Foundation January 2019 Paper 1 Q3
3 Here is a sequence of patterns made from identical pentagons.
(a)
(i) Work out the number of pentagons in Pattern number 4
(ii) Explain how you worked out your answer.
(2)A different sequence of patterns is made from identical hexagons.
The rule below can be used to find the number of hexagons in each pattern of this sequence.
| Multiply the Pattern number by 5 and subtract 1 |
(b) Work out the number of hexagons in Pattern number 7 (1)
A pattern in this sequence has exactly 59 hexagons.
(c) Work out its Pattern number. (2)
| Scheme | Marks |
|---|---|
| (i) 14 | B1 |
| (ii) Added 4 | B1 |
| (2) |
Notes
B1: Accept +4, 4 more, jumped forward by 4, difference = 4 or sight of \(4n - 2\)
| Scheme | Marks |
|---|---|
| 34 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| (59 + 1) ÷ 5 or \(59 = 5n - 1\) or 4, 9, 14, 19,……, 54, 59 (may start at 34 or 39) | M1 |
| 12 | A1 |
| (2) | |
| (5 marks) |
Notes
M1: or for 12 × 5 – 1