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1.12 I: Numerical methods (A-level only)

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Question 73

The pressure PPP (in kilopascals) at a specific depth in a hydraulic system is modelled by the equation

g(P)=P5+12P−8000 g(P) = P^5 + 12P - 8000 g(P)=P5+12P−8000
a.

Show that the equation g(P)=0g(P) = 0g(P)=0 has a root β\betaβ in the interval [6,7][6, 7][6,7].

[2]
b.

Using the iterative formula

Pn+1=8000−12Pn5withP1=6.2 P_{n+1} = \sqrt[5]{8000 - 12P_n} \quad \text{with} \quad P_1 = 6.2 Pn+1​=58000−12Pn​​withP1​=6.2

(i) Calculate the value of P2P_2P2​, giving your answer to 4 decimal places. (ii) By performing repeated iterations, find the value of β\betaβ to 4 decimal places.

[3]
Markscheme

1.12 I: Numerical methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.12 I: Numerical methods (A-level only)

125 exam-style questions on AQA A Level Maths 1.12 I: Numerical methods (A-level only), covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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