Mathematics (Matriculation)

Kedah Matriculation CollegeCHOW

Mathematics

(Matriculation)

From
2003/2004

To
2018/2019

Chow Choon Wooi Exam Papers Collection

Year CHOW Page
2018/2019 3
2017/2018 28
2016/2017 55
2015/2016 83
2014/2015 122
2013/2014 163
2012/2013 183
2011/2012 202
2010/2011 221
2009/2010 241
2008/2009 256
2007/2008 274
2006/2007 290
2005/2006 305
2004/2005 317
2003/2004 330

2

PSPM 2 CHOW
MATRICULATION MATHEMATICS

SM025
2018/2019

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PSPM 2 CHOW
MATRICULATION MATHEMATICS

QS025
2017/2018

28

STILIT QS025/1

QS025/1 Matematik

Mahernatis Kerhsl

Paprl Semester II

Semester II Sesi 201712018

Session 2017/2A18 2 iam
2 hours

KE,ME,NTE,RIAN

PENDIDIKAN
MAIAYSIA

BAHAGIAN MATRIKULASI

I,I4TNC UIATTON DIVNION

PEPERIKSMN SEMESTER PROGRAM MATRIKULASI
i,L4TNCUL,ITION PROGMMME EYAMINATION
CHOW
MATEMATIK

Kertas I
2 jtm

JANGAN BUKA KERTAS SOALAN IN!SEHINGGA DIBERITAHU,
DO NOIOPEN IHIS QUESI/ON PAPER UMIL YOU ARE IOID IO DO SO.

Kertas soalan ini mengandungi 11 halaman bercetak, 29

Ilns guesfibn papermnsafs of 11 pintd pages.

@ Bahagian Matrikulasi

SULIT QS025t1

INSTRUCTIONS TO CANDIDATE:CHOW

This question paper consists of 10 questions.

Airswer 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, sturd, fractions or up to three significant

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

ARAHANKEPADACALONz

,

Kertas soalan ini mengandungi lA soalan.

Jatyab semua soalan.

Semuaiawapan hendaklah ditutis pada buku jawapan yang disediakan. Gunakan muka surat
baharu bagi nombor soalan yang berbeza.

Marlrnh penuh yong diperuntukkan bagi setiap soalan atau bahagian soalan ditunjukkan
dalam kurungan pada penghujung soalan atou bahagian soalan.

Semuo langkah kerja hendaklah ditunjukkan dengan jelas.

Kalkulator saintifikyang tidak boleh diprogramkan sahaja yang baleh digunakan.

Jawapan beranglm boleh diberi dalam bentuk fi, e, surd, pecahan atau sehingga tiga angka
bererti, di rnana-mana yang sesuai, kecuali jika dinyatakan dalam saalon.

30

SULIT QS025l1
31
LIST OF MATHEMATICAL TORMULAE
SENARAI RUMUS MATEMATIK

Trigonometry
Trigonometri

sin (ltB)=sinl cos} + cosl sinB

I B +cos (,1* B) = cos cos sin ,4 sin .B
CHOW
tan (At B) = tanA + tanB
I + tanAtanB

sinl + sin B = zrioA+ B.o. l-B

sinl -sin B = zrorAt Bri, l-B

cosl+cos B=z"orA+ B

"orA-B

cos I -cos B : -zsinA+ B rinA- B
2

sirt 2A = 2 sinl cos I

cos 2A = cos2l-sin2l

= 2 cos? A-l

=l*2sin2 A

2tanA

l*tan'A

s.mi"4 l-cos2A

2

cos'A = l+cos?A

2

cos2 x+sin2 x =1

l+tanzJ=secz.r

cotz x+l = cosec2x

SULIT QS025/1

LIST OF' MATHEMA.TICAL FORMT'LAE
SENARAI RUMUS MATEMATIK

Differentiation and Integration
Pembezaan dan Pengamiran

d,

;Ginx) = cos n

41cosr) = -sin x CHOW

d)c'

d,

fr(tanx) = sec2 x

d- - a

frGotx) = -cosec2.r

{tu1-""'; = secntan'r

fi{"oro*) = -cosecxcotx

I f'$)rr,*) dx = ,-r(x) *,

I#* = rnlr(*)l*,

=ryJ f'{,i)tf{*)ln dx + c, n * -l

!udv=uv-!vdu

32

SULIT QS025/1

LIST OF MATHEMATICAL FORMULAE

SENAMI RUMUS MATEfuIATIK

Numerical Methods
Kaidah Berangka

Newton-Raphson Method:
Kaedah Newto n-Rap h sonl

-ffi,xn+t = ., 7t =1,2,3,.... CHOW

Trapezoidal Rule:
Petua Trapezium:

