PSPM 1 Exam Papers Collection

QS015/1

LIST OF MATHEMATICAL FORMULAE

Quadratic equation m2 +bx+c =0:,

*--ut'[* -+*
2a

Arithmetic series: CHOW CHOON WOOI

Tn = o+(n-t)d

s, =llzo+(n-r)dl

Geometric series:

Tn = arn-\

t,=ffl*l

Sum to infinity:

s. =r_",lrl<t
\- Binomial expansion:

(a+b)'=an +(:)"",.(;)"-,uz + ..+(:)"-,. + ..+bn,

where neN and(:)=@+W

*(t + ax), = t + n(m). t*f * n(n -t)(n - z) (*)' * ...

laxf <t where neZ- or n eQ

151

QS015/1

1 [; -" *. dGiven matrice, ,n=
r,*3l , =1" l.l. the values of c, and,e
looz) [o;,)
"such that AB: 14 .I, where .I is the identity matrix. Hence, determine l-r.

16 marksl

2 Consider the function f (*)= I + ln x, x) l. Determine -f-t (x) and state its range. CHOW CHOON WOOI
Hence, evaluate f'(3).

16 marksl

3 Find the value of x which satisfies the equation

logrx=(log, x)2, x>1.

l7 marksl

4 Solve the equation 22x-2 -T*t =2' -23.

17 marksl

5 #,Given g(x) = - * lwhere fr is a constant.

(a) Find the value of /r if (g. S)(r): r.

(b) Find the value of & so that g(x) is not a one-to-one function. 15 marksl
15 marksl

152

QS015/1

6 f(rt:Given e3' + 4, x e "R.

(a) Find /-r(x).

15 m.arksf

O /(r)On the ffurre axes, skctch the graphs of arrd 7-t (x) . State the domain of CHOW CHOON WOOI

"f(x) and ,f-'(;),

16 marlcsl

4-2i 4+2i 2

16 narkd

(b) Given logo2=ril atrd lo&u7=z. Expressr intemsof n and n if

(l4t*txs'*)= z'

16 marksl

153

QS015/1 CHOW CHOON WOOI

8 An osteoporosis patient was advised by a doctor to take enough magnesium,

vitamin D and calcium to improve bone density. In a week, the patient has to take
8 units magnesium, I I units vitamin D and 17 units calcium. The following are three
types of capsule that contains the three essential nutrients for the bone:

Capsule of type P: 2 units magnesium, 1 unit vitamin D and I unit calcium.

Capsule of type Q: I unit magnesium, 2 units vitamin D and 3 units calcium.

Capsule of type R: 4 units magnesium, 6 units vitamin D and l0 units calcium.

yLet x, and z represent the number of capsule oftypes P, Q andR respectively that

the patient has to take in a week.

(a) Obtain a system of linear equation to represent the given information and write
[,]

the system in the form of matrix equation AX = B, where X =ltty l.
lz)

13 marks)

(b) Find the inverse of matrix,4 from part (a) by using the adjoint method. Hence,
findthevalues of x,y and z.

[8 marks]

(c) The cost for each capsule of type P, Q andrR are RMl0, RMl5 and RMlT

respectively. How much will the expenses be for 4 weeks if the patient follows

the doctor's advice?

12 marl<s)

11

154

QS015/1 CHOW CHOON WOOI

9 (a) In an arithmetic progression, the sum of the first four terms is 46 and the

seventh term exceeds twice of the second term by 5. Obtain the first term and
the common difference for the progression. Hence, calculate the sum of the
first ten even terms of the progression.

16 marl<s)

(b) A ball is dropped from a height of 2 m. Each time the ball hits the floor, it
]bounces vertically to a height that is of its previous height.

4

(i) Find the height of the ball at the tenth bounce.

12 marksl

(ii) Find the total distance that the ball will travel before the eleventh

bounce.
15 morksl

10 (a) Find the solution set of lZ -lxl < lx + 31. 18 marlal

(b) If x+1< 0, show that 13 marlcsl
(i) 2x-l<0. 14 marksl

(ii) #,r.

