Skip to content
MathsGenie logo
Quick links
Open app

Course home

  1. A Level
  3. Maths CCEA
  5. Question bank

3.7.3 Numerical methods (A-level only)

Medium
1234567891011121314151617181920212223242526272829303132333435363738394041424344
Question 23

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]

3.7.3 Numerical methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.7.3 Numerical methods (A-level only)