AQA D1 2009 January — Question 5

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2009
SessionJanuary
TopicFixed Point Iteration

5 A student is using the algorithm below to find an approximate value of \(\sqrt { 2 }\).
Line 10 Let \(A = 1 , B = 3 , C = 0\)
Line \(20 \quad\) Let \(D = 1 , E = 2 , F = 0\)
Line 30 Let \(G = B / E\)
Line \(40 \quad\) Let \(H = G ^ { 2 }\)
Line 50 If \(( H - 2 ) ^ { 2 } < 0.0001\) then go to Line 130
Line 60 Let \(C = 2 B + A\)
Line 70 Let \(A = B\)
Line 80 Let \(B = C\)
Line 90 Let \(F = 2 E + D\)
Line 100 Let \(D = E\)
Line 110 Let \(E = F\)
Line 120 Go to Line 30
Line 130 Print ' \(\sqrt { 2 }\) is approximately', \(B / E\)
Line 140 Stop
Trace the algorithm.