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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 16
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

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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