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+48Show that
E(t)=at+bct+d,t>5 E(t) = \frac{at + b}{ct + d}, \quad t > 5 E(t)=ct+dat+b,t>5where a,b,c a, b, c\,a,b,c and d d\,d are integers to be found.
Find an expression for E−1(x)E^{-1}(x)E−1(x).
Determine the domain of E−1E^{-1}E−1.
303 exam-style questions on OCR (MEI) A Level Maths 1.2 Algebra, covering 1.2.1 Algebraic vocabulary and notation, 1.2.2 Solve linear equations, 1.2.3 Change the subject of a formula, 1.2.4 Solve quadratic equations, 1.2.5 Discriminant of a quadratic, 1.2.6 Linear simultaneous equations, 1.2.7 One linear one quadratic simultaneous equations, 1.2.8 Points of intersection and solutions, 1.2.9 Linear inequalities, 1.2.10 Quadratic inequalities, 1.2.11 Expressing solutions of inequalities, 1.2.12 Use and manipulate surds, 1.2.13 Rationalise the denominator, 1.2.14 Laws of indices, 1.2.15 Negative, fractional and zero indices, 1.2.16 Proportional relationships, 1.2.17 Partial fractions (A-level only), and 1.2.18 Simplify rational expressions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.