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3.1 Algebra and functions (A-level only)

3.1 Algebra and functions (A-level only)

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Question 117
40%

A logistics company models the operating efficiency, EEE, of its delivery fleet as a function of the average daily hours in service, ttt. For t>5t > 5t>5, the efficiency is defined by

E(t)=5−t+5t−2+16t+48t2+t−6 E(t) = 5 - \frac{t + 5}{t - 2} + \frac{16t + 48}{t^2 + t - 6} E(t)=5−t−2t+5​+t2+t−616t+48​
a.

Show that

E(t)=at+bct+d,t>5 E(t) = \frac{at + b}{ct + d}, \quad t > 5 E(t)=ct+dat+b​,t>5

where a,b,c a, b, c\,a,b,c and d d\,d are integers to be found.

[6]
b.

Find an expression for E−1(x)E^{-1}(x)E−1(x).

[3]
c.

Determine the domain of E−1E^{-1}E−1.

[4]
Markscheme

3.1 Algebra and functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.1 Algebra and functions (A-level only)

281 exam-style questions on CCEA A Level Maths 3.1 Algebra and functions (A-level only), covering 3.1.1 Algebra and functions (A-level only), 3.1.2 Algebra and functions (A-level only), 3.1.3 Algebra and functions (A-level only), 3.1.4 Algebra and functions (A-level only), 3.1.5 Algebra and functions (A-level only), 3.1.6 Algebra and functions (A-level only), 3.1.7 Algebra and functions (A-level only), 3.1.8 Algebra and functions (A-level only), 3.1.9 Algebra and functions (A-level only), and 3.1 Algebra and functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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