OCR MEI D1 2012 January — Question 2 8 marks

Exam BoardOCR MEI
ModuleD1 (Decision Mathematics 1)
Year2012
SessionJanuary
Marks8
PaperDownload PDF ↗
TopicNumber Theory
TypeAlgorithm tracing and properties
DifficultyEasy -1.8 This is a purely procedural algorithm-tracing exercise requiring only arithmetic operations (reversal, subtraction, addition) with no mathematical insight, proof, or problem-solving. The investigation in part (iii) requires minimal exploration of cases rather than rigorous analysis. Well below average A-level difficulty.
Spec7.03a Algorithm definition: input, output, deterministic, finite7.03c Working with algorithms: trace, interpret, adapt
2 The following is called the '1089' algorithm. In steps 1 to 4 numbers are to be written with exactly three digits; for example 42 is written as 042. Step 1 Choose a 3-digit number, with no digit being repeated.
Step 2 Form a new number by reversing the order of the three digits.
Step 3 Subtract the smaller number from the larger and call the difference D. If the two numbers are the same then \(\mathrm { D } = 000\). Step 4 Form a new number by reversing the order of the three digits of D , and call it R .
Step 5 Find the sum of D and R .
  1. Apply the algorithm, choosing 427 for your 3-digit number, and showing all of the steps.
  2. Apply the algorithm to a 3-digit number of your choice, showing all of the steps.
  3. Investigate what happens if digits may be repeated in the 3 -digit number in step 1 .
2 The following is called the '1089' algorithm. In steps 1 to 4 numbers are to be written with exactly three digits; for example 42 is written as 042.

Step 1 Choose a 3-digit number, with no digit being repeated.\\
Step 2 Form a new number by reversing the order of the three digits.\\
Step 3 Subtract the smaller number from the larger and call the difference D. If the two numbers are the same then $\mathrm { D } = 000$.

Step 4 Form a new number by reversing the order of the three digits of D , and call it R .\\
Step 5 Find the sum of D and R .\\
(i) Apply the algorithm, choosing 427 for your 3-digit number, and showing all of the steps.\\
(ii) Apply the algorithm to a 3-digit number of your choice, showing all of the steps.\\
(iii) Investigate what happens if digits may be repeated in the 3 -digit number in step 1 .

\hfill \mbox{\textit{OCR MEI D1 2012 Q2 [8]}}
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