PSPM 1 Exam Papers Collection

QSo16/1

1 Dividing M(x)=r'* ax+b by (r+1) and G-t) givearemainderof -12 and
-16 respectively. Determine the vaiues of a and b.

16 marl<s)

2 Solve the equation CHOW CHOON WOOI

lnx- 3 = -2.

lnx

[6 marlrs]

3 Thequadraticequation x2+3mx+2=0 hasroots aand pwhere m isa
v constant. Form a quadratic equation with roots (" * F)' and (a - p)' interms

of m.

l7 marl<sl

4 The sum S, ofthe first rz terms ofan arithmetic progression is givenby

5,,= pr1*cytt. Thesumof thefirstfiveandtentermsare 40 and 155 respectively.

(.a) pFrnd the values ol and q.

13 marksl

(b) Hence, find the ruth term of the arithmetic progression and the values of the
.-l7 first term, a and the common difference, d.

14 marlc;l

7

101

QS016/1 14 marl<sl CHOW CHOON WOOI
[8 marks]
5 Solve the following inequalities.
(a) _ai-x2 -. +,_r >- 40.
2x- -3x-2

(b) ll*^-'rl<I 2.
l.r + 31

6 (a) Given two complex numbers Zr :2 + i and zz =I-ZL

v (i) Express ,,t *l in the form x+ yi, where x and y are real
z)
numbers and iz is the conjugate of zr.
14 marksl

(ii) Hence, find the modulus of z,'+-l-. 12 marksl
[6 marlrs]
z2

(b) Find the square roots of -3 + |i.

..,v

I

102

QSo16/1

7 The following table shou,s the price (RM) per type of 0.5 kg cakes sold at the shops

P, Q and R together u'ith the total expenditure if a customer buys a number of each
type of cake tiom the listed shops.

Cake Banana Chocolate Vanilla Total CHOW CHOON WOOI
Expenditure
Jl'pes 5 8 5
4 6 aM)
Shops 5 9 6
1 36
P 30

a 40

R

Let the number of banana, chocolate and vanilla cakes bought from each shop be x,

.v and z respectively.

] (a) :Write the matrix equation AX B using the above information.

11 marlc)

(b) l.Obtain the adjoint matrix of Hence, find the inverse of matrix ,4.

{8 marksl

(c) Determine the values of .r. -r, and z using the inverse matrix of ,,4 obtained

in (br.

l2 marksl

8 A polynomiat /G) = px3 *(p* q)*' +(p +2q) x +l has a factor (x+l).

3

(a) Express q in terms of p.

13 marks)

(b) Write /(x) in terms of p and x. Determine the quotient when f(r) t

divided by (x + 1).

l3 marlal

(c) p ifHence, find the value of x = 3 is one of the roots for "f(*)=0. Using

the value of p, factonze f (x) completely.

[5 marks]

11

103

QSo16/1

(a) Giventhat 1=0.015151515... = p+q+s+..., where p,q and s arethe
u
Iffirst three terms of geometric progression. p = 0.015, state the value of q
and s in decimal form. Hence, find the value of u.

14 marlcs)

I CHOW CHOON WOOI

Find the expansion (t-*)t * to the term x2. State the range of x

".

for which the expansion is valid. Show trhrra*rt 11//su- "z : z'\'(t-iric)i). '
"Hence, by substituting x :2, approximat t,lT correct to four siguificant

figures.

- 19 marl<s)

Y

13

104

QS016/1 CHOW CHOON WOOI

10 Thegraphof aquadratic function !=o)cz +bx+c, where a, b and c areconstants

passes through the points (- 2, -10), (1, 8) and (2,6).

(a) Obtain a system of linear equations to represent the given information.

12 marks)

O) Write the system of linear equations in the form of a matrix equation AX: B,

where

r:lu[,.ll 12 marks)
[2 marks]
Lc_l

Y

(c) Find the determinant of the matrix A.

(d) By using the Cramer's Rule, solve the matrix equation.

