SPM Additional Mathematics 2017, Paper 2 (Question 10 & 11)

Question 11:
Diagram 6 shows a curve y = 2x2 – 18 and the straight line PQ which is a tangent to the curve at point K.

It is given that the gradient of the straight line PQ is 4.
(a) Find the coordinates of point K
(b) Calculate the area of the shaded region.
(c) When the region bounded by the curve, the x-axis and the straight line y = h is rotated through 180o about the y-axis, the volume generated is 65π unit3.
Find the value of h.

Solution:
(a)

(b)

(c)