| Exam Board | AQA |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sorting Algorithms |
| Type | Deducing Original List Properties |
| Difficulty | Easy -1.2 This is a straightforward algorithmic trace question requiring only basic understanding of bubble sort and shuttle sort mechanics. Students simply follow the algorithm rules to deduce constraints on x (e.g., x < 6 from first pass, x > 2 from second pass), then combine inequalities to find x = 3. No problem-solving insight needed—just careful bookwork application of standard D1 algorithms. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable7.03j Sorting: bubble sort and shuttle sort |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(x \leq 6\) | B1 | Accept \(x < 6\) if appropriate reasoning shown |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(x \leq 4\) | B1 | Must be a new/tighter inequality |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(x \leq 11\) | B1 | From shuttle sort first pass |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(x \geq 2\) | B1 | From second pass result |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Combining inequalities: \(2 \leq x \leq 4\) | M1 | Using results from (a) and (b) together |
| \(x = 3\) (only integer satisfying all constraints and being different from others) | A1 | Must be integer, must differ from \(2, 4, 6, 11\) |
# Question 2:
## Part (a)(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $x \leq 6$ | B1 | Accept $x < 6$ if appropriate reasoning shown |
## Part (a)(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $x \leq 4$ | B1 | Must be a new/tighter inequality |
## Part (b)(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $x \leq 11$ | B1 | From shuttle sort first pass |
## Part (b)(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $x \geq 2$ | B1 | From second pass result |
## Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Combining inequalities: $2 \leq x \leq 4$ | M1 | Using results from (a) and (b) together |
| $x = 3$ (only integer satisfying all constraints and being different from others) | A1 | Must be integer, must differ from $2, 4, 6, 11$ |
---2 Five different integers are to be sorted into ascending order.
\begin{enumerate}[label=(\alph*)]
\item A bubble sort is to be used on the list of numbers $\quad 6 \quad 4 \quad 5 \quad x \quad 2 \quad 11$.
\begin{enumerate}[label=(\roman*)]
\item After the first pass, the list of numbers becomes
$$\begin{array} { l l l l l }
4 & x & 2 & 6 & 11
\end{array}$$
Write down an inequality that $x$ must satisfy.
\item After the second pass, the list becomes
$$\begin{array} { l l l l l }
x & 2 & 4 & 6 & 11
\end{array}$$
Write down a new inequality that $x$ must satisfy.
\end{enumerate}\item The five integers are now written in a different order. A shuttle sort is to be used on the list of numbers $\quad \begin{array} { l l l l l } 11 & x & 2 & 4 & 6 . \end{array}$
\begin{enumerate}[label=(\roman*)]
\item After the first pass, the list of numbers becomes
$$\begin{array} { l l l l l }
x & 11 & 2 & 4 & 6
\end{array}$$
Write down an inequality that $x$ must satisfy.
\item After the second pass, the list becomes
$$\begin{array} { l l l l l }
2 & x & 11 & 4 & 6
\end{array}$$
Write down a further inequality that $x$ must satisfy.
\end{enumerate}\item Use your answers from parts (a) and (b) to write down the value of $x$.
\end{enumerate}
\hfill \mbox{\textit{AQA D1 2011 Q2 [6]}}