TMJC Term 4 Revision Chapter 9 Maclaurin Series Questions

Term 4 Revision Topical Quick Check: Maclaurin Series TMJC 2024 Page 1 of 2 JC1 H2 Mathematics (9758) Term 4 Revision Topical Quick Check Chapter 9 Maclaurin Series 1 EJC Promo 9758/2022/Q2 It is given that 2e cos .xyx= (a) Show that 2 2 dd 4 5 .dd yy yxx =− [3] (b) Find the Maclaurin series for y up to the term in 2x . [2] (c) Hence, show that the Maclaurin series for e cosx x is 211, 4xx++ up to the term in 2.x [2] 2 MI PU2 P2 Promo 9758/2022/Q6(modified) It is given that ( )ln cosyx= . (i) Find the Maclaurin series for ( )ln cos x up to and including the term in 4x . [2] (ii) Hence, by substituting π 3x= , show that 24ππln 2 18 972+ . [2] 3 ASRJC Promo 9758/2022/Q1 By finding the expansion of ( ) 1 13 x − + or otherwise, find the expansion of 13 12 x x + + in ascending powers of x, up to and including the term in 2x . Find the range of values of x for which the expansion is valid. [4] 4 MI PU2 P2 Promo 9758/2022/Q2 In triangle ABC , angle A is π 4  + radians and angle B is 1 3 radians. Show that when  is sufficiently small for terms in 3 and higher powers of  to be neglected, ( ) 26 12 AC kBC  − + where k is a constant to be found. [6]

Term 4 Revision Topical Quick Check: Maclaurin Series TMJC 2024 Page 2 of 2 Answer Key No. Year JC Answers 1 2022 EJC (b) 231 22yx x + + 2 2022 MI (i) ( ) 24 ln cos ... 2 12 xxx =− − + 3 2022 ASRJC 2111 2 ... 2xx− + + 11 33 x−   4 2022 MI 3 2k =