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AP Calculus BC Syllabus

2016-2017

Mrs. Kayla Smith

Planning Hour: 12:38-1:52

Tutoring Times: MTWHF 7:00-7:15 MTHF 3:10-4:00

Phone: 502-839-5118 E-mail: kayla.smith@anderson.kyschools.us

Website:

Course Overview

My main objective in Teaching AP Calculus BC is to provide students with an opportunity to explore the higher levels of mathematics. Through this exploration and interaction with mathematics I hope to enable students to appreciate the higher intricacies of problems, and develop a solid foundation in the Calculus BC topic outline as it appears in the AP Calculus Course Description, which they can take with them into their higher level classes. I expect a lot of my students, whether that is in class in discussion and group work time, or at home writing up assignments and AP sample problems.

Textbook

Calculus of a Single Variable AP Edition, Ninth Edition. Larson & Edwards. Published by Brooks/Cole, Cengage Learning.

Prerequisites

Pre-AP Algebra II, Pre-AP Pre-Calculus, and AP Calculus AB (Completing the course with a B or better).

Required Materials

• Graphing Calculator (TI-84 preferred; TI-83 permitted)

• 3 Ring Binder

• Loose Leaf Paper

• Required Text

• Supplemental Review Materials (provided)

Goals (Adapted from the AP Calculus Course Description)

• Students should be able to work with functions numerically, graphically, analytically, and verbally.

• The derivative should be understood as the instantaneous rate of change of a function and as the local linear approximation of the function.

• The definite integral should be understood as the limit of a Riemann Sum and as the net accumulation of a rate of change.

• The relationship between derivatives and the definite integral should be understood in terms of both parts of the Fundamental Theorem of Calculus.

• Students learn to communicate about mathematics verbally and in writing.

• Students should be able to model a written description of a physical situation with a function, a differential equation, or an integral.

• Students learn to use technology to analyze problems, experiment, and verify/interpret results.

• Students are expected to learn to judge reasonableness of their solutions.

• Students develop an appreciation of the wonderful world of calculus and for their personal accomplishment in learning calculus.

• Every student completing the AP Calculus BC course also take the AP exam (Not required).

• All students complete the course with an example of expectations and rigor of a college-level Calculus course.

Teaching Strategies

Connections in mathematics are stressed frequently. For instance: not all students realize at the beginning of the study of limits that the definition relates back to the study of slope in Algebra I. For comprehension of calculus concepts, students must make the mathematical connections to previous learning in order to have a true understanding of new calculus concepts and applications. Solutions to problems are found graphically, numerically, analytically, and verbally in order to demonstrate knowledge of the calculus curriculum being studied. In addition, proper vocabulary and symbolism are used in the classroom and expected of the students. Students are taught early on to answer questions in complete sentences.

Students will begin Calculus chapter 1.1 the first day of school. Pre-Calculus will be reviewed as needed. Students are taught proper form in putting their work on paper, justifying their solutions, and how to state their solutions in written form. Students are encouraged to ask questions immediately during lecture, no hand raising necessary. Consequently, problems and misconceptions are addressed promptly and no student/classmate is in a quandary due to lack of understanding.

Students are made comfortable with working in collaborative groups with peers, asking questions of the teacher, presenting ideas on the white board/through demonstrations, and taking chances in problem solving. Students are placed into study groups at the beginning of the year to employ the use of cooperative learning. A positive learning environment is modeled and encouraged for the students in the classroom. Examples of some (but not all) homework problems are illustrated by the instructor. Students are expected to extend their knowledge to problems that are different from the homework examples.

Course Format/Homework Policy

Students in AP Calculus BC are seniors that have completed AP Calculus AB (with a B or higher) their junior year. Generally speaking there are a number of students seeking to further their mathematical knowledge and seeking a challenge in their senior year. Students enroll in AP Calculus BC, students are placed into my classroom during the same period and are expected to participate class regularly. Calculus BC students are completing a wide range of review materials to keep their previous knowledge fresh. Students complete a variety of AP Multiple Choice and Free Response questions released by the College Board for AP Calculus AB material. In addition to the review, these students learn a variety of concepts as specified in the course outline below. I have included AB topics in the course outline to demonstrate the specific topics that are reviewed, and what BC topics are covered throughout the duration of the course.

