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1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

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Question 59

The gain response, GGG, of a specialized amplifier is modeled by the function G(t)=log⁡2(4t)G(t) = \log_2(4t)G(t)=log2​(4t), where ttt is the signal frequency in kHz. The table below shows values of GGG for specific frequencies recorded during a test.

t246810G3.004.004.585.005.32\begin{array}{|c|c|c|c|c|c|} \hline t & 2 & 4 & 6 & 8 & 10 \\ \hline G & 3.00 & 4.00 & 4.58 & 5.00 & 5.32 \\ \hline \end{array}tG​23.00​44.00​64.58​85.00​105.32​​

Using the trapezium rule with all the values of GGG in the given table,

a.

obtain an estimate for ∫210log⁡2(4t) dt\int_{2}^{10} \log_2(4t) \, dt ∫210​log2​(4t)dt, giving your answer to one decimal place.

[4]
b.

Using your answer to part (a) and making your method clear, estimate

(i) ∫210log⁡2(64t3)5 dt\int_{2}^{10} \frac{\log_2(64t^3)}{5} \, dt ∫210​5log2​(64t3)​dt

(ii) ∫210log⁡2(16t) dt\int_{2}^{10} \log_2 \left(\frac{16}{t}\right) \, dt ∫210​log2​(t16​)dt

[5]
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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