Numeracy Intermediate November 2024 Unit 1 Q10
10.
(a)
Delia invests £4000 in an account that pays 3% compound interest per annum.
She does not withdraw money or make any other payments into her account.
How much will Delia have in her account after two years? [3]
Amount in Delia’s account after two years £ ……………
(b)
Delia bought a gold bracelet at a car boot sale a few years ago.
(i)
Delia’s bracelet has increased in value by 40%.
Her gold bracelet is now worth £42.
Calculate how much Delia paid for the bracelet in the car boot sale. [2]
Delia paid £ ……………
(ii)
The density of the gold in Delia’s bracelet is 20 g/cm3.
The bracelet has a mass of \(6 \times 10^{-3}\) kilograms.
Calculate the volume of Delia’s bracelet.
Give your answer in cm3. [3]
| Scheme | Marks | Comments |
|---|---|---|
| 0.03 × 4000 + 4000 or 1.03 × 4000 (= £4120) or equivalent | M1 | Allow for sight of one of the following:
|
| 0.03 × 4120 + 4120 or 1.03 × 4120 or equivalent | M1 | FT ‘their 4120’ (the mark is for the method) (= £123.6(0) + £4120) |
| (£)4243.6(0) | A1 | CAO. Answer space takes precedence if completed, otherwise mark final answer for the amount If no marks, award SC1 for (£)3763.6(0) (from depreciation) |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Sight of \(1.03^{2} \times 4000\) | M1 | |
| 1.0609 × 4000 | A1 | |
| (£)4243.6(0) | A1 | CAO. Answer space takes precedence if completed, otherwise mark final answer for the amount If no marks, award SC1 for (£)3763.6(0) (from depreciation) |
The alternative method is printed in italics in the original.
| Scheme | Marks | Comments |
|---|---|---|
| (i) 100 × 42 ÷ (100 + 40) or 42 ÷ 1.4 or equivalent | M1 | |
| (£) 30 | A1 | CAO. Answer space takes precedence Accept a correct answer from trial and improvement |
| (ii) (Volume of gold = mass ÷ density =) \(6 \times 10^{-3} \times 1000 \div 20\) or 6 ÷ 20 or \(6 \times 10^{-3} \div (20 \div 1000)\) or \(6 \times 10^{-3} \div 0.02\) or equivalent | M2 | Must be dimensionally correct M1 for any one of the following:
|
| 0.3 (cm3) or \(\tfrac{3}{10}\) (cm3) | A1 | CAO, allowing \(3 \times 10^{-1}\) (cm3) |