2014 T2 Trial SSI JB Answer

8/11/2019 2014 T2 Trial SSI JB Answer

1/7

SEK KEB MEN

SULTAN

ISMAIL,

JOHOR

BAHRU

Pre-U

95412 MATIDMATICS

T

TERM

2

TRI,AL EXAMINATION 2OI4

MARKING

SCHEME

I

l.

The

functions/is

defined

as

:

_

1x+lxl

, x*0

flx):

I

z

12,

r=0

(a)

Without

using

graphs,

determine

whether

the

function/is

continuous

atx:

0.

(b)

Skefth

the

graphs

of

the firnctions/.

[5

marks]

[2

marks]

Marks

(a)

(0'

.fli

=|'2,

(r,

r(0

r=0

r)0

I

, -/(r)

=,\3-

o:

o

lim

f(r)

=

lim

r:0

f+0*''

'

r+0*

lim

f(x)

=

lim.

f(x):0

x+O-'-

'

x+Ol'

frg/(r):

o

fQ)=2

1

I

I

}gftr)

+f(o)

;;fis

not continuous at

x

:

0

I

(b)

1+1


2/7

)

A

cylinder

is

inscribed

inside a sphere

of

radius

r.

Given

that

the volume of

the cylinder

is

a

maximum, show

that the

ratio

(volume

of sphere)

:

(volume

of

cylinder)

is

r/5

:

1.

[9

marks]

,':r'-T

V=

ttxzh

v:nh(rz

-+)

Y=

n(r'n-

T)

1

To:o(

-T)

I

Volume

ma:rimum,

ff=

O

n(,'-lfJ

=

o

h:

*4r

-v3

'

h>

0, h:

h,

I

1

o=h,,r=n(h4V-#)

V

=

4=TEr3

3V3

I

d.zv

3

,

-:--h

hz

2

o:h',#:-:G')

:-{3r(


3/7

3(b)

fi

ortr'" a*

:

li

3x27zxe*"1d,x

Letu=3x2,9*=6x

n:t2xex'dx=er'

=13x2e,'13-

I:6xe,"dx

l+l

:

l3xz

ex2

-

ger"llo

I

=

13(4)e4

-

3enl-

[0

-

3eo] I

=9e+

+3

1

4.

(a)

Find the

general

solution

ofthe

differential equation

dv

fr:kdx+fi

where t is

a

constant,

giving your

answer

in

the

formy

=

f(r).

[5

marks]

(b)

The

gradient

at any

point

P(x,

.y)

of

a curve is

proportional

to the

surn

of

the

coordinates

of

P.

The

curve

passes

through the

pornt (1,

-2)

and its

gradient

at

(1,

-2)

is

-4.

Find

the equation

of

the

curye.

[4

marksJ

(a)

*-nr=

*

I

Integrating factor

=

sl

-n*c

=

e-tu

I

e-k

9-kve-k*-lsr-kx

dx

d

Ero"-u)

-

k*"-o'

le-kx

=

f

ftys-x*6a

I

le-kx=-xe-tu-f-e-tudx

1

le-kx =

-xe-w

- "-t,

*,

=

-X

- -Y

gat'x

I

o)

H"


4/7

6.

Given ttrat the equation ln

x

+

x2

=

8

(a)

Show

that the

equation

has

only one real root.

[2

marks]

(b)

Verifi,

by calculationthatthis root lies

betweenx=2 andr

=

3.

[2

marks]

(c)

Use the Newton-Raphson

method to find the

of the equation ln

x

*

xz

-

8o

giving

your

answer correct to two

decimal

places.

[4

marks]

(a)

lnx:

8

-

x2

.y

-

ktx

;

the

equatisn

has

only one real root.

I

I

(b)

lnx+rz-8:0

Letf

(x)

=

lnr

+

xz

-

8

f

(2)=

ln 2

+

22

-8:

-3.307

(

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2014 T2 Trial SSI JB Answer