LEARN NC

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

Advanced Placement Calculus

Goal 2: Geometry and Measurement - The learner will use derivatives to solve problems.

Objective 2.06. Apply the derivative in graphing and modeling contexts.

  • Analyze curves, with attention to monotonicity and concavity.
  • Optimize with both absolute (global) and relative (local) extrema.
  • Model rates of change, including related rates problems.
  • Use implicit differentiation to find the derivative of an inverse function.
  • Interpret the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration.
  • Interpret differential equations geometrically via slope fields and the relationship between slope fields and solution curves for differential equations.

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

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