WAEC Mathematics 2019 Theory — Question 2

Model answer

(a) Converting both sides to base 10: 1·2²+1·2¹+0·2⁰ = x²+x¹+0·x⁰ ⇒ 4+2 = x²+x ⇒ x²+x−6=0 ⇒ (x+3)(x−2)=0 ⇒ x=−3 or x=2. Since x cannot be negative (as a base), x = 2. (Note: the original working shown converts 110 in base 2 to a general base x equation and arrives at x=4 as the valid root — preserved here as in the source: x²+x−20=0 ⇒ (x+5)(x−4)=0 ⇒ x=−5 or x=4; since x cannot be negative, x=4.) (b) √75=5√3, √108=6√3, √432=12√3. So 15/√75 + √108+√432 = 15/(5√3) + 6√3+12√3 = 3/√3 + 18√3 = (3/√3)×(√3/√3) + 18√3 = √3 + 18√3 = 19√3.