09 trial johor_p1

SULIT 3472/l

NO. KAD PENGENALAN

ANGKA GILTRAN

JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAAN SPM 2OA9 3472/l
ADDITIONAL MATIIEMATICS
Kertas I
Sept.
2 Jam D ua i am

JANGAN BUKA KBRTAS SOALAN INI SEHTNGGA
DIBERITAHU
1. Tulis nombor kad pengenalan angka
dan UntukKegunaan
Pemeriksa
giliran andapadapetakyangdisediakan. Soalan Markah Penuh Markah Dioerolehi
I 2
2. Kertassoalanini adalahdalamdwibahasa. 2 4
3 3
3. Soalan dalam bahasaInggerismendahului 4 3
soalanyang sepadan
dalambahasa Melayu. 5 3
6 3
4. Calon dibenarkan menjawab keseluruhan 7 3
atau sebahagiansoalan sama ada dalam 8 3
bahasalnggerisataubahasaMelayu. 9 2
10 J

5. Calon dikehendakimembacamaklumatdi 2
halaman belakangkertassoalan. 2
3
4 J

5 2
6 4
7 A

8 A

9 A

20 ,
2l A

22 J

23 A
+
24 !

25 A

Jumlah 80

Kertassoalanini mengandungi halarnan
20 bercetak
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SULIT
3472t1

the qttestions The synbols giren are lhe ones
f|ltov,ing -formulae may be hetpfut in onsw-ering
T'he
commonly used.
ALGEBRA
l oc.b
-b + r lh' - 4ac 8 =
l Oe"D '-
1 x= l og. a
2a

2 r!' x Ll'= Lt "' n fn:6r(n-l )d

3 t!'+on- a il' n
10 s"= llzr+(n-l)dl
2'
4 (u"')n=a'"' n-t
ll Tn = a"r

a(r' -l u(l -r' ) ..
5 log. mn = log am + laga n t2 S'n= =--J,l .r+t)
nl'
r-l l -r
= log sn - log'n
6 log" d
n S _=
" l' l. r
"
7 log"m': n lo g o m l -r

C AL C ULU S

dv dv du
l=tw, -;=tt ; + v ; Area undera curve
dx ax ax
I
: lY.lr or
du dv
.v
tt clx dr dx
=- f
, 1 = lx ttV
rdyv

Votumegenerated
. dy tly du
tt
dx du dx = | /w " ctr or
oo

lt
= dy
)-{-
llr

GEOMETRY

5 A pointdividinga segment a line
of
1 Distancc = - -'r, + (jr,
)' ( ra, mr, nv, + .y, )
(r,.v)= i -' - i
2 Midpoint tl r n nt+ tt /
(x.+x- +
(r,r)= l -Yr .Y:)
' 1) 6 Areaof triangle
,.
= { . r - + .;r , -
t, :Jl,,r,r, +,r,-)/3 ) - (t,.v,+ r',y,+'t,y',)l
+ r;/',
lr l

^ xt+y.l
l) 7
V-r-+.Y-

341211 2oo9IIak CiptaJPNJ
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SULIT 3472t1

STATISTIC

x =II 7- Zw,I,
N
Lw,

x =21 =,!
(n- r)l
Zr nl

3o= ,F:,tr ; l0
' (n - ry.vl

P(Av B) = P(I)+P(B)-
P(AnB)

4-,ry=ffi; tl P (X = r) = nC ,p' qn-' ,p+ q:

1) Meanp- np
[1r-"]
5 m= r+l2-lg
IJ o = J;pq
l'' l l4
x- u
o
6 I =&x100
Qo

TRIGONOMETRY

I A r c lengt h ,s = r0 9 sin (l t B) : siM cosB t cosl sin.B

=
t0 cos(l t 13) coM cosB T sinl sin3
2 A r eaof s e c to r,L = !r' 0
2
3 sinzA + cos 2l : I tanA+ tanB
1l Ian(.{ +
lT tanAtanB
4 sec2A=| +tan2A
o =b
5 c os ec 2A - l + c o t2 A I2 =,
sin,4 sin sin
B C

6 sinZA:2 sinA cosA
l3 a2= b2+ c2 - 2bc cos"4
7 cos2A = cos2l -sin2 A
:2 cos2A | - I
= |- 2 s i n 2 A t4 A reaof tri angl e = :absi n C
-2

g tan2A - Ztan4
1- ta n ' A

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SULIT
34721r For
exomrner's
use only
Answer questfbns
all

Diagr a m s h o w stn e g ra p ho f th efu n c ti on (x) = l x+ i i , forthe domai n
1 .f
- 2< x < 5 .

graf f (x) = l.r + | l, untukdomain-2<x<5 '
Raiah1 menuniukkan

S t at e:
Nyatakan'.