END OF QUESTION PAPER

13

155

QS015/2 QS015,2
Mahematia
Matematik
Papr2
Kertas 2
ISemester
Semester I
Session 201 3/2014
2 hours Sesi 2013/2014

2 jam

BAHAGIAN MATRIKULASI CHOW CHOON WOOI
KEMENTERIAN PENDIDIKAN MALAYSIA

M4TRICWTIONDIVNION
MINNIRY OF EDUCANON MAI-4WA

PEPERIKSMN SEMESTER PROGMM MATRIKULASI
MATNC UIANON PROGMMME FX,4MINANON

MATEMATIK

Kertas 2
2 ja,m

I NJANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU.
NOT OtrN 7HlS 8UES77ON PAPER UAINLYOU ME TUD IO DO SO.

I

Kertas soalan ini mengandungi 19 halaman bercetak.
This question paper oonsrsfs of 19 pinted pages.

O Bahagian Matrikulasi

156

QS015l2

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 CHOW CHOON WOOI

question.

The firll 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, surd, fractions or up to three significant

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

157

QS(lr5/2

LIST OF' MATHEMATICAL tr'ORMULAE

Trigonometry

sin (l t B) = sin,4 cos B + cos,4 sin B

I +cos (; t B) = cos cos .B sin,4 sin.B CHOW CHOON WOOI

tan (A+.8) = tanA + tan8

1 + tanAtanB

sinl + sinB : 2 rinA+ B ro"A-',

sin,{ - sinB : 2 "orA* B *inA- B
cosl * cos B =2 "orA* B "or4- B
cosr4 - cos B : -2 rinA* B "inA- B

sin 2A=2sinA cosl

cas 2A = cos2 A-stnz A

= 2 cosz A-l

= l-2sinz A

tan 2A = 2tanA
l-tanz A

l-cosZA

gin2 A =

2

l+cos2A
cos' A =

2

158

QS015/2

LIST OF MATHEMATICAL FORMULAE

Differentiation

f(.) f'(*)

cot x )

- cosec"x CHOW CHOON WOOI

xsec sec x tan x

cosecx -cosecxcotx

If x= f (t) ana t = s(t), then !dx= 4dt*Ldx

d(dv\

dd2xyz=!,aldAx )

Sphere Y=!n'3 S=4nr2

Right circular cone V =: nr2h $ = nrs
3
S =2nrh
Rightcircularcylinder V = r,r2h

159

QS01s/2

I Expr.r,x,f+3x+2 in partial fractions form.

15 marksl

2 Statethevaluesof Rand a suchthat 3sind+6cosd=r?sin(9+a) where R>0 CHOW CHOON WOOI

and 0" <a<90". Hence, solve 3sind+6cosd=.rE for 0 <0<180".

16 marksl

\- 3 (a) Findthevalue of m if ti* T**?t =1.

r-+0 4x -8X'

(b) E-6. 13 marl*l

Evaluate rr-ir+n0 X 14 marks)

4 (a) LFind if y =cosec{sin[rn(x+r)]].

13 marksl

tive of y = cos3x and express your answer in the
(b) deriva fObtain the second

simplest form.

[4 marks]

160

QS015/2 CHOW CHOON WOOI

5 A cubic polynomial P(x) has remainders 3 and I when divided by (, - 1) and

(x -2), respectively.

(a) Let Q@) be a linear factor such that P(x) = (x - 1)(x -2)Q$) + ax + p,

where a and B are constants. Find the remainder when P(x) is divided by
(x -t)(x -2).

15 marlcsl

(b) Use the values of a and B frompart (a) to determine Q(x) if the coefficient

of x3 for P(x) is l and P(3)=7. Hence,solvefor x if P(x)=7-3x.

16 marlesl

11

161

QS015/2

6 (a) State the definition of the continuity of a function at a point. Hence, find the

value of d such that

f(x\=[,"'*o' x<o

[3x+5, x>0

is continuous at x = 0. [5 marl<s] CHOW CHOON WOOI

(b) /A tunction is defined by

f (x)={;,,_;,, ;:i 13 marksl
14 marksl
/Determine the value(s) of fr if is:
(D continuous for all x e IR.

(ii) differentiable for all x e lR.

