| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sorting Algorithms |
| Type | Describing Sorting Algorithm Steps |
| Difficulty | Easy -1.8 This is a fragment of a question about tracing through a sorting algorithm, requiring only the ability to follow simple instructions and increment a variable. It involves no mathematical reasoning or problem-solving—just mechanical execution of an algorithm step, making it significantly easier than typical A-level questions. |
| Spec | 7.03j Sorting: bubble sort and shuttle sort |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| e.g. \(0, 1, 2 \rightarrow 1\); \(3, 4, 5, 6, 7 \rightarrow 2\); \(8 \rightarrow 3\); \(9 \rightarrow 4\) | M1 | either 3 numbers for 1 or 5 numbers for 2 |
| A1 | all proportions correct | |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| random number: \(5, 3, 2, 4, 7, 9, 1, 1, 8\) | M1 | all outcomes achieved with first 2 correct for their rule |
| time interval (mins): \(2, 2, 1, 2, 2, 4, 1, 1, 3\) | A1 | all correct FT |
| arrival times: \(0, 2, 4, 5, 7, 9, 13, 14, 15, 18\) | B1 | accumulation |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| e.g. \(00\)–\(13 \rightarrow 0.1\); \(14\)–\(41 \rightarrow 0.25\); \(42\)–\(83 \rightarrow 1\); \(84\)–\(97 \rightarrow 2\); \(98, 99\) ignore and "redraw" | M1 | ignore some |
| A1 | proportions correct | |
| A1 | efficient (fewer than 7 rejected) | |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| random number: \(23, 15, 01, 32, 45, 47, 86, 71, 17, 83\) | M1 | first 4 customers correct for their rule |
| processing time: \(0.25, 0.25, 0.1, 0.25, 1, 1, 2, 1, 0.25, 1\) | A1 | all correct FT |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| e.g. \(0\)–\(5 \rightarrow 1\); \(6\)–\(9 \rightarrow 0.25\) | B1 | |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| random number: \(8, 3, 0, 1, 4, 0, 2, 5, 7, 6\) | B1 | FT |
| payment time: \(0.25, 1, 1, 1, 1, 1, 1, 1, 0.25, 0.25\) | ||
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| arrival: \(0, 2, 4, 5, 7, 9, 13, 14, 15, 18\) | M1 | deals with a wait correctly |
| departure: \(0.5, 3.25, 5.1, 6.35, 9, 11, 16, 18, 18.5, 19.75\) | A1 | all correct FT |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| arrival: \(0, 2, 4, 5, 7, 9, 13, 14, 15, 18\) | M1 | deals with last 3 correctly |
| departure: \(0.5, 3.25, 5.1, 6.35, 9, 11, 16, 18, 15.5, 19.25\) | A1 | all correct FT |
| [2] |
# Question 6:
## Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| e.g. $0, 1, 2 \rightarrow 1$; $3, 4, 5, 6, 7 \rightarrow 2$; $8 \rightarrow 3$; $9 \rightarrow 4$ | M1 | either 3 numbers for 1 or 5 numbers for 2 |
| | A1 | all proportions correct |
| **[2]** | | |
## Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| random number: $5, 3, 2, 4, 7, 9, 1, 1, 8$ | M1 | all outcomes achieved with first 2 correct for their rule |
| time interval (mins): $2, 2, 1, 2, 2, 4, 1, 1, 3$ | A1 | all correct FT |
| arrival times: $0, 2, 4, 5, 7, 9, 13, 14, 15, 18$ | B1 | accumulation |
| **[3]** | | |
## Part (iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| e.g. $00$–$13 \rightarrow 0.1$; $14$–$41 \rightarrow 0.25$; $42$–$83 \rightarrow 1$; $84$–$97 \rightarrow 2$; $98, 99$ ignore and "redraw" | M1 | ignore some |
| | A1 | proportions correct |
| | A1 | efficient (fewer than 7 rejected) |
| **[3]** | | |
## Part (iv):
| Answer | Marks | Guidance |
|--------|-------|----------|
| random number: $23, 15, 01, 32, 45, 47, 86, 71, 17, 83$ | M1 | first 4 customers correct for their rule |
| processing time: $0.25, 0.25, 0.1, 0.25, 1, 1, 2, 1, 0.25, 1$ | A1 | all correct FT |
| **[2]** | | |
## Part (v):
| Answer | Marks | Guidance |
|--------|-------|----------|
| e.g. $0$–$5 \rightarrow 1$; $6$–$9 \rightarrow 0.25$ | B1 | |
| **[1]** | | |
## Part (vi):
| Answer | Marks | Guidance |
|--------|-------|----------|
| random number: $8, 3, 0, 1, 4, 0, 2, 5, 7, 6$ | B1 | FT |
| payment time: $0.25, 1, 1, 1, 1, 1, 1, 1, 0.25, 0.25$ | | |
| **[1]** | | |
## Part (vii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| arrival: $0, 2, 4, 5, 7, 9, 13, 14, 15, 18$ | M1 | deals with a wait correctly |
| departure: $0.5, 3.25, 5.1, 6.35, 9, 11, 16, 18, 18.5, 19.75$ | A1 | all correct FT |
| **[2]** | | |
## Part (viii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| arrival: $0, 2, 4, 5, 7, 9, 13, 14, 15, 18$ | M1 | deals with last 3 correctly |
| departure: $0.5, 3.25, 5.1, 6.35, 9, 11, 16, 18, 15.5, 19.25$ | A1 | all correct FT |
| **[2]** | | |6 Let the new value of $j$ be $j + 1$.\\
\hfill \mbox{\textit{OCR MEI D1 2013 Q6 [16]}}