Higher June 2024 Paper 2 Q10
10 A bus route had 90 000 passengers last year.
The number of passengers was predicted to increase
- by 3% this year
- and then
- by 8% next year.
Is the predicted number of passengers for next year more than 100 000 ?
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: works year by year | ||
| \(90\,000 \times 1.03\) or 92 700 or \(90\,000 \times 1.08\) or 97 200 | M1 | oe eg \(90\,000 + 90\,000 \times 0.03\) |
| \(90\,000 \times 1.03 \times 1.08\) or 100 116 | M1dep | oe eg \(92\,700 \times 1.08\) |
| 100 116 and Yes | A1 | oe eg \(100\,116 \gt 100\,000\) SC1 99 900 seen |
| Alternative method 2: uses multipliers | ||
| \(1.03 \times 1.08\) or 1.112(4) | M1 | oe |
| \(\dfrac{100\,000}{90\,000}\) or 1.111(…) or \(\dfrac{100\,000}{1.03 \times 1.08}\) or [89 895, 89 900] | M1 | oe \(\dfrac{100\,000}{1.03 \times 1.08}\) or [89 895, 89 900] is M2 |
| 1.112(4) and 1.111(…) and Yes or [89 895, 89 900] and Yes | A1 | oe eg 1.112(4) and 1.111(…) so it is more SC1 99 900 seen |
Additional guidance
| M1 or SC1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| A correct value is sufficient for showing working eg1 Alt 1 100 116 eg2 Alt 1 100 116 and Yes | M2A0 M2A1 |
| Alt 1 \(90\,000 \times 103\%\) not recovered | M0 |
| Alt 2 Yes cannot be implied only by an inequality | |
| SC1 is from increasing 90 000 by 11% |