| Date | November 2010 | Marks available | 4 | Reference code | 10N.1.hl.TZ0.1 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
Find the set of values of x for which \(\left| {x - 1} \right| > \left| {2x - 1} \right|\).
Markscheme
EITHER
\(\left| {x - 1} \right| > \left| {2x - 1} \right| \Rightarrow {(x - 1)^2} > {(2x - 1)^2}\) M1
\({x^2} - 2x + 1 > 4{x^2} - 4x + 1\)
\(3{x^2} - 2x < 0\) A1
\(0 < x < \frac{2}{3}\) A1A1 N2
Note: Award A1A0 for incorrect inequality signs.
OR
\(\left| {x - 1} \right| > \left| {2x - 1} \right|\)
\(x - 1 = 2x - 1\) \(x - 1 = 1 - 2x\) M1A1
\( - x = 0\) \(3x = 2\)
\(x = 0\) \(x = \frac{2}{3}\)
Note: Award M1 for any attempt to find a critical value. If graphical methods are used, award M1 for correct graphs, A1 for correct values of x.
\(0 < x < \frac{2}{3}\) A1A1 N2
Note: Award A1A0 for incorrect inequality signs.
[4 marks]
Examiners report
This question turned out to be more difficult than expected. Candidates who squared both sides or drew a graph generally gave better solutions than those who relied on performing algebraic operations on terms involving modulus signs.