Homework is given daily and the work should be completed daily. Homework is designed to enhance skills developed in class and graded (typically) for completeness. Some problems will be extremely challenging. I expect something logical and intelligent to be attempted for all assignments. Student work should be his/her own, however study groups are encouraged and built into the design of the course. Students are given my contact information with the best way to contact me for homework help in the evenings. Other online resources are available on my website for calculus help. Homework should be complete and turned in on time. Late work will NOT be accepted.

Assessment

Students are assessed daily, weekly, and once a unit. Each day student’s complete an assignment addressing the topics covered that day. Each week students receive a “POW!” (Packet Of the Week!) which has problems from released AP exams, both multiple choice and free response designed to target the subject from the week before. On both assignments students are encouraged to work together to complete problems, but are required to write up their own solutions and explanations. Each student’s responses should be distinct, display individual and original thought, and be complete answering all parts of the problem. Once or twice each unit students will have a quiz over unit materials taught up until the day before the quiz. Students will be permitted to use a calculator approximately half of the time on the quizzes. At the conclusion of each unit students are given an exam covering all material in the unit. These exams are generally written in two parts: Calculator: ACTIVE and Calculator: INACTIVE. The exams will consist of some multiple choice questions, but primarily of open ended questions. Students are required to show work to receive full credit. Often at least one of the items on the exam is an AP released Free Response question. Any item used from an AP released exam is scored according to the AP rubrics/scoring guidelines.

At the conclusion of our AP test review, each student will complete a mock AP exam worth 100 points. This exam is graded like the real AP exam, and students will be awarded a score of 1 to 5. More information on the mock exam will be given as the end of the year approaches.

Students’ grades are determined by the ratio of points earned to total points possible. A cumulative exam will be administered at the end of each trimester. Trimester exams are 20% of the students’ final average. If the AP exam is taken at the end of the year it will count as the final trimester exam.

Calculators

Students should come to AP Calculus BC already knowing the basics of operating a graphing calculator. While many operations should be done without the aid of a calculator, several calculus problems require the support of technology to arrive at a solution. This course will teach students how to use a graphing calculator to help solve problems, interpret results, and support conclusions. Specifically, the calculator will be used to:

1. Increase the speed of normal calculations

2. Verify hand drawn graphs of functions

3. Create lines of best fit (based on entered data)

4. Verify hand computation of derivative and integral values.

5. Verify limits graphically.

6. Evaluate sequences and series.

7. Evaluate trigonometric functions and values.

8. Verify or explain various non-calculator results.

9. Justify solutions to complex problems.

As with the AP exam, portions of each unit test will require the use of a graphing calculator and portions will prohibit its use.

AB Outline (Review Topics)

Section from our (Ninth Edition) Larson, Edwards book.