13

162

QS015/2

7 (a) *Find the derivative of /(x) = by using the first principle.

(b) Use implicit differentiation to find: [4 marks) CHOW CHOON WOOI

(i) ! x ykrx=e'-!. 13 marksl
frc 15 marksl

(ii) thevalue $+&ciyf x12- I =3 when r=1.

I A curve is defined by parametric equations
r=ln (l+r), | = e" for / >-1.

(a) #Find Le *o interms of t.

16 marksl

O) Show that the curve has only one relative extremum at (0,1) and determine

the nature of the point.
16 marlal

15

163

QS01s/2

(a) A cylindrical container of volume l28n m3 is to be constructed with the same

material for the top, bottom and lateral side. Find the dimensions of the

container that will minimise the amount of the material needed.

16 morl<sl

(b) Gravel is poured onto a flat ground at the rate of * -' per minute to form a CHOW CHOON WOOI

20

conical-shaped pile with vertex angle 60o as shown in the diagram below.

Compute the rate of change of the height of the conical pile at the instant
/ = l0 minutes.

l7 marksl

17

164

QS015/2 14 marl<sl

ro (a) show,n"ffiffi=*r(ry)

(b) Use trigonometric identities to verify that

(D ztan9 CHOW CHOON WOOI

sind: 2

l+tarr'9'
2

13 marlxl

r-tarf q

(iD cosd =

l+tarr'9'
2

13 marlal

Hence, solvetheequation 3sind+cosd =2 for 0 <e <180'. Giveyour

answers correct to three decimal places.

15 marl<sl

(.*
END OF QUESTION PAPER

19

165

2014/2015

166

CHOW CHOON WOOI

QS015/1 QSo15/1
Mahematix
Paperl Matematik

ISemester Keftas 1

Session 2014/2015 Semester I
2 hours
Sesi 2014/2015

2 iam

KF.ME,NTE,RtAN CHOW CHOON WOOI

PENDIDIKAN
MATAYSIA

BAHAGIAN MATRIKULASI

M4TRICU- TTON DIVBION

PEPERIKSMN SEMESTER PROGMM MATRIKULASI
IT UTNCULAfiON PROGRAIUIME EXAMINATION

MATEMATIK

Kertas L
2 jam

JANGAN BUIG KERTAS SOALAN INISEHINGGA DIBERITAHU.

N NOTOPEN IHISQUESI/ON PAPERUNNLYOU ARETOLD IODOSO.

Kertas soalan ini mengandungi 13 halaman bercetak.

This question papermrsfs of13 pnhfedp4ges.

167@ Bahagian Matrikulasi

QSo15/1 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 fi, e, swd, fractions or up to three significant
figures, where appropriate, unless stated otherwise in the question.

163 8

QS01s/1

LIST OF MATHEMATICAL FORMULAE

Quadratic equation ax' + bx + c = 0'. CHOW CHOON WOOI

*--ott[o'-+*
2a
Arithmetie series:

T,=o+(n-a)d

s,=;Ba+@-a)dl

Geometric series:
Tn = arn-l

s,=ff,r*r

Sum to infinity:

S''-=14-r .rl <l

'

Binomial expansion:

(a + b)' = on +(i).".(;)o'u' + .(i)"-'u' + + b' ,

where neN *d [f'r)/ - (n n''
- r)tr
r.

(t + ax)' = ! + n(ax). @?b-y * n(n - D@ - 2)-(*I * . .

laxl<t where neZ-orneQ

165 9

QS01il1

I Solve the equation 3' +3G-*) =12.

16 marl<s)

2 Soive the inequality +6-x . -x]--l CHOW CHOON WOOI

16 marks)

[r o ol [r o ol

l, r-l v3 Givenmatrices a=l + I 0 I and B=l z I 0 I where B istheinverseof A.
b L, rj

Find x, "y and e in terms of a and b.

16 marlrsl

4 Using algebraic method. find the least value of n for which the sum of the first n terms

of a geometric series

0.88 + (0.88)'] - (0.88)3 + (0.88)a +...

is greater than half of its sum to infinity.
[7 marlu]

5 (a) State the interval for r such that the expansion for (4 + 3r)i 1, valid.

