WAEC Mathematics 2022 Paper

Concept:The constant of proportionality combines direct and inverse variations into a single equation.Explanation:Since $M$ varies directly as $n$ and inversely as the square of $p$, we can write $M \propto \frac{n}{p^2}$.Introduce a constant $k$: $M = \frac{kn}{p^2}$.Substitute the given values $M=3$, $n=2$, and $p=1$:$3 = \frac{k \cdot 2}{1^2}$.Since $1^2 = 1$, this becomes $3 = 2k$.Solve for $k$: $k = \frac{3}{2}$.Replace $k$ in the original relation: $M = \frac{\frac{3}{2}n}{p^2}$.Simplify the fraction: $M = \frac{3n}{2p^2}$.Answer:$M = \frac{3n}{2p^2}$, which is option A.