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1.12 I: Numerical methods (A-level only)

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Question 73

A physicist is measuring the net magnetic flux density BBB inside a custom solenoid as the control current III is adjusted. The physicist correctly evaluates the flux density at two specific current levels:

B(−5)=−2 and B(5)=2 B(-5) = -2 \text{ and } B(5) = 2 B(−5)=−2 and B(5)=2

and concludes that there must be an equilibrium current level in the interval I∈(−5,5)I \in (-5, 5)I∈(−5,5) where the flux density is exactly zero (B=0B = 0B=0), citing the change of sign. For which of the following models for B(I)B(I)B(I) is this conclusion incorrect?

  • B(I)=0.4IB(I) = 0.4IB(I)=0.4I
  • B(I)=10IB(I) = \frac{10}{I}B(I)=I10​
  • B(I)=0.016I3B(I) = 0.016I^3B(I)=0.016I3
  • B(I)=6II+10B(I) = \frac{6I}{I+10}B(I)=I+106I​
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1.12 I: Numerical methods (A-level only) Questions

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

Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions 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), 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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