Standard +0.3 This is a standard discriminant problem requiring students to recall that b²-4ac < 0 for no real roots, then solve a quadratic inequality. It's slightly above average difficulty for C1 as it involves manipulating the discriminant condition k² < 144 to get -12 < k < 12, but remains a routine textbook exercise with no novel problem-solving required.
Question 12:
12 | b2 − 4ac soi
k2 − 4 × 2 × 18 < 0 o.e.
−12 < k < 12 | M1
M1
A2 | allow in quadratic formula or clearly
looking for perfect square
condone ≤; or M1 for 12 identified as
boundary
may be two separate inequalities; A1 for
≤ used or for one ‘end’ correct
if two separate correct inequalities seen,
isw for then wrongly combining them
into one statement;
condone b instead of k;
if no working, SC2 for k < 12 and SC2
for k > −12 (ie SC2 for each ‘end’
correct) | 4