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Algebraic Methods

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Question 157

The fuel consumption rate S(t)S(t)S(t) (in kg/s) of a prototype hypersonic engine, where ttt is the time in minutes since ignition, is modelled by the polynomial S(t)=2t3+Pt2+Qt−20S(t) = 2t^3 + Pt^2 + Qt - 20S(t)=2t3+Pt2+Qt−20, where PPP and QQQ are constants.

It is given that:

  • when S(t)S(t)S(t) is divided by (t−1)(t - 1)(t−1), the remainder is RRR
  • when S(t)S(t)S(t) is divided by (t+2)(t + 2)(t+2), the remainder is 2R+62R + 62R+6
a.

Show that P−2Q=3P - 2Q = 3P−2Q=3.

[4]
b.

Given also that (2t−5)(2t - 5)(2t−5) is a factor of S(t)S(t)S(t),

Find the value of PPP and the value of QQQ.

[3]
c.

Hence find the quadratic expression g(t)g(t)g(t) such that S(t)=(2t−5)g(t)S(t) = (2t - 5)g(t)S(t)=(2t−5)g(t).

[2]
Markscheme

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.

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