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1.1 Algebra and functions

1.1 Algebra and functions

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Question 140

A chemical engineer models the temperature gradient G(s)G(s)G(s) (in °C/cm) along a cooling fin, where s s\,s is the distance from the heat source in cm, as:

G(s)=as3−9s2+bs+14 G(s) = as^3 - 9s^2 + bs + 14 G(s)=as3−9s2+bs+14

where a a\,a and b b\,b are constants.

When G(s)G(s)G(s) is divided by (s−4)(s - 4)(s−4), the remainder is 30.

a.

Use the remainder theorem to show that

16a+b=40 16a + b = 40 16a+b=40
[3]
b.

Given also that (s−1)(s - 1)(s−1) is a factor of G(s)G(s)G(s),

find the value of a a\,a and the value of bbb.

[3]
c.

Find G′(s)G'(s)G′(s).

[2]
d.

Hence find the exact coordinates of the stationary points of the curve with equation y=G(s)y = G(s)y=G(s).

[4]
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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