Prime DSE Series - Mathematics Mock Exam Papers (Extended Part) Module 2 Set 3

HKDSE-MATH-EP(M2)(Set 3) − 14 14 © United Prime Educational Publishing (HK) Ltd. Answers written in the margins will not be marked. Answers written in the margins will not be marked. Answers written in the margins will not be marked. SECTION B (50 marks) 9. Let 2 2 f ( ) 3 x x x x − − = − , where 3 x ≠ . Denote the graph of f ( ) y x = by H . (a) Find the asymptote(s) of H . (3 marks) (b) Find the maximum point(s) and minimum point(s) of H . (4 marks) (c) Let c be a real constant. If 3 y x c = − + is a tangent to H at P , find the possible coordinates of P . (2 marks) (d) Consider H for 4 x ≥ . Let R be the region bounded by H , the tangent to H at P and the straight line 6 x = . Find the area of R . (3 marks) Sample © United Prime Educational Publishing (HK) Limited All rights reserved; no part of this publication may be reproduced, photocopied, recorded or otherwise, without the prior written permission of the Publisher.