Standard +0.3 This is a standard FP2 rational inequality requiring algebraic manipulation to a common form, finding critical points, and sign analysis. While it involves Further Maths content, the technique is routine: rearrange to single fraction, find zeros/discontinuities, test intervals. Slightly above average difficulty due to the algebraic manipulation required and potential sign errors, but follows a well-established algorithm taught in FP2.
Critical values \(1\frac{1}{2}\) and 3 are 'critical values', e.g. used in solution, or both seen as asymptotes
B1
\((x+1)(x-3) = 2x - 3 \Rightarrow x(x-4) = 0\)
\(x = 4, x = 0\)
M1A1, A1
M1: Attempt to find at least one other critical value
\(0 < x < 1\frac{1}{2}\), \(3 < x < 4\)
M1A1, A17
M1: An inequality using \(1\frac{1}{2}\) or 3
First M mark can be implied by the two correct values, but otherwise a method must be seen (The method may be graphical, but either \((x = 4)\) or \((x = 0)\) needs to be clearly written or used in this case). Ignore 'extra values' which might arise through 'squaring both sides' methods
\(\leq\) appearing: maximum one A mark penalty (final mark)
Total: [7]
**Critical values** $1\frac{1}{2}$ and 3 are 'critical values', e.g. used in solution, or both seen as asymptotes | B1 |
$(x+1)(x-3) = 2x - 3 \Rightarrow x(x-4) = 0$ | |
$x = 4, x = 0$ | M1A1, A1 |
M1: Attempt to find at least one other critical value | |
$0 < x < 1\frac{1}{2}$, $3 < x < 4$ | M1A1, A17 |
M1: An inequality using $1\frac{1}{2}$ or 3 | |
First M mark can be implied by the two correct values, but otherwise a method must be seen (The method may be graphical, but either $(x = 4)$ or $(x = 0)$ needs to be clearly written or used in this case). Ignore 'extra values' which might arise through 'squaring both sides' methods | |
$\leq$ appearing: maximum one A mark penalty (final mark) | |
**Total: [7]**
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