This course is preparation for Calculus. Topics of study include polynomial, rational, exponential, logarithmic and trigonometric functions as well as their inverses. An introduction to matrices, analytic geometry, and sequences and series are also included. The application of these topics is stressed to enhance conceptual understanding of the material.
The course is designed based upon the topics outlined in the AP Calculus AB Course Description. The objectives of the course are as below
· Students will develop an understanding of the two major concepts of Calculus (of a single variable): differentiation and integration.
Ø Students will under differentiation as a local linear operation on functions, as a rate of change and as the slope of tangent lines of a curve at different points.
Ø Students will understand integration as a linear operation on functions, as a summation of change, and as the limit of Riemann sums.
Ø Students will know the Fundamental Theorem of Calculus and understand that integration is the anti-derivative of a function.
· Students will learn the both concepts and techniques of Calculus, and be able to apply them to problem solving.
Ø Students will develop proficiency in the techniques of Calculus and be able to find numerical and analytic solutions by pencil and paper.
Ø Students will be able to experiment, interpret results and verify conclusions using technology (graphing calculators or other software).
Ø Students will develop their ability to read and analyze a problem, model the problem mathematically, and solve the problem correctly.
Ø Students will learn to evaluate the validity of arguments and solutions and provide written justification of one’s thinking in solving a problem.
· Students will accurately communicate and discuss mathematics verbally and in writing
· Students will be able to represent functions analytically, numerically, and graphically. Students will be able to understand the connections among these representations.