Numeracy Higher June 2025 Unit 1 Q7
7. The diagram shows Davina’s garden.
Diagram not drawn to scale
(a) Davina wants to put a 5 cm layer of topsoil on her garden.
What volume of topsoil will Davina need for her garden?
Give your answer in cm3 in standard form. [5]
(b) Topsoil is sold in \(1{\cdot}5 \times 10^{4}\) cm3 bags.
Calculate the number of bags of topsoil that Davina needs to buy.
You must show all your working. [1]
Calculate the number of bags of topsoil that Davina needs to buy.
You must show all your working. [1]
From the formula list: Area of trapezium \(= \dfrac{1}{2}(a+b)h\)
| Scheme | Marks | Comments |
|---|---|---|
| (Volume of topsoil) ½ × 400 × (600 + 900) × 5 or 300 000 × 5 or 400 × 600 × 5 + ½ × 400 × (900 – 600) × 5 or 240 000 × 5 + 60 000 × 5 | M2 | May be seen in stages M1 for any one of the following:
|
| 1.5 × 106 (cm3) | A3 | From M2 for volume or M1 awarded for correct area calculation A2 for any of the following:
A3 for ‘their volume’ correctly evaluated in standard form A2 for any of the following:
|
Working in metres (may include incorrect conversion to cm3 in further working)
Award any one of the following M marks:
M2 volume ½ × 4 × (6 + 9) × 0.05 (= 1.5 m3)
M1 area ½ × 4 × (6 + 9) (= 30 m2)
M1 volume calculation ‘½ omission’ in m3
Award any one of the following A marks, with units stated:
A2 volume 1.5 × 100 m3
A2 volume ‘½ omission’ correctly evaluated in standard form
A1 volume 1.5m3
A1 volume ‘½ omission’ correctly evaluated
| Scheme | Marks | Comments |
|---|---|---|
| 100 (bags) | B1 | Allow an answer of (1 ×) 102 FT ‘their (a)’ ÷ (1.5 × 104)’ correctly evaluated, rounded up to a whole number of bags provided ‘their (a)’ > 3 × 104 Allow FT from ‘their (a)’ as ‘their final answer’ using: either ‘their final answer’ expressed as digits or ‘their final answer’ in standard form |