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3.1 Algebra and functions (A-level only)

3.1 Algebra and functions (A-level only)

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Question 192
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]
Markscheme

3.1 Algebra and functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.1 Algebra and functions (A-level only)

281 exam-style questions on CCEA A Level Maths 3.1 Algebra and functions (A-level only), covering 3.1.1 Algebra and functions (A-level only), 3.1.2 Algebra and functions (A-level only), 3.1.3 Algebra and functions (A-level only), 3.1.4 Algebra and functions (A-level only), 3.1.5 Algebra and functions (A-level only), 3.1.6 Algebra and functions (A-level only), 3.1.7 Algebra and functions (A-level only), 3.1.8 Algebra and functions (A-level only), 3.1.9 Algebra and functions (A-level only), and 3.1 Algebra and functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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