Numeracy Foundation June 2022 Unit 2 Q10
10.
Esme has a pond and a flowerbed in her garden.
The pond is circular and the flowerbed is in the shape of a quadrilateral, as shown below.
Diagrams not drawn to scale
The diameter of the pond is 140 cm.
The perimeter of the pond and the perimeter of the flowerbed are equal.
Esme needs to know the lengths of all the sides of her flowerbed.
Complete the following statement for Esme.
“The lengths of the sides of the flowerbed are 176 cm, 128 cm, 60 cm and …………… cm.”
You must show all your working. [4]
Bill has a vegetable plot in his garden.
It is in the shape of a trapezium, as shown below.
Diagram not drawn to scale
Fertiliser is sold in small bags.
Each bag contains enough fertiliser to treat an area of 0·9 m2.
A bag of fertiliser costs £1.15.
How much will it cost Bill to buy enough bags of fertiliser to treat his vegetable plot?
You must show all your working. [5]
From the formula list: Area of trapezium \(= \dfrac{1}{2}(a+b)h\)
| Scheme | Marks | Comments |
|---|---|---|
| (Circumference) π × 140 | M1 | Do not accept embedded within an incorrect calculation for the circumference |
| Answer in the range 439 (cm) to 440 (cm) | A1 | May be implied in later working |
| π × 140 – 176 – 128 – 60 or π × 140 – 364 or equivalent | M1 | FT ‘their derived circumference’ from a calculation involving π (including use of πr or πr2), including from previous truncation or rounding errors |
| Answer in the range 75.6 (cm) to 76 (cm) | A1 | CAO, answer must be in the range stated. If no final answer given, check if an answer has been inserted in the statement in the question |
| Scheme | Marks | Comments |
|---|---|---|
| (Area =) ½ × (4.3 + 5.6) × 2.5 or 2.5 × 4.3 + ½ × 2.5 × (5.6 – 4.3) or equivalent | M1 | |
| 12.375 (m2) | A1 | Allow 12.37(m2), 12.38(m2) or 12.4 (m2) provided not from incorrect working (e.g. 4.3 + 2.5 + 5.6 = 12.4) May be implied in further working |
| (Number of bags) 12.375 ÷ 0.9 or 13.75 | M1 | FT ‘their 12.375’ including the use of 12.375 rounded or truncated Allow for a trial and improvement method provided the final trial gives 14 bags, e.g. for sight of 0.9 × 14 = 12.6 |
| 14 (bags) | A1 | Must be rounded up to a whole number of bags Allow for an embedded answer of 14 (e.g. from within a multiplication) |
| (Cost of fertilizer is 14 × £1.15) (£) 16.1(0) | B1 | FT provided a whole number of bags considered and at least 1 mark (M1) previously awarded |