Numeracy Higher November 2022 Unit 2 Q4
4.
(a)
The population of Barbados in 1644 was said to be 30 000.
By 1964, the population of Barbados had increased by 682%.
From 1964 to 2014, the population of Barbados increased by a further 20%.
Calculate the population of Barbados in 2014.
You must show all your working. [3]
(b)
The area of Barbados is 432 km\(^2\).
The population of Barbados in September 2019 was 287 106.
Calculate the population density of Barbados in September 2019.
Give your answer correct to 2 significant figures. [3]
(c)
The density of some of the sand in Barbados is 1442 kg/m\(^3\).
Express this density in g/cm\(^3\). [2]
| Scheme | Marks | Comments |
|---|---|---|
| (Population in 1964) \(\dfrac{100 + 682}{100}\) × 30000 or 7.82 × 30000 or 30000 + 30000 × \(\dfrac{682}{100}\) or equivalent | M1 | (= 234600 people) M0 for 6.82 × 30000 (= 204600) or 1.682 × 30000 (= 50460) |
| (Population in 2014) \(\dfrac{100 + 20}{100}\) × 234600 or 1.2 × 234600 | M1 | FT ‘their derived 234600’ including 1.2 × 204600 (= 245520) 1.2 × 50460 (= 60552) |
| 281520 (people) | A1 | CAO |
| Scheme | Marks | Comments |
|---|---|---|
| 287 106 ÷ 432 660 (people per km\(^2\)) | M1 A2 | A1 for sight of 664.597…. rounded or truncated |
| Scheme | Marks | Comments |
|---|---|---|
| 1442 × 1000 ÷ 1 000 000 1.4(42 g/cm\(^3\)) | M1 A1 | Mark final answer Allow M1 A1 for 1442 ÷ 1000 = 1.4(42) Do not accept from incorrect working, e.g. M0 A0 if 1.442 seen with an incorrect statement, e.g.
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