JAMB Mathematics 2013 Paper

Concept:In a pie chart, the sum of all sector angles is $360^{\circ}$, and each sector’s number of students is proportional to its angle.Explanation:From the pie chart, the five sector angles are $5x^\circ$, $(16x - 24)^\circ$, $5x^\circ$, $(4x + 12)^\circ$, and $(6x + 12)^\circ$.The sum of these angles equals $360^\circ$:$$5x + (16x - 24) + 5x + (4x + 12) + (6x + 12) = 360.$$Simplifying the left side:$$36x - 24 + 12 + 12 = 360 \Rightarrow 36x = 360.$$Therefore,$$x = \frac{360}{36} = 10.$$Mathematics is represented by the sector with angle $5x^\circ$, so its angle is:$$5(10) = 50^\circ.$$Number of students who offer Mathematics:$$\frac{50}{360} \times 80 = \frac{4000}{360} \approx 11.11.$$Since the number of students must be a whole number, we take it as approximately $11$.Answer:B. 11