(a) Jenny is planning to sow grass seed in her garden. The plan for her garden is shown below.
Diagram not drawn to scale
Grass seed to cover 1 m2 costs 30p. Calculate how much it will cost Jenny to buy the grass seed she needs. [4]
(b)
(i) Jenny’s neighbour, Hubert, has a quote from a gardener to landscape his garden. The gardener will charge a total of £175, excluding VAT. This total charge includes £55 for plants. The remainder of the charge is for labour.
The gardener says it will take 8 hours to landscape Hubert’s garden. Calculate how much per hour the gardener is charging for labour. [2]
(ii) VAT at 20% is payable on the charge of £175. Calculate the total charge of the landscaping, including the VAT. [3]
(c) The following summer, Hubert picked 10 different flowers from his garden. He measured the height of each flower. He also counted the number of leaves on each flower. Here are his results.
(i) Is it possible to estimate the number of leaves on a flower of height 6 cm?
Yes ☐ No ☐
You must give a reason for your answer. [1]
(ii) How tall is the flower with the greatest number of leaves? Circle your answer. [1]
26 cm 2·5 cm 7·5 cm 5 cm 17·5 cm
(iii) There are two flowers that each have 19 leaves. Calculate the difference in the heights of these two flowers. You must show all your working. [2]
Difference in the heights is …………… cm
(iv) Calculate the percentage of the flowers that have fewer than 23 leaves. [2]
…………… % of the flowers have fewer than 23 leaves.
Mark scheme (a)
Scheme
Marks
Comments
(Area of lawn) ½ × 3 × 4 + ½ × 5 × 12
M2
(= 6 + 30 = 36 m2)
M1 for any one of the following:
sight of ½ × 3 × 4 and ½ × 5 × 12
½ × 3 × 4 + …..
…. + ½ × 5 × 12
Sight of either area correct, 6 or 30
(To find cost of seed) × (0.)30
m1
FT from M1
(£) 10.8(0) or 1080(p)
A1
FT from M1, m1 provided it is from the sum of 2 areas of triangles Allow if FT correctly evaluated area rounded up to the nearest m2 If units are given they must be correct
If no marks, award SC1 for an answer of (£)21.60 or 2160(p)
Mark scheme (b)
Scheme
Marks
Comments
(i) (175 – 55) ÷ 8 or 120 ÷ 8
M1
May be seen in stages
(£) 15
A1
CAO. Allow an embedded answer of 15, e.g. 8 × 15 = 120
(ii) (Total including VAT is) 175 + 175 × 0.2(0) or 175 × 1.2(0) or equivalent
M2
May be seen in stages
M1 for (VAT) 175 × 0.2(0) or 17.5 + 17.5 (= 35) or equivalent
(£) 210
A1
If no marks, award
either SC2 for total including VAT correctly evaluated starting with charge 55, 15 or ‘their 15’ from (b)(i), i.e. 66, 18 or correctly evaluated ‘their 15’ × 1.20
or SC1 for a calculation for total including VAT starting with charge 55, 15 or ‘their 15’ from (b)(i), i.e. 55 × 1.20, 15 × 1.20 or ‘their 15’ × 1.20 or equivalents
Mark scheme (c)
Scheme
Marks
Comments
(i) ‘No’ selected or unambiguous implied with reason, e.g. ‘no correlation’ ‘no pattern’ ‘(points are) random’ ‘no trend’ ‘number of leaves is not affected by height’
E1
Allow, e.g. ‘No’ with ‘different flowers have different (numbers of) leaves’ ‘scattered’ ‘ the data (or answers) are not consistent’
Do not accept, e.g. ‘No’ with ‘there isn’t a leaf with height 6cm’ ‘it does not show on the graph’ ‘there is no data for 6’ ‘it doesn’t say how many there are’ ‘not enough research’ ‘sample too small’ ‘some points close together’ ‘data is not reliable’
(ii) 7.5 cm
B1
(iii) 17.5 – 13 or 9 × 0.5 4.5 (cm)
M1 A1
Allow 13 – 17.5 Answer space takes precedence Allow FT -4.5 (cm) from 13 – 17.5
If no marks, award SC1 for the difference correctly evaluated provided either 17.5 or 13 is correct
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