FP2 June 2013 (R) Q2

Notes

M1 for multiplying through by \((x + 1)^2(3 - x)^2\)
OR: for collecting one side of the inequality and attempting to form a single fraction (see alternative in mark scheme)

M1dep for collecting on one side of the inequality and factorising the result of the above (usual rules for factorising the quadratic)
OR: for factorising the numerator – must be a three term quadratic – usual rules for factorising a quadratic (see alternative in mark scheme)
Dependent on the first M mark

B1 for the critical values \(3,\ -1\)

A1 for either \(-\dfrac{3}{2}\) or \(\dfrac{1}{3}\)

A1 for the second of these

NB: the critical values need not be shown explicitly – they may be shown on a sketch or just appear in the ranges or in the working for the ranges.

M1 using their 4 critical values to obtain appropriate ranges e.g. use a sketch graph of a quartic, (which must be the correct shape and cross the \(x\)-axis at the cvs) or a table or number line

A1cso for both of \(-\dfrac{3}{2} < x < -1,\quad \dfrac{1}{3} < x < 3\)

Set notation acceptable i.e. \(\left(-\dfrac{3}{2}, -1\right) \cup \left(\dfrac{1}{3}, 3\right)\) All brackets must be round; if square brackets appear anywhere then A0.

If both ranges correct, no working is needed for the last 2 marks, but any working shown must be correct.

Purely graphical methods are unacceptable as the question specifies “Use algebra…”.

Q2 – Alternative 1