# Question 1:

## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{131}{40} = 3.275$, so lower bound is **4** | M1 A1 **(2)** | M1: Attempt to find lower bound $(131 \pm 28)/40$. A value of 3.275 with no corresponding calculation can imply this mark. Allow for clear intention of adding all ten values and dividing by 40. A1: cao - correct calculation followed by 4, or correct value of 3.275 followed by 4. Answer of 4 with no working scores 0. |

## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Container 1: 17, 9, 8, 4 | $\overline{\text{M1}}$ A1 A1 **(3)** | M1: First four values placed correctly and at least eight values placed in containers. Condone cumulative totals for M1 only (e.g. Container 1: 17 26 34 38). A1: First eight values placed correctly (boxed and underlined values). Cannot be awarded if any repeated values or more than ten values in containers. A2: cso – no additional or repeated values (dependent on both previous marks). |
| Container 2: 15, 20, 5 | | |
| Container 3: 13, 12 | | |
| Container 4: 28 | | |

## Part (c)
| Answer/Working | Marks | Guidance |
|---|---|---|
| **Middle right pivots:** | M1 | M1: Quick sort, pivot chosen (must be choosing middle left or right). After first pass list must read (values less than pivot), pivot, (values greater than pivot). M0 if sorting into descending order. Mark can be scored if one number is either missing/incorrect or an additional number is added to the list. |
| 17 9 15 8 20 **13** 28 4 12 5 → pivot: 13 | | |
| 9 8 **4** 12 5 $\underline{13}$ 17 15 **20** 28 → pivots: 4, 20 | A1 | A1: First two passes correct and next pivots chosen correctly for third pass (third pass does not need to be attempted or correct). |
| $\underline{4}$ 9 8 5 **12** 13 **15** 17 $\underline{20}$ 28 → pivots: 12, 15, (28) | | |
| $\underline{4}$ 9 **8** 5 $\underline{12}$ 13 $\underline{15}$ 17 $\underline{20}$ 28 → pivots: 8, (17) | A1 **(3)** | A2: cso – if middle right, either a fifth pass or a 'sort complete' statement is required after the fourth pass. If middle left, a fifth pass (with value of 9) is required. |
| $\underline{4}$ 5 $\underline{8}$ 9 $\underline{12}$ 13 $\underline{15}$ 17 $\underline{20}$ 28 → Sort complete | | |

## Part (d)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\left\lceil\frac{1+10}{2}\right\rceil = 6$ → 13 – reject 13–28 | M1 | M1: Choosing middle right pivot and an attempt at discarding/retaining half the list. (Choosing middle left '12' is M0.) Condone if retaining the wrong half or retaining items 1–6. |
| $\left\lceil\frac{1+5}{2}\right\rceil = 3$ → 8 – reject 4–8 | A1 | A1: First and second passes correct, i.e. selecting 6th item in first pass and using 1st to 5th items in second pass (must not use 6th item for second pass), then correctly selecting 3rd item (the 8) in second pass and rejecting 1st to 3rd items. |
| $\left\lceil\frac{4+5}{2}\right\rceil = 5$ → 12 – reject 12 | A1 **(3)** | A2: cao – search completed correctly (rejecting 12 in third pass) together with 'found'. Condone candidates who state that after 12 is rejected the only value left is 9 so it has been found. Must be clear that 9 has been 'found' and not just stated as the final value. |
| $[4] = 4$ → 9 – **found** | | |

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