Higher November 2024 Paper 2 Q6
6. A new supermarket is about to open in a town with 8000 houses.
For the first four weeks, £10 vouchers will be sent out to encourage people to visit the supermarket.
At the start of the first week, 30% of the houses in the town will each be sent a voucher.
At the start of each of the next three weeks, a voucher will be sent to 30% of the houses that have not yet received a voucher.
The vouchers need to be used in the supermarket by the end of the four weeks.
(a) John, the supermarket manager, says
“By the end of the four weeks, 6079 of the vouchers will have been used.”
Show that John could be correct. [4](b)
(i) State an assumption that John has made in part (a). [1]
(ii) If John’s assumption was not correct, what effect would this have on the number of vouchers used by the end of the four weeks? [1]
| Scheme | Marks | Comments |
|---|---|---|
| \(8000 \times (1 - 0.3)^4\) oe | M2 | M1 for \(8000 \times (1 - 0.3)^n\) oe when \(1 \leqslant n \lt 4\) \(8000 \times (1 - 0.3)\ (= 5600)\) |
| = 1920.8 or 1921 | A1 | |
| 8000 – 1920.8 = 6079.2 therefore 6079 (£10 vouchers) or 8000 – 1921 = 6079 (£10 vouchers) | B1 | CAO |
Alternative method
| Scheme | Marks | Comments | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A full method for the number of vouchers sent for the 4 weeks.
| M2 | M1 for \(8000 - 8000 \times 0.3\ (= 5600)\) oe | |||||||||||||||
| 2400 + 1680 + 1176 + 823.2 or 2400 + 1680 + 1176 + 823 | m1 | FT provided M2 awarded | |||||||||||||||
| = 6079.2 therefore 6079 (£10 vouchers) | A1 | CAO |
| Scheme | Marks | Comments |
|---|---|---|
| (b)(i) A valid assumption that John made e.g. ‘Every house that was sent a voucher used the voucher.’ ‘Every house that was sent the voucher received the voucher.’ ‘Every house that received the voucher used the voucher by the end of the four weeks.’ ‘Every house that received the voucher uses that supermarket.’ ‘They had time to use the voucher.’ | E1 | Allow e.g. ‘None got lost in the post.’ ‘They use that supermarket.’ ‘That every house will use their voucher’ Do not allow e.g. ‘6079 vouchers would be used’ ‘The vouchers would encourage people to go to the supermarket’ |
| (b)(ii) A valid effect of their assumption e.g. ‘Less than 6079 vouchers would have been used.’ | E1 | If no valid assumption is made, then this mark cannot be awarded. Cannot award E0 E1. Allow e.g. ‘Less vouchers used.’ |
| (6) |
Corrected by Westie's Workshop
- The board's mark scheme printed “6039”. Changed to “6079” because the number in John’s claim is 6079; 6039 does not appear anywhere in the question.
Original: see the board's mark scheme PDF (link above).