A2 June 2025 Q1
1.
| 4.7 | 2.9 | 5.5 | 1.4 | 5.8 | 2.8 | 3.8 | 6.5 | 5.1 | 6.3 | 4.1 |
(a) Use the first-fit bin packing algorithm to determine how the numbers listed above can be packed into bins of size 13 (3)
(b) Use the first-fit decreasing bin packing algorithm to determine how the numbers listed above can be packed into bins of size 13 (2)
| Scheme | Marks | AO |
|---|---|---|
| Bin 1: \(\boxed{4.7}\) \(\boxed{2.9}\) \(\boxed{1.4}\) 2.8 Bin 2: \(\boxed{5.5}\) 5.8 Bin 3: 3.8 6.5 Bin 4: 5.1 6.3 Bin 5: 4.1 | M1 A1 A1 | 1.1b 1.1b 1.1b |
| (3) |
Notes
a1M1: First four items placed correctly (the boxed values) and at least eight values placed in bins – condone cumulative totals for M1 only
a1A1: First eight items placed correctly (the boxed and bold values)
a2A1: CSO (no additional/repeated values)
| Scheme | Marks | AO |
|---|---|---|
| Bin 1: \(\underline{6.5}\) \(\underline{6.3}\) Bin 2: \(\underline{5.8}\) \(\underline{5.5}\) 1.4 Bin 3: \(\underline{5.1}\) \(\underline{4.7}\) 2.9 Bin 4: \(\underline{4.1}\) \(\underline{3.8}\) 2.8 | M1 A1 | 1.1b 1.1b |
| (2) | ||
| (5 marks) |
Notes
b1M1: First eight items placed correctly (the underlined values) and at least ten values placed in bins (no additional/repeated values) - condone cumulative totals for M1 only
b1A1: CSO