| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Number Theory |
| Type | Algorithm tracing and properties |
| Difficulty | Moderate -0.8 This is a straightforward algorithm tracing exercise (Russian peasant multiplication). Parts (i) and (ii) require only mechanical following of instructions with basic arithmetic (doubling, halving, adding). Part (iii) asks students to identify the pattern, which becomes obvious after working the examples—it computes multiplication. This is easier than average A-level work as it requires no algebraic manipulation, proof, or mathematical insight beyond pattern recognition. |
| Spec | 7.03a Algorithm definition: input, output, deterministic, finite7.03c Working with algorithms: trace, interpret, adapt |
2 The following steps define an algorithm which acts on two numbers.\\
STEP 1 Write down the two numbers side by side on the same row.\\
STEP 2 Beneath the left-hand number write down double that number. Beneath the right-hand number write down half of that number, ignoring any remainder.
STEP 3 Repeat STEP 2 until the right-hand number is 1.\\
STEP 4 Delete those rows where the right-hand number is even. Add up the remaining left-hand numbers. This is the result.\\
(i) Apply the algorithm to the left-hand number 3 and the right-hand number 8.\\
(ii) Apply the algorithm to the left-hand number 26 and the right-hand number 42.\\
(iii) Use your results from parts (i) and (ii), together with any other examples you may choose, to write down what the algorithm achieves.
\hfill \mbox{\textit{OCR MEI D1 2010 Q2 [8]}}