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2.7 Solving Modulus Problems

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Question 6

The height of a drone path during a test flight is modeled by the function y=f(x)y = f(x)y=f(x), where

f(x)=∣4x+3k∣+k f(x) = |4x + 3k| + k f(x)=∣4x+3k∣+k

and where kkk is a positive constant and xxx is the horizontal distance from a start point. The graph of y=f(x)y = f(x)y=f(x) has a vertex at the point PPP.

a.

Find, in terms of kkk, the coordinates of PPP.

[2]
b.

Sketch the graph with equation y=g(x)y = g(x)y=g(x), where g(x)=∣x−5k∣g(x) = |x - 5k|g(x)=∣x−5k∣. On your sketch, show the coordinates, in terms of kkk, of each point where the graph cuts or meets the coordinate axes.

[3]
c.

The drone path with equation y=f(x)y = f(x)y=f(x) is monitored by a sensor following the path y=g(x)y = g(x)y=g(x). The paths intersect at two points.

Find, in terms of kkk, the coordinates of these two intersection points.

[6]
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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