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Mathematics · Grade 12

Vectors and Parametric Representations

Learners represent quantities with both size and direction as vectors, combine them, use the dot product to measure angles and work, solve navigation and force problems, and describe motion with parametric equations such as the path of a launched ball. An optional honors lesson introduces polar coordinates.

  • 5 lessons
  • About 145 minutes
  • Vectors and parametric equations check: 11 questions
  • Ways to answer: choose an answer, plot points, match pairs, type a number, put in order and sort into groups
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What learners will discover

  • Represent vectors in component and magnitude-direction form, and add, subtract and scale them.
  • Use the dot product to find angles between vectors, test orthogonality and compute work.
  • Solve applied problems with resultant forces and relative velocities.
  • Describe motion and curves with parametric equations and eliminate the parameter.

Lessons

  1. Vectors and their operations 5 steps3 practiceabout 30 min
  2. The dot product 5 steps3 practiceabout 30 min
  3. Forces and navigation 5 steps2 practiceabout 28 min
  4. Parametric equations of motion 6 steps4 practiceabout 32 min
  5. Going further (honors): polar coordinates 4 steps2 practiceabout 25 min
  6. Vectors and parametric equations check 11 questions at the end

Keep exploring

More 12th grade math

Guide for grown-ups