1MA0 Higher November 2012 Paper 2 Q11

EdexcelHigherOld spec6 marksForming Equations Iterations

11 The diagram shows a cube and a cuboid.

Cube with edges x and a cuboid measuring x by 5 by 2

Diagram NOT accurately drawn

All the measurements are in cm.

The volume of the cube is 100 cm\(^3\) more than the volume of the cuboid.

(a) Show that \(x^3 - 10x = 100\) (2)

(b) Use a trial and improvement method to find the value of \(x\).
Give your answer correct to 1 decimal place.
You must show all your working. (4)

Answer	Mark	Notes
show	2	M1 for \(x \times x \times x\) or \(2 \times 5 \times x\) or vol of cube \(= x^3\) or vol cuboid \(= 10x\) A1 correct completion leading to \(x^3 - 10x = 100\)

Mark scheme (b)

Working

Answer

Mark

Notes

\(x = 1\)	−9
\(x = 2\)	−2
\(x = 3\)	−3
\(x = 4\)	24
\(x = 5\)	75
\(x = 6\)	156
\(x = 10\)	900
\(x = 5.1\)	81.(651)
\(x = 5.2\)	88.(608)
\(x = 5.3\)	95.(877)
\(x = 5.4\)	103.(464)
\(x = 5.5\)	111.(375)
\(x = 5.6\)	119.(616)
\(x = 5.7\)	128.(193)
\(x = 5.8\)	137.(112)
\(x = 5.9\)	146.(379)
\(x = 5.35\)	99.6(30375)
\(x = 5.36\)	100.3(90656)
\(x = 5.355\)	100.0(101139)

5.4

B2 for a trial \(5 \leqslant x \leqslant 6\) evaluated correctly
(B1 for any two trials evaluated correctly for positive values of \(x\))
B1 for a different trial \(5.3 \lt x \lt 5.4\) evaluated correctly
B1 (dep on at least one previous B1) for 5.4
Accept trials correct to the nearest whole number (rounded or truncated) if the value of \(x\) is to 1 d.p., but correct to 1 d.p. (rounded or truncated) if the value of \(x\) is to 2 or more d.p.
NB. Allow 100 for a trial of \(x = 5.355\)