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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 200

The cooling efficiency, EEE, of a high-performance server rack is modelled by the function

E(v)=5v−2v−4,v>4 E(v) = \frac{5v - 2}{v - 4}, \quad v > 4 E(v)=v−45v−2​,v>4

where v v\,v is the coolant flow rate in litres per minute.

a.

Use differentiation to show that E E\,E is a decreasing function on its domain.

[3]
b.

Find an expression for E−1(v)E^{-1}(v)E−1(v) and state its domain.

[4]
ci.

Show that the composite function EE(v)EE(v)EE(v) can be written in the form av+bv+c\displaystyle \frac{av + b}{v + c}v+cav+b​, where a,b, a, b,\,a,b, and c c\,c are integers to be found.

[3]
cii.

Deduce the range of EEEEEE.

[3]
Markscheme

3 Unit A2 1: Pure Mathematics (A-level only) Questions

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