(a) The concrete base of Miss Morgan’s new bungalow is shown below.
Diagram not drawn to scale
The concrete base of Miss Morgan’s bungalow is 0·2 m thick.
Diagram not drawn to scale
Calculate the volume of the concrete base. You must show all your working. [4]
Volume of concrete is …………… m3
(b) Mr Graham is building a garage. A concrete mixer lorry holds a maximum load of 6 m3 of concrete. There is a fixed standard delivery charge of £35 per load. The concrete costs £45 per m3.
Mr Graham orders \(\dfrac{2}{3}\) of the maximum load of concrete for the base of his garage floor.
What is the total cost of Mr Graham’s order? [4]
Total cost is £ ……………
Mark scheme (a)
Scheme
Marks
Comments
(Total area =) 15×15 + 4×5 or 20×4 + 11×15 or 20 × 15 - 11 × 5 or equivalent
M1
Note: check diagram for the area Accept any correct area calculation
(Volume = total area ) × 0.2
M1
Allow for ‘their total area’ × 0.2 where ‘their area’ includes a product, or for one rectangular (or square) area × 0.2
(Volume =) 49 (m3)
A2
FT from 1 measurement error in a sum or difference of two products, i.e. only one measurement incorrect within one product (M0 M1 A2 is possible to award)
A1 for calculations with evaluated terms as shown (in bold and underlined)
FT from M1, M0 (area 225+ 20 or 80 + 165 or 300 - 55) 245(m2),
OR
FT from M1, M1: for one area product correctly evaluated within ‘their area’ AND ×0.2 correctly evaluated
45 + 4×5× 0.2 (m3), or 15×15×0.2 + 4(m3), or 16 + 11×15×0.2 (m3), or 20×4×0.2 + 33(m3), or 60 – 11 × 5 × 0.2 (m3), or 20 × 15 ×0.2 – 11 (m3)
Accept implied correctly evaluated area product, e.g. 4×5 + 15×15 = 20 + 125 = 145 With 145 × 0.2 = 29 (m3), award M1, M1, A1 (although 125 is incorrect)
Mark scheme (b)
Scheme
Marks
Comments
2/3 × 6 OR 2/3 × 45 × 45 × 6 or equivalent
M1 m1
Allow sight of 2/3 of 6 or 2/3 of 45 (= 4 × 45 or 30 × 6 or 2/3 × 270) (= 180)
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