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Date November 2015 Marks available 2 Reference code 15N.1.sl.TZ0.4
Level SL only Paper 1 Time zone TZ0
Command term Find Question number 4 Adapted from N/A

Question

Let \(f(x) = 3\sin (\pi x)\).

Write down the amplitude of \(f\).

[1]
a.

Find the period of \(f\).

[2]
b.

On the following grid, sketch the graph of \(y = f(x)\), for \(0 \le x \le 3\).

[4]
c.

Markscheme

amplitude is 3     A1     N1

a.

valid approach     (M1)

eg\(\;\;\;{\text{period}} = \frac{{2\pi }}{\pi },{\text{ }}\frac{{360}}{\pi }\)

period is 2     A1     N2

b.

      A1

A1A1A1     N4

 

Note:     Award A1 for sine curve starting at (0, 0) and correct period.

Only if this A1 is awarded, award the following for points in circles:

A1 for correct x-intercepts;

A1 for correct max and min points;

A1 for correct domain.

c.

Examiners report

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

Syllabus sections

Topic 3 - Circular functions and trigonometry » 3.4 » The circular functions \(\sin x\) , \(\cos x\) and \(\tan x\) : their domains and ranges; amplitude, their periodic nature; and their graphs.
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