AP CALCULUS AB
Sample of Handouts
This class at TEC takes less than three hours of lecture per week and 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 Differential Equations. AP Calculus can be applied to the study of many other college courses in various fields including business, science, and engineering. Hence, it has become a standard material of math education in high school for almost all countries in the world. Calculus is the mathematical tool used to analyze changes in physical quantities. It studies differentiation and integration and their applications, including the rate of change of quantity and the optimization of quantity, or the determination of the volume of a solid of revolution or the area of the region formed by some curves in a plane.
Syllabus of AP Calculus AB for 2025 - 2026
Instructor: Spencer Way
Time: 8/23/2025 - 1/17/2026 Sat 9 - 11:40am
1/24/2026 - 4/25/2026 Sat 8:40 - 11:40am
Aug. 23 Notation of limit means “approaching to”
Mathematical definition of general limit and continuity
Find limits by tracing the curve
Relationship between “limit existence” & “continuity” & differentiability”
Find limit by algebra, some popular mistakes
Limit involving trig functions
Aug. 30 Theorems involving continuity
Rational function and it’s asymptotes
Symmetric property of graph of an even or odd function
Curve sketching of a function involves asymptote
Definition of e and it’s variation
Definition of one-side continuity at a point
Removable or non-removable discontinuous point
Theorems involving limit
Squeeze theorems
Sep. 6 Definition of tangent/normal line of a curve
Slope of a line or a curve
Definition of derivative function
Definition of differentiation/differentiable
Definition of higher order of derivative
5 derivative rules and their chain rule
Theorems involving derivative
Derivative of even or odd function
Derivative of inverse function
Sep. 13 Verification of 5 derivative rules
Another way of looking at chain rule
Log differentiation
Sep. 20 Implicit differentiation
L’Hõpital’s rule
Derivative of
Sep.27 Instantaneous and average rate of change
Differential and linear approximation
Oct. 4 Related rates
Definition of increasing/decreasing functions
Con cavity and inflection point
Relative maximum/minimum
Curve sketching of a function by using relative extremism/inflection point
Oct. 11 Absolute maximum/minimum
Application of absolute extremum
Oct. 18 Graph of derivative/antiderivative function
Oct. 25 5 antiderivative rules
Technique of integration: integration by substitution
Comparison of derivative and antiderivative function
Operation on graphing calculator
Some theorems involving antiderivative
Integration of even or odd functions
Nov. 1 Instantaneous/average velocity and acceleration of rectilinear motion
Rectilinear motion
Nov. 8 Second fundamental theorem of calculus
Separable differential equation
Differential equation y’ = my
Growth and decay problems
Nov. 15 Riemann sum: area as limit
Rectangular/trapezoidal rules
Nov. 22 Roll’s theorem and mean value theorem
Average value of a function
Nov. 29 Application of integration: volume
Dec. 6 Slope field
Jan. 3,10,17 Riemann sum of unequal increment
Difference of function values is expressed in integral form
Derivative of piecewise or absolute function
Jan. 24 - Feb. 28 Review of AP Calculus
Mar.7- April 25 Review of AP Calculus & Practice of sample tests