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1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

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Question 75

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​
[3]
Markscheme

1.10 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.10 Numerical Methods (A-level only)

137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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