Foundation June 2023 Paper 2 Q13
13 Ryan is making a sequence of patterns using counters.
Here are the first four patterns in the sequence.
(a) Ryan started with 80 counters.
Ryan says
I still have enough counters to make Pattern 5 and Pattern 6.
Is Ryan correct?
Show how you decide. [4]
(b)
(i) Complete the table below for the addition of counters in consecutive patterns.
| Patterns to add | Counters to add | Total counters |
|---|---|---|
| Pattern 1 + Pattern 2 | \(3 + 6\) | 9 |
| Pattern 2 + Pattern 3 | \(6 + 10\) | 16 |
| Pattern 3 + Pattern 4 |
[1]
(ii) The number of counters in Pattern \(k\) + Pattern \((k + 1)\) is 144.
Find the value of \(k\). [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| No and 83 oe or No and 49 and 46 or No and 25 and 28 | 4 | M3 for 3 + 6 + 10 + 15 + their 21 + their 28 or for their 21 + their 28 and 80 – their 34 or for 80 – (their 21+15+10+6+3) and their 28 or B2 for 21 and 28 or B1 for 21 or 28 OR M2 for 80–(their 21+15+10+6+3) or 80–their 34 or M1 for [80–] 3 + 6 + 10 + 15 | implied by 83 implied by 49 and 46 implied by 25 and 28 their 21 > 15 and their 28 > their 21 B2 implied by 49 M2 implied by 25 or 46 M1 implied by 34 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) \(10 + 15\) and 25 | 1 | ||
| (ii) 10 | 2 | M1 for recognition of square number pattern If 0 scored SC1 for answer 11 | e.g. \(\sqrt{144}\), \(11 \times 11\), 36, 49, [64, ….] |