BECE Mathematics 2021 Paper

Concept:The mapping has a constant difference between consecutive $y$-values, so its rule is a linear equation.Explanation:For $x = 1, 2, 3, 4, 5$, the corresponding $y$-values are $5, 9, 13, 17, 21$.Find the differences: $9 - 5 = 4$, $13 - 9 = 4$, $17 - 13 = 4$, $21 - 17 = 4$.Since the common difference is $4$, use the linear rule: $y = \text{first term} + (x - 1)d$.Substitute the first term $5$ and $d = 4$: $y = 5 + (x - 1) \times 4$.Simplify: $y = 5 + 4x - 4 = 4x + 1$.Verify with $x = 3$: $y = 4(3) + 1 = 12 + 1 = 13$, which matches the mapping.Therefore, the rule of the mapping is $y = 4x + 1$.Answer:Option C: $y = 4x + 1$.