JAMB Mathematics 2016 Paper

Concept:A fraction of a circle covered by the shaded parts is found by dividing the total shaded angle by the full angle of a circle, $360^\circ$.Explanation:From the diagram, use the three angles in the given triangle.The two known angles are $90^\circ$ and $60^\circ$.So the remaining angle is $\theta = 180^\circ - (90^\circ + 60^\circ)$.This gives $\theta = 180^\circ - 150^\circ = 30^\circ$.The shaded portion consists of two sectors, each with an angle of $30^\circ$.Therefore, the shaded fraction is $\frac{30^\circ}{360^\circ} + \frac{30^\circ}{360^\circ}$.This simplifies to $\frac{1}{12} + \frac{1}{12} = \frac{1}{6}$.Answer:D. $\frac{1}{6}$