17 marks)

(e) Hence. urite the quadratic function of the graph and determine whether the

graph has a masimum or minimum value.
[2 marks]

-

END OF QUESTION BOOKLET

15

105

QS016/2 QS016/2
Mathemattcs
Matematik
Paper 2
Kertas 2
ISemester
Semester I
Session 2010/2011
2 hours Sesi 2010/2011

2 jam

I dL I CHOW CHOON WOOI
=Y=a"%:: XlX-:-F-,"S'

BAHAGIAN MATRIKULASI
KEMENTERIAN PELAJARAN MALAYSIA

MATRIC ULATION DIVISION
MINISTRY OF EDUCATION MALAYSIA

PEPERIKSMN SEMESTER PROGRAM MATRIKULASI
MATRIC ULATION P ROGRAMME EXAMINATION

MATEMATIK

Kertas 2
2 iam

JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU.
DO NOT OPEN IHIS BOOKLET UNTILYAU ARE TOLD IO DO SO.

Kertas soalan ini mengandungi 15 halaman bercetak.

Thisbooklet conslsfs of 15 printedpages.

@ Bahagian Matrikulasi

106

QS016/2 CHOW CHOON WOOI

INSTRUCTIONS TO CANDIDATE:
This question booklet consists of 10 questions.
Answer all questions.
The firll marks for each question or section are shown in the bracket at the end of the question

or section.
A1l steps must be shown clearly.
Only non-programmable scientific calculators can be used.

Numerical answers may be given in the form of fi, e, svrd, fractions or up to three

significant figures, where appropriate, unless stated otherwise in the question.

!7

3

107

QSo16/2

LIST OF MATHEMATICAL FORMULAE

Differentiation CHOW CHOON WOOI

If y=g(r) *a x=f|\then !d=x4d"t4dx

d(dv)l

dd'xv2-AldAx )

dt

Integration

v
ludv=uv- lvdu

rt

E

108

QS()16/2 12 marl<sl CHOW CHOON WOOI
14 marl<s)
1 !Find foreach of the following:
aIx [6 marl<s]
(a) 1 = (ln x)' . 16 marksl

(b) xy' - ye* =3. l7 marl<sl

2 fofFind the exact value f ,t,' -t a,

.y

3 If f is a tunction with .f '(l) =2, find xlir+nl"f GL- f Q)

riX _1

4 ff{fExpr.r, as partial fractions.

Hence, evaluate J[ 2!'x]'+*31xt ,r.

v

7

109

QSo16/2 14 marlcs] CHOW CHOON WOOI

5 Given the functions f and g as follows: 13 marla)
f(x)=2-*', 12 marksl

8Q) = x +2' 13 marl<sl

(a) Find /.g and g.f.

(b) fState the domain and range of " g.

(c) Find (g " f)'.

v

(d) rDetermine the value of such that f .g(x) = g" f (x).

6 (a) State the conditions of continuity of a function at a point x = c.

12 marksl

(b) A tunction / defined by

I x-21 - -5<.r<2
x'+3x-10
fG)=1 A
2<x<3
v Ax+B , x=3

is continuous at x :2 and x : 3. [6 marlrs)
[5 marl<s)
(i) Find lrry_ /(x).

(ii) Determine the values of the constants A and B.

I

110

QSo16/2

7 (a) Evaiuate.

(i) rli+m€!+lt -{Ix++1za x-L

(ili . 2- VrxT'-5 13 marl<s) CHOW CHOON WOOI
14 morl<sl
til-il..-i -1 .r + 3 13 marks)

-.

(b) If li* /(')- 5 = 1, find lri-m4"/(x).

x+{ X-2

v

8 Consider the curve given by the equation .f (x) = 2 - x' .

(a) Sketch the region bounded by the curves -f (x) , g(x) = x2, the lines
x : 0 and x:2. Hence, find the area of the region.

l7 marks)

(b) Find the volume of solid generated when the region bounded by the curve
/(x), lines x=1 and x=2 isrotatedcompletelyaboutthe x-axis.

15 marl<s)

Y

11

111

QS016/2

9 Consider the parametric equations

x=2t-t-' , !=2tlt'' , />1.

(a) Show that

dy 2r2 -1 CHOW CHOON WOOI
dx 2r: -l

(b) +Er aluate at the point (1, 3). 13 marl<sl
(L\ 14 marks)

Y 16 marksl

(c) 4!pin6 in term of r. Hence, show that

dx'

ddrxy2= g

Y3'

-

13

112

QS016/2

10 Atunction / isdefinedby f(x)="5'Y2x-:r'-+"R-x. -r'- 4

'

(a) Find the vertical and horizontal asymptotes of /.

