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AS91578 Differentiation

Optimisation

AAchieved

  1. 1A Christchurch irrigation channel has a rectangular cross-section. Its two sides and its base have a total length of 12 m, so with depth d m the width is 12 − 2d m and the cross-sectional area is A = d(12 − 2d) m². Find the depth that gives the greatest cross-sectional area. You may assume this gives a maximum.Free
  2. 2A Dunedin packaging line makes open-top boxes from 40 cm × 40 cm squares of card by cutting a square of side x cm from each corner and folding up the sides. The volume of a box is V = (40 − 2x)²x cm³, for 0 < x < 20. Find the value of x that gives the greatest volume. You may assume this gives a maximum.Free
  3. 3The running cost of a ferry, in dollars per kilometre, is C = 0.2v + 500/v, where v is its speed in km/h. Find the speed that gives the lowest running cost. You may assume this gives a minimum.Free
  4. 4A Achieved question, in the pass🔒 Pass
  5. 5A Achieved question, in the pass🔒 Pass

MMerit

  1. 6A Merit question, in the pass🔒 Pass
  2. 7A Merit question, in the pass🔒 Pass
  3. 8A Merit question, in the pass🔒 Pass
  4. 9A Merit question, in the pass🔒 Pass
  5. 10A Merit question, in the pass🔒 Pass

EExcellence

  1. 11A Excellence question, in the pass🔒 Pass
  2. 12A Excellence question, in the pass🔒 Pass
  3. 13A Excellence question, in the pass🔒 Pass
  4. 14A Excellence question, in the pass🔒 Pass
  5. 15A Excellence question, in the pass🔒 Pass
  6. 16A Excellence question, in the pass🔒 Pass