JAMB Mathematics 2020 Paper

Concept:Adding and subtracting base-$3$ numerals requires carrying over when a column sum reaches $3$ and borrowing $3$ from the next higher column, just like in base $10$.Explanation:First add $(212)_3$ and $(222)_3$.Units: $2 + 2 = 4 = 1 \cdot 3 + 1$, so write $1$, carry $1$.Threes place: $1 + 2 + 1 = 4 = 1 \cdot 3 + 1$, write $1$, carry $1$.Nines place: $2 + 2 + 1 = 5 = 1 \cdot 3 + 2$, write $2$, carry $1$.Thus, $(212)_3 + (222)_3 = (1211)_3$.Now subtract $(121)_3$ from $(1211)_3$.Units: $1 - 1 = 0$.Threes place: $1 - 2$ needs a borrow, making it $1 + 3 = 4$; $4 - 2 = 2$.Nines place: originally $2$, reduces to $1$ after the borrow; then $1 - 1 = 0$.Twenty-sevens place: $1 - 0 = 1$.Therefore, the result is $(1020)_3$.Answer:Option C: $(1020)_3$