AP/Advanced Calculus Part 2 begins with additional topics related to derivatives, specifically first and second derivatives and their graphs. The study of derivatives concludes with optimization, linearization, and related rates. Students will study definite integrals and area under a curve. The topics include antiderivatives, the Fundamental Theorem of Calculus, the trapezoidal rule, slope fields, and antidifferentiation by substitution. The course concludes with the application of definite integrals. Students will study the integral as an accumulation function, the area under a curve, and the volume of a surface of revolution.
This course meets the Advanced Placement criteria required by the College Board.
*Note: AP/Advanced Calculus Parts 1 and 2 are intended to prepare students for the AP Calculus AB exam.
It is recommended that students successfully complete AP/Advanced Calculus Part 1 or equivalent course work before enrolling in this course. Successful completion of both Part 1 and Part 2 of this course is required for students to earn the AP designation.
Unit 1: Essential Content and Skills
- Use the first derivative test for local extrema.
- Define the phrase “point of inflection.”
- Read the graph of a derivative.
- Analyze the Second Derivative Test for local extrema.
- Solve application problems involving finding minimum or maximum values of functions.
- Use Newton’s method to approximate the zeros of a function.
- Estimate the change in a function using differentials.
Unit 2: Essential Content and Skills
- Find distance traveled when velocity varies.
- Discover rectangular approximation method (RAM).
- Analyze the definite integral and area.
- Evaluate integrals of constant functions.
- Integrate discontinuous functions.
- Apply rules for definite integrals.
- Find the average value of a function over a closed interval.
Unit 3: Essential Content and Skills
- Apply the Fundamental Theorem of Calculus.
- Use the Trapezoidal Rule and Simpson’s Rule.
- Construct and interpret slope fields as visualizations of differential equations.
- Compute indefinite integrals by the method of substitution.
- Solve exponential growth and decay problems by separation of variables.
- Solve problems involving exponential growth and decay in a variety of applications.
Unit 4: Essential Content and Skills
- Examine integrals as net change.
- Use integration to calculate area between curves, area enclosed by intersecting curves, and area using subregions.
- Integrate with respect to y to find the area of the region.
- Discover volume as an integral.
- Evualuate cross sections of unusually shaped solids.
- Adapt knowledge of integral calculus to model problems involving rates of change in a variety of applications.
- Calculus Graphical, Numerical, Algebraic (textbook, practice book, and CD)