functions E. Find the Area bounded by polar functions F. Intersection of Polar Curves G. Area in Polar Coordinates H. Parametric Equations and Curves I. Tangents with Parametric Equation J. Arc Length and Surface Area with Parametric Equation

Unit 9: Vector Calculus (3 weeks) all BC Topics A. Graphing and Analysis of Vector Functions B. Cartesian Space Coordinates C. Analysis of velocity and acceleration vectors D. Derivatives of vector functions E. Displacements and Forces F. The Dot Product G. Lines H. Planes I. The Cross Product

Unit 10: Sequences and Series (3 Weeks) all BC Topics A. Sequences B. Series Convergence and Divergence C. Geometric Series with applications D. Harmonic Series E. Motivating examples, including decimal expansion F. Alternating series with error bound G. Integral Test and its use in testing the convergence of p -series H. Comparison/Limit Comparison Test for Convergence and Divergence I. Ratio Test for Convergence and Divergence J. Root Test for Convergence and Divergence

Unit 11: Taylor Series (2 Weeks) all BC Topics A. Taylor Polynomial Approximation B. Maclaurin Series and the general Taylor Series 1 C. Maclaurin Series for e x , sin x, cos x, and . 1  x D. Functions defined by Power Series E. Radius and Interval of Convergence for Power Series F. Lagrange Error Bound for Taylor Polynomials The AP Exam Tuesday, May 5, 2018, A-Day

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