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1.9 Numerical Methods (A-level only)

1.9 Numerical Methods (A-level only)

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Question 82

An engineer is monitoring the output voltage V(t)V(t)V(t) of a circuit at different times ttt (measured in seconds). He correctly evaluates:

V(1)=−5 V and V(3)=5 V V(1) = -5 \text{ V and } V(3) = 5 \text{ V} V(1)=−5 V and V(3)=5 V

and concludes that there must be at least one time t∈(1,3)t \in (1, 3)t∈(1,3) where the voltage is zero, due to the change of sign. For which of the following models is this conclusion incorrect?

  • V(t)=5t−10V(t) = 5t - 10V(t)=5t−10
  • V(t)=5t−2V(t) = \frac{5}{t-2}V(t)=t−25​
  • V(t)=54(t−2)3+154(t−2)V(t) = \frac{5}{4}(t-2)^3 + \frac{15}{4}(t-2)V(t)=45​(t−2)3+415​(t−2)
  • V(t)=10t−20t+1V(t) = \frac{10t - 20}{t+1}V(t)=t+110t−20​
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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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