1CONFIDENTIAL*(SULIT*) PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN MATHEMATICS (T) [MATEMATIK (T)]PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PAPER 2 (KERTAS 2) PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN One and a half hours (Satu jam setengah) PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN 954/2 STPM 2015 SMK DESA MAHKOTA, KUALA LUMPUR PEPERIKSAAN PERCUBAAN PENGGAL 2 SIJIL TINGGI PERSEKOLAHAN MALAYSIA (MALAYSIA HIGHER SCHOOL CERTIFICATE) Instruction to candidates: DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO. Answer all questions in Section A and ONLYone question in Section B. Answers may be written in either English or BahasaMelayu. All necessary working should be shown clearly. Non-exact numerical answers may be given correct to three significant figures, or one decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. Scientific calculators may be used. Programmable and graphic display calculators are prohibited. A list of mathematical formulae is provided on page 4 of this question paper. This question paper consists of 4 printed pages. STPM 954/2 *This question paper is CONFIDENTIAL until the examination is over. [Turn over CONFIDENTIAL* 8. b) find the values of k and q if xlim 3 x0 [4marks] c) Hence. show that the non-linear differential equation dv v dy y ex 2e x .in m3. 1The function his defined by h(x) = e x q .2 CONFIDENTIAL* 2 Section A[45 marks] Answer all questions in this section. V. [3 marks] 3 Express x 2 2 x 14 in partial fractions. [6marks] 6 Show that x3 = 954/2 *This question paper is CONFIDENTIAL until the examination is over. x0 h x =2 a) determine the value of p if lim x-1 [2marks] h x and lim h x exist. the x 3 volume.Use the Newton-Raphson method. with 1 x2 the initial approximation x0= 0. 3 x 0. ( x 3)( x 5) 5 8 [7marks] By using substitution v = y2. in terms of π. of the water is given by V . to find the root correct to two decimal places. If the volume of water in the container is 12 increasing at the constant rate of 3m3s-1 . obtain y2 in terms of x. [3 marks] 2 At the instant when the depth of water in a large water storage container is xmeter. given that y = 1 when x = 1. and hence. [9marks] 5 Given that y ln(1 sin x) d2 y dy ( )2 ey 1 . up to and including the term x3. calculate. ( x 3)( x 5) Hence. [4marks] 2 dx dx b) Find the Maclaurin’s series for yin ascending powers of x. CONFIDENTIAL* .sketch the graph of y= h(x). x2 k . show that 4 5 4 x 2 2 x 14 1 9 dx = 1 + ln . x 3 x p . a) the rate of increase in depth of water in ms-1 at the instant when the depth is 3m [3marks] b) the time taken in seconds for the depth to increase from 5m to 10m. [4marks] a) show that 1 has a root between 0 and 1.Solve this may be reduced into the linear differential equation dx 2 x y dx x linear differential equation. 5y -2 [4 marks] (b) Find theMaclaurin series for e-x sin 2x in ascending powers of x up to and including the term in x4 [5 marks] (c) Hence. 7On the same axes.3 CONFIDENTIAL* 3 Section B[15 marks] Answer ONLY onequestion in this section. find the value of [3marks] ********** END OF QUESTION PAPER ********** Prepared by: (MohdZaki bin HjMdSalleh) Mathematics T Teacher Verified by: (Chang SS. find the Maclaurin series for e-xcos 2x in ascending powers of x up to and including the term in x3 [3 marks] (d) Hence. Catherine) Head of Mathematics Unit 954/2 Checked by: (Khung Sow Wah) Committee of Mathematics T Unit . (a) Sketch the curves y = 6 – ex and y = 5e-x [3marks] (b) Find the coordinates of the points of intersection [4 marks] (c) Calculate the area of the region bounded by the curves [4 marks] (d) Calculate the volume of the solid formed when the region is rotated through 2 radians about the x-axis [4marks] 8Given that y = e-x sin 2x (a) Show that = . CONFIDENTIAL* .4 *This question paper is CONFIDENTIAL until the examination is over.