Date | May 2017 | Marks available | 2 | Reference code | 17M.2.SL.TZ2.S_4 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 2 |
Command term | Find | Question number | S_4 | Adapted from | N/A |
Question
The depth of water in a port is modelled by the function d(t)=pcosqt+7.5d(t)=pcosqt+7.5, for 0⩽t⩽12, where t is the number of hours after high tide.
At high tide, the depth is 9.7 metres.
At low tide, which is 7 hours later, the depth is 5.3 metres.
Find the value of p.
Find the value of q.
Use the model to find the depth of the water 10 hours after high tide.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
valid approach (M1)
egmax−min2, sketch of graph, 9.7=pcos(0)+7.5
p=2.2 A1 N2
[2 marks]
valid approach (M1)
egB=2πperiod, period is 14, 36014, 5.3=2.2cos7q+7.5
0.448798
q=2π14 (π7), (do not accept degrees) A1 N2
[2 marks]
valid approach (M1)
egd(10), 2.2cos(20π14)+7.5
7.01045
7.01 (m) A1 N2
[2 marks]