D1 January 2012 Q5
5.
| 5 | 1 | 8 | 13 | 16 | 5 | 8 | 2 | 15 | 12 | 10 |
| Scheme | Marks |
|---|---|
| Bin 1: 5, 1, 8, 5 Bin 4: 8, 12 | M1 (1st 6 terms) |
| Bin 2: 13, 2 Bin 5: 15 | A1(next 3) |
| Bin 3: 16 Bin 6: 10 | A1 |
| (3) |
Notes
a1M1: Bin 1 correct 13 and 16 in bins 2 and 3.
a1A1: Bin 2 correct 8 in bin 4.
a2A1: CAO
| Scheme | Marks | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
E.g Bubbling left to right (see alts)
| M1 A1 A1ft A1ft A1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| (5) |
Notes
b1M1: End number (greatest/least) in place. Consistent direction throughout.
b1A1: first pass correct.
b2A1ft: 2nd and 3rd passes correct – so end three numbers in place.
b3A1ft: 4th and 5th passes correct – so end five numbers in place.
b4A1: cso including ‘sorted’, or extra pass (es), ruling off, boxed, ticked etc.
Alternatives for Question 5(b)
Right to left
| 5 | 1 | 8 | 13 | 16 | 5 | 8 | 2 | 15 | 12 | 10 | 1M1 |
| 16 | 5 | 1 | 8 | 13 | 15 | 5 | 8 | 2 | 12 | 10 | 1A1 |
| 16 | 15 | 5 | 1 | 8 | 13 | 12 | 5 | 8 | 2 | 10 | |
| 16 | 15 | 13 | 5 | 1 | 8 | 12 | 10 | 5 | 8 | 2 | 2A1ft |
| 16 | 15 | 13 | 12 | 5 | 1 | 8 | 10 | 8 | 5 | 2 | |
| 16 | 15 | 13 | 12 | 10 | 5 | 1 | 8 | 8 | 5 | 2 | 3A1ft |
| 16 | 15 | 13 | 12 | 10 | 8 | 5 | 1 | 8 | 5 | 2 | |
| 16 | 15 | 13 | 12 | 10 | 8 | 8 | 5 | 1 | 5 | 2 | |
| 16 | 15 | 13 | 12 | 10 | 8 | 8 | 5 | 5 | 1 | 2 | |
| 16 | 15 | 13 | 12 | 10 | 8 | 8 | 5 | 5 | 2 | 1 | + Stop 4A1 |
Misreads – allow recovery if list reversed.
Left to right ascending
| 5 | 1 | 8 | 13 | 16 | 5 | 8 | 2 | 15 | 12 | 10 | 1M1 |
| 1 | 5 | 8 | 13 | 5 | 8 | 2 | 15 | 12 | 10 | 16 | 1A1 |
| 1 | 5 | 8 | 5 | 8 | 2 | 13 | 12 | 10 | 15 | 16 | |
| 1 | 5 | 5 | 8 | 2 | 8 | 12 | 10 | 13 | 15 | 16 | 2A1ft |
| 1 | 5 | 5 | 2 | 8 | 8 | 10 | 12 | 13 | 15 | 16 | |
| 1 | 5 | 2 | 5 | 8 | 8 | 10 | 12 | 13 | 15 | 16 | 3A1ft |
| 1 | 2 | 5 | 5 | 8 | 8 | 10 | 12 | 13 | 15 | 16 | + stop 4A1 |
Right to Left ascending
| 5 | 1 | 8 | 13 | 16 | 5 | 8 | 2 | 15 | 12 | 10 | 1M1 |
| 1 | 5 | 2 | 8 | 13 | 16 | 5 | 8 | 10 | 15 | 12 | 1A1 |
| 1 | 2 | 5 | 5 | 8 | 13 | 16 | 8 | 10 | 12 | 15 | |
| 1 | 2 | 5 | 5 | 8 | 8 | 13 | 16 | 10 | 12 | 15 | 2A1ft |
| 1 | 2 | 5 | 5 | 8 | 8 | 10 | 13 | 16 | 12 | 15 | |
| 1 | 2 | 5 | 5 | 8 | 8 | 10 | 12 | 13 | 16 | 15 | 3A1ft |
| 1 | 2 | 5 | 5 | 8 | 8 | 10 | 12 | 13 | 15 | 16 | + stop 4A1 |
| Scheme | Marks |
|---|---|
| Bin 1: 16, 2, 1 Bin 4: 12, 8 | M1 (to 8s) |
| Bin 2: 15, 5 Bin 5: 10, 8 | A1 (to 5s) |
| Bin 3: 13, 5 | A1 |
| (3) |
Notes
c1M1: Bins 4 and 5 correct, others started.
Special case: If list at end of (b) wrong give M1 only for their 1st 7 terms placed correctly.
c1A1: Bins 2 and 3 correct up to the 5s.
c2A1: cao
| Scheme | Marks |
|---|---|
| E. g. \(\dfrac{95}{20} = 4.75\) so a minimum of 5 bins needed. | M1 A1 |
| (2) | |
| (13 marks) |
Notes
d1M1: Numerical argument. E.g. Attempt to find lower bound o.e., consideration of ‘spare room’. Etc. (Accept ‘5 items \(\geqslant\) 10’ o.e for M1 only)
d1A1: correct numerical argument; conclusion (the yes/no) may follow from (c).