13 marl<s)

(b) /Find the coordinates of,the point where the curve cuts the horizontal CHOW CHOON WOOI

asymptote.

[2 marlcs]

(c) Determine the coordinates of the point where /'(x) = Q.

13 marksl

(d) :fBy writing y (x), show that

(y-5)r'+(f-8)x-4=0

Hence, for real x, show that f (x) < -4 or f (x)>4. 14 marl<s)
(e) Sketchthe graph of f . 13 marl<s)

END OF QUESTION BOOKLET

15

113

2011/2012

114

CHOW CHOON WOOI

QS015/1 QS{t15/1
thMb
PWl Matematik
SS2eersmsteioosntue2r rI0slI/2012
Kertas f

Semester I

Sesi 2011/2012

2jam

I 'v 4L CHOW CHOON WOOI
qef1:Y---

== 5--

BAHAGIAN MATRIKT]LASI
KEMENTERIAN PELAJARAN MALAYSIA

n IATRIC\I-,IflON DIVNON
MIMtrRY OF EDUCATION MAI-AYSIA

PEPERIKSMN SEMESTER PROGRAM MATRIKULASI
I,IATRICU-4UON PROGRAMME EX,4MINATION

MATEMATIK

Kertas I

2 jam

JANGAN BUKA KERTAS SOAI.AN INISEHINGGA DIBERITAHU.
DO NOT @EN IHIS QUESNON PA,PER UI,NL YOU A,RE lCI.D IO DO SO,

Kertas soalan ini mengandungi 15 halaman bercetak.
This quesiriat paperconslsts of 15 pnfied pages.

@ Bahagian Matrikulasi

115

QS015/1 CHOW CHOON WOOI

INSTRUCTIONS TO CANIDIDATE:
This question paper consists of 10 questions.
Answer all questions.
All answers must be written in fte mswer booklet provided. Use a new page for each

question.

The full ma*s for each question or section ae shown in the bracket at the end of the question

or section.

All steps must be shown clearly.

Only non-programmable scientific calculators can be used.

Numerical answers may be given in the form of fi, e, strd, fractions or up to three significant

figures, where appropriate, unless stated otherwise in the question.

-

3

116

QSo1s/1

LIST OF MATHEMATICAL FORMULAE

Quadratic equation ax2 +bx*c=0l
--:--

-b=r b- -|ac

Arithmetic series: CHOW CHOON WOOI

Tn = ct*(n-l)d

s, =lrlz"+(n_ldl

ry

Geometric series:
T, = arn-l

s,=ff,r*t

Sum to infinity:

s*=*,l.l.r

ry Binomial expansion:

(a+b)^ = an +(i)"".(;)"-u'+ + (:)"'', + +bn ,

*.where neN [;j =@lW

(t+ax)n =t+n(ax).9tax12 *n(n-)!n-z) @13 +...

lo*1.1 where neZ- or n ee

5

117

QSo15/1

I Solve the equation 3zx+t - 28 (3') * 9 : 0.

16 marksl

2 The functions "f and g are defined as: CHOW CHOON WOOI

f(x)=JA, x>1

g(x)=x', x>0.

Find the inverse function, f-t (*) and determine its range. Then, evaluate

("F " s)el. 16 marksl

v

3 The ninth term and the sum of the first fifteen terms of an arithmetic progression are
24 arrd 330 respectively. Find the first term, a and the common difference, d.

Hence, find the least possible value n, such that the sum of the first n terms is

-qreater than 500.

[6 marlrs]

, -,f

[r4 Matrix .{ is given as lZ 3 -3 l.

lz 2 -t)

[: x+y -21
(a) Giventhecofactormatrixof e is | 0 | 2 | *n... x>0.
[-: x'
-t_]

rDetermine the values of and y.

{3 marl<sl

(b) Given A2-4A+1=0,showthat A3=l5A-41 where 1 isthe3x3

identity matrix. Hence, find, A3.

