The sequence of diagrams below shows small black and small white squares in an arrangement to form large squares. [Figure 11.1] Diagram 1 Diagram 2 Diagram 3 The table below shows the numbers of black and white squares in each diagram. Diagram (n) 1 2 3 4 Black squares 5 13 25 White squares 4 12 24 Total number of black and 9 25 49 white squares
- (a)For each diagram, how many more black squares are there than white squares?[1]
- (b)On the table, complete the column for Diagram 4.[1]
- (c)Write down an expression, in terms of n, for the total number of black and white squares in Diagram n.[1]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.
- [1] (a) 1
- [1] (b) 41 40 81 (all three)
- [1] (c) (2n + 1)² oe
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