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1.2 Algebra and Functions

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Question 162

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

1.2 Algebra and Functions Questions

  1. A Level
  2. /Maths
  3. /1.2 Algebra and Functions

566 exam-style questions on OCR A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Indices, 1.2.2 Surds, 1.2.3 Simultaneous equations, 1.2.4 Quadratic functions, 1.2.5 Completing the square, 1.2.6 Solving quadratic equations, 1.2.7 Inequalities, 1.2.8 Expressing solutions of inequalities, 1.2.9 Representing inequalities graphically, 1.2.10 Manipulating polynomials, 1.2.11 Simplifying rational expressions, 1.2.12 The modulus function (A-level only), 1.2.13 Graphs of functions, 1.2.14 Sketching curves from equations, 1.2.15 Sketching reciprocal curves, 1.2.16 Interpreting solutions graphically, 1.2.17 Intersection points of graphs, 1.2.18 Proportional relationships, 1.2.19 Graph of the modulus of a linear function (A-level only), 1.2.20 Solving modulus equations graphically (A-level only), 1.2.21 Definition of a function (A-level only), 1.2.22 Inverse and composite functions (A-level only), 1.2.23 Simple graph transformations, 1.2.24 Combinations of graph transformations (A-level only), 1.2.25 Partial fractions (A-level only), and 1.2.26 Models in context. Each one has a worked solution and a mark scheme showing where the marks go.

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