LEARN NC

K–12 teaching and learning · from the UNC School of Education

Advanced Placement Calculus

Goal 3: Algebra - The learner will use integrals to solve problems.

Objective 3.04. Define and use appropriate integrals in a variety of applications.

  • Interpret the integral of a rate of change to give accumulated change.
  • Find specific anti-derivatives using initial conditions.
  • Set up and use an approximating Riemann sum or trapezoidal sum and represent its limit as a definite integral.
  • Find the area of a region.
  • Find the volume of a solid with known cross sections.
  • Find the average value of a function.
  • Find the distance traveled by a particle along a line.
  • Solve separable differential equations and use them in modeling. In particular, study the equation y' = ky and exponential growth.

Additional related resources

We’re in the process of aligning our content for students to the Standard Course of Study. As we do, you’ll find it here.

General resources

Aligned lesson plans

Slice it! Rotate it!: Volumes of revolution
The students will first view the animated slicing and rotating of various area about the x-axis or about different lines at internet sites. Then the student will complete a lab experience in which various food items will be examined as to what planar region created them.
Format: lesson plan (grade 9–12 Mathematics)
By Sharon Whitted.

Resources on the web

Fretting
In this lesson, one of a multi-part unit from Illuminations, students use their discoveries from the first lesson to place frets on a fretless instrument. They then compare geometric sequences with exponential functions. (Learn more)
Format: lesson plan (grade 9–12 Mathematics)
Provided by: National Council of Teachers of Mathematics