AP/Honors Calculus Credits: 6
Text: Calculus: Graphical, Numerical, Algebraic. (Finney, Demana, Waits, & Kennedy)
Mathematics 21st Century Expectation for Student Learning:
Every Hull High School student will be a competent problem solver.
Course Overview:
The intent of the course is to give students the chance to earn college credit while still in high school by teaching them the content defined for the College Board’s Calculus AB advanced placement exam. Students should have a real desire to place out of the first semester of college calculus to help maintain their motivation throughout this very challenging course. Students are taught the concepts of single variable differentiation and integration, applying these concepts to the solution of rigorous mathematical problems. This course is intended for students who have a thorough knowledge of analytic geometry, algebra, and elementary functions and a grade of at least a B in Honors Pre-Calculus is a prerequisite. There are also important prerequisites of attitude. Students should be ready to work hard both in and out of class and they should be prepared to help each other master the material.
Graphing calculators are an essential tool for the course and are required on the AP Calculus exam. They will be used in class, on the homework, and on the tests. Consequently, students are required to have a graphing calculator and students are expected to bring it to each class session. Any graphing calculator approved for use on the AP Calculus test may be used. For a list see http://apcentral.collegeboard.com/repository/ap06_calculator_polic_36720.pdf. However, since class demonstrations and instruction will use the TI 83 Plus, there may be an advantage to having this particular model. The newer TI-84 offers the same functionality as the TI-83 with
better speed and memory. Currently there are good deals available on TI-83 Plus calculators as they are phased out of inventory, and there is no reason why they should not be used for this course, despite the availability of the newer model.
Students who are taking AP credit are expected to take the Advanced Placement Examination in Calculus AB. The deadline to pay for the exam is October 1st. Any student who does not pay the fee or make arrangements to do so will receive Honors credit for the course.
Course Objectives:
Students will work with functions graphically, numerically, and analytically, and demonstrate understanding of the connections among these multiple representations.
Students will define and apply the properties of limits of functions.
Students will describe asymptotic and unbounded behavior of functions.
Students will define continuity and determine where a function is continuous or discontinuous at a point, or over a closed interval both algebraically and using graphical interpretations.
Students will understand the meaning of derivatives and apply rules of differentiation.
Students will apply the derivative to solve problems, including tangent and normal lines to a curve, and related rates of change problems.
Students will demonstrate an understanding between the relationship of the function and its derivative both algebraically and geometrically.
Students will apply the characteristics of the graphs of the function and its first and second derivatives to sketch a function.
Students will explore varied applications of derivatives both algebraically and geometrically.
Students will find the derivatives of various functions using a variety of differentiation techniques.
Students will know the definition of the definite integral by using Riemann sums.
Students will demonstrate knowledge and proof of the Fundamental Theorem of Calculus and use it to interpret integrals as antiderivatives.
Students will compute the integrals of a wide variety of functions by using techniques of integration, such as substitution, integration by parts, and trigonometric substitution.
Students will use definite integrals in problems involving accumulated change, volume of a solid, area of a region, average value of a function, and the distance traveled by a particle along a line.
Students will approximate definite integrals.
Students will construct and interpret slope fields.
Students will solve separable differential equations.
Students will find specific antiderivatives using initial conditions, including applications to motion on a line.
Course Content:
Analyze the connection between the geometric and algebraic information.
Predict and explain the observed local and global behavior of a function.
Analyze the limiting process.
Calculate limits using algebra.
Estimate limits from graphs or tables of data.
Analyze asymptotes in terms of graphical behavior.
Describe asymptotic behavior in terms of limits involving infinity.
Compare relative magnitudes of functions and their rates of change.
Analyze the concept of continuity.
Analyze continuity in terms of limits.
Use the Intermediate Value Theorem and the Extreme Value Theorem to understand the graphs of continuous functions.
Present derivatives graphically, numerically, and analytically.
Interpret the derivative as an instantaneous rate of change.
Define the derivative as the limit of the difference quotient.
Analyze the relationship between differentiability and continuity.
Determine the slope of a curve at a point.
Analyze the tangent line to a curve at a point and the local linear approximation.
Determine the instantaneous rate of change as the limit of average rate of change.
Approximate the rate of change from graphs and tables of values.
Analyze the characteristics of graphs of f and f'.
Analyze the relationship between the increasing and decreasing behavior of f and the sign of f'.
Analyze the Mean Value Theorem and its geometric consequences.
Translate verbal descriptions into equations involving derivatives and vice versa.
Analyze the characteristics of the graphs of f, f', f".
Analyze the relationship between the concavity of f and the sign of f".
Identify the points of inflection as places where concavity changes.
Analyze curves, including the notions on monotonicity and concavity.
Identify both absolute (global) and relative (local) extrema.
Model rates of change, including related rates problems.
Use implicit differentiation to find the derivative of an inverse function.
Analyze the interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration.
Determine derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
Use the basic rules for the derivatives of sums, products, and quotients of functions.
Use the chain rule and implicit differentiation.
Compute Riemann sums using left, right, and midpoint evaluation points.
Identify the definite integral as a limit of Riemann sums over equal subdivisions.
Identify the definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval.
Use basic properties of definite integrals.
Use the Fundamental Theorem to evaluate definite integrals.
Use the Fundamental Theorem to represent a particular anti-derivative, and the analytical and graphical analysis of functions so defined.
Identify and use antiderivatives from derivatives of basic functions.
Identify and use antiderivatives by substitution of variables, including change of limits for definite integrals.
Identify specific antiderivatives using initial conditions, including applications to motion along a line.
Solve separable differential equations and use them in modeling, particularly studying the equation y'=ky and exponential growth.
Calculate areas under curves.
Calculate volumes of solids with known cross-sections.
Use Riemann and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values.
Course Evaluation Criteria
· Tests 60%
· Quizzes 40%
Course Policies
· Students are expected to follow the attendance, tardiness, behavioral, academic honesty, and make-up of missing work policies as outline in the Hull High School Student Handbook.
· Students are expected to be on time.
· Students are expected to be respectful and courteous and use appropriate language at all times.
· Students are expected to behave in a responsible manner.
· Students are expected to bring the textbook, math binder, pens/pencils, and a daily planner or agenda book to each class period. Being properly prepared for class will be counted as part of the class participation evaluation.
· Students are expected to take part in class on a daily basis. Students will be called on to answer questions and to do problems on the board.
· Homework is an integral part of this course. Homework will be given each class period, as an aid in understanding the concepts and skills presented in class. In order to be successful in this course, it is imperative that each student does his/her homework on a daily basis.
Extra Help
Extra help will be available after school Monday through Thursday, except when faculty commitments conflict, or by appointment for other times. Since much of this course builds on that which the student has learned earlier, it is important that students seek help as soon as s/he encounters difficulty with the material. It is a sign of a responsible student to seek help promptly when it is needed.
Communication
I can be reached by:
· Telephone 925-3000 ext.2202
Follow the prompts to Schools…High School…Faculty…Math…Mrs. Canniff
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