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1.2 Algebra and Functions

1.2 Algebra and Functions

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Question 108

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

1.2 Algebra and Functions Questions

  1. A Level
  2. /Maths
  3. /1.2 Algebra and Functions

302 exam-style questions on WJEC A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Algebra and Functions, 1.2.2 Algebra and Functions, 1.2.3 Algebra and Functions, 1.2.4 Algebra and Functions, 1.2.5 Algebra and Functions, 1.2.6 Algebra and Functions, 1.2.7 Algebra and Functions, 1.2.8 Algebra and Functions, 1.2.9 Algebra and Functions, 1.2.10 Algebra and Functions, 1.2.11 Algebra and Functions, and 1.2.12 Algebra and Functions. Each one has a worked solution and a mark scheme showing where the marks go.

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