Numeracy Foundation June 2022 Unit 2 Q3
3. Glyn is running a game stall at a village fête.
Each player who wins a game at the stall receives a prize.
These prizes are selected at random from those available.
At the start of the fête, Glyn drew a vertical line diagram to show the number of each prize available.
At the start of the fête, one player said:
There is an equal chance of winning a box of chocolates, a cuddly toy, a book or a photo frame.
Do you agree? [1]
Yes ☐ No ☐
Give a reason for your answer.
In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
Glyn bought all of the prizes for his stall from a shop.
The number of each prize is shown in the vertical line diagram above.
The cost of buying one of each prize is shown in the table below.
| Box of chocolates | £1.80 |
| Cuddly toy | £2.30 |
| Book | £3.20 |
| Photo frame | £4.70 |
Glyn received a discount of 10% off the total cost of all the prizes.
How much did Glyn pay for all the prizes at his stall?
You must show all your working. [6 + 2 OCW]
| Scheme | Marks | Comments |
|---|---|---|
| Cuddly toy | B1 | Allow cuddly toy and 12 given together B0 for 12 alone |
| Scheme | Marks | Comments |
|---|---|---|
| No and reason given e.g. ‘The frequencies would all need to be the same for an equal chance’ ‘no as it seems that there are more cuddly toys than anything else’ ‘There aren’t equal numbers of each prize’ ‘more of some prizes than others’ ‘numbers are not equal’ ‘different number of prizes’ ‘not equal to each other’ ‘different amounts of different prizes’ ‘cuddly toy is most common’ ‘more of one thing than another’ ‘more likely to win a cuddly toy or box of chocolates’ ‘less chance to win a book or photo frame’ ‘less of certain prizes’ | E1 | Ignore additional spurious or incorrect statements for accepted and allowed responses Allow ‘different amounts available’ ‘different amount of stock for the prizes’ ‘there’s only 5 books, 9 boxes of chocolates and there are 12 cuddly toys’ ‘there’s 12 cuddly toys and 2 photo frames’ (comparison of any 2 or more) ‘more prizes than others’ Do not allow ‘there are only 2 photo frames’ (with nothing else said – no comparison with any other prize) ‘different prizes’ |
| Scheme | Marks | Comments |
|---|---|---|
| (Cost of prizes without discount) 9 × 1.80 + 12 × 2.30 + 5 × 3.20 + 2 × 4.70 (16.20 + 27.60 + 16 + 9.40) | M2 | May be seen in stages Award M1 for:
|
| (£)69.2(0) | A1 | CAO |
| (Discount) (£)6.92 | B1 | Allow (£)6.9(0) if 6.92 seen FT 10% of ‘their (£)69.2(0)’ including 10% of (£)12 This may be implied in their final answer. |
| (Cost of prizes with discount) (£)69.2(0) – (£)6.92 | M1 | FT ‘their (£)69.2(0)’ – ‘their (£)6.92’ provided there has been an attempt at finding 10% and 10 or 0.10 is not used as their value of 10% |
| (£)62.28 | A1 | |
| Organisation and communication | OC1 | For OC1, candidates will be expected to: • present their response in a structured way • explain to the reader what they are doing at each step of their response • lay out their explanations and working in a way that is clear and logical • write a conclusion that draws together their results and explains what their answer means |
| Writing | W1 | For W1, candidates will be expected to: • show all their working • make few, if any, errors in spelling, punctuation and grammar • use correct mathematical form in their working • use appropriate terminology, units, etc. |
Alternative
3(c) Alternative method 1 (printed in italics in the mark scheme)
| Scheme | Marks | Comments |
|---|---|---|
| (10% discount for each prize) (£)0.18 or (£)0.23 or (£)0.32 or (£)0.47 | B1 | Accept 18(p) or 23(p) or 32(p) or 47(p). If units stated, they must be correct |
| Correct cost of all reductions 1.62 AND 2.07 AND 2.88 AND 4.23 | B2 | Award B1 for any one correct reduction |
| 9 × 1.62 + 12 × 2.07 + 5 × 2.88 + 2 × 4.23 (£14.58 + £24.84 + £14.40 + £8.46) | M2 | FT from B1, B1 Award M1 for the sum of 3 correct products |
| (£)62.28 | A1 |
Alternative
3(c) Alternative method 2 (printed in italics in the mark scheme)
| Scheme | Marks | Comments |
|---|---|---|
| (10% discount for each prize) (£)0.18 or (£)0.23 or (£)0.32 or (£)0.47 | B1 | Accept 18(p) or 23(p) or 32(p) or 47(p). If units stated, they must be correct |
| (Total discount) 9×(£)0.18 + 12×(£)0.23 + 5×(£)0.32 + 2×(£)0.47 (£1.62 + £2.76 + £1.60 + £0.94) | M2 | FT ‘their (£)0.18 or (£)0.23 or (£)0.32 or (£)0.47’ Award M1 for the sum of 3 correct products |
| (Total discount) (£)6.92 | A1 | CAO |
| (Cost of prizes with discount) (£)69.2(0) – (£)6.92 (£)62.28 | M1 A1 | FT ‘their (£)69.2(0)’ – ‘their (£)6.92 |