14 marks)

7

118

QS015/1 lI markl CHOW CHOON WOOI

5 Giventwocomplexnumbers zr:Ja3i and zr=2-i. 13 marl<sl
(a) State z, ""d 4. 16 marl<sl

(b) ifDetermine the value of k | = k1. 12 morksl
zr 12 marksl

(c) Find zrzr.Hence,showthat 21 zz=2F2. 15 marl<sl
14 marks)
v
6 (a) Given -f (x)= e ' and g(x)= x'.

(i) fFind the domain and range of and g.
(ii) Show that (g " -f)(*) = e-" .

(b) Given

I

I (i) Find ft-'(.r).

(ii) Sketchthegraph for h(x) and h-t(x).

I

119

QS015/1 15 marlal CHOW CHOON WOOI
17 marksl
7 (a) Solve the equation log(r-4)+ 2log3:r.*(;)

(b) Find the solution set of the inequality

141.,

lx+ll

y I (a) -(i)"Given that the sum of the first n terms, S, of a series as E = ,

Find an expression for the zth term. Show that the series is a geometric series

and find the sum to infinity, ^S-.

16 marlal

I

(b) Expand (r4)' intheasce,ndingpowersiof r uptothetermin x3.

,EHence, by substituting r = 3, evaluat" correct to three decimal places.

y [6 marks)

11

120

QSo15/1

9 (a) A tunction /(x) is defined by f(i=4x-o for x * 6.

Show that f (x) is a one-to-one function.
Find the values of x such that (f . "f)(x) = 0.

(b) Given -f (r)=.'/l= x l7 marks) CHOW CHOON WOOI
16 marksl
and Su\(-r,)= -1.

2

Find /[s'(j))

v

13

121

QS015/1

l0 The following table shows the quantities (unit) and the amount paid (RM) for pens

bought from three shops.

Pen Pilot Kilometrico Papermate Amount paid CHOW CHOON WOOI
Shop (unit) (uni0 (unit) (RM)

S I p 2p 18.00
I 3q 31.00
T q 4r 37.00
U 1
r

Given the price in RM per unit of pilot, kilometrico and papermate pens be x, y Md

z respectively.

(a)V Obtain a system of linear equations to represent the given information.

ll mark)

(b) BWrite the system in the form of a matrix equation AX = where
/x\

* =l ,1.

l,)

I mark)

(c) Giventheminor 4r, ozt arrtd azz ofmatrix A is 9, 12 and 8

v respectively. Find the values of p, q and r.

14 marksl

(d) Find the determinant, cofactor, adjoint and A-t of matrix l. Hence, find the
values of x, y and z.

19 marksl

END OF QUESTION PAPER

15

122

QS(}15I2 QS015/2

ftffitsndis Matematik

Pw2 Kertas 2

ISemester Semester I

Session 201l/2012 Sesi 2011/2012
2 ja,m
2 hours

A CHOW CHOON WOOI
ffid

BAHAGIAN MATRIKULASI
KEMENTERIAN PELAJARAN MALAYSIA

IqI4TRICUI-AflON DIWSION
MIMSIRY OF EDUCANON M4I-AYSIA

PEPERIKSMN SEMESTER PROGRAM MATRIKU LASI
NATRICUI.,ITION PROGRAMME EXAMINATTON

I MATEMATIK
I Kertas 2

2 jam

E JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU.

DO NOIOPEN 7HlS QUESTTO,\/ PAPER UNNL YOU ARE TOI-D IO DO SO.

Kertas soalan ini mengandungi 15 halaman bercetak.
ThisquMion paperconslsts of 15 printed pages.

123@ Bahagian Matrikulasi

QS015r2 CHOW CHOON WOOI

INSTRUCTIONS TO CAITDIDATE :
This question paper consists of 10 questions.
Answer all questions.
All answers must be written in the ailiwer booklet provided. Use a new page for each

question.
The fuIl marks for each question or section are shown in the bracket at the end of the question
or section.

All steps must be shown clearly-

Only non-programmable scie,ntific calculators can be used.

'v Numerical answers may be given in the form of r, e, srttd, firactions or up to three significant

figures, where appropriate, unless stated otherwise in the question.

