Moderate -0.8 This is a straightforward algebraic proof requiring students to express consecutive odd integers as Q and Q+2, expand (Q+2)² - Q² to get 4Q+4, then factor as 4(Q+1) and note that Q+1 is even since Q is odd. The structure is simple with clear steps, making it easier than average but not trivial since it requires understanding parity arguments.
$P$ and $Q$ are consecutive odd positive integers such that $P > Q$.
Prove that $P^2 - Q^2$ is a multiple of 8. [3]
\hfill \mbox{\textit{OCR MEI AS Paper 2 2018 Q3 [3]}}