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World 5 · The shape of change · 6 min · PRO

Two directions, two slopes

Probe a surface at one point

PRO · Calculus & Probability

World 5: The shape of change is part of PRO

The first world of Calculus & Probability is free. PRO opens the other 48 lessons in 6 worlds — simulations, quizzes and all.

  • Walk without climbing
  • Find the steepest climb
  • The best view on a circular trail
  • Lift a hill through its contours
  • Read steepness from a map
PRO includes
  • All 26 labs — every world, every lesson
  • Practice exams and certificates

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