Find the value of $\theta$ .

Find the area of the shaded region.

correct substitution     (A1)

e.g. $8.5 = \theta (6.8)$ , $\theta  = \frac{{8.5}}{{6.8}}$

$\theta  = 1.25$ (accept ${71.6^ \circ }$ )     A1     N2

[2 marks]

METHOD 1

correct substitution into area formula (seen anywhere)     (A1)

e.g. $A = \pi {(6.8)^2}$ , $145.267 \ldots$

correct substitution into area formula (seen anywhere)     (A1)

e.g. $A = \frac{1}{2}(1.25)({6.8^2})$ , 28.9

valid approach     M1

e.g. $\pi {(6.8)^2} - \frac{1}{2}(1.25)({6.8^2})$ ; $145.267 \ldots - 28.9$ ; $\pi {r^2} - \frac{1}{2}{r^2}\sin \theta$

$A = 116$ (${\text{c}}{{\text{m}}^2}$)     A1     N2

METHOD 2

attempt to find reflex angle     (M1)

e.g. $2\pi - \theta$ , $360 - 1.25$

correct reflex angle     (A1)

${\rm{A}}\widehat {\rm{O}}{\rm{B}} = 2\pi - 1.25$ ($= 5.03318 \ldots$)

correct substitution into area formula     A1

e.g. $A = \frac{1}{2}(5.03318 \ldots )({6.8^2})$

$A = 116$ (${\text{c}}{{\text{m}}^2}$)     A1     N2

[4 marks]

Part (a) was almost universally done correctly.

Many also had little trouble in part (b), with most subtracting from the circle's area, and a minority using the reflex angle. A few candidates worked in degrees, although some of these did so incorrectly by using the radian area formula. Some candidates only found the area of the unshaded sector.