D1 January 2013 Q1

EdexcelOld spec6 marksAlgorithms

Figure 1: flow chart. Start; Input N and E; R = (N/E + E)/2; Is −10^−6 < R − E < 10^−6? No: E = R and loop back; Yes: Output R; Stop — Figure 1

Hero’s algorithm for finding a square root is described by the flow chart shown in Figure 1.

Given that \(N = 72\) and \(E = 8\),

(a) use the flow chart to complete the table in the answer book, working to at least seven decimal places when necessary. Give the final output correct to seven decimal places. (4)

The flow chart is used with \(N = 72\) and \(E = -8\),

(b) describe how this would affect the output. (1)

Mark scheme (a)

Scheme

Marks

N	E	R	Qn
72	8	8.5	N
	8.5	8.485 294 118	N
	8.485 294 118	8.485 281 374	N
	8.485 281 374	8.485 281 374	Y

M1
A1

A1

Output is R = 8.485 281 4

A1ft

(4)

Notes

a1M1 At least two rows of cells in just E and R completed.

a1A1 CAO first two rows correct giving exact values or awrt 7dp (the exact second value for R is \(\frac{577}{68}\)).

a2A1 CAO third and fourth rows awrt 7dp

a3A1ft Output for R must follow through from their final value for R awrt 7dp – candidate must have answered ‘yes’ to score this mark. Output either on the answer line (or on the second page) or stated in the table but must be in the column for R below the row which contains ‘yes’.

Condone N = 72 on each row and entries appearing on separate rows throughout for full marks. Allow e.g. ticks/crosses etc. for yes/no.

Mark scheme (b)

Scheme	Marks
We would get a negative output for R/ We would get the negative square root	B1
	(1)

Notes

b1B1 Mention of ‘negative’ scores B1 however do not accept incorrect statements but bod that ‘negative’ only is implicitly describing the effect on the output. Accept ‘other square root’.

Scheme	Marks
E cannot be zero	B1
	(1)
	(6 marks)