3

1234

QS015/2

LIST OF MATHEMATICAL FORMULAE

Trigonometry

Isin (,{ t B)= sin,4 cos B + cos sin B CHOW CHOON WOOI

cos (.1t B) = cos .-1 cos -B + siri,-1 sin B

\ '/ I +tan ( -4+ .B ) = L'ul '

tan.{ tan B

'v sin,4 +sin,B :2rinA+ B B

22 "orA-

sin A -sin B :2 B ,inA- B

"rrA*22

cos -4 t cos B: 2 cos A+ B B

22 "oro-

cos,{ - cos :.B -z rinA*2B2 ,inA- B

sin 2J = 2 sin.-{ cos --1

cos 2.{ = cos: .l -sinr ,l

v = I cos: -l -1
= L-2sinr I

2tan A

1-tan'A

sin' A = l-cos2A

2

cos' A = 1+cos2A

1525

QS015/2 LIST OF MATHEMATICAL FORMULAE

Limit

li*'inft =1 CHOW CHOON WOOI

h">o h

lim l-cos ft =0
h--+0 h

Differentiation

=y f(*) f'(*)

cot r - cosec2x
xsec
sec x tan x

cosecx -cosec xcotx

rf y=g(r) and *=f(t),tnen f=*"*

d(dv\
dd'xv2-Alddx- )

dt

.,

Sphere v =! nr3 s = 4xr2
3
-^S 7c rs
Right circular cone V =L nrzh
3 S =2nrh

Rightcircularcylinder V = nrzh

1726

QS015'2 15 marksl CHOW CHOON WOOI

I -Expr"*. (,t!xr:-1+?)u' in the form of partial fractions. [3 marks]
13 marl<sl
2 Evaluate the following limits:
(a) lrm xo -16

x-+2 X-2

-.

..EI*G

(b) rl+lm@- J,

3 Fkd +dx forthefollowingequations: 13 marlal
13 marksl
(a) ! =32'*1.

O G) ery+y-5a.

4 The surface area of a balloon in the shape of a sphere is decreasing at the rate of

2 cmzf min Find the rate at which the volume is decreasing when the radius of the

balloon is 5 cm.

l7 marks)

9

127

QS()15l2 -3The function f (x) = x' - 6x' +9x is defined on the interval [0, 5].

s (a) Find the critical points of f (x) on this interval and determine whether the

critical points are local minimum or maximum.

[6 marks]

(b) ffi.Find the horizontal and vertical asymptotes for /(x) = CHOW CHOON WOOI

[7 marks)

a6 The polynomial p(*) = x' -Zx' + ax +b, where ba1|J are constants, has a
factor of (x-2) dand leaves aremainder of when it is divided by (x-a).

(a) aFind the values of and b.

f6 marlcsl

(b) Factorize f (.r) completely by using the values of a and b obtained from
bpart 6(a). Hence, find the real roots of p(x)= 0, where a and are not

equal to zero.
16 marksl

Giyen that ., =^,-lLt+t' ,:ry, where / is a non zero parameter.

(a) Show that dy -l-+---t:2- 16 marksl
16 marksl
dx tt

(b) ,rno t4 when t =1.

11

128

QS01s/2 15 marl<sl CHOW CHOON WOOI
[6 marks]
8 (a) lf y=sin(x'+l), showthat
x!t2(-?*,4x3y=g. 14 marksl
13 marksl
dx" dx
16 morlal
(b) Fild the gradient of a curr e x eu = e2' - e3v at (0, 0).

v 9 (a) Given f I *'-64 ' x+4

(*)=l ,-o
L 40, x=4.

(D Find li]l t (*).

(ii) Is / continuous at x=4? Giveyourreason.

(b) Determine the values of A arrd B such that the function

v *- a, x<-l
+3Ax+ B, -l < x<l
h(x)= |
x>1.
l2x: 4,

[

is continuous for all values of x.

13

129

QS015'2

10 (a) Given t*13=4,1-l and tanL=\.
Express t^# intheformof a+Ji where a and b areintegers.

.Hence, show that r^g\6A\/= +Jt. CHOW CHOON WOOI

16 marl*l

(b) aFind R and suchthattheexpression gsing +l2cos? canbeexpressed
in the form of Rsn(O + a), ofrer" R > 0, 0o < a < 90".

Hence,if 9sind+l2cos0:5, solve for 0 intheinterval O" <0 <360".

