AP CALCULUS BC
Sample of Handouts
This class covers all AP Calculus AB topics, as well as additional topics, but takes less than four hours of lecture per week at TEC. This class not only ensures a good test result on the AP exam, but also provides a solid background for taking many other college-level courses such as Multi- Variable Calculus. Additional topics include advanced integration techniques and improper integrals and Taylor series and applications on the polar coordinate system or parametric equations.
Syllabus of AP Calculus BC for 2025 - 2026
Instructor: Spencer Way
Time: Sat 4 - 7pm as below
Dec. 27 (9-12:30pm), Jan 2 (noon - 3:30pm)
Nov. 1 IBP: Integration by parts
ITI: Integration of trig integrand
ITS: Integration of trig substitution
ICS: Integration by completing the square
Nov. 15 IPF: Integration by partial fraction
IMS: Integration by miscellaneous substitution
Nov. 29 Improper integral
more of L’Hõpital’s rule
Sequence and series
10 tests of infinite series
Dec. 27 ( 9- 12:30pm)
Error approximation of convergence
Power series
Interval and radius of convergence
Taylor and Maclaurin series
Taylor polynomial and its remainder, Lagrange error approximation
Algebra of Taylor series
Calculus of Taylor series
Jan. 2 (noon - 3:30pm)
Parametric equations. 2D SVA curvilinear motion
Position, velocity and acceleration vectors of 2D curvilinear motion
Application of integration: arc length of a curve
Slop/concavity/arc length of parametric equation
Area of surface of a solid of revolution
Jan.3 (4 - 7pm)
Polar coordinates and the conversation to rectangular coordinates
Intercept and symmetric properties of the graph of polar equation
Graph of polar equations
Point of intersection of the graphs of polar equation
Area formed by polar curves
Slopes/arc length of polar curves
Jan. 10 Logistics differential equation and it's biological application
Solving differential equation by Euler's method
Work, Rigorous definition of limit
Jan. 24, Feb.7,21 Mar 7,21 Apr. 4 Review of Calculus BC
Mar. 7 - Apr. 25 (Sat 8:40 - 11:40am) Review of AP Calculus & Practice of sample tests