Further Mathematics Paper 2, Nov/Dec. 2010
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
Weakness/Remedies
Strength
Question 3

Find the equation of the tangent to the curve y = X2 - 3x + 4 at the point where the tangent makes an angle of 1350 with the positive x - axis.

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Observation

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.