Y 19 marksl

END OF QUESTION PAPER

v

15

130

2012/2013

131

CHOW CHOON WOOI

QS01st1 QS015/1
Mathematia
Paprl Matematik

1Semester Kertas 1
Session 2012/2013
2 hours Semester I

Sesi 2012/2013

2 jam

==4-::t-6q^GeLf5-J:sI :! CHOW CHOON WOOI
l:-.\

BAIIAGIAN MATRIKULASI
KEMENTERIAII PELAJARAN MALAYSIA

I,IATRICU-,ITION DIVBION
MINNTRY OF EDUCATION MAL4YSU

v' PEPERIKSMN SEMESTE R PROG RAM MATRIKULASI

IT UTNC UI-4TTON PRrcRAMME EXAMI|,{ATION

MATEMATIK

Kertas L
2 ja'm

JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU.
DO NOT OPEN IFI/S QUESNON PAPER UI{NL YOU ARE TAD IO DO SO.

v

CHOW CHOON WOOI

Kertas soalan inimengandungi 13 halaman bercetak.
This question paper consists of 13 pinted pagx.

@ Bahagian Makikulasi

132

QSo15/1 CHOW CHOON WOOI

INSTRUCTIONS TO CAI\DIDATE :
This question paper consists of L0 questions.
Answer all questions.
All answers must be written in the answer booklet provided. Use a new page for each

question.

The full marks for each question or section are shown in the bracket at the end of the question
or section.
All steps must be shown clearly.
Only non-programmable scientific calculators can be used.

Numerical answers may be given in the form of r, e, stJrd, fractions or up to three significant

figures, where appropriate, unless stated otherwise in the question.

Y

CHOW CHOON WOOI

133

QS015l1

LIST OF MATHEMATICAL FORMULAE

Quadratic equation ax2 +bx+c=02

x= -t+.[6'-a*

Arithmetic series: CHOW CHOON WOOI

To = a*(n-l)d

s, =llzo+(n_\dl

U

Geometric series:

Tn = ar*l

Sum to infinity:

s- =fr, l'l<t

t Binomial expansion:

*(a + b). = an *(i)"" t .(i)o- + + (i)"'u' + ...+ b' ,

*.where neN =@+ya

[;)

*:W(t + m)n = r + n(ax).$r*y * -2(*)' *...

laxf<twhere neZ- orn eQ

CHOW CHOON WOOI

134

QS015/1

1 Find the value of x which satisfies the equation

log, (5 - x) - log, (* - z) : 3 -lo1z(t + r).

16 marksl

2 Determine the solution set of the inequality CHOW CHOON WOOI
2x1-1l <_x+.2

16 marlcsl

3 Given k+2,k-4,k-7 arc the firstthree terms of a geometric series. Determine the

value of k Hence, find the sum to infinity of the series.

f6 marksl

1 Givenacomplexntrmber z:l-$i. Deteminethevalue of ,tif 7 =UvL.

[7 marksl

Ir5 -11
(a) MatrixMisgiven* tr"*that M2:7M-8.I, where ^I isthe
L_O O-l

2x2 identitymatrix. Deduce that M-t =818r-lr.

15 marksl

lr*t -r(b) Given matrix l: | 3 I24 I ana lZl =27. Findthe value

-,L |
o p*2)

ofp, wherep is an integer.

15 marlcs)

CHOW CHOON WOOI

135

QSo15/1

6 =:::,The tunctions ,f and g are defined as f (x) x +2 and 8(x) = 3-x.

(a) Find /-t(x) and s-'(x). 15 marksl CHOW CHOON WOOI
13 marks)
o) Evaluate (/.s-,)t:). 14 marksl

(c) If (g' f')(k):1, *O the value of fr.

s

7 (a) Solve lx' -x-rl::.

2x2 +9x - 4 15 narlcsl
x+2 l7 morl<sl
(b) .Find
the solution set of the inequality o.

CHOW CHOON WOOI

136

QSo15/1 CHOW CHOON WOOI

8 The first four terms of a binomial expansion (1+ axl is
l+ *-L*'+ oxj + ...

2

Find

(a) the values of a and nwharc n*A.

16 narksl

O) *=!, "" \Ethe value of p. Hence, by substitutingshow is approximately

equal to 9r2.8

[7 marks]

9 Given -f(r):h(2t+3) md g(r.),= +
2

(a) 5trourfint "f (r)it a one-to-one fuuction algebraically.

