AP Calculus AB Syllabus 2012/2013
Philosophy
The school provides a differentiated curriculum in math that includes remedial, core, regular,
enriched and accelerated choices. For enrichment the school has an extensive math contest
program including ASMA, ATPAC, CNML, AMC/AIME, and the Canadian National Contest
Pascal, Cayley, Fermat and Euclid. For acceleration, the school has AP Calculus AB to provide
talented math students with continuous learning. Also, one way to deepen understanding of Math
8-12 is by studying calculus.
Assessment/Evaluation
Both formative and summative evaluation is used. Smaller quizzes occur unannounced in class.
There are unit tests after each chapter and review tests, including a number of chapters. Larger
cumulative tests occur at mid-year, before the May AP exam and at year end to complete the
school mark in the course.
Text
Stewart, James Single Variable Calculus 4th edition. Brookes/Cole Publishing Co. 1999 ISBN
0-534-35562-5*
Support Text: Be Prepared for the AP Calculus Exam. Mark Howell and Martha Montgomery.
Skylight Publishing, Andover, Mass. ISBN 0-9727055-5-4
*each topic has assigned questions for student from student text*
Support:
1. college board AP materials – course outline, old exams
2. Support Text: Be Prepared for the AP Calculus Exam. Mark Howell and Martha
Montgomery. Skylight Publishing, Andover, Mass. ISBN 0-9727055-5-4
3. Support Text: Theory and Problems of Beginning Calculus. Elliott Mendelson. Schaum’s
Outline Series McGraw-Hill, INC. ISBN 0-07-041465-3
4. Guided notes and exercises.
5. Calculator used: TI-83 or better
Chapter 2: Limits and Rates of Change ( 3 weeks)
1.
2.
3.
4.
5.
6.
Velocity, as tangent to a curve. Slope of secant with/without calculator.
Limit of a function, so that x  0 - secant line becomes a tangent line.
Calculating limits using limit laws. Using calculator to estimate limit to compare with
analytic answer.
Continuity of functions.
Velocities and the rate of change (eg. Temperature). Work problems.
Chapter review exercises.
Chapter 3: Derivatives (4 weeks)
1.
2.
3.
Slope of a function at a point. Check with dy/dx on calculator.
Derivative: Another function that reports on the original’s slope at any point. The
lim f ( x  h)  f ( x)
f ' ( x) 
h0
h
Differentiation formulas- rule to calculate f ' more easily from f.
4.
5.
6.
7.
8.
9.
10.
11.
Applications of the derivative: velocity, linear density, electric current, chemical
reactions, population growth, marginal cost.
Deriviatives of trigonometric functions including numerical estimate of
lim sin 
, Calculations and problems.
 0 
Chain rule.
Implicit differentiation.
Higher derivatives.
Related rates.
Linear approximations and differentials.
Chapter Review exercises…… Chapter 2/3 Test.
Some Classroom notes to date:
1.
2.
3.
4.
5.
Students must keep a list of homework assignments at the front of homework
section in notebooks. Homework assignments must be ordered, work shown,
answers marked. Most homework assignments 15-25 questions.
Quizzes happen about once every week or two. Could be a surprise.
Students asked to come to the whiteboard/smartboard at front of room to present
full solutions to questions.
Students are encouraged to write math contests in our school contest program.
These include CNML and various Canadian contests COMC, Euclid, etc.
Stewart text has word problems for most topics. Guided notes in class have many
exercise questions for students to attempt.
Chapter 4: Applications of Differentiations (5 weeks)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Maximum and minimum values. Check on TI-83/84.
Mean value theorem.
What does f’ and f” say about f.
Asymptotes
Summary of curve sketching A-H procedure. (A) domain/range, (B) intercepts, (C)
symmetry, (D) asymptotes, (E) intervals increase/decrease, (F) local max/min, (G)
concavity, (H) the curve. Interactions between analytic and graphing calculators
approaches (including zoom, trace, CALC….)
Optimization problems. Students present solutions at the board.
Applications to economics.
Newton method. Program TI-83/84 to run many-step calculations
Anti-derivatives F  f  f '
Chapter Review exercises ……..Chapter 4 test
Chapter 5 Integrals (5 weeks)
1.
2.
Areas and distance
The definite integral as the sum on an infinite number of infinitesimally thin
rectangles. Use TI-83/84  f (x) approx.
3.
4.
Fundamental Theorem of Calculus.
Indefinite integrals and total change including relations between s(t), v(t) and a(t).
5.
Substitution rule – allows you to “
inverse
” the chain rule. Later integration by parts
reverse
inverse
” the product rule. F  f  f '
reverse
Chapter Review exercises ………Chapter 5 test.
will “
6.
More Classroom notes to date:
1.
2.
3.
Sources for questions for tests include Brookes/Cole website Calculus test bank (free
with text purchase) , LXR databank and Access testbank for calculus. Tests include
multiple choice and full response questions.
Quiz questions most frequently based on lesson exercises and text homework questions.
Study chart technique used. Students must identify main topics with explanations and
examples (in own words).
Chapter 6: Applications of Integration (5 weeks)
1.
2.
3.
4.
Areas between curves.
Volumes – Disk, washer.
Volume by cylindrical shells.
Work =  fds
5.
6.
Average value of a function
Review Exercises…….Chapter 6 test.
Chapter 7: Inverse functions (exponential, logarithmic and inverse trig. functions) (5 weeks)
1.
2.
3.
4.
5.
6.
1
f ' ( g (a ))
Exponential functions and their derivatives.
Logarithmic functions and their derivatives.
Inverse trigonometric functions and their derivatives.
Indeterminate forms and l’Hopital’s rule.
Chapter review exercises ……. Chapter 7 test.
Inverse function g ' (a ) 
Chapter 8: Techniques of Integration/ Chapter 10: Differential Equations / Review for may AP
exam (3 weeks)
1.
2.
3.
4.
5.
6.
Integration by parts (8.1) (Optional for AB course)
Modelling with differential equations (10.1)
Direction fields (10.2)
Separable differential equations. (10.3)
Exponential growth and decay (10.4)
Review AP course description. Practice AP multiple choice and full response
questions. Students work in small groups helping each other to solve problems. For
some exercises, students must provide the “answer key”, for the class.
Total 30 weeks.