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1.3 Functions

1.3 Functions

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Question 113

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

1.3 Functions Questions

  1. A Level
  2. /Maths
  3. /1.3 Functions

181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 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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