Numeracy Higher November 2023 Unit 1 Q7
7. Trains using electrified railway tracks produce fewer emissions than other trains.
In 2020, the USA had the longest total length of railway track of any country in the world.
| Approximate length of electrified railway track (km) | Approximate total length of railway track (km) | |
|---|---|---|
| USA | \(2 \times 10^{3}\) | \(2 \times 10^{5}\) |
| Rest of the world | \(3{\cdot}98 \times 10^{5}\) | \(1{\cdot}2 \times 10^{6}\) |
Answer the following questions using information from the table.
(a) Calculate the percentage of track in the USA that was electrified in 2020. [2]
(b) Calculate the fraction of the whole world’s railway track that was electrified in 2020.
Give your answer in its simplest form. [5]
Give your answer in its simplest form. [5]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{2 \times 10^{3}}{2 \times 10^{5}}\) (× 100) or equivalent | M1 | e.g. \(\dfrac{2000}{200\,000}\) (× 100) |
| = 1 (%) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| (0.02 × 105) + (3.98 × 105) or 2000 + 398 000 OR (0.2 × 106) + (1.2 × 106) or 200 000 + 1 200 000 | M1 | Or equivalents |
| = 400 000 AND 1 400 000 | A2 | Or equivalents e.g. (4 × 105) AND (1.4 × 106) Note: these do not need to be in correct standard form notation A1 for each |
| (Fraction that was electrified =) \(\dfrac{400\,000}{1\,400\,000}\) or equivalent | B1 | e.g. \(\dfrac{4 \times 10^{5}}{1.4 \times 10^{6}}\) Must not involve sums within the numerator or denominator FT ‘their 400 000’ and ‘their 1 400 000’ provided not the USA figures e.g. for use of the rest of the world’s data B1 for \(\dfrac{3.98 \times 10^{5}}{1.2 \times 10^{6}}\) or equivalent |
| = \(\dfrac{2}{7}\) | B1 | Mark final answer FT ‘their 400 000’ and ‘their 1 400 000’ provided equivalent level of difficulty e.g. for use of the rest of the world’s data B1 for \(\dfrac{199}{600}\) Ignore attempt to convert to a % |