Find the values of k for which the line y+kx - 2 = 0 is a tangent to the curve y = 2x² – 9x + 4.

Mark scheme

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

1. [M1] Correctly eliminate y - kx + 2 = 2x² - 9x + 4 oe
2. [A1] 2x² + (k-9)x+2[= 0] oe allow even if x terms not collected; condone = y provided later work implies it should be 0
3. [M1] Use b²-4ac oe must be applied to a 3 term quadratic expression containing k as a coefficient; condone < 0 etc.
4. [M1] Reach their(k−9 = ±4) or solves their(k² -18k+65)= 0 condone 9-k=±4; condone an inequality at this stage
5. [A1] k = 5 and 13 cao mark final answer, do not isw; A0 if inequalities for final answers