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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 235

In a fluid dynamics simulation, the pressure deviation PPP at distance ddd from a source is modeled by the function

P(d)=d(d−k)(d−16) P(d) = d(d - k)(d - 16) P(d)=d(d−k)(d−16)

where kkk is a constant such that 0<k<160 < k < 160<k<16.

a.

Sketch the graph of y=P(d)y = P(d)y=P(d) on axes, showing the coordinates of the points where the graph meets the ddd-axis.

[3]
b.

A secondary model suggests the pressure behaves according to the transformation y=P(−4d)y = P(-4d)y=P(−4d). Sketch this transformed graph on separate axes, showing the coordinates of the points where the graph meets the ddd-axis in terms of kkk.

[3]
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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