1CALCULUS FINAL REVISION PAST PAPER EXAMPLES1.Differentiate with respect to x: (a)(x2 + l)2 (b)1n(3x 1).(Total 4 marks)2.Given that = 10, deduce the value of(a)(b)(Total 6 marks)3.Let f(x) = + 5cos2x. Find f (x).(Total 6 marks)4.The parabola shown has equation y2 = 9x.(a)Verify that the point P (4, 6) is on the parabola.(2)The line (PQ) is the normal to the parabola at the point P, and cuts the x-axis at Q.(b)(i)Find the equation of (PQ) in the form ax + by + c = 0.(5)(ii)Find the coordinates of Q.(2)S is the point .(c)Verify that SP = SQ.(4)(d)The line (PM) is parallel to the x-axis. From part (c), explain why(QP) bisects the angle SPM.(3)(Total 16 marks)5.The function f is such that f (x) = 2x 2.When the graph of f is drawn, it has a minimum point at (3, 7).(a)Show that f (x) = x2 2x 3 and hence find f(x).(6)(b)Find f (0), f (1) and f(1).(3)(c)Hence sketch the graph of f labelling it with the information obtained in part (b).(4)(Note: It is not necessary to find the coordinates of the points where the graph cuts the x-axis.)(Total 13 marks)