| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sorting Algorithms |
| Type | Algorithm Tracing |
| Difficulty | Moderate -0.8 This is a straightforward trace-through of the bisection method requiring only arithmetic and sign checking. The algorithm recognition and completion are standard textbook material for D1, with no novel problem-solving or proof required—simpler than typical A-level pure maths questions. |
| Spec | 7.03a Algorithm definition: input, output, deterministic, finite7.03c Working with algorithms: trace, interpret, adapt |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(M = 1\), \(f(M) = -1\), \(L = 1\) | B1 B1 B1 | |
| \(M = 1.5\), \(f(M) = 0.25\), \(R = 1.5\) | B1 B1 B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Solves equations (Allow "Finds root 2") | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| A termination condition | B1 |
**Part (i)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $M = 1$, $f(M) = -1$, $L = 1$ | B1 B1 B1 | |
| $M = 1.5$, $f(M) = 0.25$, $R = 1.5$ | B1 B1 B1 | |
**Part (ii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Solves equations (Allow "Finds root 2") | B1 | |
**Part (iii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| A termination condition | B1 | |3 An incomplete algorithm is specified in Fig. 3.\\
$\mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 2$\\
Initial values: $\mathrm { L } = 0 , \mathrm { R } = 2$.\\
Step 1 Compute $\mathrm { M } = \frac { \mathrm { L } + \mathrm { R } } { 2 }$.\\
Step 2 Compute $\mathrm { f } ( \mathrm { M } )$.\\
Step 3 If $\mathrm { f } ( \mathrm { M } ) < 0$ change the value of L to that of M .\\
Otherwise change the value of $R$ to that of $M$.\\
Step 4 Go to Step 1.
\section*{Fig. 3}
(i) Apply two iterations of the algorithm.\\
(ii) After 10 iterations $\mathrm { L } = 1.414063 , \mathrm { R } = 1.416016 , \mathrm { M } = 1.416016$ and $\mathrm { f } ( \mathrm { M } ) = 0.005100$.
Say what the algorithm achieves.\\
(iii) Say what is needed to complete the algorithm.
\hfill \mbox{\textit{OCR MEI D1 2006 Q3 [8]}}