(b) $\dfrac{5}{4}$
Given $\cos A = \dfrac{1}{2}$, so $\sin^2 A = 1 - \cos^2 A = 1 - \dfrac{1}{4} = \dfrac{3}{4}$.
$\sin^2 A + 2\cos^2 A = \dfrac{3}{4} + 2 \times \dfrac{1}{4} = \dfrac{3}{4} + \dfrac{2}{4} = \dfrac{5}{4}$
Source: Chapter 8, Section 8.4 Trigonometric Identities
Use the identity $\sin^2 A + \cos^2 A = 1$ to find $\sin^2 A$, then substitute both values. Note that $2\cos^2 A = 2 \times \frac{1}{4}$, not $\cos^2(2A)$. This is a straightforward substitution question — examiners award the mark for the correct option with brief working shown.