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1.5 B: Algebra and functions

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Question 276
a.

(i) Find the binomial expansion of (1+3x)−1(1 + 3x)^{-1}(1+3x)−1 up to and including the term in x2x^2x2.

(ii) Show that the first three terms in the binomial expansion of

15−2x \frac{1}{5 - 2x} 5−2x1​

form a geometric sequence and state the common ratio.

[5]
b.

It is given that

85x(1+3x)(5−2x)≡P5−2x+Q1+3x \frac{85x}{(1 + 3x)(5 - 2x)} \equiv \frac{P}{5 - 2x} + \frac{Q}{1 + 3x} (1+3x)(5−2x)85x​≡5−2xP​+1+3xQ​

where PPP and QQQ are integers. Find the value of PPP and the value of QQQ.

[3]
c.

(i) In a structural model, the stress SSS on a beam at distance xxx from the support is given by S(x)=17x(1+3x)(5−2x)S(x) = \frac{17x}{(1 + 3x)(5 - 2x)}S(x)=(1+3x)(5−2x)17x​. Using your answers to parts (a) and (b), find the binomial expansion of S(x)S(x)S(x) up to and including the term in x2x^2x2.

(ii) Determine the range of values of xxx for which the binomial expansion of S(x)S(x)S(x) is valid.

[5]

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.

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