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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 271

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

1.5 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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