October 2021 Paper 1 Q5

OCR ACurrent spec8 marksDifferentiationModelling

5 The fuel consumption of a car, \(C\) miles per gallon, varies with the speed, \(v\) miles per hour. Jamal models the fuel consumption of his car by the formula

\(C = \frac{12}{5}v - \frac{3}{125}v^2\), for \(0 \leqslant v \leqslant 80\).

(a) Suggest a reason why Jamal has included an upper limit in his model. [1]
(b) Determine the speed that gives the maximum fuel consumption. [4]

Amaya’s car does more miles per gallon than Jamal’s car. She proposes to model the fuel consumption of her car using a formula of the form

\(C = \frac{12}{5}v - \frac{3}{125}v^2 + k\), for \(0 \leqslant v \leqslant 80\), where \(k\) is a positive constant.

(c) Give a reason why this model is not suitable. [1]
(d) Suggest a different change to Jamal’s formula which would give a more suitable model. [2]
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