Solve the equation \({{\rm{e}}^x} = 4\sin x\) , for \(0 \le x \le 2\pi \) .

evidence of appropriate approach     M1

e.g. a sketch, writing \({{\rm{e}}^x} - 4\sin x = 0\) 

\(x = 0.371\) , \(x = 1.36\)     A2A2     N2N2

[5 marks]

Although many students started with an analytical approach, many also realized they were not going further and successfully used their GDC to find the intercepts with the x-axis if they had set the equation equal to 0, or in other cases, they found the intersection of the two graphs. The better candidates drew a reasonable sketch and found the two values without difficulty. A good number of candidates did not provide a sketch, however, and they had more trouble earning the mark for showing method. Accuracy penalties were relatively common on this question.