AP Calculus BC 2011-2012
Welcome to the second year of AP Calculus! This course is divided into 3 types of
material;
i) review of AP Calculus AB – basic derivatives, limits, integrals, etc
ii) new material that will be tested on the AP Calculus BC exam
iii) topics which are part of a second year college calculus course (these topics
will not be tested on the AP exam but will be tested during the year.)
There will be a lot of handouts given during class for class work and homework. Please
make sure that they are organized so that you can refer back to them easily when you
need to review for your quizzes, tests and the AP Exam.
These are some of the topics that will be covered in our class this year:
** Calc 2 topics will be handled this year as time permits.
** Specific topics from AP Calculus AB class will be reviewed briefly either as a warm up
problem or through practice AP exam problems.
Topic
Symmetry, Transformation & Differentiability
L’Hopital’s Rule for Indeterminate Forms
Business and Economics Applications
Newton’s Methods of Roots
Hyperbolic Trig
Approximation Using Differentials
The Definite Integral as Area
The Accumulation Function
Area Under Curve
Sigma Notation
Riemann Sums
Simpson’s Rule
Volume by Disks and Washers
Volume by Shells
Length of a Plane Curve
Area of a Surface of Revolution
Work Problems
Fluid Force Problems
Center of Mass Problems
Natural Logs and Exponentials
Differential Equations – Separation of
Variables
Exponential Growth
Integration by Parts
Curriculum
AB
BC
BC
Calc 2
Calc 2
BC
AB
AB
AB
AB
AB
BC
AB
BC
BC
BC
Calc 2
Calc 2
Calc 2
AB
AB
AB
BC
Integration of Powers of Sin and Cos
Integration by partial Fractions
Improper Integrals
Slope Fields
Differential Equations by Euler’s Method
Logistic Growth
Inverse Trig Functions
Inverse Trig Functions Derivatives and
Integrals
Curves Defined by Parametric Equations
Parametric Equations and Calculus
Polar Equations
Polar Equations Area, Arc Length, Surface
Area
Vectors in the Plane
Vector-valued Functions
Vector-valued Functions Velocity &
Acceleration
Taylor Polynomials and Approximations
Sequences
Infinite Series
Convergence of Infinite Series
Comparison of Series
Alternating Series
Ratio and Root Tests
Power Series
Representation of Functions by Power Series
Taylor and Maclaurin Series
Calc 2
BC
BC
AB
BC
BC
AB
AB
BC
BC
BC
BC
BC
BC
BC
BC
BC
BC
BC
BC
BC
BC
BC
BC
BC