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Grade 12 · Calculus
Optimisation & Rates of Change (Grade 12)
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Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    A rectangle has a perimeter of 40 m. Determine its maximum possible area.
    (2)
  2. 2
    The height of a ball is s(t) = 20t − 5t². Determine its velocity after 1 second.
    (2)
  3. 3
    For the same ball, determine when it reaches its maximum height.
    (2)
  4. 4
    For the same ball, determine its maximum height.
    (2)
  5. 5
    For the same ball, determine its velocity when it strikes the ground.
    (2)
  6. 6
    Determine the acceleration of the ball.
    (2)
  7. 7
    Why must you use the constraint before differentiating?
    (2)
  8. 8
    What does a negative velocity tell you?
    (2)
TOTAL: 16 marks
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