| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sorting Algorithms |
| Type | Algorithm Tracing |
| Difficulty | Easy -1.8 This is a straightforward algorithm tracing exercise requiring only careful step-by-step execution of given instructions with no problem-solving, insight, or understanding of why the algorithm works. It's purely mechanical bookwork testing ability to follow a flowchart, which is significantly easier than typical A-level questions requiring mathematical reasoning. |
| Spec | 7.03c Working with algorithms: trace, interpret, adapt |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Trace table completed with at least 3 rows of \(x\), \(y\), \(t\) with correct first row (\(x=26\), \(t=5\)) | M1 (3 rows + 1st correct) | Values in parentheses indicate values carried forward from previous row |
| 2nd and 3rd rows correct (columns \(x\), \(y\), \(t\) only) | A1 | Row 1: \(x=26, y=(5), t=5\); Row 2: \(x=13, y=10, t=(5)\) |
| 4th, 5th and 6th rows correct (columns \(x\), \(y\), \(t\) only) | A1 | Row 3: \(x=12, y=(10), t=15\); Row 4: \(x=6, y=20, t=(15)\); Row 5: \(x=3, y=40, t=(15)\); Row 6: \(x=2, y=(40), t=55\) |
| Output \(= 135\) | A1 (CSO) | Must be absolutely clear output is the final \(t\) value; all yes/no columns must be present with no additional/incorrect entries |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(x\) must be a (positive) integer, therefore \(x = 122\) | B1 | Any attempt at a reason |
| \(x = 122\) with correct valid reason | DB1 | \(x\) must be integer/whole number or \(\frac{1}{2}\) is not odd or even or halving \(\frac{1}{2}\) means \(x=0\) is never reached; must explain why \(x\) will never become 0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(61\) | B1 | CAO |
# Question 5:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Trace table completed with at least 3 rows of $x$, $y$, $t$ with correct first row ($x=26$, $t=5$) | M1 (3 rows + 1st correct) | Values in parentheses indicate values carried forward from previous row |
| 2nd and 3rd rows correct (columns $x$, $y$, $t$ only) | A1 | Row 1: $x=26, y=(5), t=5$; Row 2: $x=13, y=10, t=(5)$ |
| 4th, 5th and 6th rows correct (columns $x$, $y$, $t$ only) | A1 | Row 3: $x=12, y=(10), t=15$; Row 4: $x=6, y=20, t=(15)$; Row 5: $x=3, y=40, t=(15)$; Row 6: $x=2, y=(40), t=55$ |
| Output $= 135$ | A1 (CSO) | Must be absolutely clear output is the final $t$ value; all yes/no columns must be present with no additional/incorrect entries |
## Part (b)(i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $x$ must be a (positive) integer, therefore $x = 122$ | B1 | Any attempt at a reason |
| $x = 122$ with correct valid reason | DB1 | $x$ must be integer/whole number **or** $\frac{1}{2}$ is not odd or even **or** halving $\frac{1}{2}$ means $x=0$ is never reached; must explain **why** $x$ will never become 0 |
## Part (b)(ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $61$ | B1 | CAO |
---5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{22ff916a-4ba8-4e0c-9c53-e82b0aff0b98-06_1388_1648_246_221}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}
An algorithm is described by the flow chart shown in Figure 4.
Given that $x = 27$ and $y = 5$,
\begin{enumerate}[label=(\alph*)]
\item complete the table in the answer book to show the results obtained at each step when the algorithm is applied. Give the final output.
The numbers 122 and $\frac { 1 } { 2 }$ are to be used as inputs for the algorithm described by the flow chart.
\item \begin{enumerate}[label=(\roman*)]
\item State, giving a reason, which number should be input as $x$.
\item State the output.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2016 Q5 [7]}}