(a)In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
Malik has two orchards. He has apple trees and pear trees in his north orchard. He has pear trees and cherry trees in his west orchard.
In the north orchard,
Malik has a total of 35 trees
number of apple trees : number of pear trees = 4 : 3.
In the west orchard,
Malik has twice as many pear trees as he has pear trees in the north orchard
number of pear trees : number of cherry trees = 5 : 11.
How many cherry trees does Malik have? You must show all your working. [5 + 2 OCW]
(b) Malik’s crop of apples this year has a total mass of 5280 pounds. He makes apple juice from \(\frac{1}{6}\) of the mass of his apple crop. Malik makes 2 litres of apple juice from every 5 kg of apples.
Calculate the number of litres of apple juice Malik makes. [6]
(c) Malik makes cherry jam using some of the fruit from his trees. Malik makes a poster to advertise his jam. He also makes labels for the jars. The poster and the labels are mathematically similar.
Diagrams not drawn to scale
Calculate the height of the poster. [2]
Mark scheme (a)
Scheme
Marks
Comments
(North orchard, number of pear trees is) 3 × 35 ÷ (4 + 3) or 3 × 5 or equivalent
M1
15 (pear trees)
A1
(West orchard number of pear trees is 2 × 15) 30 (pear trees)
B1
FT ‘their derived 15’
(West orchard number of cherry trees is) 11 × 30 ÷ 5
M1
FT ‘their derived number of pear trees’ Allow M1 for a final answer of 88 (cherry trees from use of 40 apple trees as pear trees), but A0
66 (cherry trees)
A1
FT answer must be evaluated correctly and lead to a whole number
Organisation and communication
OC1
For OC1, candidates will be expected to: • present their response in a structured way • explain to the reader what they are doing at each step of their response • lay out their explanations and working in a way that is clear and logical • write a conclusion that draws together their results and explains what their answer means
Writing
W1
For W1, candidates will be expected to: • show all their working • make few, if any, errors in spelling, punctuation and grammar • use correct mathematical form in their working • use appropriate terminology, units, etc.
Mark scheme (b)
Scheme
Marks
Comments
(Mass of apples to make juice) 5280 ÷ 6
M1
Method may be seen in either order M0 for statement ‘1/6 of 5280’ without calculation
÷ 2.2
M1
400 (kg)
A2
Ignore incorrect units given May be seen or implied in later working
A1 for any one of the following:
(5280 ÷ 2.2 =) 2400
(5280 ÷ 6 =) 880
a correct evaluation of ‘their 2400’ ÷ 6
a correct evaluation of ‘their 880’ ÷ 2.2
(Number of litres of juice produced) 400 × 2 ÷ 5 or 2 ÷ (5 ÷ 400) or 2 × \(\dfrac{400}{5}\)
M1
FT ‘their derived 400(kg)’ (not 5280) If ‘their derived 400’ is used as g (rather than kg) allow M1 for ‘their derived 400’ × 2 ÷ 5000 or 2 ÷ (5000 ÷ ‘their derived 400’), but A0
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