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1.3 Functions

1.3 Functions

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Question 147

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

1.3 Functions Questions

  1. A Level
  2. /Maths
  3. /1.3 Functions

181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 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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