1MA0 Higher November 2016 Paper 1 Q22

EdexcelHigherOld spec4 marksExpanding Brackets Forming Equations

22 The diagram shows a prism.

Prism with a U-shaped cross section: overall width 4x - 1, height x + 2, depth x + 1; each upright is x wide and the gap is 2x deep

Diagram NOT accurately drawn

All measurements are in centimetres.
All corners are right angles.

Find an expression, in terms of \(x\), for the volume, in cm\(^3\), of the prism.
You must show your working.
Give your answer in its simplest form. (4)

Mark scheme

Answer	Mark	Notes
\(9x^2 + 7x - 2\)	4	M1 for finding an expression for a missing length eg \(4x - 1 - x - x\) (\(=2x - 1\)) or \(x + 2 - 2x\) (\(=2 - x\)) M1 for a correct expression for one area from the cross-section, eg. \(x \times 2x\) or \((4x - 1)(x + 2 - 2x)\) or for one volume of cuboid(s), eg. \(x \times 2x \times (x + 1)\) M1 for a complete method to find the volume A1 for \(9x^2 + 7x - 2\) or \((9x - 2)(x + 1)\) oe