WAEC Further Mathematics 2025 Paper

Concept:Since $x \in \mathbb{R}$, treat each set as a continuous interval on the real number line and find their common region.Explanation:The set $P = \{x : 1 \leq x \leq 6\}$ contains all real numbers from $1$ to $6$, including both $1$ and $6$.The set $Q = \{x : 2 < x < 9\}$ contains all real numbers strictly greater than $2$ and strictly less than $9$.For $P \cap Q$, a real number must lie in both intervals at the same time.The lower end is decided by $2 < x$, because $2$ is excluded from $Q$, even though $1$ is included in $P$.The upper end is decided by $x \leq 6$, because $6$ is included in $P$, while $Q$ extends only up to $9$.Thus, every number greater than $2$ and less than or equal to $6$ belongs to the intersection.So $P \cap Q = \{x : 2 < x \leq 6\}$.Answer:Option D: $\{x : 2 < x \leq 6\}$.