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.
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.