Numeracy Higher November 2017 Unit 2 Q2
2.
Alvaro knows it is possible to keep between 4 and 6 alpacas on each acre of suitable farmland.
They have 13 hectares of farmland that they want to use to keep the alpacas.
Bronwen knows that 1 acre is 4046·86 m2 and that 10 000 m2 = 1 hectare.
Use this information to advise Bronwen and Alvaro on the number of alpacas they could keep on their farmland.
State any assumption that you make.
You must show all your working. [6]
Assumption:
The water container has a diameter of 1·4 metres.
The small paddock is rectangular, measuring 7 metres by 5 metres.
On screen this diagram may not be shown at actual size. To measure it, use the question paper (PDF) printed at 100%.
Bronwen decides to place the centre of the water container so that it is:
- equidistant from the south fence and the east fence,
- 3 metres from the south fence.
Show the placement of the water container on the scale diagram of the small paddock above.
Your diagram should include an accurate plan view of the water container. [4]
Calculate the height of the water container in centimetres. [4]
The height of the water container is …………… cm
Alvaro sells alpaca fleeces from Patagonia.
His fleeces are priced in Argentine pesos.
Tom lives in Wales and buys fleeces from Alvaro.
Tom pays for the fleeces in pounds.
Tom’s purchases are shown in the table below.
| Number of fleeces bought | Price per fleece, in Argentine pesos | Exchange rate | |
|---|---|---|---|
| January 2015 | 80 | 19.20 | £1 = 15.47 Argentine pesos |
| March 2016 | 20 | 22.30 | £1 = 15.21 Argentine pesos |
| April 2017 | 100 | 24.50 | £1 = 14.93 Argentine pesos |
For each of Tom’s 3 purchases he paid correct to the nearest penny.
How much did Tom pay for these 200 fleeces, in pounds?
Give your answer correct to the nearest penny.
You must show all your working. [4]
Tom paid £ …………… , correct to the nearest penny
| Scheme | Marks | Comments |
|---|---|---|
| An appropriate calculation that could lead to an answer of approximately 32 (acres), e.g. 13 × 10000 ÷ 4046.86 (=32.12367…) 13 × 10000 ÷ 4050 (=32.098…) 10000 ÷ 4046.8 (≈ 2.5), 2.5 × 13 (= 32.5) 13 × 10000 ÷ 4000 ( = 32.5) 13 ÷ 0.4 ( = 32.5) | M2 | M1 for a calculation such as
|
| × any number between 4 and 6 inclusive | m1 | FT from M2 only |
| Number of alpacas from appropriate correct calculation: Answer given as a whole number of alpacas in the inclusive range 128 to195 | A2 | Must be correct working FT from rounding to 32 (acres) Accept an answer as a range with bounds given as whole numbers Award A1 for
Note: Only accept answers outside the given range if fully justified, e.g. 32.5 rounded to 33 with use of 6 alpacas to give 198 alpacas |
| Statement of their assumption, e.g. ‘used the mid number 5 alpacas’, ‘used a range of numbers of alpacas’, ‘used the least number of alpacas per acre’, ‘used the greatest number of alpacas per acre’, ‘all the 13 hectares are suitable for keeping alpaca’, 'used 1 acre as 4000m2', ‘they left 6 alpacas in every acre’, ‘they would keep as many alpacas in every acre as they could’ (following use of ‘6’), 'not all their land is suitable' | E1 | The assumption must match their working Allow, e.g. ‘as they could have many small fields, not possible to fit all the alpacas in’ (with 4 alpacas used) (fields not being hectares implied) Do not accept, e.g. ‘all alpacas weigh the same’, ‘they will be able to keep .... alpacas on 13 acres’, 'alpacas not all the same size', ‘they can afford all the alpacas’, ‘same amount of alpacas on each bit of land’ (unless accompanied by further explanation) |
| Scheme | Marks | Comments |
|---|---|---|
| (i) Line 6 cm ± 2mm from the south fence AND Bisector from south and east fences (±2º), or Line 6cm ± 2mm from the east fence | B2 | Mark intention Any lines must be of sufficient length to find the intersection for B2 Award B2 for the unsupported or unambiguous correct location indicated provided not from incorrect working, such as spurious or incorrect arcs B1 for sight of one of the following:
|
| Circle with radius 1.4cm ± 2mm centred at the intersection of the 2 lines | B2 | FT ‘their intersection’ of two straight lines B1 for sight of one of the following:
|
| (ii) (900 litres = 900 000 cm3) 900 000 = π × 702 × height or 0.9 = π × 0.72 × height or equivalent | M2 | May be shown in stages M1 for sight of any 1 of the following:
|
| (Height =) \(\dfrac{900\,000}{\pi \times 70^2}\) or \(\dfrac{0.9}{\pi \times 0.7^2}\) | m1 | FT from M1 or M2 Allow for correct rearrangement (intended calculation) including place value error with digits 9 and/or 7 and use of diameter as radius |
| Answers in the range 58.4 to 58.5 (cm) | A1 | CAO, must be in centimetres Accept 58(cm) from correct working |
| Scheme | Marks | Comments |
|---|---|---|
| 80 × 19.20 ÷ 15.47 + 20 × 22.30 ÷ 15.21 + 100 × 24.50 ÷ 14.93 | M2 | M1 for sight of any 1 year calculation seen (£99.288…, £29.322…, £164.099..) |
| For any 2 of the 3 correct amounts of money (£)99.29, (£)29.32, (£)164.1(0) OR an answer in the inclusive range (£)292 to (£)293 | A1 | |
| (£)99.29 + (£)29.32 + (£) 164.1(0) leading to (£) 292.71 | A1 | CAO not from incorrect working |