assignment math matrikulasi sm025

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Update: 03/12/2019

CHOW CHOON WOOI

Kolej Matrikulasi

SM025 Mathematics

Rationale of the course.

This course is to equip students with knowledge of mathematics and the ability to solve problems and propose solutions using mathematical terms, notation, principles and methods to pursue education in the field of science and technology.

Course Learning Outcomes (CLO)

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Matriculation Notes (Semester 1)

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MOCK UPS 1 (PART 1)

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Chap 1: Integration

Chap 2 : First Order Differential Equation

Chap 3 : Numerical Methods

Chap 4 : Conics

Chap 5 : Vectors

Chap 6 : Data Description

Chap 7 : Permutations and Combinations

Chap 8 : Probability

Chap 9 : Random Variables

Chap 10 : Special Probability Distribution

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Mathematics (Matriculation)

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Kedah Matriculation CollegeKWKANG Mathematics (Matriculation) From 2003/2004 To 2018/2019 KANG KOOI WEI Exam Papers Collection Year KWKANG 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 KWKANG MATRICULATION MATHEMATICS SM025 2018/2019 3 KWKANG 4 KWKANG 5 KWKANG 6 KWKANG 7 KWKANG 8 KWKANG 9 KWKANG 10 KWKANG 11 KWKANG 12 KWKANG 13 KWKANG 14 KWKANG 15 KWKANG 16 KWKANG 17 KWKANG 18 KWKANG 19 KWKANG 20 KWKANG 21 KWKANG 22 KWKANG 23 KWKANG 24 KWKANG 25 KWKANG 26 KWKANG 27 PSPM 2 KWKANG 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 KWKANG KE,ME,NTE,RIAN PENDIDIKAN MAIAYSIA BAHAGIAN MATRIKULASI I,I4TNC UIATTON DIVNION PEPERIKSMN SEMESTER PROGRAM MATRIKULASI i,L4TNCUL,ITION PROGMMME EYAMINATION 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:KWKANG 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 KWKANG 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 KWKANG 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,.... KWKANG 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) KWKANG 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.KWKANG 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| KWKANG 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 KWKANG 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.KWKANG 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. KWKANG [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 KWKANG KEMENTERIAN PE,NDIDIKAI.{ MALAYSIA BAHAGIAN MATRIKULASI IqUTRIC UlilnON DII/EIA],{ PEPERIKSMN SEMESTER PROGRAM MATRIKULAS] M4TNCUI.,ITION PROGMMME EXAMINANON 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;KWKANG 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 KWKANGwh-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)KWKANG P(A)=t- P(A) P(AtBp)(=A^fBf)i 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:KWKANG 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 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. KWKANG 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 KWKANG 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 dailyKWKANG 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 ringgitKWKANG per day. Tentukan gaji harian k yong mana 80o/o daripada pekerja itu memperoleh poling banyak k ringgit seltari. 12 marl*l 12 markahl 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?KWKANG 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. KWKANG 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

AKU BUDAK MATRIKULASI

Search this blog, lecture note mathematics matrikulasi semester 2 sm025.

 NOTA KULIAH MATEMATIK SEMESTER 2 MATRIKULASI KPM

CREDIT : 

• Chapter 1 : Integration
• Chapter 2 : First Order Differential Equation
• Chapter 3 : Numerical Methods
• Chapter 4 : Conics
• Chapter 5 : Vectors
• Chapter 6 : Data Description
• Chapter 7 : Permutations & Combinations
• Chapter 8 : Probability
• Chapter 9 : Random Variables
• Chapter 10 : Special Probability Distribution

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