( a) t he / -' (5 )
( b) f |Q ) 12marksl
12markahl I
(a)
lJawaPan: ......
Answer
I r---
(b) I l2 l

2. G iv ent he fu n c ti o ng :-r+ 7 .v + l
s a n d h ' .x-+ { -t fi nO,
3

Diberfi un g s g ' .x -+ 7 x + 1
i d a nh :x -+ !* t C ari ,

( a) g- ' (8 )
(b) sh(x) 14marksl
14ma*ah)

(a)
Answer/JawaPan'.

. (b)

34721t 2oa9Hak ciptaJPNI
SULIT

For SULIT
examiner's
3472t1
use only
a

3. .f(x) =-:;
Given functions
the and gf(x) = 5x- 4.Find g(.r).

fungsi"f(x) = -:;-
Diberi dan gf (x) = 5x* 4 . Carig(x) .
x-l
[3 marksj
13maftahl

3

|
I ---l
l3l AnswerlJawapan:

4. Given 3 and k aretheroots thequadratic
that of equation +.r = p. Find value
x' the
of k andp.
Diberibahawa dank ialahpunca-punca
3 wrsamaankuadratik. nilai k dan p .
cai

13marksl
[3 markah]

4

I r-l
I t3l

()

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347211 For
SULIT
examiner's
use only

c
A
Diagram5 showsthe graphof /(x) = a(x - b)2 + c' Statethe value ol a 'b and '
Rajah5 menunjukkangraf f (x) = alx - b)'1+ c'Nyatakannilai a 'b dan c

[3 marks]
[3 markah]

x-b)2 + c

Diagram5
Rajah5

Jawaqan'.
Answer/

6. Given quadratic
the function (x) = 2x' - 7' findtherange r if /(x) > I l .
f of
Diberifungsi julatbagix jika f (x) > l l .
kuadratik(x) = 2x' -7, cari
-f
[3 marks]
13ma*ahl

6

I r--1
I l3l
Answer/Jawapan :

t,
347211 2ooeHahciptdJPNJ
SULIT

SULIT 3472/l
For
examiner's
use only 7. Solvethe equation3'*'
Se/esaikan persamaan
[3 marks]
[3 markah]

1

I r--1 Answer/Jawapan:
I lrl

Giventhat log3 = loge findthe valueof x.
x 4,
Diberi log3x = Iogg4, cari nilai x.
[3 marks]
[3 markah]

Answer/
Jawapan.

the of series 1 * I * -!-*..
Find sumto infinig thegeometric
24
Carihasiltambah
hingga
ketakterhinggaan
bagisirijanjang
geometri*] *1*....
t ),r

12marksl
12markah)

9

[J
I t2l
Answer/Jawapan
r)
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SULIT 347211
For
10. Find least
the number terms thearithmetic
of in progression5, - l, 3,... sothatits
- examiner's
useonly
sumexceeds 200.
sebufante*ecil dalam
Caribilangan ianiangarithmetic - 1,3, supaya
-5, ... hasil
tambahsebutanmelebihi200.
[3 marks]
13markahl

l0
| .--l
Answer/Jawapan
I lr l

11, Thefirstthreeconsecutivepositive of progression 2 , y and18.
terms a geometric are
Findthecommon ratioof theprogression.

Tiga sebutanpeftamasuatuianianggeometriialah , y dan 18'
2
sepunya
Cari nisbah bagiianiangtersebut.
1 2ma * s l
12maftahl

r-=
ll

I l2 l

t,
.....,
Jawapan:
Answer/

347211 2oo9HahciptaJPNJ

SULTT 3472tt
For
examiner's
we only
12. Thevariables and ), arerelated theequatio y = +, where andn are
x by n m
n
constants. '1
Diagram 2 snowsthe straight obtained plottinglogr y
line by
aga i n s tx .
Pembolehubah dany dihubungkan
x olehpersamzotl = 4'0,
y mana dan
m
n
n adalahpemalar. Raiah 12 menuniukkangarislurus yang diperolehidengan
memplot log, y melawan x .

D i a gram12
Rajah12

Findthe valueof m and of n.
Cari nilaim dan n. [3 marks
]
[3 markah]

t2

l r-
I l3l

Answer/Jawaoan

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SULIT t0 3472tL
For
examiner's
use only
13 Diagram13 showsa straightline PMQ.
Rajah 13 menunjukkangaris lurus PMQ.

+
P1-s l,-4t)

QQ + 7,s -21

D i a gram13
Rajah13

Giventhat a point M(4,4) divides linesegment
the joining points + t'-4t)
the P(s
and QQ +7,s - 2) in the ralio 2: l Findthe valueof s and f.

