| Exam Board | AQA |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2005 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Fixed Point Iteration |
| Type | Apply iteration to find root (pure fixed point) |
| Difficulty | Easy -1.2 This is a straightforward algorithm tracing exercise requiring only systematic substitution into a given formula. Students follow mechanical steps with no problem-solving, conceptual understanding of fixed point iteration, or analysis required. The omitted line question is trivial observation about infinite loops. |
| Spec | 7.03c Working with algorithms: trace, interpret, adapt |
| LINE 10 | INPUT \(X\) |
| LINE 20 | LET \(K = 1\) |
| LINE 30 | LET \(Y = \left( X ^ { * } X + 16 \right) / \left( 2 ^ { * } X \right)\) |
| LINE 40 | PRINT \(Y\) |
| LINE 50 | LET \(X = Y\) |
| LINE 60 | LET \(K = K + 1\) |
| LINE 70 | IF \(K = 4\) THEN GO TO LINE 90 |
| LINE 80 | GO TO LINE 30 |
| LINE 90 | STOP |
5 A student is using the following algorithm with different values of $X$.
\begin{center}
\begin{tabular}{|l|l|}
\hline
LINE 10 & INPUT $X$ \\
\hline
LINE 20 & LET $K = 1$ \\
\hline
LINE 30 & LET $Y = \left( X ^ { * } X + 16 \right) / \left( 2 ^ { * } X \right)$ \\
\hline
LINE 40 & PRINT $Y$ \\
\hline
LINE 50 & LET $X = Y$ \\
\hline
LINE 60 & LET $K = K + 1$ \\
\hline
LINE 70 & IF $K = 4$ THEN GO TO LINE 90 \\
\hline
LINE 80 & GO TO LINE 30 \\
\hline
LINE 90 & STOP \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Trace the algorithm, giving your answers to three decimal places where appropriate:
\begin{enumerate}[label=(\roman*)]
\item in the case where the input value of $X$ is 2 ;
\item in the case where the input value of $X$ is - 6 .
\end{enumerate}\item Another student used the same algorithm but omitted LINE 70. Describe the outcome for this student.
\end{enumerate}
\hfill \mbox{\textit{AQA D1 2005 Q5 [8]}}