[2 marksl

(b) *lt1iExpand {+ in ascending power ofx up to the term in 13.

14 marlul

(c) Hence, by substifuting an appropriate value ofx, evaluat. 1S;i correct to three

decimal places.

14 marlcsl

1770

QSo15/1

6 (a) Given f(*)=2x+l and g(r) =x'+2x-1.

(i) Find (/ - g)(x). [2 marksl CHOW CHOON WOOI
14 marksl
(ii) Evaluate (3s -zf)(t).

(b) EGiven .f (*) = state the domain and range of /(r).

Hence, on the same ixes, sketch the graph of /(x) and f-t(x).

16 marlal

7 lr;t z = a+bi be a nonzero complex number.

ft(a) !show that =

14 marks)

O) Show that if i = -2, then z is a complex number with only an imaginary part.

13 marlal

(c) Find the value of a and b if z(2-i) =(i+1)(t+;).

15 marksl

1I 71

QSo15/1

8 (a) Solve the following equation le*, +x_l tl= +.

(b) Find the solution set for the inequality 16 marlu)
l7 marlesl
( x+2\ _ CHOW CHOON WOOI

2-l
\x-t-<4)).

9 Two companies P and Q decided to award prizes to their employees for three work

ethical values, namely punctuality (x), creativity (y)and efficiency (e). Company p

decided to award a total of RM3850 for the three values to 6, 2 and3 employees

respectively, while compary Q decided to award RM3200 for the three values to

4' I and 5 employees respectively. The total amount for all the three prizes is

RMl000.

(a) Construct a system of linear equations to represent the above situation.

13 marksl

(b) By forming a matrix equation, solve this equation system using the elimination

method.

[7 marks\

(c) with the same total amount of money spent by company p and e, is it possible

for company P to award 15 employees for their creativity instead of 2
employees? Give your reason.

13 marla)

11172

QSo15/1

l0 (a) Determinewhether f(x)=* *O g(x)= T areinversefrurctionof

each other by computing their composite functions.

[5 marks)

(b) Given .{(x)=ln(l-3r). CHOW CHOON WOOI

(1) Determine the domain and range of f (x). Then sketch the graph of

f (x).

[6 marks]

(ii) Find /-r(x), if it exists. Hence, state the domain and range of f-t(x).

[4 marks]

END OF QUESTION PAPER

113 73

QS015/2 QS015/2

Mathematia Matematik

Papr2 Kertas 2

ISemester Semester I

Session 2014/2015 Sesi 2014/2015
2 hours
2 jam

KEN,IENTERIAN CHOW CHOON WOOI

PENDIDiKAN
MALAYSIA

BAHAGIAN MATRIKULASI

M4TRICUATION DIVNION

PEPERIKSMN SEMESTER PROGRAM MATRIKULASI
II,IATNC UIATTON PRrcMMME EXAMINATION

MATEMATIK

Kertas 2
2 jam

JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU.
DONOTOPEN THIS QUESflON PAPERUNNLYOU ARE IOLD IODOSO.

Kertas soalan ini mengandungi 15 halaman bercetak.
This quxlbn paperconsisfs of 15 pinted pages.

@ Bahagian Matrikulasi

174

QS015/2 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 tr, e, stJrd, fractions or up to three significant
figures, where appropriate, unless stated otherwise in the question.

1735

QSo15/2

LIST OF MATHEMATICAL FORMULAE

Trigonometry

Isln (e+ A)= sin,4 cos .B + cos sin.B CHOW CHOON WOOI

(exA)=cos AcosB + sinl sinB

tan (A+ B) = tanA * tan B

1 + tanAtanB

sin I + sin B: 2 ,inA+2B2 "orA- B

sinl - sinB: 2 B rinA- B
"orA*22

cosA* cos B:2 B B

"o"A*22 "rrA-

cosA- cos B : -2 rinA+ B ,inA- B

sin2A=2sinAcosA

cos 2A= cos2 A-sin2 A

= 2 cos2 A-l
= l-Zsin2 I

tan 2A= 2tan 4

l-tar," A

sinz A = l-cosZA

2

cos' A = l+cos2A

175 6

QS015/2

LIST OF MATHEMATICAL FORMULAE

Limit

li* si'ft = I CHOW CHOON WOOI

h-+0 h

hlm+0l-cohs fr =0

Differentiation

f(*) "f'(*)