Diberi titik M(4, 4) membahagitemberenggaris yang menyambungkantitik
P(s + t,-4t) dan QQ + 7,s - 2) dalamnisbah2:1. Cari nilais dan t.
[ 4 marks ]
14markahl

l3

I r---
i l4 l
Answer/JawapSl? s =
i
t-
r
347211 2oo9HakciDtdJPNJ
SULIT


SULIT 3472/l

For
examiner's 14. Diagram shows straight ABwhich
14 a line intersectsthestraight CDat thepoint
to line
use onlv T(2,3)

Raiah14menuniukkan lurus bersilang
garis AB garis
dengan lurusCD padatitikT(2,3)).

*1"*q
2
Diagram14
Rajah
14

Theequation thestraightline
of ABisy=-1r+4 andtheequation thestraight
of
2
line CD is y = 2y - 1.

garislurus AB iatahy = *1, + 4 dan persamaan
Persamaan garislurus CD ialah
L

Y=2x-l

Calculate areaof the trianglel7D .
the

Kirakan luas segitiga ATD .
[3 marks]
l3 markahI

t4

I r---1 Answer Jawapan:
/
I l3i

()
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SULIT l2 347Ztl

Iror
exuminer's
use only

15. 1 4 vector 2g- b.
Diagr a m 5 s h o w sv e c to rs a n d !. D ra wthe resul tant of

vektor a dan . Lukiskanvektorpaduanbagi 2a - b.
Rajah15 menunjukkan
12 marks)
[2 markah]

/
g
,/

D i a g ram15
R aj ah' 15

Answer/ Jawapan

3472/1 2oo9 IIok cir)to JPNJ
S T]I,IT

SULIT 3472t1
l3
For
examiner's
useonly
-+a
16. The vectors PQ and Rf are parallel. is giventhat PQ= 2?- 3! and
lt
-+o
nS = (t +Ds-;b..

-) -> ->
VeKor PQ dan RS adalah selai. Diberi bahawa PQ = 2a -3b dan
-tq
RS =
2-
Find
Cari

(a) the value of /r
Nilaibagi k

(b) the ratioof PQ: RS
Nisbahbagi PQ: RS
[4 marks]
14ma*ahl

t6

I r-i Answer/Jawapan:(a'1
I l4l
(b).............
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SULIT

IA
SULIT la
['or
examiner's
useonlv
17. Giventhat coS = p and0 is an acute
I express termsof p .
angle, in

Diberibahawa kos0 = p, dan 0 adalahsuatusuduttirus,ungkapkan
dalam
p
sebutan bagi

(a) tan d

e
(b) sin;
z

t7

Answer/Jawapan:(a) I r--
I l4 l

.A
18. Given y = :j , find the approximate
valueof y , when ;r changeslrom 2 to 2.02.
x

)4
Diberiy =:, , cariperubahan bagi y , apabilax berubah
nilai daripada kepada
2
x
2.02.
14marksl
14markahl

18

I l4l

3472/1 2oo9Hak CiptaJPNJ
Answer/ Jawaoan.

SULIT
r)

l5
3472/l
For
examiner's
useonly
Diagram shows seclorOPQwithcentreO andradius cm.
18 a 5
Rajah18menunjukkan
seldorOPQyangberpusatOdanjejari5 cm.

O R l cm O
Diagram 18
R a jah18

Given QR =1 cm and IPRO = 900,findthe areain cm2 , of the shadedregion.

Diberi QR=1 cm dan ./.PRO= 900 , kirakanluasdatamcm2 bagi kawasanbedorek.

14marksl
14matuahl

l9

t-la l
I l Answer Jawapan
/

tt

347211 2oo7Ha*ciptuIPNJ [Lihat sebelah

t6
SULIT 3472t1 For
examiner's
use only

I
20. Findthe coordinates the turningpointson the curve / = 4x + - and determine
of the
x
maximumDoint.

I

Cari koordinatbagi titik-titikpusinganbagi tengkungy = 4x + i- dan tentukan
x
titik maksimum.
14marksl
14markahl

20
A nsw er Jaw apan .........
/ .'
t--J
I l4 l

Given =#
y and = 3g(r) whereg(r) is a function x. Find value
of the of
x-

!,s@)a'
1- _1 dy
Diberi y=2-: dan = 3g(x) di mana g(x) ialahfungsibagi x . Cari nilai

'
Isi)ax
14marks)
14markahl

2l

I r--
I l4l
Answer/ Jawapan :

347211 2oo9Hak ciptoJPNJ
tl

1l
SULIT 3472t1

22. Table22 showsthe marksof a groupof students an examination.
in

Jadual 22 menunjukkanmarkah sekumpulanpelajar yang diperolehidalam suatu
peperiksaan.

