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1.1 Algebra and functions

1.1 Algebra and functions

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Question 157

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

1.1 Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.1 Algebra and functions

306 exam-style questions on CCEA A Level Maths 1.1 Algebra and functions, covering 1.1.1 Algebra and functions, 1.1.2 Algebra and functions, 1.1.3 Algebra and functions, 1.1.4 Algebra and functions, 1.1.5 Algebra and functions, 1.1.6 Algebra and functions, 1.1.7 Algebra and functions, 1.1.8 Algebra and functions, 1.1.9 Algebra and functions, 1.1.10 Algebra and functions, 1.1.11 Algebra and functions, 1.1.12 Algebra and functions, 1.1.13 Algebra and functions, and 1.1.14 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.

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