| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sorting Algorithms |
| Type | Binary Search Execution |
| Difficulty | Easy -1.8 This is a straightforward execution of the binary search algorithm on a given list, requiring only mechanical application of a learned procedure with no problem-solving or insight. Part (c) asks for basic recall of why the algorithm works, making this significantly easier than average A-level questions. |
| Spec | 7.03a Algorithm definition: input, output, deterministic, finite |
| Answer | Marks |
|---|---|
| List of 14 names has midpoint = 8th = KINCARDINE. After removing PENICUIK alphabetically, reduced list is: LARGS, MALLAIG, MONTROSE, PENICUIK, ST. ANDREWS, THURSO. List of 6 names has midpoint = 4th = PENICUIK and found | M2 A1 |
| Answer | Marks |
|---|---|
| List of 14 names has midpoint = 8th = KINCARDINE. PENDINE is after this alphabetically so reduced list is: LARGS, MALLAIG, MONTROSE, PENICUIK, ST. ANDREWS, THURSO. List of 6 names has midpoint = 4th = PENICUIK. PENDINE is before this alphabetically so reduced list is: LARGS, MALLAIG, MONTROSE. List of 3 names has midpoint = 2nd = MALLAIG. PENDINE is after this alphabetically so reduced list is: MONTROSE. List of 1 name, not PENDINE, therefore not in list | M2 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Each new list is at most half of previous list | B1 | (7) |
**Part (a)**
List of 14 names has midpoint = 8th = KINCARDINE. After removing PENICUIK alphabetically, reduced list is: LARGS, MALLAIG, MONTROSE, PENICUIK, ST. ANDREWS, THURSO. List of 6 names has midpoint = 4th = PENICUIK and found | M2 A1 |
**Part (b)**
List of 14 names has midpoint = 8th = KINCARDINE. PENDINE is after this alphabetically so reduced list is: LARGS, MALLAIG, MONTROSE, PENICUIK, ST. ANDREWS, THURSO. List of 6 names has midpoint = 4th = PENICUIK. PENDINE is before this alphabetically so reduced list is: LARGS, MALLAIG, MONTROSE. List of 3 names has midpoint = 2nd = MALLAIG. PENDINE is after this alphabetically so reduced list is: MONTROSE. List of 1 name, not PENDINE, therefore not in list | M2 A1 |
**Part (c)**
Each new list is at most half of previous list | B1 | (7) |
---\begin{enumerate}
\item (a) Use the binary search algorithm to locate the name PENICUIK in the following list.
\end{enumerate}
\begin{displayquote}
ANKERDINE CULROSS DUNOON ELGIN FORFAR FORT WILLIAM HADDINGTON KINCARDINE LARGS MALLAIG MONTROSE PENICUIK ST. ANDREWS THURSO\\
(b) Use the same algorithm to attempt to locate PENDINE.\\
(c) Explain the purpose of the mid-point in dividing up the ordered list when using this algorithm.
\end{displayquote}
\hfill \mbox{\textit{Edexcel D1 Q1 [7]}}