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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 349

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

1.5 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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