Foundation June 2023 Paper 2 Q4
4 Here is a sequence of patterns made from sticks.
(a) In the space below, draw Pattern number 4 (1)
(b) Complete the table.
(1)
| Pattern number | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Number of sticks | 5 | 9 | 13 |
(c) Work out the number of sticks in Pattern number 10 (1)
Connor says that in Pattern number 25 there are 102 sticks.
(d) Explain why Connor is wrong. (1)
| Scheme | Marks |
|---|---|
 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| 17, 21 | B1 |
| (1) |
Notes
B1: Ignore any extra numbers if the 2 that are required are there
| Scheme | Marks |
|---|---|
| 41 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| A correct reason | B1 |
| (1) | |
| (4 marks) |
Notes
B1: The numbers of sticks are always an odd number (always ends in 1,3,5,7,9)
102 is even,
pattern 25 has 101 sticks,
The pattern goes …97, 101, 105…
It is \(4n + 1\) oe
\(4 \times 25 + 1 = 101\) (or does not =102)
The pattern never ends in a 2