WAEC Mathematics 2014 Paper

Concept:We need to subtract one algebraic expression from another, so we first add the two given expressions and then subtract the third one.Explanation:First, write the sum of the first two expressions.$\frac{1}{2}(a-b+c) + \frac{1}{2}(a+b-c)$Now subtract $\frac{1}{2}(a-b-c)$ from this sum.$\frac{1}{2}(a-b+c) + \frac{1}{2}(a+b-c) - \frac{1}{2}(a-b-c)$Expand each term inside the brackets.$\frac{1}{2}a - \frac{1}{2}b + \frac{1}{2}c + \frac{1}{2}a + \frac{1}{2}b - \frac{1}{2}c - \frac{1}{2}a + \frac{1}{2}b + \frac{1}{2}c$Group the like terms.For $a$: $\frac{1}{2}a + \frac{1}{2}a - \frac{1}{2}a = \frac{1}{2}a$For $b$: $-\frac{1}{2}b + \frac{1}{2}b + \frac{1}{2}b = \frac{1}{2}b$For $c$: $\frac{1}{2}c - \frac{1}{2}c + \frac{1}{2}c = \frac{1}{2}c$Combining these gives $\frac{1}{2}a + \frac{1}{2}b + \frac{1}{2}c$.Factor out $\frac{1}{2}$ to obtain $\frac{1}{2}(a+b+c)$.Answer:$\frac{1}{2}(a+b+c)$Therefore, the correct option is A.