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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 41

A physical experiment measures the spectral intensity III of a pulsed laser relative to its frequency shift sss. The measurements are modeled by the parametric equations

s=5+4sin⁡t s = 5 + 4 \sin t s=5+4sint I=187+cos⁡2t I = \frac{18}{7 + \cos 2t} I=7+cos2t18​

where −π2≤t≤π2-\frac{\pi}{2} \le t \le \frac{\pi}{2}−2π​≤t≤2π​.

a.

Show that the relationship between intensity and frequency shift can be expressed as

I=144(13−s)(s+3)p≤s≤q I = \frac{144}{(13 - s)(s + 3)} \quad p \le s \le q I=(13−s)(s+3)144​p≤s≤q

where ppp and qqq are constants to be found.

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b.

Hence, determine a Cartesian equation for this relationship in the form

I=as+b+cs+dp≤s≤q I = \frac{a}{s + b} + \frac{c}{s + d} \quad p \le s \le q I=s+ba​+s+dc​p≤s≤q

where a,b,ca, b, ca,b,c and ddd are constants.

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Markscheme

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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