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Mathematics · Grade 12

Rates of Change and Limits Readiness

Learners prepare for calculus by moving from average to instantaneous rates of change: secant slopes that approach a tangent slope, difference quotients simplified with algebra, limits read from tables, graphs and formulas, informal continuity, and limits at infinity that describe end behavior.

  • 4 lessons
  • About 135 minutes
  • Rates and limits check: 11 questions
  • Ways to answer: choose an answer, match pairs, type a number, place on a number line, put in order and sort into groups
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What learners will discover

  • Distinguish average and instantaneous rates of change and estimate instantaneous rates from secant slopes.
  • Simplify difference quotients algebraically and interpret the result as h approaches 0.
  • Evaluate limits from tables, graphs and algebra, including one-sided limits, and decide informally whether a function is continuous.
  • Use limits at infinity and infinite limits to describe end behavior and asymptotes.

Lessons

  1. From average to instantaneous rates 6 steps3 practiceabout 33 min
  2. Difference quotients 5 steps3 practiceabout 32 min
  3. Limits and continuity 5 steps3 practiceabout 36 min
  4. Limits involving infinity 5 steps3 practiceabout 34 min
  5. Rates and limits check 11 questions at the end

Keep exploring

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Guide for grown-ups