Higher November 2021 Paper 2 Q14
14 The population of butterflies in a park is 4200
Show that after 20 days the population would be greater than 40 000 [2 marks]
increases by 13% each day for 19 days
then
decreases by 8% for 1 day.
After the 20 days, is the actual population greater than 40 000 ?
Tick a box.
- Yes
- No
Show working to support your answer. [2 marks]
| Temperature | Expected number of visitors each day |
|---|---|
| Less than 21°C | 700 |
| 21°C or more | 900 |
On each of the 30 days in June
the park is open
the probability that the temperature is less than 21°C is 0.4
Work out the total number of expected visitors to the park in June. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(4200 \times 1.12^{20}\) | M1 | oe allow \(4200 \times [9.64, 9.65]\) |
| 40 514(…) or 40 515 or 40 500 or 40 510 or 40 489 or 40 509 or 40 548 | A1 |
Additional guidance
Day on day calculations
Consistently rounding down to nearest integer leads to 40 489
Consistently rounding to nearest integer leads to 40 509
Consistently rounding up to nearest integer leads to 40 548
| Answer | Mark | Comments |
|---|---|---|
| \(4200 \times 1.13^{19} \times 0.92\) or [39 402, 39 403] or 39 400 or 39 372 or 39 407 or 39 435 | M1 | oe allow \(4200 \times [10.19, 10.2] \times 0.92\) |
| No and [39 402, 39 403] or No and 39 400 or No and 39 372 or No and 39 407 or No and 39 435 | A1 |
Additional guidance
Day on day calculations
Consistently rounding down to nearest integer leads to 39 372
Consistently rounding to nearest integer leads to 39 407
Consistently rounding up to nearest integer leads to 39 435
| Answer | Mark | Comments |
|---|---|---|
| \(0.4 \times 700\) or 280 or \((1 - 0.4) \times 900\) or \(0.6 \times 900\) or 540 or \(30 \times 0.4\) or 12 or \(30 \times (1 - 0.4)\) or \(30 \times 0.6\) or 18 | M1 | oe implied by 820 |
| \(30 \times 0.4 \times 700\) or 8400 or \(30 \times (1 - 0.4) \times 900\) or 16 200 | M1dep | oe implied by \(820 \times 30\) |
| 24 600 | A1 |
Additional guidance
Up to M2 may be awarded for correct work, with no or incorrect answer, even if this is seen amongst multiple attempts