cot x - cosec2,
xsec
sec x tan x

cosecr -cosec xcotx

*"*rf y =g(r) and * = fk), tnen ff=

d(dv\

dd'xv2-AldAx )

dr

Sphere V A nr3 S = 4nr2

=1 =g rE rs
J -,S 2 nrh

Right circular cone Y =! nr2h
3

Right circular cylinder V = nrzh

1777

QSo15/2

Given that (x-2) is afactot of thepolynomial "f(*)= axt -l}x' +bx-2 where
a and b arc real numbers. lt f (x)is divided by (x + 1) the remainder is -24,
find the values of aand D. Hence, find the remainder when /(x) is divided

by(2x+1).

16 marksl

2 Solve the equation 2cos2 x -l =sinx for0 I x 12n. Give your answer in terms of a. CHOW CHOON WOOI

16 marksl

3 Find the relative extremum of the curve ! = x3 -4x2 +4x.

16 marksl

Car X is travelling east at a speed of 80 km/h and car Y is travelling north at 100 km/h
as shown in the diagram below. Obtain an equation that describes the rate of change
of the distance betlr,een the two cars.
Hence, evaluate the rate of change of the distance between the two cars when
car X is 0.15 km and car Y is 0.08 km from P.

Car X

[7 marks)

1789

QSo15/2

Expand (x+a)(x+ b)' , o and b are real numbers with b > 0. Hence, find the

values of a and b if (x+ a)(x+b)'=*t -3x-2.

-Express #xo -4x'+5x-l in the form of partial fractions.
x'-3x-2

ll2 marksl CHOW CHOON WOOI

(a) Express sin 6x - sin 2x in a product form. Hence, show that [6 marlcsl
l7 marksl
sin 6x - sin2x + sin 4x = 4 cos 3r sin 2x cos x .

(b) Use the result in (a) to solve

sin 6x - sin 2x + sin 4x = sin 2x cos x
for 0<x<180".

7 Find the limit of the following, if it exists.

-.(a) lx[--f>l-.3-_vrx+q)3J

(b) l.l.m--Z--:x.-l 13 marksl
x+-* *z -g 13 marks)
r ^f 14 marksl

l,

(c) l,xl.m+4x',-l/3X- x_2-4 .

17911

QSo15t2 x<0
0<x<4
lt+r-,
x>4
8 lr-,Given rhat /(,r)= ]-
lc,
u'here C isaconstant.

(a) Determine whether /(x) is continuous at x = 0. CHOW CHOON WOOI

15 marksl

(b) fGiven that (x) is discontinuous at x = 4, determine the values of c.

13 marksl

(c) fFind the vertical asymptote of (x).

14 marksl

18103

I

QS015/2

9 Consider the parametric equations of the curve

.tr=cos30 and y=sin30, 0<0<2r.

(a) Find 4L and express your answer in terms ofd.

dx

(b) Find the value ot Ldxf4f x =O 14 marksl CHOW CHOON WOOI
14 marksl
- 44dxz(c) Show ,,nur 3 cosa 0 sin?' [5 marksl
15 marksl
*iHence, calculate " 0 =L
ll0 marksf
(a) J;.10 Use the first principle to find the derivative ofg(x) =

(b) Given that ev + xy +ln{l+Zx) =1, x > 0.

lff ffishow that (ev *
*,' (U*)' . rff- =o

#Hence, find the value "f at the point (0,0).

END OF QUESTION PAPER

18115

2015/2016

182

CHOW CHOON WOOI

QS()I5I1 QS015/1

Mathendix Matematik

Paprl Kertas 1

ISemester Semester I

Session 201 5/2016 Sesi 2015/2016
2 hours
2 jam
I
KEMEI{TE,RIAI{ CHOW CHOON WOOI
PEI{DIDIKAI\J
MALAYSIA

BAHAGIAN MATRIKI]LASI

&vI,4TNCUI-ATIONDIVNION

PEPERIKSMN SEMESTER PROGRAM MATRIKULASI
I,L4TRICU-,IffiON PROGMMME FXAMINAITON

MATEMATIK

Kertas 1

2 jam

JANGAN BUI(A KERTAS SOALAN INI SEHINGGA DIBERITAHU.
DO NOIOPEN IHIS QUESI/ON PAPERUMILYOU /RE IOLO IO DO SO,

Kertas soalan ini mengandungi 13 halaman bercetak.
This question paper consisfs of 13 prhfedpryes.

