Numeracy Foundation November 2023 Unit 2 Q9
9.
Maggie sees a Bluetooth speaker in a sale.
The price of the speaker is reduced by 18% in the sale.
The original price of the speaker was £45.
Maggie’s mum says she will share the cost of buying this speaker.
The ratio of the amount Maggie’s mum pays to the amount Maggie pays is 8 : 1.
Calculate the amount Maggie’s mum will pay towards buying this speaker in the sale.
You must show all your working. [4]
The diagram below shows a flowerbed at Maggie’s house.
Maggie’s mum will pay her £2.50 per m2 to weed the flowerbed.
Diagram not drawn to scale
Calculate how much Maggie will get paid for the weeding. [4]
From the formula list: Area of trapezium \(= \dfrac{1}{2}(a+b)h\)
| Scheme | Marks | Comments |
|---|---|---|
| (Sale price) 45 – 0.18 × 45 or 45 × (1 – 0.18) or 45 – 8.1(0) or 45 × 0.82 | M1 | |
| (£)36.9(0) | A1 | May be seen or implied in further working |
| (Maggie’s mum pays) 8 × 36.9(0) ÷ (8 + 1) or 36.9(0) – 36.9(0) ÷ (8 + 1) 8 × 4.1(0) or 36.9(0) – 4.1(0) | M1 | FT ‘their £36.90’ |
| (£)32.8(0) | A1 | On FT allow rounded or truncated to a penny |
Alternative
The alternative method is printed in italics in the mark scheme.
9(a) Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Maggie’s mum’s share of original price) 8 × 45 ÷ (8 + 1) or 45 – 45 ÷ (8 + 1) | M1 | |
| (£) 40 | A1 | May be seen or implied in further working |
| (Maggie’s mum pays) 40 – 0.18 × 40 or 40 × (1 – 0.18) or 40 – 7.2(0) or 40 × 0.82 | M1 | FT ‘their £40’ |
| (£)32.8(0) | A1 | On FT allow rounded or truncated to a penny |
| Scheme | Marks | Comments |
|---|---|---|
| (Area) ½ × 1.5 × (3.1 + 4.5) 5.7 (m2) | M1 A1 | Accept rounding to 6 (m2) May be seen or implied in further working |
| (Charge) 2.5(0) × 5.7 | M1 | FT ‘their 5.7’ (including if previously rounded to 6), including if ‘their 5.7’ is not an area Allow if ‘their area’ is costed in parts provided there is an attempt to sum all of the part costs, provided ‘their 5.7’ ≠ 1.5, 3.1 or 4.5 |
| (£) 14.25 | A1 | CAO |