Moderate -0.8 This is a straightforward algorithm tracing exercise requiring only careful arithmetic and following instructions step-by-step. No conceptual understanding of why the algorithm works is needed, just mechanical execution of the given lines until the stopping condition is met.
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.
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.
\hfill \mbox{\textit{AQA D1 2009 Q5 [6]}}