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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 299

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

1.5 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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