Walter Hines Page High School - Mr. Mack- AP Calculus BC H ...



Phillip O Berry High School

Advanced Placement Calculus-AB

2017-2018

Mr. Brandon A. Mack

Email: brandona.mack@cms.k12.nc.us

Tutoring Hours: Room 815, After School – Tuesday 2:20-3:00pm

Any students needing accommodations should inform the instructor.

Students with disabilities who may need accommodations for this class are encouraged to notify the instructor. All information will remain confidential. IEP’s and 504’s will be followed and together we will do whatever is necessary to create a positive learning environment for you.

Congratulations, you have made it to the pinnacle of your high school experience! This year you are going to be standing on the shoulders of giants who have created the calculus. We will be building on all of the math that you have learned in the previous years to complete this course in differential and integral calculus. If you are like I was at your age, this will be the most challenging course you will have encountered in your academic career – so far (unfortunately, there are other courses you will take in college that will take over that title.) But you will find that this course will open up new thought processes and opportunities to explore subjects that you can only dream of now. This is a college level course and one of your goals should be to score well enough on the AP exam to be able to exempt at least one calculus course in college. If you put your best effort into this year I can promise you three things – you will work as hard as you ever have in a course, you will grow intellectually as much as you ever have in a course, and we will have a great time as we triumphantly wrestle with the concepts that Newton and Leibnitz presented to the human race.

Text: Calculus 7th edition by Larson, Hostetler, and Edwards. Houghton Mifflin Company, copyright 2002

Calculators: You must have your own TI-83. I also make use of a TI-83 view-screen calculator that is especially helpful when studying slope fields and other visual concepts.

Other resources:

▪ Calculator Labs published by Skylight Publishing, authors Phyllis Hillis and Benita Albert.

▪ Access Software which has an extensive bank of Calculus multiple choice questions.

▪ A full collection of AP Exam Review Books (Baron’s, ARCO, D&S, Kaplan ect.)

▪ Released Exams: 1969-2009

Weekly Topics & Assignments

|Approximate Time |Topics & Assignments |

|5 days |Functions |

|6 days |Limits and Continuity |

|6 days |Differentiability and Early Derivative Rules |

|5 days |More Complex Derivatives |

| 5 days |Derivatives of Inverses |

|5 days |Local Linearity |

|5 days |Applications of Derivatives-Graphs |

|4 days |More Applications of Derivatives |

|4 days |Sum Review and Anti-derivatives |

|5 days |The Area Problem and Definite Integrals |

|6 days |Applications of the Definite Integral |

|4 days |Differential Equations |

|3 days |Graphing Calculator Unit |

|10 days |Exam Review |

Note: Our school is structured on a Block A/B Day bell schedule. Classes meet every other day for 90 minutes. The time allotments shown above do not include test days of which there will be approximately 10. We will also conduct labs (approximately 10) one after each test.

Topics to be covered in each area

Functions

The first task is to make sure that you understand key features of the members in our “Library of Functions.” You will be given a handout which lists the basic function classes; Linear, Polynomial, Rational, Radical, Trigonometric, Exponent, Logarithmic, and Piecewise Defined Functions. You will sketch graphs of the functions and specify their domain and range. Next we will study other properties including symmetry, intercepts, and asymptotes. Lastly we will cover the specifics of solving equations and inequalities involving each of these types of functions. Due to the rigor of our honors classes that are prerequisites to Calculus we have the luxury of only spending 10 days here. Of course we always do “mini-reviews” to activate prior knowledge when we focus on a certain topic; for example, reinforcing the laws of logarithms before introducing the logarithmic derivatives.

Limits and Continuity

The topics covered will be: concept of a limit; notation, including one-sided and overall limits; evaluating limits given a graph; algebraic evaluation of limits with special care given to techniques for handling the indeterminate form”0/0;” numeric approach to evaluate limits using the table feature of the calculator; infinite limits (Type I-“non-zero”/”zero” leading to +/- infinity, Type II- end behavior in limits as x approaches infinity all with heavy emphasis on graphs and the concept of how fast something approaches infinity); graphically show the connection between limits and asymptotes; continuity of basic functions; continuity at a point.

