3570 Timpview Dr. Provo, Utah 84604 Phone: (801)221-9720 Fax: (801)224-4210

AP Calculus BC

Course Description/Overview/Welcome Statement

Instructor:   Anne Crosland

Email: annec@provo.edu

School: 801-221-9720 ext. 3608

Course: This course is designed for those students who have successfully completed Beginning and Intermediate Algebra, Geometry, Trigonometry (Secondary Math I, II, and III) and College Algebra and/or Pre‑Calculus. This course is an Advanced Placement course and as such, students can receive college calculus credit by scoring a 3, 4 or 5 on the AP exam. This class differs from the AP calculus-AB in that the BC course covers more topics and a potential for higher calculus proficiency. The topics that we will cover will be Functions, Graphs, Limits, Derivatives, Integrals, Sequences and Series. There will be homework nearly every day. Students work at different speeds, but students should allow at least one hour for homework every day.

Learning Expectations

Assessment of Progress

Course Materials

Primary Text:  Finney, Ross L., Franklin Demana, Bert Waits, Daniel Kennedy, David M. Bressoud. Calculus:  Graphical, Numerical, Algebraic—5th Ed. Boston, Mass.: Pearson , 2016

Calculators: I will be making limited use of the TI83 (Texas Instruments) calculator in my class. If you have any of the following calculators; TI82, TI83, TI85, TI86, TI89 and you know (or are willing to learn on your own) how to use them, you will be fine. They are appropriate for calculus and are approved for use on the AP test. Please note: Calculators are only allowed on 1/3 of the AP test. There are also many other graphing calculators that are acceptable for use on the AP exam. Come see me if you have questions about your calculator. The Math department has calculators to rent for $20 per year and you can do so by paying for the rental in the bookstore then taking the receipt to Mrs. Gerstner (in the library), and filling out the rental agreement form.

Classroom Procedures

Attendance: Missing class will affect your grade as it is easy to get behind and difficult to catch up. Truancies, tardies, and absences will also affect your grade as explained in the Timpview High School Attendance Policy in the Timpview Handbook. You may earn an extra 2% by having no tardies and at most one excused absence per term.

 

Grading: There will be approximately three chapter tests each term, and usually an assignment every day. Seventy percent (70%) of your grade will be determined by your average test score and the other thirty percent (30%) will be determined by homework and quiz scores. Late homework is only worth half credit and will be accepted up until the current chapter test. After the chapter test, late homework will not be accepted.   Also, missing a test and taking it late will result in a 5% reduction the first time, 10% the second time and 15% the third. I use the standard grading scale for Timpview. 94% and above = A, 90-93% = A-, 87-89% = B+, 83-86% = B, 80-82% = B-, etc.

 

Calendar of Due Dates for Major Assignments

Course Plan:

 

 

CHAPTER ONE: PREREQUISITES FOR CALCULUS                                           (week 1)

  • 1.1 Lines • 1.2 Functions and Graphs • 1.3 Exponential Functions • 1.4 Parametric Equations • 1.5 Inverse Functions and Logarithms • 1.6 Trigonometric Functions

 

CHAPTER TWO: LIMITS AND CONTINUITY                                                       (week 2-week 3+) TEST

  • 2.1 Rates of Change and Limits • 2.2 Limits Involving Infinity  • 2.3 Continuity
  • 2.4 Rates of Change and Tangent Lines

 

CHAPTER THREE: DERIVATIVES                                                                        (week 4-­week 7) TEST 

  • 3.1 Derivative of a Function  • 3.2 Differentiability  • 3.3 Rules for Differentiation
  • 3.4 Velocity and Other Rates of Change • 3.5 Derivatives of Trigonometric Functions

 

CHAPTER FOUR: MORE DERIVATIVES                                                              (week 8- week 10) TEST

  • 4.6 Chain Rule • 4.7 Implicit Differentiation  • 4.8 Derivatives of Inverse Trigonometric Functions
  • 4.9 Derivatives of Exponential and Logarithmic Functions

 

(End of Term 1)

 

CHAPTER FIVE: APPLICATIONS OF DERIVATIVES                                         (week 11­-week13+) TEST

  • 5.1 Extreme Values of Functions • 5.2 Mean Value Theorem • 5.3 Connecting f ’ and f ”with the Graph of f
  • 5.4 Modeling and Optimization  • 5.5 Linearization, Sensitivity, and Differentials • 5.6 Related Rates

