The rate of change of a bio-reactant R R\,R over a period of time t t\,t minutes is modelled by the function:
R(t)=11t+1(1−3t)(t+2),0≤t<13 R(t) = \frac{11t + 1}{(1 - 3t)(t + 2)}, \quad 0 \le t < \frac{1}{3} R(t)=(1−3t)(t+2)11t+1,0≤t<31Express R(t)R(t)R(t) in partial fractions.
(i) Hence find the binomial series expansion of R(t)R(t)R(t) in ascending powers of ttt, up to and including the term in t2t^2t2. Give each coefficient as a simplified fraction.
(ii) State the range of values of t t\,t for which the expansion in (b)(i) is valid.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
