Higher November 2019 Paper 2 Q10
10. Candice has been given a bracelet.
The dimensions of the bracelet are given below.
Diagram not drawn to scale
Candice knows it is made entirely from one metal. She is not sure if it is copper, silver or gold.
Her bracelet has a mass of approximately 18 g.
| Metal | Density (g/cm³) |
|---|---|
| Copper | 8·96 |
| Silver | 10·49 |
| Gold | 19·32 |
Convince Candice that her bracelet is made from silver.
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| Inner cuboid \((62-2-2) \times (48-2-2) \times 4\) | B1 | Accept equivalents in cm throughout |
| Volume \(62 \times 48 \times 4 - (62-2-2) \times (48-2-2) \times 4\) \((11904 - 10208\ \text{mm}^3)\) | M1 | FT ‘their inner cuboid volume’ provided \(\ne 62 \times 48 \times 4\) |
| 1.696 (cm³) | m1 | |
| Mass \(1.696 \times 10.49\) OR Density \(18 \div 1.696\) | M1 | FT ‘their 1.696’ |
| Mass 17.7(9... g) 17.8 (g) or 18 (g) OR Density 10.6(13... g/cm³) or 11 (g/cm³) | A1 | CAO |
| (5) |
Notes
Alternative: treated as one long cuboid of metal
| Scheme | Marks |
|---|---|
| Overall length \((2\times(48+62)=)\ 220\) (mm) | B1 |
| Volume of cuboid: \(2\times(48+62) \times 2 \times 4\ (= 1760\ \text{mm}^3)\) | M1 |
| 1.76(0 cm³) | m1 |
| Mass OR density: FT ‘their 1.76’ Mass \(1.76 \times 10.49\) OR Density \(18 \div 1.76\) | m1 |
| Mass 18(.46...g) OR Density 10.2(2.... g/cm³) | A1 CAO |