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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 182

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]
Markscheme

1.5 B: Algebra and functions Questions

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

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, 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). Each one has a worked solution and a mark scheme showing where the marks go.

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