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1.5 B: Algebra and functions

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Question 184

The growth rate H(s)H(s)H(s) of a synthetic crystal, where sss is the concentration of an additive, is modeled by the function:

H(s)=9s+4(1−3s)(2+s) H(s) = \frac{9s + 4}{(1 - 3s)(2 + s)} H(s)=(1−3s)(2+s)9s+4​
a.

Express H(s)H(s)H(s) in partial fractions.

[4]
b.

Hence find the binomial series expansion of H(s)H(s)H(s) in ascending powers of sss, up to and including the term in s2s^2s2. Give each coefficient as a simplified fraction.

[6]
c.

Determine the range of values of sss for which the expansion in (b)(i) is valid.

[2]

1.5 B: Algebra and functions Questions

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

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.

Question bank