Express 12x2 - 6x + 5 in the form p(x – q)² + r, where p, q and r are constants to be found.

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

1. [B3, 2, 1,0] 12(x-1/4)²+17/4 isw one mark for each of p, q, r correct in a correctly formatted expression; allow correct equivalent values; If B0 then SC2 for 12(x-1/4)²+17/4 or SC1 for correct 3 values seen in incorrect format e.g. 12(x - 1/4) + 17/4 or 12x² - x + 17/4 or for a correct completed square form of the original expression in a different but correct format. e.g. 3(2x-1/2)² + 17/4
2. [B1ft] their 4/17 or their 0.235 strict ft; their 4/17 must be a proper fraction or decimal rounded to 3sig figs or more or truncated to 4 figs or more
3. [B1ft] their x = 1/4 oe strict ft; x must be correctly attributed