AP CALCULUS AB
Instructor: Mr. Morrissey, kmorrissey@portsmouthabbey.org, St. Hugh’s DormText: Calculus: Graphical, Numerical, Algebraic, 3d Edition; Finney, Demana, Waits, Kennedy, Prentice Hall, 2007Calculator: TI-89/89 Plus preferred (see AP Calculus Guide for list of acceptable Calculators)
Course Description
AP Calculus AB is a demanding, college-level course designed with the goal of helping you prepare for the AP Calculus AB Exam administered in May. While specific requirements, evaluation criteria, test format and topics to be covered can be found at www.apcentral.collegeboard.com , generally, by the end of this course you will be able to:· Understand and be able to apply the curriculum of the AP course· Use numerical, analytical and geometric approaches to solving problems and be able to write a logical explanation of your solution and approach· Take individual responsibility for the acquisition of mathematical knowledge· Communicate mathematics both orally and in well-written sentences· Model a written description of a physical situation with a function, differential equation or integral· Use technology to solve problems, experiment, interpret results and verify conclusions· Be adequately prepared for the next level of learning
Evaluation
You will receive a term mark, calculated as follows. TERM Tests 55% Quizzes/Projects 30% Homework 10% Participation 5%
We will have at least 1 test per chapter and 2-3 quizzes per chapter. Tests will be announced; quizzes may or may not be announced. There will by an end of term exam for both fall and winter terms.
Student expectations
At this level, you should know what I expect of you. Act as mature young adults and I will treat you as such. The PAS Student Handbook has a code of conduct that outlines acceptable behavior but a few areas I want to emphasize are: · You need your calculator everyday· Homework must be done everyday, late assignments result in a zero· Quizzes and tests missed must be made-up with-in 2 days of returning to school· Notebooks must be neatly organized, keep all notes, quizzes and tests· I expect you to purchase an AP Calculus review book and use it to prepare for class and the AP Exam· In order to best prepare for the AP Calculus exam in May, you must actively participate in this class, to include seeking extra help when you need it
Course Outline
Fall TermA. Functions and Graphs1. Properties of Functionsa. Domain and rangeb. Sum, product, quotient and compositionc. Inverse functionsd. Odd and even functionse. Zeros of a function2. Properties of Graphsa. Interceptsb. Symmetryc. Asymptotesd. Trig functions: amplitude, period and phase shifts, identitiese. Absolute value functionsB. Limits and Continuity1. Finites Limitsa. Limits of constants, sum, product or quotientb. One-sided limitsc. Limits at infinity2. Nonexistent Limitsa. Types of nonexistenceb. Infinite limitsc. L’Hopital’s Rule for 0/0, and
3. Continuitya. Definitionb. Graphical interpretation of continuity and discontinuityc. Existence of absolute extrema of a continuous function on a closed intervald. Applications of the Intermediate Value Theorem and Extreme Value Theoreme. Relationship between continuity and differentiabilityC. Differential Calculus1. The Derivativea. Definition of derivative1. Derivatives of elementary functions2. Derivatives of sums, products and quotients3. Derivatives of composite functions (Chain Rule)4. Derivatives of implicitly defined functions5. Derivatives of higher order6. Derivatives of inverse functions7. Logarithmic differentiation2. Statements and applications of derivative theoremsa. Relationship between differentiability and continuityb. The Mean Value Theorem and Rolle’s TheoremWinter Term
3. Applications of the Derivativea. Geometric applications1. Slope of a curve; tangent and normal lines2. Average and instantaneous rates of change3. Increasing and decreasing functions4. Critical numbers5. Concavity6. Points of inflection7. Curve sketchingb. Optimization problems1. Relative and absolute max and min values2. Extreme value problemsc. Rate-of-change problems1. Average and instantaneous rate of change2. Position, velocity and acceleration in linear motion3. Related rates of change
D. Integral Calculus1. Antiderivatves (indefinite integrals)a. Techniques of integration1. Basic integration formulas2. Integration by substitution (change of variable)3. Simple integration by partsb. Applications of antiderivatives1. Distance and velocity from acceleration with initial conditions2. Separable differential equations3. Applications for growth and decay
Spring Term2. The Definite Integrala. Definitions of the definite integral as a limit of sumsb. Properties-Integration by trig substitutionc. Approximations to the definite integral1. Rectangles (Riemann Sums)2. Trapezoids (Trapezoid Rule)d. Fundamental theoremse. Applications of the definite integral1. Area under a curve; area between curves2. Average value of a function on an interval3. Volumes of solids with known cross section, including solids of revolution (disc and washer method)4. Volumes of solids of revolution (shell method)5. Extended review and practice exams
