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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 178

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

1.5 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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