! +*Io, f f*> a. f;Xro + y n) + 2(yr + yz * ...* n-r)),, =

Conics
Keratan Kon

Circle:
Bulatanz

(x-h)' +(y-k)2 = 72

*' + y' +2gx+Zfy*c = 0

xxr + yyr+ g(x+xr)+ f (y+ y.')+c =0

r= .f' + g' -"

, _loh+bk + cl

a2 +b2

33

SULIT QSo25/1

Parabola: LIST OF MATIIEMATICAL F'ORMULAE
Parubolaz SENARAI RUMAS MATEMATIK

(x-h)'=4P(Y-k)

(Y - k)' = 4P(x- h) CHOW
F(h+ p,k)

F(h,k + p)

Ellipse:
Elipst

(x-h)' _(y k), =_,t
q;'-.r
-;- b'

F{h+s,lc1

F(h,k+ s1

Yectors
Yektor

Line and Plane:
Goris dan Sataht

V:d+ti

i.fi, =d,fi

34

SULIT QS025ll

1 Evaluate 16 marks)
16 markah)
Nilailmn

l6 tan20 cos'20 d0.
I
Jo

Givenvectors p=3i-6j+ak and q = Bi-4i+5k where a and 0 we constants.CHOW

Diberi vektor p = 3i - 6j+ak dan q= Bi-4i+5k dengan a dan p adalah

pemalar.

(a) fFind the values of a and if p and q are parallel. 13 marl<s)

Cari nilai a dan p jika p dan q adalah selari. [3 markah]

(b) Given a, =1, frnd B if p and q are perpendicular. l3 marksl
13 markahl
Diberi a =1, cari B iika p dan q adalah serenjang.

Given three points P(-3,2,-l), g(1,4,5) and .it(L-2,4). Calculate the area of

triangle PQR.

Diberi tiga titik P(-3,2,--l), 8(-2,4,5) dan R(1,-2,4). Kira luas segitiga pgR.

16 marks)
16 morkahl

35

SULIT QS025/1

Detennine the vertices and foci of the ellipse 25x2 +4y2 -250x-16y+541= 0.

Sketch the ellipse and label the foci, center and vertices.

Tentukon bucu danfokus bagi elips 25xz +4y' -251x-fiy+541=A. Lakorkan elips

tersebut dan labelkanfokus, pusqt dan bucu.
l7 marksl

17 marlrah|
CHOW
Showthattheequation lnx+x-4=0 hasarootbetween I and 3.

From the Newton-Raphson formula, show that iterative equation ofthe root is

Hence, if the initial value ir ,, - 2, calculate the root correct to

three decimal places.

Tunjukkanpersamaan lnx+ x-4=0 mempunyaipunca antara I dan 3.

Daripada rumus Newton-Rophson, tunjukkan persamaan lelaran bagi punca tersebut

adalah xn*t J,IHC . Seterusnya, jika nilai awal adalah x, = Z, hitunglmn

punca tersebut betul kepada tiga tempat perpuluhan.

|l marksl
|l markah)

Show that the line 2y -5x t 4 = 0 does not intersect the circle
x' + y' +3x-2y+2=0. Find centre and radius of the circle.

Hence, determine the shortest distance between the line and the circle.

Tunjuklran garis 2 y - 5 x + 4 = 0 tidak menyilangi bulaton x' + y' + 3x - Zy + 2 = 0.

Cari pusat dan jejari bulatan tersebut.
seterusnya, tentukan jarak terdekat dntora garis dan bulatan tersebut.

ll2 marksl
ll2 markahl

36

SULIT QSo25/1

7 Giventheline t, *:2, -l-3 ., =z-! andtheplanes rr: Zx-y*Zz=17 and,

nzi -4x-3y+52=10.

Diberig-a2r-is1t-,3 *:' ,' :' dansatah rr: 2x-y*22=17 dsn
=2
fizi -4x-3y+52=10.

Find CHOW
Cari

(a) the intersection point between L and rr.

titik persilangan dntard L dan n,

f4 marlcsl
f4 markahl

(b) the acute angle between tr, and rr.

sudut tirus antarq n, dan zr.

