Higher November 2020 Paper 2 Q14
14 A marathon takes place each year.
In 2020 there were 6500 runners.
| Prediction For each of the next 3 years the number of runners will increase by 5% |
Does this predict that in 2023 there will be more than 7500 runners?
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(6500 \times 1.05\) or 6825 | M1 | oe eg \(6500 + 0.05 \times 6500\) or \(6500 + 325\) may be implied eg 7475 |
| \(6500 \times 1.05^3\) or 7524.(…) or 7525 | M1dep | oe eg their \(6825 \times 1.05\) or 7166.25 and their \(7166.25 \times 1.05\) \(6825 \times 1.05^2\) is M2 |
| 7524.(…) and Yes or 7525 and Yes | A1 | oe eg 7524.(…) which is more than 7500 |
| Alternative method 2 | ||
| \(1.05^3\) or 1.157… or 1.158 or 1.16 or \(\dfrac{7500}{6500}\) or 1.15(3…) or 1.154 | M1 | oe |
| \(1.05^3\) or 1.157… or 1.158 or 1.16 and \(\dfrac{7500}{6500}\) or 1.15(3…) or 1.154 | M1dep | oe |
| 1.157… or 1.158 or 1.16 and 1.15(3…) or 1.154 and Yes | A1 | |
Additional guidance
| Working is implied by a correct value 7524.(…) and Yes with no working 7525 and Yes with no working 7524.(…) with no working 7525 with no working | M1M1A1 M1M1A1 M1M1A0 M1M1A0 |
| \(7525 > 7500\) | M1M1A1 |
| \(7525 < 7500\) | M1M1A0 |
| For year on year working allow truncation/rounding eg \(6825 \times 1.05 = 7166\) \(7166 \times 1.05 = 7524.30\) Yes | M1 M1A1 |
| Increasing by 5% four or more times can score a maximum of M1M1A0 | |
| Increasing by 5% two times can score a maximum of M1M0A0 | |
| Do not allow misreads of 5% |