Raffles Institution 2022 Y4 RP Math Supp WS

Page 1 of 4 RAFFLES INSTITUTION MATHEMATICS DEPARTMENT 2022 YEAR 4 RP MATHEMATICS TOPIC 3B: DIFFERENTIATION (MATHS 2) SUPPLEMENTARY WORKSHEET Name: Class: Sec 4 ( ) Date: 1 2020/Y4RP/M2/T1/Q1 Differentiate ( ) 5ln cos 3 x with respect to x, leaving your answer as a single trigonometric term. [2] [Ans: 15 tan 3x− ] 2 2020/Y4RP/M2/T1/Q3 Given that tan 5y x= , show that 2 2 d d y x can be written in the form d d yky x , where k is a constant to be determined. [4] [Ans: k = 10] 3 2019/Y4RP/M2/T1/Q1 Differentiate the following with respect to x, simplifying your answer: (i) 2 sin 3x x , [2] (ii) 23eln cos3 x x       . [2] [Ans: (i) 3 3 cos3 2sin 3x x x x − (ii) 6 3tan 3x x+ ] 4 2019/Y4RP/M2/T1/Q4 (i) By writing sec x as ( ) 1 cos x − , show that ( )d sec sec tand x x xx = . [1] (ii) Hence find the following in terms of sec x , (a) ( )d sec tand x xx ’ [2] (b) ( )d ln sec tand x xx +  . [2] [Ans: (ii)(a) ( ) 2sec 2sec 1x x − (b) sec x ] 5 2018/Y4RP/CT/Q1 Differentiate each of the following with respect to x, leaving your answer in the simplest form. (b) 5tan 5 2x( ) . [2] [Ans: (b) ( ) ( ) 4 250 tan 2 sec 2x x ] 6 2018/Y4RP/CT/Q6 It is given that 1 siny x=− . Downloaded by chocomint (mohamadamiyaz@gmail.com) lOMoARcPSD|19327920

Page 2 of 4 (i) Find an expression for d d y x , leaving your answer in the simplest form. . [2] (ii) Show that 2 2 d d y kyx = , where k is a constant to be determined. [4] [Ans: (i) cos 2 1 sin x x − − (ii) 1 1 sin4 x−− ] 7 2017/Y4RP/CT/Q1 A curve has the equation y = xtan(1- 3x). Find the gradient of the curve at the point where 1x= . [3] [Ans: − 15.1] 8 2017/Y4RP/CT/Q3 Given that y = cos2 2x , find dy dx and d 2 y dx2 , simplifying your answers. Hence show that d2 y dx2 æ èç ö ø÷ 2 +16 dy dx æ èç ö ø÷ 2 - 128y = k cos4x, where k is a constant to be determined. [5] [Ans: 2 2 d d 2sin 4 , 8cos 4d d y y x xx x=− =− ] 9 2016/Y4RP/CT/Q1 Differentiate each of the following with respect to x, expressing your answers as a single fraction. (ii) ( ) 4 2 3 1 tan 5 x x + . [3] [Ans: (ii) ( ) ( ) 3 2 3 2 3 1 6 tan 5 5 3 1 sec 5 tan 5 x x x x x + − + ] 10 2016/Y4RP/CT/Q4 It is given that y = 1+ cosx . (i) Find dy dx , leaving your answer in its simplest form. [1] (ii) Show that d2 y dx2 = - 1 4 y . [4] [Ans: (i) sin 2 1 cos x x − + ] 11 2015/Y4RP/CT/Q2 Given that ( )ln 1 siny x=+ , (a) write down an expression for dy dx in terms of x, [1] (b) show that d2 y dx2 = - secx dy dx æ èç ö ø÷ . [3] [Ans: (a) cos 1 sd i d n y x x x= + ] Downloaded by chocomint (mohamadamiyaz@gmail.com) lOMoARcPSD|19327920

Page 3 of 4 12 2015/Y4RP/CT/Q4