The report stated that although this question was equally attempted by majority of the
candidates, their performance was poorer than it was in question 2. Some candidates were said
not to recall that the tangent of the angle between the line and the x-axis is equal to the gradient
of the curve at the point of contact between the line and the curve.

Gradient of the curve = __dy__= 2x - 3, tan 135° = -1. This implied that 2x - 3 = -1. Hence, x = 1.

* dx *

Substituting 1 for x in y = X² - 3 + 4, we obtained y = 2. Thus, the point of contact is (1,2).

Equation of the line passing through the point (1, 2) and having a slop of -1 is given by:

y - 2 = -1(x -1) == x + y - 3 = O.