[3 marlu]

O) Find (,f "sxr) and (s'l)(r). Hence, state the conclusion about the results,

15 narksl

(c) /(x)Sketch the graphs of and g(x) on the same axes. Hence, state the

&main and range of /(x).

15 marksl

CHOW CHOON WOOI

13'171

QS015l1

10 Given

lz23l

.n=Lttlr3st44)1.

(a) Find the determinant of matrixl. 12 mark*l CHOW CHOON WOOI
(b) l.Find the minm, cofactor and adjoint of matrix 15 marksl

O G) Given /(a{ioint( A))=lAllwhere.(is 3 x 3 identity matrix, showthat

f :fr"ai"iot(,1). Hence, find l-r.

15 narlxl

(O Byusing A-rinpart (c), solve the follswing simultaneous equations.

2x+2y+32=49
x +5y+42=74
3x + y +42=49

[3 marks]

END OF QUESTION PAPER

CHOW CHOON WOOI

13183

QSo15/2 QS015/2
Mathematkx
PaprZ Matematik

/Semester Kertas 2
Session 2012/2013
2 hours Semester I

Sesi 201212013

2jam

GL CHOW CHOON WOOI

==-=
,,

BAHAGIAN MATRIKULASI
KEMENTERIAN PELAJARAN MALAYSIA

MATRICU./TTTON DII/BION
MINNIPJ OF EDUCATION MAI-4YSU

U PEPERIKSMN SEMESTER PROGMM MATRIKULASI

AATRIC U-/TNON PROGRAMME FXIUNUruON

MATEMATIK

Kertas 2

,' i'^

JAt{CrAl{ BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU.

IfiTffE'DCI I}dS Q,fiESTffi,' FAPER UNTL YW ME TW IO DO SO.

\,

Kertas soalan ini mengandungi 17 halaman bercetak,

Thls quNion paper mnsrisfs of 17 pintd pagx.

@ Bahagian Matrikulasi

139

QS015/2 CHOW CHOON WOOI

INSTRUCTIONS TO CAI\iDIDATE :
This question paper consists of 10 questions.
Answer all questions.
All answers must be written in the answer booklet provided. Use a newpage for each

question.

The full marks for each question or section are shown in the bracket at the end of the question
or section.
All steps must be shown clearly.
Only non-programmable scientific calculators can be used.

1. Numerical answers may be given in the form of T, e, sltrd, fractions or up to three significant
- figures, where appropriate, unless stated otherwise in the question.

v

140

QS()15/2

LIST OF MATHEMATICAL FORMULAE

Trigonometry

I ftsin (,,4 A) = sin cos .B cos A sin B

cos (r4tB)=*t AcosB + sin,4 sinB CHOW CHOON WOOI

tan I\/A.r. B-\'l'= tanA + tanB
l+@LAtanB

T sinl +sinB: 2"ioA*2B2 .o* l-B

sinl - sinB : 2 rn*A*2B2 r*A- B

cosl +cos6 :z*n*A* B ,rro- u

22

ml-G(E B:1*' l+B rio1-B

sn 2A:2smA cos,{

w2A: cG2 A-sinz A
I =2cos2 A-l

=l-Zsinz A

:tafl 2A 2*'! A

l-tarf

. 1 . l-cos2A

Sfn'.4 =

2

). -l+cosZA

COS'A = 2

-

141

QS015/2

LIST OF MATIIEMATICAL TORMULAE

Limit

hli+- 0thhfr = I CHOW CHOON WOOI
h,.-+lA-cohs ft _O

Differentiation

f(.) f'(*)

cotx - cosec2x
rsec
sec x tan x

cosecr -cosecx cotx

tf y:st) *a *=fk\uenfi=*"*

d(dv)l

d&'y2&-AIA)

&

Sphere Y =! nr} S = 4nr2
3 Sl = firS
Right circular cone
Right circular cylinder , S:Zxrh
V =! nrrh

3

V = rcr2h

142

QS015/2

1 Giventhat f(*)=j ll+nt,., x<1

x=l

12-x, x>1.

