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1.1 Algebra and functions

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Question 101

A specialized sensor measures the displacement D(s)D(s)D(s) of a robotic arm as a function of the system's stress level sss. The displacement is modeled by the function

D(s)=3s3−13s2+17s−15 D(s) = 3s^3 - 13s^2 + 17s - 15 D(s)=3s3−13s2+17s−15
a.

Use the factor theorem to prove that (s−3)(s - 3)(s−3) is a factor of D(s)D(s)D(s).

[2]
bi.

Prove that the graph of the displacement function y=D(s)y = D(s)y=D(s) intersects the sss-axis at exactly one point.

[4]
bii.

State the coordinates of this point of intersection.

[1]
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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