| Exam Board | OCR |
|---|---|
| Module | Further Discrete AS (Further Discrete AS) |
| Year | 2022 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sorting Algorithms |
| Type | Algorithm Tracing |
| Difficulty | Easy -1.2 This is a straightforward flowchart tracing exercise requiring students to follow simple arithmetic operations (doubling X, halving Y) and record changes. Part (b) asks for basic reasoning about why Y→0 ensures termination. Both parts are routine procedural tasks with no problem-solving or novel insight required, making this easier than average A-level work. |
| Spec | 7.03a Algorithm definition: input, output, deterministic, finite7.03c Working with algorithms: trace, interpret, adapt |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Initial values: \(X=1, Y=2, N=0, M=2, H=0.5, D=1\) | B1 | Initial values of \(X\), \(Y\), \(N\), \(M\), \(H\) and \(D\) |
| First updated values: \(X=1.5, Y=2.5, N=1, D=1.13\) | M1 | First updated values of \(X\), \(Y\), \(D\) (with \(D\) to 3 s.f. or better) (17/15) |
| Second updated: \(X=2, Y=3.07, N=2\) | ||
| Display: 3.07 | A1 | Or seen in table as second updated value of \(Y\) (to 3 s.f. or better) (46/15) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| e.g. \(N\) is initially 0 and increases by 1 in each pass until it reaches \(M\), when the algorithm displays the output and stops | B1 | Explain why algorithm is finite. e.g. \(N\) (starts at 0 and) increases (through positive integer values) until it passes \(M\) |
# Question 1:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Initial values: $X=1, Y=2, N=0, M=2, H=0.5, D=1$ | B1 | Initial values of $X$, $Y$, $N$, $M$, $H$ and $D$ |
| First updated values: $X=1.5, Y=2.5, N=1, D=1.13$ | M1 | First updated values of $X$, $Y$, $D$ (with $D$ to 3 s.f. or better) (17/15) |
| Second updated: $X=2, Y=3.07, N=2$ | | |
| Display: 3.07 | A1 | Or seen in table as second updated value of $Y$ (to 3 s.f. or better) (46/15) |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| e.g. $N$ is initially 0 and increases by 1 in each pass until it reaches $M$, when the algorithm displays the output and stops | B1 | Explain why algorithm is finite. e.g. $N$ (starts at 0 and) increases (through positive integer values) until it passes $M$ |
---1 The flowchart below has positive inputs $X , Y$ and $M$.\\
\includegraphics[max width=\textwidth, alt={}, center]{74b6f747-7045-4902-8b21-0b59c007f7f6-2_1274_643_392_242}
\begin{enumerate}[label=(\alph*)]
\item Trace through the flowchart above using the inputs $X = 1 , Y = 2$ and $M = 2$. You only need to record values when they change.
\item Explain why the process in the flowchart is finite.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Discrete AS 2022 Q1 [4]}}