O-LevelComputer ScienceAlgorithm design and problem-solving2210/11 · May/June 2016 · Q95 Marks

Check digits are used to ensure the accuracy of entered data. A 7-digit number has an extra digit on the right, called the check digit. digit position: 1 2 3 4 5 6 7 8 digit: check digit The check digit is calculated as follows: • each digit in the number is multiplied by its digit position • the seven results are then added together • this total is divided by 11 • the remainder gives the check digit (if the remainder = 10, the check digit is X)

(a)Calculate the check digit for the following number. Show all your working. 4 2 4 1 5 0 8 ... Check digit[2]
(b)An operator has just keyed in the following number: 3 2 4 0 0 4 5 X Circle below correct if the check digit is correct OR incorrect if the check digit is incorrect. Explain your answer. correct incorrect[3]

Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

[1] (a) (4 × 1) + (2 × 2) + (4 × 3) + (1 × 4) + (5 × 5) + (0 × 6) + (8 × 7)
[1] (a) = 4 + 4 + 12 + 4 + 25 + 0 + 56 = 105
[1] (a) 105/11 = 9 remainder 6
[1] (a) check digit is: 6
[1] (b) incorrect check digit
[1] (b) check digit should be 1
[1] (b) (3*1) + (2*2) + (4*3) + (0*4) + (0*5) + (4*6) + (5*7) // 3 + 4 + 12 + 0 + 0 + 24 + 35 // Total = 78
[1] (b) 78/11 gives 7 remainder 1

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