A sequence of patterns is created with black counters and white counters. Pattern 1, Pattern 2 and Pattern 3 are illustrated by black and white circular counters set out in square arrangements that grow in size.
(a)[1]
Draw Pattern 4 exactly.
(b)[2]
Complete the table in full.
(c(i))[2]
Write an expression, in terms of $n$, for the number of black counters in Pattern $n$.
(c(ii))[1]
Write an expression, in terms of $n$, for the number of white counters in Pattern $n$.
(d)[2]
Can she make Pattern 12 using her counters? Explain your answer.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The shaded-circle pattern is correct.” …