|Section |Topic |# of Days |

| |Chapter 1: Limits and Their Properties | |

|1.1 |A Preview of Calculus |2 |

|1.2 |Finding Limits Graphically and Numerically |2 |

|1.3 |Evaluating Limits Analytically |2 |

|1.4 |Continuity and One-Sided Limits |2 |

|1.5 |Infinite Limits |2 |

|3.5 |Limits at Infinity |2 |

| |Review and Assessment |3 |

| | | |

| |Chapter 2: Differentiation | |

|2.1 |The Derivative and Tangent Line Problem |5 |

|2.2 |Basic Differentiation Rules and Rates of Change |4 |

|2.3 |Product and Quotient Rules and Higher-Order Derivatives |3 |

|2.4 |The Chain Rule |3 |

|2.5 |Implicit Differentiation |3 |

|2.6 |Related Rates |3 |

| |Review and Assessment |3 |

| | | |

| |Chapter 3: Applications of Differentiation | |

|3.1 |Extrema on an Interval |3 |

|3.2 |Rolle’s Theorem and the Mean Value Theorem |3 |

|3.3 |Increasing and Decreasing Functions & the First Derivative Test |2 |

|3.4 |Concavity and the Second Derivative Test |2 |

|3.6 |A Summary of Curve Sketching |2 |

|3.7 |Optimization Problems |5 |

|3.9 |Differentials |3 |

| |Review and Assessment |3 |

| | | |

| |Chapter 4: Integration | |

|4.1 |Antiderivatives and Indefinite Integration |3 |

|4.2 |Area |3 |

|4.3 |Riemann Sums and Definite Integrals |3 |

|4.4 |The Fundamental Theorem of Calculus |3 |

|4.5 |Integration by Substitution |3 |

|4.6 |Numerical Integration |1 |

| |Review and Assessment |3 |

| | | |

| |Chapter 5: Logarithmic, Exponential, & Other Transcendental Functions | |

|5.1 |The Natural Logarithmic Function: Differentiation |3 |

|5.2 |The Natural Logarithmic Function: Integration |2 |

|5.3 |Inverse Functions |3 |

|5.4 |Exponential Functions: Differentiation and Integration |3 |

|5.5 |Bases Other than e and Applications |2 |

|5.6 |Inverse Trigonometric Functions: Differentiation |2 |

|5.7 |Inverse Trigonometric Functions: Integration |1 |

| |Review and Assessment |3 |

| | | |

| |Chapter 6: Differential Equations | |

|6.1 |Slope Fields |3 |

|6.2 |Differential Equations: Growth and Decay |5 |

|6.3 |Separation of Variables and the Logistic Equation |3 |

| |Review and Assessment |3 |

| | | |

| |Chapter 7: Application of Integration | |

|7.1 |Area of a Region Between Two Curves |3 |

|7.2 |Volume: The Disk Method |5 |

| |Review and Assessment |3 |

| | | |

| |Chapter 8: Integration Techniques, L’Hopital’s Rule, & Improper Integrals | |

|8.1 |Basic Integration Rules |2 |

| |Review and Assessment |3 |

| | | |

| |Review AP Calculus AB | |

| |AP Exam | |

| | | |

AP Calculus BC –Topic Overview

Timeline is approximate and includes reviews and testing. Students are completing many of the AB assignments and topics as review. Students are being taught each of the new topics. Students in the BC course are encouraged to work together and develop mathematical maturity. Students are encouraged to self teach AB topics that are unclear or lacking in depth of understanding.

Sections correspond to Larson and Edwards (Ninth Edition)

|Section |Topic |# of Days |

| |Unit 1 – Planar Curves |40 |

|7.4 |Arc Length and Surfaces of Revolution | |

|10.2 |Plane Curves and Parametric Equations | |

|10.3 |Parametric Equations and Calculus | |

|10.4 |Polar Coordinates and Polar Graphs | |

|10.5 |Area and Arc Length in Polar Coordinates | |

| |Review and Quiz | |

|11.1 |Vectors in the Plane | |

|11.2 |Space Coordinates and Vectors in Space | |

|12.1 |Vector-Valued Functions | |

|12.2 |Differentiation and Integration of Vector-Valued Functions | |

|12.3 |Velocity and Acceleration | |

| |Review and Assessment | |

| | | |

| |Unit 2 – Techniques and Uses of Derivatives and Antiderivatives |30 |

|6.1 |Slope Fields and Euler’s Method | |

|6.3 |Separation of Variables and the Logistic Equation | |

| |Review and Quiz | |

|8.2 |Integration by Parts | |

|8.5 |Partial Fractions | |

|8.7 |Indeterminate Forms and L’Hopital’s Rule | |

|8.8 |Improper Integrals | |

| | | |

| |Unit 3 – Polynomial Approximations and Series |40 |

|9.1 |Sequences | |

|9.2 |Series and Convergence | |

|9.3 |The Integral Test and p-Series | |

|9.4 |Comparisons and Series | |

|9.5 |Alternating Series | |

| |Review and Quiz | |

|9.6 |The Ratio and Root Tests | |

|9.7 |Taylor Polynomials and Approximations | |

|9.8 |Power Series | |

|9.9 |Representation of Functions by Power Series | |

|9.10 |Taylor and Maclaurin Series | |

| |Review and Assessment | |

| | | |

| |Unit 4 – Review |40 |

| | | |

| |Review of AB and BC Material by Topic | |

| |Multiple Released MC and Free-Response Practice | |

| |Mock Exams | |

| |Review Games/Activities | |

| |Barron’s Assignments | |

| | | |

*Dates and Time frame are adjustable based on teacher need.

*Multiple projects, released AP material, and problem sets will be incorporated into each unit.

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