Edexcel D1 2023 June — Question 3

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2023
SessionJune
TopicFixed Point Iteration

3. In this question, the function \(\operatorname { INT } ( X )\) is the largest integer less than or equal to \(X\). For example, $$\begin{aligned} \mathrm { INT } ( 5.7 ) & = 5
\mathrm { INT } ( 8 ) & = 8
\mathrm { INT } ( - 2.3 ) & = - 3 \end{aligned}$$ Consider the following algorithm.
Step 1 Input \(N\)
Step 2 Calculate \(A = N \div 10\)
Step 3 Let \(B = \operatorname { INT } ( A )\)
Step 4 Calculate \(C = B \times 10\)
Step 5 Calculate \(D = N - C\)
Step 6 Output \(D\)
Step \(7 \quad\) Replace \(N\) by \(B\)
Step 8 If \(N = 0\) then STOP, otherwise go back to Step 2
  1. Complete the table in the answer book, using \(N = 4217\), to show the results obtained at each step of the algorithm.
  2. Explain how the output values of the algorithm relate to the original input \(N\), where \(N\) is any positive integer.