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Date November Example question Marks available 1 Reference code EXN.1.SL.TZ0.6
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number 6 Adapted from N/A

Question

The size of the population (P) of migrating birds in a particular town can be approximately modelled by the equation P=asin(bt)+c,  a,b,c+, where t is measured in months from the time of the initial measurements.

In a 12 month period the maximum population is 2600 and occurs when t=3 and the minimum population is 800 and occurs when t=9.

This information is shown on the graph below.

Find the value of a.

[2]
a.i.

Find the value of b.

[2]
a.ii.

Find the value of c.

[1]
a.iii.

Find the value of t at which the population first reaches 2200.

[2]
b.

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

2600-8002=900        (M1)A1

 

[2 marks]

a.i.

36012=30        (M1)A1

 

Note: Accept 2π12=0.524 0.523598.

 

[2 marks]

a.ii.

2600+8002=1700         A1

  

[1 mark]

a.iii.

Solve 900sin30t+1700=2200        (M1)

t=1.12 1.12496         A1

  

[2 marks]

b.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
a.iii.
[N/A]
b.

Syllabus sections

Topic 2—Functions » SL 2.5—Modelling functions
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Topic 2—Functions

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