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Date May 2019 Marks available 3 Reference code 19M.1.SL.TZ2.S_7
Level Standard Level Paper Paper 1 (without calculator) Time zone Time zone 2
Command term Find Question number S_7 Adapted from N/A

Question

Consider the graph of the function f(x)=2sinx,  0 ≤ x < 2π . The graph of f intersects the line y=1 exactly twice, at point A and point B. This is shown in the following diagram.

Consider the graph of g(x)=2sinpx, 0 ≤ x < 2π, where p > 0.

Find the greatest value of p such that the graph of g does not intersect the line y=1.

Markscheme

recognizing period of g is larger than the period of f        (M1)

eg   sketch of g with larger period (may be seen on diagram), A at x=2π,

      image of A when x>2π,  7π62π,  2sin(2πp)=1,  7π6×k=2π

correct working       (A1)

eg   7π61p=2π,  2πp=7π6,  127

p=712   (acceptp<712orp712)       A1  N2

[3 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3— Geometry and trigonometry » SL 3.7—Circular functions: graphs, composites, transformations
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Topic 3— Geometry and trigonometry

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