12. Gwilym is giving a talk about the amount of food that was wasted in 2019.
(a)
In 2019, the world produced 931 million tonnes of food waste. Of this:
569 million tonnes was from households
243 million tonnes was from food services
119 million tonnes was from retail sectors.
Gwilym wants to draw a pie chart to display this information.
Complete the table below. Then complete Gwilym’s pie chart. You must show all your working. [4]
Food waste
Angle in a pie chart
Household
220°
Food service
……………… °
Retail sector
……………… °
Gwilym has found some further details of food waste in 2019.
Country
Total food waste in kilograms
Population
China
91 646 213 000
1 440 000 000
France
5 522 358 000
65 400 000
United Kingdom
5 199 825 000
67 600 000
(b)
(i)
The population data seems to be given correct to a certain number of significant figures. To how many significant figures does the data seem to be given? Circle your answer. [1]
Three One Ten Eight Two
(ii)
Use the data from the table above to complete the following statements. You must show all your working. [4]
‘On average, a person in France produced …………… kilograms of food waste.
This was …………… times the average amount of food waste per person in China.’
(c)
The area of the United Kingdom is 242 500 km\(^2\). Use this information and the information in the table above to answer the following questions about 2019.
(i) What was the population density of the UK? [2]
…………… people per km\(^2\)
(ii) What was the average food waste per km\(^2\) in the UK? Give your answer in tonnes. [3]
…………… tonnes
Mark scheme (a)
Scheme
Mark
Comments
For an appropriate method to calculate a missing angle: \(\dfrac{243}{931}\) × 360 or \(\dfrac{243}{362}\) × 140 or \(\dfrac{243}{569}\) × 220 \(\dfrac{119}{931}\) × 360 or \(\dfrac{119}{362}\) × 140 or \(\dfrac{119}{569}\) × 220
M1
Or equivalent with consistent place value when attempting to write in millions in full In the calculations shown on the left, allow appropriate sight of the following:
243 + 119 for 362
360 – 220 for 140
If no working shown, M1 may be implied by the appropriate sight of correct (or allowed) angles
(Food service) 93.9(663...°) or 94(°) AND (Retail sector) 46(.015...°)
A1
Do not award A mark from incorrect method, M0 A0, (e.g. 140 ÷ 3 = 46.66….°) Allow A1 for
Food service
Retail sector
93(°)
and
46(°)
93(°)
and
47(°)
93.4(°) to 94.2(°)
and
45.7(°) to 46.2(°) *
*from premature approximation of 1° represents 2.58(…), 2.59 or 2.6 million tonnes
Award M1 A0 A0 for 97.2° and 47.6° (from premature approximation of 1° represents 2.5 million tonnes, 243 ÷ 2.5 and 119 ÷ 2.5)
Award M0 A0 A0 for 94.5° and 46.277..° (from \(\dfrac{140}{360}\) × 243 and \(\dfrac{140}{360}\) × 119 )
Pie chart completed correctly with labels for Food service AND Retail sector
A2
Tolerance for angles ± 2° For A2 or A1 FT ‘their derived angles’ provided the sum of ‘their derived angles’ = 140° ± 2° (and at least M1 previously awarded)
A1 for the pie chart completed correctly without labels
An unsupported correct pie chart, with no angles stated in the table, is awarded SC2 with labels, or SC1 without labels, not from sight of incorrect angles in the table
Corrected by Westie's Workshop
The board's mark scheme printed “1° represents 2.58(…), 2.59 or 2.6 million people” and “1° represents 2.5 million people”. Changed “people” to “tonnes” in both places because the pie chart shows food waste in millions of tonnes (931 ÷ 360 = 2.586… million tonnes per degree).
Original: see the board's mark scheme PDF (link above).
Mark scheme (b)
Scheme
Mark
Comments
(i) Three
B1
(ii) (France per person) answer in the range 84(kg) to 85 (kg)
Accept an equivalent fraction in this range FT provided at least B1 previously awarded, for ‘their France per person’ ÷ China per person accurately evaluated, provided 61 ≤ ‘their China per person’ ≤ 66
In this question, if 1 of the 2 numbers shown in an appropriate division has an initial ‘factor of 10’ place value error, treat this as a misread allowing a possible B1 (rather than B2) in either stage, may be implied by ‘their answer’
Mark scheme (c)
Scheme
Mark
Comments
(i) Answer in the range 278 to 284 (people per km\(^2\))
B2
B1 for appropriate sight of any one of the following:
67 600 000 ÷ 242 500
use of approximations, e.g.
67 600 000 ÷ 243 000 (= 278.18...)
68 000 000 ÷ 243 000 (= 279.8...)
68 000 000 ÷ 240 000 (= 283.3...)
70 000 000 ÷ 200 000 (= 350)
The answer in the statement takes precedence
In this question, if one of the two numbers shown has an initial ‘factor of 10’ place value error, treat this as a misread, allowing possible B1 (for appropriate division), may be implied by ‘their answer’
(ii) 5 199 825 000
Allow suitable approximation, e.g. 5 200 000 000 or 5 000 000 000 Method marks may be awarded in either order
÷ 1000
M1
May be implied in working, e.g. starting 5 199 825
÷ 242 500
M1
Allow suitable approximation, e.g. 200 000 or 240 000 or 242 000 or 243 000
Answer in the range 21 to 22 (tonnes)
A1
Only accept answers in the range, however allow 20 (tonnes) provided not from incorrect working
Answer space takes precedence
If no marks, award SC1 for an unsupported answer with digits 214(4…)
In this question, excluding 1000, if one of the other 2 numbers shown has an initial ‘factor of 10’ place value error, treat this as a misread
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