(ii) Estimate the population density of Wales in 2015. [3]
Population density of Wales in 2015 was …………… people / km2
(b) Cardiff is the largest city in Wales. In 2018, the population of Cardiff was approximately 360 000. The population of Cardiff increased by 20% from 1991 to 2018. Calculate the population of Cardiff in 1991. [3]
(c) DraigYma prints Welsh flags onto stickers. Three of their mathematically similar Welsh flag stickers are shown below.
Diagrams not drawn to scale
Calculate the missing length and height in the diagrams. [4]
Length is …………… cm Height is …………… cm
Mark scheme (a)
Scheme
Marks
Comments
(i) \(1 \times 10^{5}\)
B1
(ii) A suitable calculation, including an appropriate approximation, e.g. \(\dfrac{3\,100\,000}{21\,000}\) or \(\dfrac{3\,100\,000}{20\,000}\) or \(\dfrac{3\,000\,000}{20\,000}\) or \(\dfrac{3\,000\,000}{21\,000}\) or equivalent
M2
Place value must be correct Must include an approximation
M1 for the idea to divide (in the correct order), that may also include one place value error, e.g. \(\dfrac{3.1\text{ million}}{20\,735}\), \(\dfrac{31\,000\,000}{20\,000}\), \(\dfrac{3\,100\,000}{20\,700}\)
Answer in the range 142 (people/km2) to 155 (people/km2)
A1
ISW. Allow 142.8, 142.9 and 143 rounded to 140 Accept equivalents, e.g. 150 written as \(1.5 \times 10^{2}\)
Mark scheme (b)
Scheme
Marks
Comments
Idea that 360 000 is 120%
B1
Accept from sight of trial to increase ‘their value’ by 20% provided ‘their value’ <360 000
360 000 ÷ 1.2 or equivalent
M1
Award of M1 also implies previous B1
300 000 (people)
A1
Mark scheme (c)
Scheme
Marks
Comments
(Length) 6.6 ÷ (4.2 ÷ 1.4) or 6.6 ÷ 3 or equivalent
M1
Length 2.2 (cm)
A1
(Height) 4.2 × (9.9 ÷ 6.6) or 4.2 × 1.5 or 1.4 × (9.9 ÷ 2.2) or equivalent
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