Higher June 2025 Paper 2 Q18
18 At the start of year \(n\), the population of deer in a park is \(D_n\)
At the start of the following year, the population of the deer is \(D_{n+1}\)
At the start of 2019, the population of the deer was 2000
At the start of 2020, the population of the deer was 2400
Show that, at the start of 2022, the population of the deer was greater than 3000 (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| Shown | M1 | for beginning to find \(K\) eg \(2400 = K \times 2000\) or \(K = 1.2\) oe |
| M1 | For a correct method to find the value for 2021 or 2022, eg \(2400 \times \text{``}1.2\text{''}\ (= 2880)\) or \(2400 \times (\text{``}1.2\text{''})^2\ (= 3456)\) or \(2000 \times (\text{``}1.2\text{''})^2\ (= 2880)\) or \(2000 \times (\text{``}1.2\text{''})^3\ (= 3456)\) OR method to find rate leading to 3000 in 2022, eg \(\sqrt[3]{\dfrac{3000}{2000}}\ (= 1.144\ldots)\) | |
| C1 | for comparative figures eg 3456 (and 3000) OR \(3000 \div 2880 = 1.041\ldots\) and 1.2 OR 1.144… and 1.2 |
Additional guidance
M marks can be awarded in either order
\(1.2^2 = 1.44\)
3000 need not be restated to award this mark
If comparison made with 2023 or beyond do not award C1