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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 146
i.

The intensity of light I I\,I at a distance w w\,w from a source is modeled by the equation

I(w)=e4wsec⁡2w,−π4<w<π4 I(w) = e^{4w} \sec 2w, \quad -\frac{\pi}{4} < w < \frac{\pi}{4} I(w)=e4wsec2w,−4π​<w<4π​

(a) Find I′(w)I'(w)I′(w). (b) Determine the www-coordinate of the stationary point for the light intensity curve.

[7]
ii.

In a separate experiment, the relationship between a signal s s\,s and a phase angle θ \theta\,θ is given by

s=ln⁡(5cos⁡θ),0<θ<π2 s = \ln(5 \cos \theta), \quad 0 < \theta < \frac{\pi}{2} s=ln(5cosθ),0<θ<2π​

Show that

dθds=−esf(s) \frac{d\theta}{ds} = -\frac{e^s}{f(s)} dsdθ​=−f(s)es​

where f(s)f(s)f(s) is a function of es e^s\,es to be determined.

[7]
Markscheme

3.6 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Differentiation (A-level only)

333 exam-style questions on WJEC A Level Maths 3.6 Differentiation (A-level only), covering 3.6.1 Differentiation (A-level only), 3.6.2 Differentiation (A-level only), 3.6.3 Differentiation (A-level only), 3.6.4 Differentiation (A-level only), 3.6.5 Differentiation (A-level only), 3.6.6 Differentiation (A-level only), 3.6.7 Differentiation (A-level only), and 3.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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