User interface language: English | Español

Date May 2008 Marks available 3 Reference code 08M.1.sl.TZ1.4
Level SL only Paper 1 Time zone TZ1
Command term Sketch Question number 4 Adapted from N/A

Question

Consider \(g(x) = 3\sin 2x\) .

Write down the period of g.

[1]
a.

On the diagram below, sketch the curve of g, for \(0 \le x \le 2\pi \) .


[3]
b.

Write down the number of solutions to the equation \(g(x) = 2\) , for \(0 \le x \le 2\pi \) .

[2]
c.

Markscheme

\({\text{period}} = \pi \)     A1     N1

[1 mark]

a.

      A1A1A1     N3

 

Note: Award A1 for amplitude of 3, A1 for their period, A1 for a sine curve passing through \((0{\text{, }}0)\) and \((0{\text{, }}2\pi )\) .

[3 marks]

b.

evidence of appropriate approach     (M1)

e.g. line \(y = 2\) on graph, discussion of number of solutions in the domain

4 (solutions)     A1     N2

[2 marks]

c.

Examiners report

Many candidates were unable to write down the period of the function.

a.

Many candidates were unable to write down the period of the function. However, they were often then able to go and correctly sketch the graph with the correct period.

b.

The final part was poorly done with many candidates finding the number of zeros instead of the intersection with the line \(y = 2\) .

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.
Show 59 related questions

View options