• ADVANCED PLACEMENT CALCULUS

    BC - AP LEVEL
Code: M681 Full Year (12) (1 credit) (rank weight 1.10)

    NOTE: This full year course covers a solid year of college calculus and is considerably more intensive than Advanced Placement Calculus AB. The curriculum closely follows the Advanced Placement Program of the College Board. The syllabus has been reviewed and approved by the AP audit. Each student is expected to take the Advanced Placement BC Calculus Examination in May. A score of 3, 4, or 5 can result in a year’s credit in coursework at many colleges. The fee for this exam is determined by the College Board and is the responsibility of the student. In the event that a student does not take the AP Exam, the student’s report a rank weight of 1.05.

    Areas of Study Include:

    - Simplify expressions, solve equations, transform functions, and graph functions involving the functions used in calculus including functions in parametric form.

    - Use of a graphing calculator to draw a complete graph intersections of functions, storing functions, and performing algebraic manipulations

    
- Distinguish between determinate and indeterminate limits - Evaluate limits graphically, numerically and analytically
- Recognize the three ways a Limit does not exist

    and end behavior models using limits
- Recognize the ways pixels can be deceiving on a graph-

    numerically and graphically

    • -  Evaluate derivatives numerically, and recognize when a 

derivative does not exist 


    • -  Recognize the four ways a derivative does not exist 


    • -  Understand the relationship between continuity and dif
ferentiability 


    • -  Given the graph of a function approximate the rate of change 
and produce a feasible graph of the derivative of the function 


    • -  Determine derivatives using differentiation rules and tech- niques for polynomial rational, radical, trigonometric, inverse trigonometric, logarithmic, exponential, and piecewise 

quotients, powers, and compositions of these functions 


    • -  Determine derivatives of functions and their inverses using 
implicit differentiation 


    • -  Determine derivatives using logarithmic differentiation 
especially when complicated and to interpret graphically and in context 


    • -  Find equations of tangent lines and estimate function evalu- 
ations using linearization 


    • -  Demonstrate and apply the intermediate value theorem, 
extreme value theorem, Rolles Theorem, and the mean 
value theorem 
and regions of increase, decrease, monotonicity, positive concavity, and negative concavity

    • -  Use derivatives to study rates of change of a variety of phenomena including motion. 


    -  Use derivatives to model and solve a variety of optimization problems 


    -  Use derivatives to model and solve a variety of related rates problems 
derivative applications 


    -  Evaluate integrals numerically using the left, right, midpoint, 
and trapezoidal rules, and realize the possible errors 


    • -  Given the graph of the function, produce a feasible graph of the antiderivative as the net accumulation of a rate of change 


    • -  Evaluate integrals using the Fundamental Theorem of 
Calculus
- 
tions using integration rules and techniques based on antiderivatives including linearity, change of variable, and by parts 


    - Use the Variable Limits Theorem to evaluate the derivative of an integral with variable limits

    antiderivatives especially when complicated

    -  Antidifferentiation by substitution and by parts 


    • -  Modeling problems involving Exponential Change includ- 
ing Population Problems, Newton’s Law of Cooling, Con- tinuous and Discrete Compound Interest, and Radioactivity with separable differential equations and analytically solving them 


    -  Modeling Social Diffusion Problems with the Logistics Equa- tion and solving using Partial Fractions 
- ing them by Euler’s method with and without the graphing calculator 


a varying rate of change over an interval
- Determine area of a region
-Determine volumes of solids of revolution by washers 
and shells
- Determine volumes of solids of known cross section
- Determine travel distance of a particle 
the average value of a function 


    -  Solve work problems 


    • -  Analyze motion problems 


    • -  Determine curve length 


    -  Determine when to use a graphing calculator to evaluate Page 60 


    integrals, especially when complicated, which occur in these applications

    • -  Studying sequences, especially arithmetic and geometric, 


    • -  Using L’Hopital’s Rule to evaluate limits 


    • -  Using limits to study function growth rate 


    • -  Using limits to evaluate improper integrals 



    • -  Identify and use geometric series to represent repeating 
decimals and to model discrete exponential change 


    • -  Write the McLaurin series for common functions and then manipulate them by change of variable, differentiation, and 

derivatives at the center 


    • -  Use the Alternating Series Estimation Theorem and the 

Taylor polynomials 


    • -  Use Taylor series to represent and Taylor polynomials to 
estimate irrational numbers involving radicals and transcen- 
dental functions
-Graphically estimate convergence intervals and error 
bounds
- Apply convergence tests to determine the radius of conver- 
gence and convergence interval of a power series - Use a Graphing Calculator to investigate Taylor polynomial 
approximations and errors numerically and graphically 
- Take derivatives of parametric functions and use them to 
- Model and solve motion problems using derivatives of parametric equations 
- Recognize polar coordinates as a special case of parametrics. - Take derivatives of polar functions and use them to describe 


- Use a Graphing Calculator in these problems especially 
when complicated 
- A geometric series example: how mortgages work. - Balancing chemical equations with matrices
-

    • Challenge problems
- Preview to multivariable calculus and linear algebra

    

For the complete AP Curriculum see: http://apcentral.collegeboard.com