Foundation January 2023 Paper 2 Q14
14 The diagram shows a solid prism.
Diagram NOT accurately drawn
The cross section of the prism is shown shaded.
The volume of the prism is 924 cm3
Work out the value of \(x\)
(4)
| Scheme | Marks |
|---|---|
| eg 6 × 14 (= 84) or 13.5 × 14 (= 189) or 7.5 × \(x\) (= 7.5\(x\)) or 924 ÷ 8 (= 115.5) or any correct calculation that leads to an area linked to the cross section of the shape or eg 14 × 6 × 8 ( = 672) or 7.5 × \(x\) × 8 ( = 60\(x\)) or 13.5 × 14 × 8 ( = 1512) any correct calculation that leads to a volume linked to the 3D shape | M1 |
\(\dfrac{924}{8} - 84\;(= 115.5 - 84 = 31.5)\) oe or 6 × 14 + 7.5\(x\) = “115.5” oe or \(\dfrac{924 - \text{“}672\text{”}}{8}\left(= \dfrac{252}{8} = 31.5\right)\) or \(\dfrac{924 - \text{“}672\text{”}}{7.5}\left(= \dfrac{252}{7.5} = 33.6\right)\) or 8(6 × 14 + 7.5\(x\)) = 924 oe | M1 |
eg \(\left(\dfrac{924}{8} - \text{“}84\text{”}\right) \div 7.5\;(= 31.5 \div 7.5)\) or \(\dfrac{\text{“}115.5\text{”} - \text{“}84\text{”}}{7.5}\) oe or “33.6” ÷ 8 | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 4.2 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: a correct calculation linked to the area of the cross section of the shape – can be numerical or algebraic and maybe part of another calculation.
or
a correct calculation linked to the volume of the shape – can be numerical or algebraic and may be part of another calculation
M1: a calculation that leads to a value one step away from the value of \(x\) eg a calculation leading to 31.5 (one step remains which is to divide by 7.5)
or
a correct equation in \(x\)
M1: a fully correct calculation that leads to the value for \(x\)
A1: oe