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1.5 B: Algebra and functions

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Question 296

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]

1.5 B: Algebra and functions Questions

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

Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank