The diagrams show patterns made from crosses (X) and circles (O). [Figure of Patterns 1-4]

1. (a)Draw pattern 5 above.[1]
2. (b)Complete the table. Pattern number (n) | 1 | 2 | 3 | 4 | 5 | 6 Number of crosses | 1 | 3 | 6 | 10 | Number of circles | 0 | 1 | 3 | 6 | Total number of crosses and circles | 1 | 4 | 9 | 16 | 25 | 36[2]
3. (c)Find an expression, in terms of n, for the total number of crosses and circles in pattern n.[1]
4. (d)An expression, in terms of n, for the number of crosses in pattern n is ½n² + ½n. How many crosses are there in pattern 30?[1]
5. (e)Show that the number of circles in pattern n is ½n² - ½n.[1]
6. (f)The number of crosses in pattern m is equal to 5m. Find m.[3]

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.