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, 7π6→2π, 2sin(2πp)=−1, 7π6×k=2π
correct working (A1)
eg 7π6⋅1p=2π, 2πp=7π6, 127
p=712 (acceptp<712orp⩽712) A1 N2
[3 marks]