2012 A-level H2 Mathematics (9740) Paper 2 Question 2 Suggested Solutions

By KS Teng

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

Graph of 2(i)

Graph of 2(i)

(ii)
(a)
Required answer = \sqrt{7^2 + 3^2} -4 = \sqrt{58} - 4

(b)
z = 7 - 4 cos (tan^{-1}\frac{3}{7}) - i(3 - 4sin (tan^{-1}\frac{3}{7}))

z = 7 - 4 (\frac{7}{\sqrt{58}}) - i(3 - 4(\frac{3}{\sqrt{58}}))

z = 7 - \frac{28}{\sqrt{58}} - i(3 - \frac{12}{\sqrt{58}})

(iii)
arg(z) = - tan^{-1} \frac{3}{7} - sin^{-1} \frac{4}{\sqrt{58}} = -0.9579 \mathrm{~radians}

KS Comments:

For (iib), students should draw the right angled triangle out to see what the value is since its required that they leave in exact form. When there is a circle for locus, I usually remind students to always utilise the radius.

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