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1.3 Functions

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Question 32

Let f(x)=6x3+13x2−4x−15f(x) = 6x^3 + 13x^2 - 4x - 15f(x)=6x3+13x2−4x−15.

a.

Use the factor theorem to show that (2x+3)(2x + 3)(2x+3) is a factor of f(x)f(x)f(x).

[2]
b.

Hence, using algebra, write f(x)f(x)f(x) as a product of three linear factors.

[3]
c.

Solve, for π2<θ<π\frac{\pi}{2} < \theta < \pi2π​<θ<π, the equation

6tan⁡3θ+13tan⁡2θ−4tan⁡θ−15=0 6\tan^3 \theta + 13\tan^2 \theta - 4\tan \theta - 15 = 0 6tan3θ+13tan2θ−4tanθ−15=0

giving your answers to 3 significant figures.

[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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