Created by T Madas Question 303 (*****) A curve C and a straight line L have respective equations C : y = x2 − x + , x ≥ L : y = 5x − a) Show that L is a tangent to C at some point P , further determining the coordinates of P b) Show further that L does not meet C again MP1-T , P ( 4,11) Created by T Madas Created by T Madas Question 304 (*****) If a and b such that a > b > , find with justification the minimum value of 4a + 9b2 5ab SPX-R , 12 Created by T Madas Created by T Madas Question 305 (*****) A convergent geometric progression has positive first term and positive common ratio Show that the sum to infinity of the progression is at least four times as large as its second term V , SYN-W , proof Created by T Madas