The student will become conversant the language and notation math

CDRP: AP Calculus BC

Enduring Understandings

5. The student will begin to develop a meta-cognitive approach to learning. That is, the student will begin to think about his or her thinking process and how that affects his or her learning.

6. The student will develop a confidence and tenacity when approaching lengthy and intricate math problems. By breaking down a problem into its component parts, analyzing and resolving each part, and then reassembling the whole, the student will develop a sense that no problem is beyond his or her grasp.

3. How do all the problems relate to one another?

Why do some people find this interesting? Can it interest me? 4.

1.The achievement of the learning outcomes for each unit will be assessed by a Chapter Test which will be half multiple choice and half free response. These tests will be graded on the AP scale.

2.There will be a Fall Midterm Exam.

By the end of this unit, the student will be able to:

•Use the Power Rule and Exponential Rules to find Derivatives.

•Find higher order derivatives.

•Take derivatives of relations implicitly.

Unit II Anti-Derivatives

By the end of this unit, the student will be able to:

•Use the Integration by Substitution to integrate integrands involving •Secant and Tangent or Cosecant and Cotangent.

•Given a separable differential equation, find the general solution. •Given a separable differential equation and an initial condition, find a particular solution.

Unit III Integrals

By the end of this unit, the student will be able to:

•Understand the difference between displacement and total distance.

•Extend that idea to understanding the difference between the two concepts in other contexts.

•Prove continuity or discontinuity of a given function.

•Interpret Vertical Asymptotes in terms of one-sided limits.

•Recognize and evaluate Limits which are derivatives.

•Use the nDeriv function on the calculator to find numerical derivatives. •Evaluate Limits at infinity.

•Identify Sequences and Series
•Find Partial Sums of a given Series.

•Find the terms, partial sums, infinite sums, or n in a geometric sequence. •Determine the convergence or divergence of a sequence.

By the end of this unit, the student will be able to:

•Find critical values and extreme values for functions.

•Solve optimization problems.

•Use the derivative to make conclusions about motion.

•Use the graph of a function to answer questions concerning maximums, minimums, and intervals of increasing and decreasing

•Use the graph of a function to answer questions concerning points of inflection and intervals of concavity.

•Find the volume of a solid rotated when a region is rotated about a given axis

•Find the volume of a solid rotated when a region is rotated about a given line •Find the volume of a solid with given cross sections.

•Apply the Integration by Parts method.

•Integrate radical integrands using trig substitution.

•Apply Partial Fractions to the proper type of integral.

•Apply Partial Fractions to integrals with Quadratic factors.

•Eliminate the parameter to identify the function form of a parametric. •Find the slope of a tangent line to a curve in parametric mode.

•Find the concavity of a curve in parametric mode.

•Determine and interpret intervals of increasing or decreasing of a polar curve.

•Find slopes of lines tangent to polar curves.

•Create a Taylor polynomial from give numerical derivatives.

•Identify numerical derivatives from a given Taylor or Maclaurin polynomial.

•Find the Interval of Convergence for a given series.