User interface language: English | Español

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 0t12, 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.

[2]
a.

Find the value of q.

[2]
b.

Use the model to find the depth of the water 10 hours after high tide.

[2]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

valid approach     (M1)

egmaxmin2, sketch of graph, 9.7=pcos(0)+7.5

p=2.2     A1     N2

[2 marks]

a.

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]

b.

valid approach     (M1)

egd(10), 2.2cos(20π14)+7.5

7.01045

7.01 (m)     A1     N2

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 3— Geometry and trigonometry » SL 3.7—Circular functions: graphs, composites, transformations
Show 89 related questions
Topic 3— Geometry and trigonometry

View options