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1.2 Algebra and Functions

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Question 41

A mechanical engineer determines that the stability factor, SSS, of a dampening system is modeled by the function S(ω)=6ω3−5ω2−17ω+6S(\omega) = 6\omega^3 - 5\omega^2 - 17\omega + 6S(ω)=6ω3−5ω2−17ω+6, where ω\omegaω is a frequency parameter.

a.

Use the factor theorem to show that (3ω−1)(3\omega - 1)(3ω−1) is a factor of S(ω)S(\omega)S(ω).

[2]
b.

Hence, using algebraic methods, express S(ω)S(\omega)S(ω) as the product of three linear factors.

[3]
c.

Solve, for 0<ϕ<π0 < \phi < \pi0<ϕ<π, the equation

6tan⁡3ϕ−5tan⁡2ϕ−17tan⁡ϕ+6=0 6\tan^3 \phi - 5\tan^2 \phi - 17\tan \phi + 6 = 0 6tan3ϕ−5tan2ϕ−17tanϕ+6=0

giving your answers to 3 significant figures.

[4]
Markscheme

1.2 Algebra and Functions Questions

  1. A Level
  2. /Maths
  3. /1.2 Algebra and Functions

302 exam-style questions on WJEC A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Algebra and Functions, 1.2.2 Algebra and Functions, 1.2.3 Algebra and Functions, 1.2.4 Algebra and Functions, 1.2.5 Algebra and Functions, 1.2.6 Algebra and Functions, 1.2.7 Algebra and Functions, 1.2.8 Algebra and Functions, 1.2.9 Algebra and Functions, 1.2.10 Algebra and Functions, 1.2.11 Algebra and Functions, and 1.2.12 Algebra and Functions. Each one has a worked solution and a mark scheme showing where the marks go.

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