183@ Bahagian Matrikulasi

QS015r1 CHOW CHOON WOOI

ARAHAN KEPADA CALON:
Kertas soalan ini mengandungi 10 soalan.

Jawab semua soalan.
Semua jawapan hendaklah ditulis pada buku jawapan yang disediakan. Gunakan muka surat
baru bagi nombor soalan yang berbeza.
Markah penuh yang diperuntukkan bagi setiap soalan atau bahagian soalan ditunjukkan
dalam kurungan pada penghujung soalan atau bahagian soalan.
Semua langkah kerja hendaklah ditunjukkan dengan jelas.
Kalkulator saintifik yang tidak boleh diprogramkan sahaja yang boleh digunakan.
Jawapan berangka boleh diberi dalam bentuk rr, e, surd, pecahan atau sehingga tiga angka

bererti, di mana-mana yang sesuai, kecuali jika dinyatakan dalam soalan.

1284

QSo1$1 CHOW CHOON WOOI

INSTRUCTIONS TO CANDIDATE:
This question paper consists of 10 questions.
Answer all questions.
All answers must be written in the answff 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 E, e, stmd, fractions or up to three significant
figures, where appropriate, ucless stated otherwise in the question.

1385

QS015/1

SENARAI RUMUS MATEMATIK

Persamaan kuadratik m2 +bx+c=0: CHOW CHOON WOOI

_u*ly

2a -aac

Siri aritmetik:

To = Q+(n-l)d

s, =Lrlzo+(n*I)d)

Siri geometri:
To: arn-l

t,=ffl+t

Hasil tambah infiniti:

s*=fi,lrl<t

Kembangan Binomial:

(a+b)' =an +(i).-'r.(;)o-,u,. .[, an-'/b'i +...+bn,

dengan neN.*fi =@+i-il

rP(t + ax)n = r + n (ax). t*12 * n (n - \{n - z) (*), * ...

lo*l.l dengan neZ- atau n eQ

1486

QSo1s/1

LIST OF MATIIEMATICAL FORMULAE

Quadratic equation mz +bx+c=O:, CHOW CHOON WOOI

-b + "[b' 4a;

2a

Arithmetic series:

Tn = a+(n-l)d

S, = !12.a + (n _t)d1

Geometric series:

T' = or'-1

J.,=Jraf+(ll- r')

I-r

Sum to infinity:

s." =fr, lrl<r

Binomial expansion:

(a+b). =,. .(l o.u.(;)on-z6z+...+ (",)o-u, +...+b.,

, ,where
ne'N' "*.d'- fl,"l)= n! r !.

(n-r)!

(t + ax)n = t + n(ax).$ r*)' * n(n-t)(n-z) (*)' *...
3!

laxl<t where rceZ- orreQ

1587

QS(l15/1

1 Nilaikan penyelesaian bagi 4v-2 =5|. ,.ninega tiga tempat perpuluhan.

[6 markahl

2 Tiga sebutan pertama bagi suatu jujukan geometri adalah[i- - z), {z*-t) dan tz. CHOW CHOON WOOI

Tentukan rulai rn. Seterusnya, cari sebutan yang keenam bagi jujukan ini.
16 markahf

3 Selesaikan persamaan

2+log, x =!51o9,2.

17 markah)

lt x -11
4 (a) Tentukannilaixrrrurul, 0 I ladalahsingular.

[, 3 -r.]

(b) rikar=L[:l 2]l Jo*.8='L[r; 4'rll'tuti c aPabila A=BCB-|'

17 markahl

5 (a) Kembangk an (2+ x)- 1 dalam kuasa menaik x, sehingga sebutan .r3.

