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2.7 Solving Modulus Problems

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Question 3

A researcher models the depth of a sediment layer, D(p)D(p)D(p), in millimetres as a function of the pressure ppp in kilopascals using the modulus function:

D(p)=∣cp−30∣−6,p≥0 D(p) = |cp - 30| - 6, \quad p \ge 0 D(p)=∣cp−30∣−6,p≥0

where ccc is a positive constant representing the compression coefficient.

The graph of y=D(p)y = D(p)y=D(p) has a minimum point MMM and intersects the yyy-axis at the point SSS.

a.

(i) Find the yyy-coordinate of SSS. (ii) Find, in terms of ccc, the ppp-coordinate of MMM.

[2]
b.

Find, in terms of ccc, the set of values of ppp for which the sediment depth is negative.

[3]
c.

A second model suggests the depth follows the linear relationship y=18−4py = 18 - 4py=18−4p. Given that this linear model intersects the modulus model y=D(p)y = D(p)y=D(p) at two distinct points,

find the range of possible values for ccc.

[4]
Markscheme

2.7 Solving Modulus Problems Questions

  1. A Level
  2. /Maths
  3. /2.7 Solving Modulus Problems

30 exam-style questions on Edexcel A Level Maths 2.7 Solving Modulus Problems. Each one has a worked solution and a mark scheme showing where the marks go.

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