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1.9 Numerical Methods (A-level only)

1.9 Numerical Methods (A-level only)

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Question 74

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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Markscheme

1.9 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.9 Numerical Methods (A-level only)

125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 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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