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Mathematics · Grade 11

Functions and Rates of Change

Learners open the calculus elective by studying how fast quantities change. They compute average rates of change with units, estimate instantaneous rates from tables and graphs using local linearity, connect position and velocity, approximate with tangent lines, and simplify difference quotients in preparation for the formal definition of the derivative.

  • 4 lessons
  • About 135 minutes
  • Rates of change check: 11 questions
  • Ways to answer: fill in the blanks, choose an answer, match pairs, type a number, put in order and sort into groups
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What learners will discover

  • Compute and interpret average rates of change with units as slopes of secant lines.
  • Estimate instantaneous rates of change from tables and graphs, using local linearity and symmetric difference quotients.
  • Relate position and velocity, interpret the sign of velocity and speed, and approximate values with a tangent line.
  • Simplify difference quotients algebraically and find the value they approach as h → 0.

Lessons

  1. Average rate of change 5 steps3 practiceabout 30 min
  2. Estimating instantaneous rates 5 steps3 practiceabout 34 min
  3. Position, velocity and tangent lines 6 steps3 practiceabout 34 min
  4. Difference quotients 6 steps3 practiceabout 37 min
  5. Rates of change check 11 questions at the end

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