AQA D1 2005 June — Question 5

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2005
SessionJune
TopicFixed Point Iteration

5 A student is using the following algorithm with different values of \(X\).
LINE 10INPUT \(X\)
LINE 20LET \(K = 1\)
LINE 30LET \(Y = \left( X ^ { * } X + 16 \right) / \left( 2 ^ { * } X \right)\)
LINE 40PRINT \(Y\)
LINE 50LET \(X = Y\)
LINE 60LET \(K = K + 1\)
LINE 70IF \(K = 4\) THEN GO TO LINE 90
LINE 80GO TO LINE 30
LINE 90STOP
  1. Trace the algorithm, giving your answers to three decimal places where appropriate:
    1. in the case where the input value of \(X\) is 2 ;
    2. in the case where the input value of \(X\) is - 6 .
  2. Another student used the same algorithm but omitted LINE 70. Describe the outcome for this student.