Standard +0.3 This is a rational inequality requiring rearrangement to a single fraction, finding critical points, and sign analysis. While it involves multiple steps (combining terms, factoring, testing intervals), it's a standard Further Maths technique with no novel insight required. The 5 marks reflect the working needed, but the method is routine for Further Maths students, making it slightly easier than average.
Question 5:
5 | Selects a correct
approach which would
lead to solving the
inequality
eg
Multiplies the inequality by
2
or
(π₯π₯β1)
Rearranges to an
inequality with 0 on LHS
or RHS
or
Replaces β β with β=β and
multiplies by
β€ | 1.1a | M1 | 2
(π₯π₯β1) (2π₯π₯+3) 2
β€ (π₯π₯β1) (π₯π₯+5)
π₯π₯β1
2
(π₯π₯β1)(2π₯π₯+3) β€ (π₯π₯β1) (π₯π₯+5)
(π₯π₯β1){(π₯π₯β1)(π₯π₯+5)β(2π₯π₯+3 )} β₯ 0
2
(π₯π₯β1){π₯π₯ +2π₯π₯β8} β₯ 0
Consideri(nπ₯π₯gβ cu1b)(icπ₯π₯ c+ur4v)e(:π₯π₯ β2) β₯ 0
or between -4 and 1
π₯π₯Buβ₯t 2
S o π₯π₯ β 1 or
π₯π₯ β₯ 2 β4 β€ π₯π₯ < 1
Manipulates their
(π₯π₯β1)
equation/inequality to
allow the critical values to
be found | 1.1a | M1
Obtains critical values of
-4, 1 and 2 | 1.1a | M1
Gives one correct region
from
Condone
π₯π₯ β₯ 2,β4 β€ π₯π₯ < 1
Must have three critical
β4 β€ π₯π₯ β€ 1
values. | 1.1b | A1
Obtains correct solution | 1.1b | A1
Total | 5
Q | Marking Instructions | AO | Marks | Typical Solution