Higher June 2025 Paper 5 Q11
11 A solid steel cube has a mass of 1.05 kg.
The density of the steel is 7.9 g/cm\(^3\).
Orla says,
The length of one side of the cube is approximately 10 cm.
Use estimation to decide if Orla’s statement is reasonable.
Show how you decide. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Mass = 1050 or 1000 | B1 | For B1 accept 1050 or 1000 seen | |
| Volume = their mass ÷ 8 oe | M2 | M1 for their mass ÷ 7.9 oe | For M2 or M1 allow use of 1050 or 1000 or their mass ÷ 8, their mass could be in kg |
| Length = \(\sqrt[3]{\textit{their} \text{ volume}}\) | M1 | or [Volume = ]10 × 10 × 10 = 1000 | If cube root not shown allow implied by 5 nfww after 125 shown |
| Unreasonable oe and length = 5 [cm] | A1 | Dep on B1M2M1 or incorrect and shows [Volume = ]1000 and 125 | For A1 If 5 [cm] is shown in working it does not need to be stated in conclusion |
| OR | OR | ||
| [Volume =] 10 × 10 × 10 or 10\(^3\) | M1 | Accept Volume = 1000 | |
| Mass = (10 × 10 × 10) × 8 oe | M2 | M1 for (10 × 10 × 10) × 7.9 oe | |
| Their mass converted to kg or 1050 [g] or 1000 [g] | B1 | ||
| Unreasonable oe and either 8 kg with 1 kg or [1.05 kg] or 8000 g with 1050 g or 1000 g | A1 | Dep on M1M2B1 | For A1 values could be shown in working and do not need to be stated in conclusion See Appendix 1 for alternate method |
Appendix 1: Question 11
A further possibility is to show that the density of the 10 cm cube is different to 7.9 g/cm\(^3\)
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Mass = 1050 or 1000 or 0.0079 or 0.008 | B1 | For B1 accept 1050 or 1000 or 0.0079 or 0.008 seen | |
| [Volume = ]10 × 10 × 10 or 10\(^3\) | M1 | Accept Volume = 1000 | |
| 1000 ÷ (10 × 10 × 10) oe or 1[kg] ÷ (10 × 10 × 10) oe | M2 | M1 for 1050 ÷ (10 × 10 × 10) oe or 1.05[kg] ÷ (10 × 10 × 10) oe | |
| Unreasonable oe and [density =] 1 oe or [density = ]0.001 and 0.0079 or 0.008 | A1 | Dep on M1M2B1 | For A1 , [density =] 1 could be shown in working and does not need to be stated in conclusion |