Numeracy Intermediate November 2024 Unit 2 Q2
2.
Lewis buys an annual discount card to use in a sports shop.
He pays £9.95 for the discount card.
For one year, Lewis gets 15% off anything he buys in this sports shop when he shows his discount card.
During the year, Lewis buys the following three items.
| Full price before discount | ||
|---|---|---|
| Trainers £55 | Tennis racket £18 | T-shirt £12 |
How much did Lewis save during the year by using his discount card?
Remember that Lewis had to buy his discount card.
You must show all your working. [4]
Sally buys clothes from the same sports shop.
She does not have a discount card.
In a sale, there is \(\dfrac{1}{6}\) off the full price of a hoodie.
On the last day of the sale, customers could buy the hoodie for half of the sale price.
Sally buys the hoodie on the last day of the sale.
What fraction of the original full price of the hoodie does Sally pay? [2]
| Scheme | Marks | Comments |
|---|---|---|
| (Total of items 55 + 18 + 12 =) (£) 85 OR (Individual discounts) (£) 8.25, (£) 2.7(0), (£) 1.8(0) OR (Discounted costs) (£) 46.75, (£) 15.3(0), (£) 10.2(0) | B1 | All 3 discounts are required, not necessarily in a sum OR Allow 2 of the 3 individual discounts correct in a sum All discounted costs required, not necessarily in a sum OR Allow 2 of the 3 discounted costs correct in a sum |
| (Total Discount 0.15 × 85 =) (£) 12.75 OR (Total discounted cost 0.85 × 85 =) (£) 72.25 | B1 | FT from ‘their 55 + 18 + 12’ incorrectly evaluated May imply previous B1 Allow an embedded £12.75 from sight of 22.70 (= 12.75 + 9.95) or 85 – 82.20 (= 2.80) Allow an embedded £72.25 from sight of 62.30 (= 72.25 – 9.95) or 82.20 (= 94.95 – 12.75) |
| (Overall saving) (12.75 – 9.95 or 85 – 9.95 – 72.25 =) (£) 2.8(0) | B2 | CAO provided not from incorrect working If units are given they must be correct B1 for any one of the following:
FT for possible B1, provided ‘their overall saving’ > 0:
‘their total discount’ – 9.95, or ‘their 55 + 18 + 12’ – 9.95 – ‘their total discounted costs’ If no marks, award SC1 for sight of (£)94.95 (= 85 + 9.95) or (£)75.05 (= 85 – 9.95) |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{1}{2}\) × (1 – \(\dfrac{1}{6}\)) or \(\dfrac{1}{2}\) × \(\dfrac{5}{6}\) or equivalent | M1 | Allow 0.5 × 0.833(…..) Do not accept 0.5 × 0.83 |
| \(\dfrac{5}{12}\) or equivalent fraction | A1 | An answer of \(\dfrac{2.5}{6}\) is awarded M1 A0 If no marks, award SC1 for an answer of (½ × ⅙ =) \(\dfrac{1}{12}\) |
Alternative
2(b) Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Correctly evaluated \(\dfrac{1}{2}\) × \(\dfrac{5}{6}\) × an amount | B1 | May be seen in stages Must be an exact amount calculated, not rounded or truncated, e.g. £60 as ‘their amount’ to give £25 |
| \(\dfrac{5}{12}\) or equivalent | B1 | An answer of \(\dfrac{2.5}{6}\) is awarded B1 B0 |