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1.3 Functions

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Question 21

A theoretical model for the potential energy EEE in a micro-system is given by the function

E(t)=27t3+54t2+33t+6 E(t) = 27t^3 + 54t^2 + 33t + 6 E(t)=27t3+54t2+33t+6

where ttt is a dimensionless time parameter.

a.

Use the factor theorem to prove that (3t+1)(3t + 1)(3t+1) is a factor of E(t)E(t)E(t).

[2]
b.

Factorise E(t)E(t)E(t) completely.

[3]
c.

Hence, prove that 108n3+216n2+132n+24108n^3 + 216n^2 + 132n + 24108n3+216n2+132n+24 is a multiple of 24 when nnn is a positive integer.

[3]
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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