Date | May 2021 | Marks available | 2 | Reference code | 21M.1.SL.TZ1.11 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 1 |
Command term | Find | Question number | 11 | Adapted from | N/A |
Question
If a shark is spotted near to Brighton beach, a lifeguard will activate a siren to warn swimmers.
The sound intensity, I, of the siren varies inversely with the square of the distance, d, from the siren, where d>0.
It is known that at a distance of 1.5 metres from the siren, the sound intensity is 4 watts per square metre (W m-2).
Show that I=9d2.
Sketch the curve of I on the axes below showing clearly the point (1.5, 4).
Whilst swimming, Scarlett can hear the siren only if the sound intensity at her location is greater than 1.5×10-6 W m-2.
Find the values of d where Scarlett cannot hear the siren.
Markscheme
I=kd2 (M1)
4=k1.52 M1
I=9d2 AG
Note: The AG line must be seen for the second M1 to be awarded.
Award no marks for substituting 1.5 and 4 into I=9d2 (i.e., working backwards).
[2 marks]
A1A1
Note: Award A1 for correct general shape (concave up) with no I-intercept, passing through the marked point (1.5, 4); the point must be labelled with either the coordinates or the values 1.5 and 4 on the x and y axes. Award A1 for the curve showing asymptotic behavior (i.e. I tends to 0, as d tends to infinity), extending to at least d=6; the curve must not cross nor veer away from the horizontal asymptote.
[2 marks]
1.5×10-6≥9d2 (M1)
Note: Award (M1) for a correct inequality.
d≥2450 A1
Note: Award A0 for .
[2 marks]