Find the set of values of x for which $\left| {0.1{x^2} - 2x + 3} \right| < {\log _{10}}x$ .

Attempting to solve $\left| {0.1{x^2} - 2x + 3} \right| = {\log _{10}}x$ numerically or graphically.     (M1)

x = 1.52, 1.79     (A1)(A1)

x = 17.6, 19.1     (A1)

$(1.52 < x < 1.79) \cup (17.6 < x < 19.1)$     A1A1     N2

[6 marks]

This question was generally not well done. A number of candidates attempted an ‘ill-fated’ algebraic approach. Most candidates who used their GDC were able to correctly locate one inequality. The few successful candidates were able to employ a suitable window or suitable window(s) to correctly locate both inequalities.