15 marlcsJ

[5 markak]

(c) the parametric equations of the line that passes through the point (2,-t,l) and

peqpendieular to the plane nr.

persamoon berparameter bagi garis melalui titik (2,-1,3) dan berserenjang
dengan satah nr.

13 marksl
13 marknhl

37

SULIT QSO25/1

8 Ex'pres(s46-x32 x- )x(+17+x- )i'n Ipartial fra' ctions. ll2 marla)
Hence, showthat lt , u*'-,!*'--rdx=l+lnz. fiZ markahf

Jo (a-3x)(r+x)'

ffi{Jngkapkan dabm pecahan separa.

"seterusnya,tunjukkan lt (-+6-xlx2 )-(Jt++x7)'-dx=l+1n2.CHOW

Jo

9 (a) !Find the general solution of the differential equation = y'*r-".
dx
Give your answer in the form y = "f (r).

!Cari penyelesaian am bagi persamaan pembezaan ffi = ,'*r-'*.
Beri jowapan anda dalam bentuky= {(*).

16 marksl
[6 morkahJ

O) Find the particular solution of the differential 'equation +d.x3=l+=.r.,fr7,

giventhat Y=l when x=0.

Cari penyelesaian khusus bagi persamaan pembezaan +d.x*=1+.'x,'[F,
diberi !=l apabila x:A,

l7 marksl
17 markahl

38

SULIT QS025ll

10 Given the curve y2 = x and the line y = -2x +1.

Diberi lenghtng !' = x dan garis ! :4x +1.

(a) Determine the points of intersection between the curve and the line.

Tentukan titikpersilangan antara lengkung dan garis tersebut.

CHOW [3 marlcsl
13 markahf

(b) Sketch the curve and the line on the same axes. Shade the region R bounded

by the curye and the line. Label the points of intersection.

Lakarkan lengkung dan garis tersebut pada palcsi yang sama. Lorekkan

rantau R yang dibatasi oleh lengkung dan garis tersebut. Labelknn titik-titik

persilangannya.
13 marlu)

13 markahl

(c) Find the area of the region R.
Cari luas bagi rantau R.

14 marks)
14 markahl

(d) Calculate the volume of the solid generated when the region R is rotated 2r

radians about the y-axis.

Hitung isipodu bonglwhyang terjona apabila rantau R diputarkan 2n

radian pado paksi-y.
15 marlal

{5 markahl

END OF QUESTION PAPER 39
KERTAS SOAL/IN TAMAT

SIJLIT QS02512

QS025n Matematik

MilMndis Kerhs2
Papr2
Semester II
Semester II
Sesi 2017/2018
Session 2017/2018
2 hours 2 jam

KEMENTERIAN
PE,NDIDIKAI.{
MALAYSIA

BAHAGIAN MATRIKULASI

IqUTRIC UlilnON DII/EIA],{

PEPERIKSMN SEMESTER PROGRAM MATRIKULAS]
M4TNCUI.,ITION PROGMMME EXAMINANON
CHOW
MATEMATIK

Kertas 2

2 jam

I JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU.
M MNOT OPEN THIS QUESI/ON PAFER UNfiLYOIJ ARE TOI-D IO SO.

Kertas soalan inimengandungi 15 halaman bercetak, 40

Iiris gueslion paper mnssfs of 15 pintd pag,s.

@ Bahagian Matrikulasi

SULIT QS025/2

INSTRUCTIONS TO CANDIDATE;CHOW

This question papff 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 fi, e, surd, fractions or up to three significant

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

ARAHAN KEPADA CALON:

Kertas soalan ini mengandungi l0 soalan.

Jawab semua soalan,

Semuaiawapan hendaklah ditulis pada buku jawopan yang disediaknn. Gunakan muka surat
baltaru bagi nombor soalan yang berbeza.

Markah penuh yong diperuntukkan bogi setiap soalan atau bahagian soalan ditunjukkan
dalam kurungan pada penghujung saalan atau bahagian soalan.
Semua langlwh kerja hendaklah ditunjukkan dengan jelas.

Kalkulator saintiJtk yang tidak boleh diatur cara sahaja yang boleh digwnakan,

Jawapan berangka boleh diberi dalam bentuk E, e, surd, pecahan atau sehingga tiga angka
bererti, di mana-mana ysng sesuoi, kecuali jika dinyatakan dalam soalan.