Differentiability and Early Derivative Rules

The topics covered will be: average vs. instantaneous change-auto trip real life example; graphic interpretation (tangent segment vs. secant segment); definition of derivative-recognizing both forms, calculating f’(x) from graph and table of values;

power rule; scalar multiple rule; sums and difference rule; product and quotient rule;

writing equations of tangent lines and horizontal tangents.

More Complex Derivatives

Derivatives of six trig functions

Higher Order Derivatives

Chain Rule

Implicit Differentiation

Related Rates

Derivative of Inverses

General Inverses (Monotonicity and derivative and inverse at a point.)

Derivatives of Logarithmic Functions

Derivatives of Exponential Functions

Logarithmic Differentiation

Derivatives of Inverse Trig Functions

Local Linearity

Linearization/Linear Approximations

Differentials (both algebraic and graphic representation)

Applications of Derivatives

1st Derivative Test

Concavity and 2nd Derivative Test

Curve Sketching

(Note that with these topics you will be required to find solutions when provided a variety of information. An example would be my asking you relative extrema and concavity questions when you are given the original function (algebraic), the graph of the derivative (graphic), and/or a table of function values (numeric).)

More Applications of Derivatives

Rectilinear Motion

Absolute Maximums and Minimums (Extreme Value Theorem)

Optimization

Mean Value Theorem and Rolle’s Theorem

Sum Review and Anti-derivatives

The Indefinite Integral (A family of curves)

Slope Fields

Integration by Substitution

The Area Problem and Definite Integrals

Review Sigma Notation

Area estimates using midpoints and left and right endpoints

Riemann sums and definition of definite integral

The Fundamental Theorem of Calculus

Evaluating Definite Integrals-Average Value of a Function

Application of the Definite Integral

Rectilinear Motion

The Definite Integral as an accumulator (Functions defined as definite integrals with variable bounds)

Area between two curves

Volume-Disks and Washers, Shell Method, and Known Cross Sections

Differential Equations

Exponential & Logistic Growth Models

General Separable Differential Equations (Algebraic Approach)

Revisit Slope Fields (Graphical Approach)

Graphing Calculator Unit

Although we will have been using the calculator throughout the course, we will have an intense graphing calculator unit in order to help you feel more confident using that valuable tool. Using a packet written by Sergio Standler, you will explore ways to use the calculator to its full potential.

Exam Review

The exam review will start with you taking a released full exam during 3 class days. For the homework during this period you will outline the course, organizing it in a manner which makes sense to you. I will collect these to review and start a topical review of the course leading with limits and continuity, etc. You will keep everything in a review notebook which will be collected after the AP Exam and graded with a weight of two test grades. The culminating activity will include going over rubrics and previous exam statistics. Then you will complete an additional released exam. This second mock exam will be given on a Saturday morning so that you can experience the exact format and timing of the exam. I will provide the food.

Note: This leaves about 8 days unaccounted for. If we don’t miss any class days due to snow or class assemblies etc, I will incorporate some “portfolio assignments.” These assignments usually require technology and some form of investigation or modeling. They are similar to the calculator labs (Albert & Hillis) referenced earlier and incorporate either real world mathematical modeling or some form of investigation or programming.

Grading

|Quizes/HW/Classwork |30% |

|Test/Major Projects |70% |

Late Work Policy: This course is designed to prepare you for the AP Exam and is taught as a college course. Late work will not be accepted. Exceptions will be granted with school related activities and at my discretion. . If any issues arise please make it a point to discuss with me as soon as you are aware of them. Remember tutoring is available. Late work is classified as work not turned on the day it is due.

Tests

Each test will consist of both multiple choice and free response questions in order to prepare you for the format of the AP Exam. Questions are selected to give you a variety of contexts (algebraic, graphic, and numeric) in which to show your understanding. The free response section concentrates on justifying answers in complete sentences and paying attention to notation and units. A guiding principle is that good math well articulated is always worth points. The tests will stretch you and will be a vital part of our learning experience – they are not simply a chance to regurgitate facts that you have memorized.

It’s going to be a great year and I am looking forward to our journey together through the calculus. Keep up with your assignments and make sure you come to see me when need help with a concept. I know from experience that you cannot master this material if you get behind. You must keep current with your assignments and plan ahead. You provide the diligence and I will provide the good times!

Mr. Brandon Mack M.S.

Mathematics and Education

AP Calculus Instructor

Phillip O Berry High School

17 Years teaching experience

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