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Differentiation practice

QCE Mathematical Methods · Original practice questions with worked solutions

All differentiation practice questions

98 original questions · Page 5 of 5

  1. Q358 · Original practice · 5 marks
    A water level varies sinusoidally. The minimum level is 44 m, the maximum is 1212 m and the period is 1010 hours. A minimum occurs at t=0t=0.
    Further applications of differentiation
  2. Q378 · Original practice · 6 marks
    For 0≤t≤120\leq t\leq12, a reservoir level is modelled by H(t)=7+3sin⁡(πt/6)H(t)=7+3\sin(\pi t/6) metres, where tt is measured in hours. An alarm sounds only when the level is above 99 m and rising at more than 11 m/hour. An engineer claims that the alarm will sound for at least 2020 minutes during this period. Evaluate the reasonableness of the claim.
    Further applications of differentiation