 

CHAPTER SIX: THE DEFINITE INTEGRAL                                                          (week 14-­week 17) TEST

  • 6.1 Estimating with Finite Sums • 6.2 Definite Integrals • 6.3 Definite Integrals and Antiderivatives
  • 6.4 Fundamental Theorem of Calculus • 6.5 Trapezoidal Rule (Christmas Break)

 

CHAPTER SEVEN: DIFFERENTIAL EQUATIONS AND 

MATHEMATICAL MODELING                                                                              (week 18-­week 20+) TEST

  • 7.1 Slope Fields and Euler’s Method  • 7.2 Antidifferentiation by Substitution
  • 7.3 Antidifferentiation by Parts • 7.4 Exponential Growth and Decay  • 7.5 Logistic Growth

 

(End of term 2)

 

CHAPTER EIGHT: APPLICATIONS OF DEFINITE INTEGRALS                       (week 21-­week 23) TEST

  • 8.1 Accumulation and Net Change • 8.2 Areas in the Plane • 8.3 Volumes • 8.4 Lengths of Curves
  • 8.5 Applications from Science and Statistics

 

CHAPTER NINE: SEQUENCES, L’HÔPITAL’S RULE, 

AND IMPROPER INTEGRALS                                                                                (week 24­-week 26) TEST

  • 9.1 Sequences • 9.2 L’Hôpital’s Rule • 9.3 Relative Rates of Growth  • 9.4 Improper Integrals

 

CHAPTER TEN: INFINITE SERIES                                                                         (week 27­-week 29) TEST

  • 10.1 Power Series • 10.2 Taylor Series • 10.3 Taylor’s Theorem • 10.4 Radius of Convergence
  • 10.5 Testing Convergence at Endpoints

 

(End of Term 3)

 

CHAPTER ELEVEN: PARAMETRIC, VECTOR, AND POLAR FUNCTIONS     (week 30­-31)

  • 11.1 Parametric Functions • 11.2 Vectors in the Plane • 11.3 Polar Functions

 

This schedule allows four to six weeks to review for the AP exam.  The students use prepared review materials for practice on multiple-choice questions as well as using those released by College Board.  They also work many released AP Section II exams for free response question practice.

 

 

Progress Reports and Report Cards

Please refer to PowerSchool for grade information and attendance.  I update PowerSchool multiple times a day and it should be accurate and current.

Connecting Home to School

Personal Statement and other items (optional)

Teaching and Learning Philosophy:

I want my calculus students to understand calculus from more than just a mechanical point of view.  To reduce such a beautiful

subject to formulas and procedures is literally taking the life out of it.  I want them to be strong mathematicians with the skills it

takes to do the procedures and the ingenuity to solve problems.

 

Since there are many ways to look at a problem and many ways to describe its solution, we work together to fully understand it by

studying the graph(s), numerically “crunching” a few numbers to get a feel for what’s going on, and using algebraic methods to

find solutions.  The main text that we use superbly supports this kind of exploration and provides opportunities for students to

work problems in these different ways.

 

I also believe that to really understand calculus, you must be able to teach it to someone else.  There is something inherent in the

process of verbally expressing your ideas that solidifies that knowledge in you.  For this reason, students are encouraged and given

time to teach each other in small groups.

 

Ultimately, to express what you know about a mathematical problem, you must be able to write your ideas and solutions.  I stress

correct and precise use of symbols and words in writing solutions and explaining ideas.  This practice helps crystallize a students’ understanding of calculus concepts.

 

I love to teach because I take so much joy in seeing you learn. I love mathematics and believe in the power that comes from studying it.

 

I wish to have a classroom in which everyone is treated with respect. I will treat you with respect if you, in turn, will treat each other and me with respect. I fully support Timpview’s attendance policy, academic integrity procedure, cell phone policy, and dress code. I intend to follow through with the described action upon misconduct regarding these policies.

 

I have the right and responsibility to teach, you have a right and a responsibility to learn, and no one has the right to infringe on this educational process.

 

WELCOME!   And let’s have a great year!