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3.2 Algebra and Functions (A-level only)

3.2 Algebra and Functions (A-level only)

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Question 122

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

3.2 Algebra and Functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.2 Algebra and Functions (A-level only)

216 exam-style questions on WJEC A Level Maths 3.2 Algebra and Functions (A-level only), covering 3.2.1 Algebra and Functions (A-level only), 3.2.2 Algebra and Functions (A-level only), 3.2.3 Algebra and Functions (A-level only), 3.2.4 Algebra and Functions (A-level only), 3.2.5 Algebra and Functions (A-level only), 3.2.6 Algebra and Functions (A-level only), and 3.2 Algebra and Functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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