| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sorting Algorithms |
| Type | Algorithm Tracing |
| Difficulty | Standard +0.3 This is a straightforward trace-through of a given flowchart algorithm (likely interval bisection) with standard arithmetic operations. Part (a) requires mechanical execution of steps and recording values to specified decimal places. Part (b) requires understanding when the algorithm fails (likely when initial interval doesn't contain a sign change), which is a standard concept in D1. The question tests procedural fluency rather than problem-solving or novel insight, making it slightly easier than average. |
| Spec | 7.03a Algorithm definition: input, output, deterministic, finite7.03b Algorithm awareness: uses and practical limitations |
3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{44ddb176-e265-4545-b438-c1b5ffb40852-04_997_1155_223_456}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
An algorithm for finding the positive real root of the equation $8 x ^ { 4 } + 5 x - 12 = 0$ is described by the flow chart shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\item Use the flow chart, with $a = 1$, to complete the table in the answer book, stating values to at least 6 decimal places. Give the final output correct to 5 decimal places.
Given that the value of the input $a$ is a non-negative real number,
\item determine the set of values for $a$ that cannot be used to find the positive real root of $8 x ^ { 4 } + 5 x - 12 = 0$ using this flow chart.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2021 Q3 [6]}}