Higher November 2020 Paper 2R Q15
15 Platinum nuggets are in the shape of a solid cylinder.
Diagram NOT accurately drawn
The radius of each cylinder is 2.5 cm.
The length of each cylinder is 15 cm.
The density of platinum is 21.5 g/cm³
The greatest mass that Jacques can carry is 30 kg.
Can Jacques carry 5 platinum nuggets at the same time?
You must show all your working.
(5)
| Scheme | Marks |
|---|---|
| \(\pi \times 2.5^2 \times 15\) ( = 93.75π = 294.5243...) | M1 |
| \(21.5 = \dfrac{m}{\text{“}294.5243\text{”}}\) | M1 |
| (\(m\) =) 21.5 × ‘294.5243...’ ( = 6332.272692) | M1 |
| ‘6332.27269’ ÷ 1000 × 5 (=31.661…) or ‘6332.27269’ ÷ 6 ÷ 1000 (= 1.055…) or ‘6332.27269’× 5 and 30 × 1000 (=30 000) or 30 ÷ (‘6332.27269’ ÷ 1000) (= 4.7376…) | M1 |
| Working required Answer: No and correct comparable figure(s) | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for using the formula for volume of cylinder
M1: for using \(d = \dfrac{m}{v}\) with their intended volume \(v\)
M1: for rearranging for \(m = d \times v\)
M1: for a correct calculation that would enable a conclusion to be made based on mass
A1: for No oe and (31.6 to 31.7 or 1.05 to 1.06 or 4.70 to 4.74) seen
Alternative Mark Scheme for Q15
| Scheme | Marks |
|---|---|
| \(\pi \times 2.5^2 \times 15\) ( = 93.75π = 294.5243...) | M1 |
| \(21.5 = \dfrac{30\,000}{v}\) or \(21.5 = \dfrac{30\,000 \div 5}{v}\) | M1 |
\((v =)\; \dfrac{30\,000}{21.5}\;(= 1395.34\ldots)\) or \((v =)\; \dfrac{30\,000}{21.5 \times 5}\;(= 279.069\ldots)\) | M1 |
| “1395.34” and “294.52” × 5 (= 1472.62) or “279.06” and “294.52” | M1 |
| No and correct comparable figure(s) | A1 |
Notes
M1: for using the formula for volume of cylinder
M1: for using \(d = \dfrac{m}{v}\) with given \(d\) and \(m\)
M1: for rearranging for \(v = \dfrac{m}{d}\) for either one nugget, or all five nuggets.
M1: for correct calculations that would enable a conclusion to be made based on volumes
A1: awrt 3sf
(corrected from the printed mark scheme: the alternative prints “Total 6 marks”; it is worth 5 marks)