41

SULIT QS025/2

LIST OF' MATIIEMATICAL FORMULAE
SENARAI RUMUS MATEMATIK

Grouped Data Ungrouped Data
Data Terkumpal Data tak Terkumpul

Persentile: loP*=L*-[(*)'-o '1, rDk _ If[''((,t),+])-/.'(,*r)',sseezz
Persentil: l

CHOW wh-ere s =:n:x: k and [s] = the least
100

integer greater than s

- s=*nxk danls)= integer

dengan

100

terkecil lebih besar daripada s

Mode: M=LM.l#*1"
Mod:

Mean: t.r,*, In,,

Min: ir---;-1 v-,=l

"{, n
i=l
-*[t-)'
Variance: ,, -Z'f'*'' -I(Zf'*')'
Varians:
n*l

Pearson's Coefficient of Skewness:
Pekali Kepeneongsn Pearson:

- _- 3(mean-median) st = 3(min-me:dfan)
sisihan piawai
"o ,t*durd dilut[i

or atau

st= mean-mode min-mod
Jr- - sisihan piawai
standard deviation

42

SULIT QS025l2

LIST OF MATHEMATICAL FORMULAE
SENARAI RUMUS MATEMATIK

Probabilify
Kebarangkalian

P(Aw B) = P(A) + P(B) - P(An B)

P(A)=t- P(A)

P(AtBp)(=A^fBf)i
CHOW
Binomial Distribution
Taburan Binomial

X - B(n,p)

f (X =x)=nC*p'(l- p)'-', x=A,1,2,3,...,n

Poisson Distribution

Tabaran Poisson

x*1@)

4=+,P(X = x =0,1,2,3,...

Normal Distribufion
Taburan Normul

X - N(p,o2)

x-z(0,1), z- X-p

43

SULIT QS025/2

I A sample of positive integers is arranged in ascending order as follows:

3x+2, 40, 4x,2y, 59,3y-9.

If the mean and median of the sample arc 49 and 47 respectively, determine the values

of x and y. Hence, rewrite the sample in ascending order.

Suatu sampel integer positif yang disusun secara menaik adalah seperti berikut:

3x+2, 40, 4x, 2y, 59, 3y-9.
Jika min dan median sampel masing-masing ialah 49 dan 47, tentukan nilai x dan y.

Seterusnya, tulis semula sampel tersebut secora menaik.

16 marksl
16 markahl
CHOW
2 Let A and B be two events where P(A')=A.7, p(B)=0.4 and p(AwB)=0.0.

Determine P(AI.B) andthenevaluate f (AlA).
Hence, state with reason whether A and B arc independent events.

Andaiknn A dan B duaperistiwadengan P(A')=0.'1, p(B)=0.4 dan

P(AwB) =0.0. Tentukan p(Aa B) dan kemudian niraikan r{aln).

Seterusnya, nyatakan dengan alasan sama ada peristiwa A dan B odalah tak

bersandar.

16 marksl
16 markalt]

44

SULIT QS025/2

3 The number of text messages received by Rosnaida during a fixed time interval is

distributed with a mean of 6 messages per hour.

Bilangan pesanan ringkas yang diterima oleh Rosnaida dalam tempoh selang masa
tertentu tertabur dengan min 6 pesanan ringkas per jam.

(a) Find the probability that Rosnaida will receive exactly 8 text messages

between 16:00 and 18:00 on a particular day.
CHOW
Cari kebarangkalian bahawa Rosnaida akan menerima tepat 8 pesanan
ringkos di antara 16:00 dan l8:0A pada suatu hari tertentu.

13 marksf
13 markahl

(b) It is known that Rosnaida has received at least 10 text messages between
l6:00 and 18:00 on a particular day, find the probability that she received
l3 text messages during that time interval.

Diketahui bahawa Rosnaida menerima sekurang-kurangnya l0 pesanan
ringkas di antara 16:00 dan l9:Oa pado suatu hari tertentu, cori
kebarangkalian bahawa dio menerima 13 pesonan ringkas dalam selang masa
tersebut.

14 marlx)
14 markah]

45

SULIT QSo2512

4 A probability distribution for discrete random variable X is as shown in the table

below

Suatu taburan kebarangkalian bagi pembolehubah rawak dislcret X adalah seperti

yang ditunjukkan dalam jadual di bm,ah

X -2 -1 0 1 2 a
J

r(x = x) p 0.1 0.3 q 0.2 p+q CHOW

pwhere p and q areconstants. If E{X)=0.65, determinethevalues of and q.