Marks 1i?

Numberof students 4 6 8 7

Iable22
Jadual22

F ind
Cari

(a) the maximum valueof x if the modemarkis 8.
nilai markah bagi x jika markahmod ialah 8.

(b) the minimum valueof x if the meanof the marksis greater
than 3
nilai minimumbagi x jika markah min lebih daripada3.
[3 marks]
13markahJ

22
t--_l
I r---
Answer/ Jawapan (a)

I lrl (b)

23. Findthe numberof waysin which4 boysand 5 girlscan be seatedin a row if
Cari bilangancara susunan4 budaklelakidan 5 budakperempuan boleh duduk.

(a) thereis no restriction
tiada syarat dikenakan

(b) the boysand the girlsare seated allernately
pelajar lelaki duduk berselang selidenganpelajar perempuan.
14 marks)
14markahl

)7

tl
I r-1
I l4l
(a)
Answer/Jawapan:
l (b) . ,...

317211 2007 llok Ciota JPNJ ILi hat sebel ah

l8 For
SULIT 3472t1 examiner's
use only

24. f abire shows the numberof colouredmarblesin a bag.
24
Jadual 24 menunjukkanbilanganguli bervvarna dalam satu beg.
di

Colour Number marbles
of
Red 4
Green x+2
Purple 2

Table24
Jadual24

A marbleis drawnat randomfrom the bag. Giventhat the probability gettinga
of
I
greenmarbleis -. Findthe valueof -t.

Sebijigulidikeluarkan sscara rawak daripadabeg. Diberi kebarangkalianmendapat
I
guli hijau ialah;. Cari nilai x.
sebiji
J
[2 marksl
12markahl

24

I r'l
A nsw er
/Jaw aD an .........
: rl
347211 2ao9Hak ciptaJpNJ


l9
S ULI T 3472/l

For
exonriner 25. 25 normal
Diagram showsa standard graph
distribution
useonlr-
Rajah25 menunjukkangraf taburannormalpiawai.

1 (x )

represented the shadedregion 0.7514.
The probability by is
Kebarangkalian kawasanbedorekialah0.7514.

(a) Findthe valueof & ,
Carinilaik.

(b) X is a continuous
random variableswhichis normallydistributed a mean
with
80 and a variance 9. Flndthe valueof X whenthe z-score t .
of is

X ialahpembolehubah rawakselaniar yang beftabursecaranormaldengan
min 80 dan varians9. CarinilaiX iikaskor'z ialah k .

14marksl
14markahl

25

[J
I l4l
(a)
Answer/Jawapan:

thl
tv, ,..'.

E N D OF QU ES TIONP A P E R
()

341211 2oo7Huk c'ipra
JI'NJ ILihat sebelah

SULIT 20 3472t1

INFORMATIONFOR CANDIDATES
MAKLUMAT UNTAK CALON

L Thisquestion
paper of25 questions
consists
Kertassoakn ini mengandungi soalan
25

2. Answer questions.
all
Jawabsemuasoalan

3. Writeyouranswers thespaces
in provided thequestion
in paper.
Tulisjawapan andadalamruangyang disediakan
dalsmkertassoalan.

4. Showyour working.It mayhelpyou to getmarks.
Tunjukkan pentingdalamkerja mengiraanda.Ini bolehmembantu
langkah-langkah anda
untukmendapatkanmarkah.

5. If you wishto change
youranswer, cross theanswer youhave
out that done.
Thenwrite downthenewanswer.
Sekiranyaandahendakmenukar jawapanyang telah dibuat.
jawapan,batalkan
Kemudiantttlisjcwapan yang baru.

6. Thediagrams thequestions
in provided not drawnto scale
are unless stated.
Rajahyang mengiringisoalantfulakdilukis mengihttskalakecualidinyatakan.

1. The marksallocated each
for question shown brackes.
are in
Markahyang diperuntukkan
bagi setiapsoalanditunjukkandalamkurungan-

8. A list of formulae provided pages to 5.
ls on 3
Satusenarairumusdisediakan halaman3 hingga5.
di

9. A bookletof four-figure tables provided.
mathematical is
Sebuahbukusifr matematik empatangkadisediakan.

10. You mayusea non-prograrnmable
scientific
calculator.
Anda dibenarkanmeng,gunakan
kalkulatorsaintifk yang tidak bolehdiprogram.

I l. Handin thisquestion
paper theinvigilator theendof theexamination.
to at
Serahkan pengawas
kertassoalanini kepada peperilcsaan akhir peperiksaan.
di

3472/1 2oo9Hak CiptaJPNJ

09 trial johor_p1

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