15 markahl

(b) ^ E.Guna kembangan di (a) untuk menganggark

15 markahl

1688

QSo1$1

1 +Evaluate the solution of 4v-2 = )' up to three decimal places.

[6 marl<s]

z The first three terms of a geometric *"sequence (1*-Z), tZ*-1) and 12. CHOW CHOON WOOI

Determine the value of m . Hence, find the sixth term for this sequence.

[6 marks]

3 Solve the equation

2 +1og, x = 15 1og,2.

17 marks)

4 (a) [l ;*",Determine the values of x so ]'-l ,, singeular.
[r 3 -r]

[i [l(b) ,r , = ;] *. , = 1], *u c when A= BCB-,

17 marksl

5 (a) Expand (2+ x)_12 in ascending powers of x, up to the term x3.

15 marksl

O) EUse the expansion in (a) to approximat "

15 marksl

187 9

QSo15/1

6 Diberi zt=3-3f dan zz=3*2i.
(a) Tuliskan ,, a*at rbentuk polar.

(b) ' @1.3fZlUngkapkanl-r, ) dalam bentuk a+bi, a,6 e IR. 14 markah| CHOW CHOON WOOI
l8 markahl

7 Suatulengkung !=axz+bx+c yangmana a,b danc adalahpemalar,melalui

titik-titik (2,11), (-1,-16) dan (3,28).

(a) Dengan menggunakan maklumat di atas, bina satu sistem yang mengandungi

tiga persamaan linear.

13 markah)

(b) ungkapkan sistem di atas sebagai satu persamaan matriks AX = B,

ll markah)

(c) ICari songsangan bagi matriks dengan menggunakan kaedah matriks adjoin.

Seterusnya, dapatkan nilu a, b dan e.

l8 markah)

8

190

QS()15r1

6 Given Zr=3-3i and zz=3*2i.

(a) Write z, in polar form.

(b) 'Express yl;"?*\{I-1l " \ in.t. form a+bi, a,beF.. 14 narksl CHOW CHOON WOOI
13 \-r, ) l8 marlcsl

1 Acurve !=axz +bx+c where a, b and c areconstants,passesthrough

thepoints (2,11), (-1,-16) and (3,28).

(a) By using the above information, construct a system containing three linear

equations.
13 marksl

(b) Express the above system as a matrix equation AX = B.

lT mark]

{c} Find the inverse of matrix .4 by using the adjoint matrix method.

Hence, obtain the values of a, b and c.

18 marltsf

9

191

QSo15/1

8 Diberi tungsi f (*) : Ji 1x.

(a) fTunjukkan bahawa adalah fungsi satu ke satu.

12 markahl

(b) Cari domain dan julat bagi f . CHOW CHOON WOOI

f3 markahl

(c) /Tentukan fungsi songsangan bagi dan nyatakan domain dan julafrrya.

f4 markalz)

(d) f-tLakarkan graf bagi .f dw padapaksi yang sama.

[3 markah]

9 (a) Fungsi / diberi sebagai -f (x) =93!x:-24, ' * t1,

3

Jika (f . "f)(x) = x, cari nilai a.

16 markah)

(b) Katakan -f (x) = hl3x + 2l dan g(x) = e-' +2 adalah dua tungsi.

Nilaikan (g.,f)-'(3).

{7 markahl

11092

--r

QS()15/1

8 Given a tunction f (*)=,13-2l-.

(a) fShow that is a one to one function.

[2 marks]

(b) /.Find the domain and range of CHOW CHOON WOOI

[3 marksl

(c) /Determine the inverse function of and state its domain and range.

14 marlcsl

(d) / f-tSketch the graphs of and orthe same axis.

13 marksl

9 (a) /The tunction is given as f(x)=#, -*:. 16 marlul
[7 marlxl
If ("f . "f)(x) = x, find the value of a.

(b) Let f (x) = hl3x +21 md g(x) = e-* +2 be two functions.

Evaluate (8 " ,f)-'(3).