Hence, calculate the standard deviation of X.

dengan p dan q adalah pemalar. Jika E(X)= 0.65, tentukan nilai bagi p dan q.

Seterusnya, hitung sisihon piawai bagi X.
l7 marl<s)

17 markahl

5 The probability distribution function of a discrete random variable X is given as

Fungsi taburan kebarangkalian bagi suatu pembolehubah rawak diskret X diberi

sebagai

t7'

+,,/(*)= iI 34' x = 4, 5, 6, 7

0, otherwise.

selainnya.

(a) Calculate P(2<X. s).

Htung P(2sX.5).

13 marl<.s)

[3 markah]

46

SULIT QSO25I2
(b) Determine the value of Var(X).
-t)Hence, calculate the standard deviation of )z = (.fSX [7 marks]
l7 markahl
Tentukan nitat Yar(X).

fSeterusnya, hitung sisihan piawai bagi = (r6X - f ).

6 The frequency distribution for 80 employeos at a supermarket according to their dailyCHOW

wage class is as shown below.

Taburan kekerapan bogi 8A pekerja di sebuah pasoraya mengikut kelas gaji horian
adalah seperti yang ditunjukkan di bawah.

Class Boundary of Daily Wage (RM) Frequency
Sernpadan Kelas Gaji Hariaf, (RM) Kekerapan

t5 -20 4
20 -25
25 -30 t2
30-35
35-40 20
32
4A-45
8

4

(a) Find the median and standard deviation of the sample.
Cari median dan sisihan piawai bagi sampel tersebut.

16 marks)
16 markaltl

47

SULIT QS025/2

(b) Calculate and interpret the Pearson's coefficient of skewness for the data.

Hitung dan tafsir pekali kepencangan Pearson bagi data tersebut.
[4 marlrs]

[4 markah]

(c) Determine the daily wage * where 80% of the workers eam at most fr ringgit

per day.

Tentukan gaji harian k yong mana 80o/o daripada pekerja itu memperoleh

poling banyak k ringgit seltari.
12 marl*l

12 markahl
CHOW
A box contains 12 cups of similar size and shape but in different colours. There are 5
blue cups, 4 red cups and 3 yellow cups. A rack can only take up 6 cups. In how many

ways can

Sebuah kotak mengandungi 12 bualt cawon yang sama soiz dan bentuk tetapi dengan
warna yang berbeza. Terdapat 5 cawan biru, 4 cawan merah dan 3 cowon kuning,
Sebuah rak hanya boleh menampung 6 buah cowan. Dalam berapa cara boleh

(a) any 6 cups be placed on the rack?
sebarang 6 buah cswan diletak di atas rok tersebut?

12 morlul
12 markahl

(b) an equal number of colored cups that could be placed on the rack?

cqwan dengan bilangan yang sama bagi setiap warna diletak di atas rak

tersebut?

[3 marksl
13 markahl

48

SULIT QSO25'2

(c) an equal number of colored cups that could be placed on the rack with cups of

the same colour being side by side?

cawan dengan bilangan yang soma bagi setiapwarna diletak di atas rak
tersebut dengan cowan yong sotna warna mesti sebelah menyebelah?

[3 marks)
[3 markah)

(d) an equal number of yellow and red cups be placed on the rack?CHOW

cawan kuning dan merah yang sama bilangan diletak di atos rak tersebut?
14 marlxl

14 markahl

49

SULIT QS025/2

8 A survey was implemented on 400 students at a private university in order to collect

information on the popular choice of minor subjects (Language, Statistics and
Information Technology) by students of various major of study (Medicine,
Engineering and Economics). The following table describes the data collected from
the survey.

Satu kait selidik telah dilaksanakan terhadap 4A0 pelajor di sebuah universiti swasta
untuk mengumpul maklumat mengenai pilihan mata pelajaran minor yang popular
(Bahasa, Stotistik dan Telcnologi Maklumat) oleh pelajar daripada Jtelbagai
pengkhususan pengajian (Perubatan, Kejuruteraan dan Ekonomi). Jadual berikut
memperihalknn data yang dikumpul daripada kaji selidik tersebut.
CHOW
Major Medicine Engineering Economics Total
Perubatan Kejuruteraan Ekonomi Jumlah
Pengkhususan
140
Minor 50
Minor
210
Language 30 80 30
Bahasa 400

Statistics 10 30 10
Statistik

Information

Technology 60 124 30

Tebtologi Maklumat

Total 100 230 70
Jumlah

50