4MA0 Foundation January 2017 Paper 2R Q6
6 Here is a sequence of patterns made from sticks.
(a) Complete the table.
(1)
| Pattern number | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Number of sticks | 4 | 7 | 10 |
(b) Explain how you worked out your answer. (1)
(c) How many sticks are needed to make Pattern number 12? (2)
(d) Work out the Pattern number of the pattern made from exactly 67 sticks. (2)
| Scheme | Marks |
|---|---|
| 13 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| Add 3 | B1 |
| (1) |
Notes
B1: Accept +3, 3 more, jumped forward by 3, difference = 3 oe or \(3n + 1\)
| Scheme | Marks |
|---|---|
| 4 + 11 × 3 or 4 + 12 × 3 or \(3n + 1\) Or 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37 | M1 |
| 37 | A1 |
| (2) |
Notes
M1: Allow 4 + 12 × 3 or 34 or 40
List should show a clear intention of adding 3 with at least 5 terms (including 16). Condone 1 arithmetic error.
| Scheme | Marks |
|---|---|
| 67 − 1 or \(3x + 1 = 67\) | M1 |
| 22 | A1 |
| (2) | |
| (6 marks) |
Notes
A1: cao