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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 318
a.

(i) Find the binomial expansion of (1+3p)−1(1 + 3p)^{-1}(1+3p)−1 up to and including the term in p2p^2p2.

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

12−5p \frac{1}{2 - 5p} 2−5p1​

form a geometric sequence and state the common ratio.

[4]
b.

For an automated control system, the sensitivity factor S(p)S(p)S(p) depends on a small perturbation ppp, where

S(p)=55p(1+3p)(2−5p) S(p) = \frac{55p}{(1 + 3p)(2 - 5p)} S(p)=(1+3p)(2−5p)55p​

Express S(p)S(p)S(p) in the form P2−5p+Q1+3p\frac{P}{2 - 5p} + \frac{Q}{1 + 3p}2−5pP​+1+3pQ​ where PPP and QQQ are integers.

[3]
c.

(i) Using your answers to parts (a) and (b), find the binomial expansion of

G(p)=22p(1+3p)(2−5p) G(p) = \frac{22p}{(1 + 3p)(2 - 5p)} G(p)=(1+3p)(2−5p)22p​

up to and including the term in p2p^2p2.

(ii) Determine the range of values of ppp for which the binomial expansion of G(p)G(p)G(p) is valid.

[3]
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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