1MA0 Foundation November 2014 Paper 2 Q14
14 Here is a sequence of patterns made with counters.
(a) In the space below, draw pattern number 4 (1)
(b) Complete the table. (1)
| Pattern number | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Number of counters | 5 | 9 | 13 |
(c) Find an expression, in terms of \(n\), for the number of counters in pattern number \(n\). (2)
Habeeb has 50 counters.
He wants to use as many of his counters as possible to make a pattern in the sequence.
(d) What is the number of the pattern he can make using the greatest number of his counters? (2)
| Answer | Mark | Notes |
|---|---|---|
| 1 | B1 cao |
| Answer | Mark | Notes |
|---|---|---|
| 17, 21 | 1 | B1 for 17, 21 cao |
| Answer | Mark | Notes |
|---|---|---|
| \(4n + 1\) | 2 | B2 for \(4n + 1\) oe (B1 for \(4n + k\), \(k \neq 1\), or \(k\) is absent or \(n = 4n + 1\)) |
| Answer | Mark | Notes |
|---|---|---|
| 12 | 2 | M1 for \((50 - 1) \div 4\) or evidence of using their formula from part (c) if in the form \(an + b\) or repeated addition of 4 (at least 3) ft table in part (b) or 49 seen A1 cao |