Find ,li3_,f (x) anA Um /(r). Does the trq/(x) exist? State your reason. CHOW CHOON WOOI

15 marlcsl

2 Prove that 1+tan20la$0 =sec20.

16 marlrsl

3 Find the following limits:

(a) 2x2 + x-- 4

r'-')o 1- x2 '

o) 3-rf,+7 13 marks)
rH+m2 t' -4 ' 14 marlcsl

4 Express 2x3 -27x2'-7!xl7+x6- 19 intheformofpartialfractions.

l7 marksl

g

143

QS015/2

s (a) ll*' - r-zl x * 0,2
x=2.
Given that f (x) = 1L#,0,

Find the yy f (-). Is /(r) continuous at x=Z?

[6 marks] CHOW CHOON WOOI

lax+6, x <4
(b) A tunction/(r) t defined fAV (*)=) x' +2, 4< x <6

lr-B*, x>6.

J
a fDetermine the values of the constants and B ir (x) is continuous.

15 marlcsl

6 The polynomial P(x) =2x3 + mz +bx-24 has a factor (*-Z) and a remainder 15

nfren divided by (x+3).

(a) Find tre values of a and D.

[6 marks]

-o (b) Factorise P(r) completely and find all zeroes of p(x).

16 marksl

11144

QS015/2

7 Given f (0) = 3sind -2cos0.

(a) Express f (e) inthe form of Xsin(d-a), where R >0,0< "=;. CHOW CHOON WOOI
fHence, find the maximum and minimum values of (e\.

l8 marksl

(b) Solve f (o):E for oo <o<3600.

14 marks)

8 (a) =#Given that y

(i) ff.By using the first principle of derivativ e, fina 14 marksl
12 marlul
(ii) ,*#
12 marksl
(b) +Ftud of the following: 14 marlcsl
ax
(i) y=e2* tarrx.
(ii) !=xs"'.

11345

8S015t2 CHOW CHOON WOOI

9 (a) A conical tank is of height 12 m and surface diameter I m. water is pumped

into the tank at the rate of 50 m3/min. How fast is the water level increasing
when the depth of the water is 6 m?

16 morksl

(b) A cylindrical container of radius r and height h}p,s a constant volume v. The

cost of the maerials for the surface of both of its ends is twice the oost of its

,sides. state in t€ms of r and I/. Hence, find & and r in tenns of zsuch that

the cost is minimrmr.
l7 marlal

11456

QS015/2.

10 (a) Given 3y2 -ry+x2 =3.8y using implicit differentiation,

(i) findthevalue .f * at x=1.

(ii) 4*!.show that (ay - r(*)' - r*.2 = o 16 marksl CHOW CHOON WOOI
12 marksl
O) Consider the parametric equations
[3 marlal
x =3t -ut',-, =3t *? where t * o.
14 marl<s)
t

O show tn* fl=;fi;.

(ii) + t:NFid_ when l.

t,

END OF QUESTION PAPER

14177

2013/2014

148

CHOW CHOON WOOI

QS015/1 QS015/1
Mathemalix
Paprl Matematik
1Semester
Session 2013/2014 Kertas 1
2 hours
Semester I

Sesi 2013/2014

2iam

BAHAGIAN MATRIKULASI CHOW CHOON WOOI
KEMENTERIAN PENDIDIKAN MALAYSIA

MATRICUATION DIVBION
MINNIRY OF EDUCATION MAIaffSA

PEPERIKSMN SEMESTER PROGRAM MATRIKULASI
MATRICU-ATTON PROGRAMME EX,4MINATION

MATEMATIK

Kertas 1
2 jam

I JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU.
DO NOIOPEN 7H'S QUESTTON PAPER UAINLYOU ARE TAD IO DO SO.

I

Kertas soalan ini mengandungi 13 halaman bercetak.
This quxtion paperconssfs of 13 pinted pages.

@ Bahaglan Matrikulasi

149

QS015/1 CHOW CHOON WOOI

INSTRUCTIONS TO CANDIDATE:
This question paper consists of 10 questions.
Answer all questions.
All answers must be written in the answer booklet provided. Use a new page for each

question.

The full marks for each question or section are shown in the bracket at the end of the question
or section.
All steps must be shown clearly.
Only non-programmable scientific calculators can be used.
Numerical answers may be given in the form of n, e, strtd, fractions or up to three significant

\- figures, wltere appropriate, unless stated otherwise in the question.

150