Overview
AP Calculus AB is offered on a semester-long 4 x 4 schedule. That is ninety minutes every day. Enrollment in the course is open to all students, the majority of them, though, come from the Honors Pre-Calculus course. All calculus courses are taught using the
College Board AP curriculum with item objectives being linked to state and district curriculum guidelines. Taking the AP exam is part of the course requirement for each student. The course divides naturally into four parts; review of functions, limits and derivatives, integration, and review.
Review of functions . When reviewing functions particular attention is given to novel approaches and organization. Special emphasis is put on the transformation of families of functions as well as their composition and decomposition. All discussions incorporate multiple representations (graphical, numerical, analytical, and verbal). Non-explicit functions, such as data sets, are explored. During this section any graphing calculator usage weaknesses are resolved.
Limits and the derivative. Limits are approached initially from data, then, graphically and analytically. Limits to infinity are related to asymptotic behavior as well as relative function domination and other global aspects of functions. Continuity, IVT, and EVT are discussed informally and formally. Derivatives are seen as natural results of limits and are interpreted as instantaneous rates of change and linear approximations before technique is emphasized. Use of the four representations is continued in this section.
Applications required by the AP course description are covered with focus throughout on the derivative as a rate of change.
Integration. Some review of summation notation and its use is required. The integral is developed as the limit of Riemann sums then related to area under curves and the antiderivative. Several representations are used in the discussion of definite integrals and the Fundamental Theorem of Calculus. Transcendental functions are re-introduced and reviewed along with their derivatives. Applications suggested by the AP course description are covered with special emphasis on curve sketching and visualization.
Numerical methods of approximation are covered.
Review . Besides a linear review of each topic students are presented with multi-step, multi-concept problems. Confidence in approaching these and other novel questions is emphasized. In particular, both the derivative and antiderivative of a function is discussed and applied. Technique is heavily drilled as well as some formula memorization. Previous Calculus free response questions are practiced and discussed.
After the AP exam, time will often allow for the presentation of L’Hopitals rule, volumes by shell method, and other concepts.

I.
Review (1 week)
A.
Linear models
B.
Graphs
C.
Functions
1.
Power
2.
Exponential
3.
Logarithmic
4.
Inverse
5.
Piecewise
D.
Transformations and compositions.
II.
Limits, Continuity, and Derivatives (7 weeks)
A. Limits
1. Numerical, Graphical
2. Analytical
B.
Continuity
C.
Derivatives
1.
Derivative definition
2.
Differentiation rules
3.
Product/Quotient
4.
Chain rule
5.
Implicit
D.
Applications
1.
Related Rates
2.
Extrema
3.
Rolle/MVT
4.
1 st
derivative test
5.
Concavity
6.
Curve sketching
7.
Optimization
8.
Differentials
III.
Integrals (3 weeks)
A.
Antiderivative
B.
Area
C.
Riemann sums
D.
Fundamental theorem of calculus
E.
Techniques
1.
Integration by substitution
2.
Numerical integration
IV.
Transcendental functions (4 weeks)
A.
Logarithms

1.
Differentiation
2.
Integration
B.
Exponential functions
C.
Growth and decay
D.
Differential equations
E.
Slope fields
F.
Inverse Trigonometric functions
V.
Applications of Integration (3 weeks)
A.
Area between curves
B.
Volumes of revolution
C.
Volumes of cross section
D.
Summing rates of change
VI.
Review for the AP exam (until exam)
Textbooks :
Finney, Demana, Waits, Kennedy. Calculus—Graphical, Numerical, Algebraic . Upper
Saddle River:Pearson/Prentice Hall. 2010.
Larson, Hostetler, Edwards. Calculus of a Single Variable. 7ed. Boston: Houghton
Mifflin Co., 2002.
Supplements:
You Tube: patrickjmt
Davidson Next modules
Graphing Calculators :
TI-83plus, TI-84, or TI-89