1191 3

QSo15'1

10 (a) * l4lSelesaikan ketaksama r r.

lx+31

16 markahl

(b) Tunjukkan U1=2". CHOW CHOON WOOI

Seterusnya, cari seellaanngg bbaaggi x ssru.pa,ya !:{-13(2-)+36>0.
g,

19 markah)

KERTAS SOALAN TAMAT

11294

QSo1s/1

10 (a) l+lSolve the inequal* , r.

16 marks)

(b) Show sr6L!1=2". CHOW CHOON WOOI

l!'-Hence, find the interval for x so tt ut 2' -13(2')+ 36 > 0.
8',

19 marksl

END OF QUESTION PAPER

11395

QS015/2 QSo15i2

It*:runatix Matematik
PWr2
Kertas 2
ISemester
Semester I
Session 2015/2016
Sesi 2015/2016
2 hours
2 jam

I KEMENTERIAN CHOW CHOON WOOI
PENDIDIKAN
MALAYSIA

BAHAGIAN MATRIKULASI

A,TATRICULATTON DIVNION

PEPERIKSMN SEMESTER PROGMM MATRIKULASI
M4TRICUfuLNON PROGRAMME EXAMINATION

MATEMATIK

Kertas 2

2 jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU.
DO NOTOPEN IHISQUESI/ON PAFERUMILYOU ARETOLDTO DO SO,

Kertas soalan ini mengandungi 15 halaman bercetak.
Iha gueston paper mnsbfs of 15 pinted pryes.

@ Bahagian Matrikulasi

196

QS015l2 CHOW CHOON WOOI

ARAHAN KEPADA CALON:
Kertas soalan ini mengandungi 10 soalan.

Jawab semua soalan.
Semua jawapan hendaklah ditulis pada buku jawapan yang disediakan. Gunakan muka surat
baru bagi nombor soalan yang berbeza.
Markah penuh yang diperuntukkan bagi setiap soalan atau bahagian soalan ditunjukkan
dalam kurungan pada penglrujung soalan atau bahagian soalan.
Semua langkah kerja hendaklah ditunjukkan dengan jelas.
Kalkulator saintifik yang tidak boleh diprogramkan sahaja yang boleh digunakan.
Jawapan berangka boleh diberi dalam bentuk ?E, e, st)rd, pecahan atau sehingga tiga angka

bererti, di mana-mana yang sesuai, kecuali jika dinyatakan dalam soalan.

2

197

QSo15/2 CHOW CHOON WOOI

INSTRUCTIONS TO CANDIDATE:
This question paper consists of I0 questions.
Answer all questions.
All answers must be written in the answer booklet provided. Use a new page for each

question.
The fuII 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 tT, e, surd, fractions or up to three significant

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

3

198

QSo15/2

SENARAI RUMUS MATEMATIK

Trigonometri

I I+Sln (Z* A)= sin cos .B cos sin B

(ex a) = cos A cos B + sinl sin B CHOW CHOON WOOI

tan (A* B) = tanA + tanB
1 + tanAtanB

sinA+sin,B: 2rioA+ B B

"orA*

sinA -sin.B : 2 "r"A* B *inA- B

Icos * cos B:2 "orA* u "orA- B

lcos - cos.B : -2 rioA* B "inA- I

sin2A=2sinAcosA

cos 2A = cos2l -sinz A
= 2 coszA-l
= l-Zsin2 A

tan2A = 2 tanA

l-lrrfi A

sinz A = l-cos2A

2

cos'A = l+cos2A

2

1499

QS01sl2

LIST OF MATHEMATICAL FORN{ULAE

Trigonometry

IB +sin (l +,8) = sin ,{ cos
cos sin .B

cos (,atB)= cosAcosB + sinl sinB CHOW CHOON WOOI

tan (A* B)= tanA + tanB
1 + tanAtanB

sinA +sin B : z B B

"inA+22 "orA-

sinl - sinB: z B B

"orA*22 "inA-

cosl * cos.B :2 "orA*2.F2 "orA-,8
cosl -cos B = -2 rioA+ B rroA- B

sin2A=2sinAcosA

cos 2A = cos2 A-sin2 A

= 2 cos2 A-l

=l-2sin2 A

tan 2A = 2tanA

-l---t-a--n---'-A--

s.tn1'A. 1-cos2A
2

CO1S-I= l+cos2A
2
-

2500