Higher November 2024 Paper 1 Q13
13 Here are two cuboids.
All lengths are measured in centimetres.
The volume of cuboid A is 142 cm3 greater than the volume of cuboid B.
Work out the value of \(x\). (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 7 | P1 | for setting up an equation using volumes, eg \((x + 2)(2x - 1)(x - 1) = 2x(x + 3)(x - 3) + 142\) |
| P1 | for process to find an expanded expression for the area of one face, eg \((x + 2)(2x - 1) = 2x^2 - x + 4x - 2\) or \(2x^2 + 3x - 2\) or \((x + 2)(x - 1) = x^2 - x + 2x - 2\) or \(x^2 + x - 2\) or \((2x - 1)(x - 1) = 2x^2 - 2x - x + 1\) or \(2x^2 - 3x + 1\) or \(2x(x + 3) = 2x^2 + 6x\) or \(2x(x - 3) = 2x^2 - 6x\) or \((x + 3)(x - 3) = x^2 - 3x + 3x - 9\) or \(x^2 - 9\) | |
| P1 | for a complete process to find a fully expanded expression for the volume of one cuboid, eg \(2x^3 + 3x^2 - 2x - 2x^2 - 3x + 2\) or \(2x^3 + x^2 - 5x + 2\) or \(2x^3 + 6x^2 - 6x^2 - 18x\) or \(2x^3 - 18x\) | |
| P1 | (dep P3) for correct rearrangement of the expanded terms in their equation leading to a 3-term quadratic eg \(x^2 + 13x - 140\ (= 0)\) or \(x^2 + 13x = 140\) | |
| A1 | cao |
Additional guidance
May occur later in the process
Must use expressions for volumes but these may have been incorrectly expanded and simplified
Condone one incorrect term in expansion of two brackets
Expression need not be fully simplified, but must be correct