The net harvesting efficiency EEE of a solar panel array over time ttt (in years) is modeled by the function:
E(t)=3−t−2t+4+t+702t2+5t−12,t>4 E(t) = 3 - \frac{t - 2}{t + 4} + \frac{t + 70}{2t^2 + 5t - 12}, \quad t > 4 E(t)=3−t+4t−2+2t2+5t−12t+70,t>4Show that
E(t)=at+bct+d,t>4 E(t) = \frac{at + b}{ct + d}, \quad t > 4 E(t)=ct+dat+b,t>4where a,b,ca, b, ca,b,c and ddd are integers to be found.
Determine an expression for E−1(x)E^{-1}(x)E−1(x).
Find 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.