BECE Mathematics 2025 Paper

Concept:When the outputs go up by the same amount each time, the rule is $t \rightarrow mt + c$, where $m$ is that common difference.Solution:From the diagram: $1 \rightarrow 9$, $2 \rightarrow 20$, $3 \rightarrow 31$, $4 \rightarrow 42$.Outputs increase by $20 - 9 = 11$ each time, so $m = 11$.Using $1 \rightarrow 9$: $11(1) + c = 9 \Rightarrow c = -2$.Rule: $t \rightarrow 11t - 2$.Check: $11(3) - 2 = 31$ and $11(4) - 2 = 42$. Correct.Key point: The old key gave $t \rightarrow 8t + 1$, but that rule maps $2 \rightarrow 17$, not $20$. Always check the rule against every pair in the mapping.Answer:Option C ($t \rightarrow 11t - 2$)