smk desa mahkota maths t p2 trial

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CONFIDENTIAL*(SULIT*)

PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN PEPERIKSAAN PERCUBAAN


















SMK DESA MAHKOTA, KUALA LUMPUR

PEPERIKSAAN PERCUBAAN PENGGAL 2SIJIL 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

[Turn over

*This question paper is CONFIDENTIAL until the examination is over.

CONFIDENTIAL*CONFIDENTIAL*2

Section A[45 marks]Answer all questions in this section.

1The function his defined by h(x) =,a) determine the value of p if =2

[2marks]

b) find the values of k and q if and exist.

[4marks]

c) Hence,sketch the graph of y= h(x).

[3 marks]

2 At the instant when the depth of water in a large water storage container is xmeter, the volume, V,in m3, of the water is given by . If the volume of water in the container is increasing at the constant rate of 3m3s-1 , calculate, in terms of ,

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.[3 marks]3 Express in partial fractions.

Hence, show that dx = 1 + ln .

[7marks]4 By using substitution v = y2, show that the non-linear differential equation

may be reduced into the linear differential equation .Solve this linear differential equation, and hence, obtain y2 in terms of x, given that y = 1 when x = 1.

[9marks]5 Given that

a) show that .

[4marks]b) Find the Maclaurins series for yin ascending powers of x, up to and including the term x3.

[4marks]

6 Show that x3 = has a root between 0 and 1.Use the Newton-Raphson method, with the initial approximation x0= 0.8, to find the root correct to two decimal places.

[6marks]

954/2*This question paper is CONFIDENTIAL until the examination is over.

CONFIDENTIAL*CONFIDENTIAL*3

Section B[15 marks]

Answer ONLY onequestion in this section.7On the same axes,

(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 = - 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, 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, find the value of

[3marks]

********** END OF QUESTION PAPER **********

Prepared by:

Checked by:

(MohdZaki bin HjMdSalleh)

(Khung Sow Wah) Mathematics T Teacher

Committee of Mathematics T UnitVerified by:

(Chang SS, Catherine)

Head of Mathematics Unit954/2

*This question paper is CONFIDENTIAL until the examination is over.

CONFIDENTIAL*

954/2

STPM 2015

One and a half hours (Satu jam setengah)

MATHEMATICS (T) [MATEMATIK (T)]

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smk desa mahkota maths t p2 trial

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