| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sorting Algorithms |
| Type | Algorithm Tracing |
| Difficulty | Moderate -0.5 This is a straightforward algorithm tracing exercise requiring students to follow a flowchart step-by-step and complete a table. Part (a) is mechanical execution, (b) requires recognizing a simple pattern (likely factorial or powers), (c) tests understanding of termination conditions, and (d) requires identifying valid inputs. While it involves multiple parts, each step is routine for D1 students with no novel problem-solving or proof required—slightly easier than average A-level maths. |
| Spec | 7.03a Algorithm definition: input, output, deterministic, finite7.03b Algorithm awareness: uses and practical limitations7.03c Working with algorithms: trace, interpret, adapt |
| Answer | Marks | Guidance |
|---|---|---|
| \(x\) | \(a\) | \(b\) |
| 100 | 50 | 26 |
| — | 26 | 14.923 |
| — | 14.923 | 10.812 |
| — | 10.812 | 10.0305 |
| — | 10.0305 | 10.00004 |
| — | 10.00004 | 10 |
| Answer | Marks |
|---|---|
| Final Output = 10 | M2 A4 |
| Answer | Marks |
|---|---|
| It finds the square root of 100 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(x\) | \(a\) | \(b\) |
| 100 | 5 | 12.5 |
| Answer | Marks |
|---|---|
| E.g. it stops instead of looping because \((a-b)\) becomes negative | A1 B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(a \geq 10\) | A2 | (11) |
**Part (a)**
[Table showing iterations:
| $x$ | $a$ | $b$ | $(a-b) < 0.01?$ |
|-----|-----|-----|---|
| 100 | 50 | 26 | No |
| — | 26 | 14.923 | No |
| — | 14.923 | 10.812 | No |
| — | 10.812 | 10.0305 | No |
| — | 10.0305 | 10.00004 | No |
| — | 10.00004 | 10 | Yes |
]
Final Output = 10 | M2 A4 |
**Part (b)**
It finds the square root of 100 | B1 |
**Part (c)**
[Table showing:
| $x$ | $a$ | $b$ | $(a-b) < 0.01?$ |
|-----|-----|-----|---|
| 100 | 5 | 12.5 | Yes |
]
E.g. it stops instead of looping because $(a-b)$ becomes negative | A1 B1 |
**Part (d)**
$a \geq 10$ | A2 | (11) |
---5. This question should be answered on the sheet provided.
An algorithm is described by the flow chart shown in Figure 1 below.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{1e518ab0-9852-4d1d-a4c9-344a5edf9547-05_1337_937_388_404}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
\begin{enumerate}[label=(\alph*)]
\item Complete the table on the answer sheet recording the results of each instruction as the algorithm is applied and state the final output.
\item Explain what the algorithm achieves.
\item Attempt to apply the algorithm again, with the initial value of $a$, as specified in Box 2, changed to 5 . Explain what happens.\\
(2 mark)
\item Find the set of positive initial values of $a$ for which the algorithm will work.\\
(2 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 Q5 [11]}}