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1.2 Algebra and Functions

1.2 Algebra and Functions

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Question 182

Let f(x)=36x3−27x2−4x+3f(x) = 36x^3 - 27x^2 - 4x + 3f(x)=36x3−27x2−4x+3.

a.

Use the factor theorem to show that (3x−1)(3x - 1)(3x−1) is a factor of f(x)f(x)f(x).

[2]
b.

Express f(x)f(x)f(x) as a product of three linear factors.

[3]
c.

A mechanical engineer modeling the resonance of a suspension bridge determines that the equilibrium angles θ\thetaθ are given by the equation:

12sec⁡2θ+cos⁡θ4=2.25sec⁡θ+13 \frac{12\sec^2 \theta + \cos \theta}{4} = 2.25\sec \theta + \frac{1}{3} 412sec2θ+cosθ​=2.25secθ+31​

Prove that there are no real values of θ\thetaθ that satisfy this stability condition.

[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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