CAIE A-Level Mathematics 2.6.1 Root location

CAIE A-Level Mathematics 2.6.1 Root location
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise proving where a root lies by sign changes or graph sketches, including single-root arguments from intersections.

How this is tested

  • evaluate f(x) at two endpoints and use a sign change to justify a root interval
  • sketch suitable graphs on one diagram to show the number of roots in a given range

Question 6

Question 6(a)

(a)

By sketching a suitable pair of graphs, show that the equation

∣x−2∣=2sin⁡12x|x-2|=2 \sin \frac{1}{2} x

has only one root in the interval 0<x<π0<x<\pi.

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Question 6(b)

(b)

Show by calculation that this root lies between 1 and 1.5.

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