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2.7 Solving Modulus Problems

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Question 15

A laser displacement sensor is calibrated to measure the surface profile of a machined groove. The vertical height y y\,y relative to a datum, at a horizontal distance x x\,x from the start of the sensor's path, is modelled using two related functions.

Given that k k\,k and m m\,m are positive constants with k>mk > mk>m,

a.

Sketch, on separate diagrams, the graph with equation

(i) y=∣3x−k∣y = |3x - k|y=∣3x−k∣

(ii) y=∣3x−k∣−my = |3x - k| - my=∣3x−k∣−m

Show on each sketch

  • the coordinates of the minimum point on the graph
  • the coordinates of the point at which the graph crosses the yyy-axis
[4]
b.

Solve the equation

∣3x−k∣−m=7x |3x - k| - m = 7x ∣3x−k∣−m=7x

giving any solution for x x\,x in terms of k k\,k and mmm.

[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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