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SULIT 1 3472 / 1
SEK. MEN. KEB. JOHOR JAYA 2
PEP. PERTENGAHAN TAHUN TING. 4 3472 / 1
MATEMATIK TAMBAHAN
Kertas 1
Untuk Kegunaan Pemeriksa
Soalan Marks
Penuh
Marks
Diperoleh1 3
2 3
3 2
4 3
5 3
6 3
7 4
8 2
9 3
10 411 4
12 4
13 3
14 3
15 2
16 3
17 3
18 3
19 4
20 3
21 3
22 4
23 3
24 3
25 6
J!"a# $%
Me& 2%1'
2 jam
JANGAN BUKA KERTAS SOALAN INI
SEHINGGA (IBERITAHU
1. Keras soalan ini men!an"un!i 25 soalan.
#a$a% se!a soalan.
2. &ulis ja$apan an"a pa"a ruan! 'an!
"ise"iakan "alam keras soalan ini.
3. (n"a "i%enarkan men!!unakan kalkulaor
saini)ik 'an! i"ak %oleh "ipro!ramkan.
4. Serahkan keras soalan ini kepa"a
pen!a$as peperiksaan pa"a akhir
peperiksaan.
Dise"iakan oleh*
++++++++++++..
Pn Serene ,eap -in -in
Ketua Panitia Matematik Tambahan
Disahkan oleh*
++++++++++++..Puan ! Poh Sim
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NAMA ) ****************** TINGKATAN ) ......................
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STATISTIK
1.
N
x x ∑=
2.
∑∑=
f
fx x
3.
( ) 22
2
x N
x
N
x x−=
−= ∑∑
σ
4.
( ) 222
x f
fx
f
x x f −=
−=
∑∑
∑∑
σ
5.
c f
F N
Lmm
−+= 2
1
6.
1000
1 ×=Q
Q
7.
∑∑=
i
ii
!
!
8.
( )7
7
r n
n P r n
−=
9.
( ) 77
7
r r n
n" r
n
−=
10.
( ) ( ) ( ) ( ) # $ P # P $ P # $ P ∩−+=∪
11.
( ) 1* =+== −% &% &" r ' P
r nr
r
n
12. Min*
n&= µ
13.
n&%=σ
14.
σ
µ −= '
(
TRIGONOMETRI
1. Panjan! len!kok*
θ j s =
2. -uas sekor*
θ 2
2
1 j L =
3.
1ossin 22 =+ $ $
4.
$ $ sek 22 an1+=
5. $k)t $k)sek
22
1+=
6.
k)s$ $ $ sin22sin =
7.
$ $k)s $k)s 22
sin2 −=
12 2 −= $k)s
$2sin21−=
8.
( ) # $k)s #k)s $ # $ sinsinsin ±=±
9.
( ) # $ #k)s $k)s # $k)s sinsin=±
10.
( ) # $
# $ # $
anan1
ananan
±=±
11.
$
$ $
2an1
an22an
−=
12.
"
c
#
b
$
a
sinsinsin==
13.
$k)sbccba 2222 −+=
14. -uas se!i i!a
" ab sin2
1=
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#a$a% se!a soalan
1
is !ien ha he relaion %e$een se
{ }12*8*6*4*2= P
an" se
{ }6*5*4*3*2*1=Q
is :$o imes;
*iberi baha+a hubungan antara set
{ }12*8*6*4*2= P
dan set
{ }6*5*4*3*2*1=Q
ia,ah
-dua ka,i ganda./
a <in" he ima!e o) 8"ari imej bagi 0
% =>press he relaion in he )orm o) or"ere" pairsUngka&kan hubungan itu da,am bentuk &asangan bertertib/
?3 marks@
(ns$er 1 ja+a&anA
a
%
2 &he "ia!ram %elo$ sho$s he relaion %e$een se M an" se .
2ajah di ba+ah menunjukkan hubungan antara set M dan set N/
Sae B 'aakan
a he o%je o) 2*
)bjek bagi 34
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% he ran!e o) he relaion. ju,at hubungan tersebut/
?3 marks@
(ns$er B ja$apanA
a
%
3
Cien he )union
( ) 4−= x x f
* )in" he alues o) > suh ha
( ) 9= x f
.
*iberi fungsi
( ) 4−= x x f
4 cari ni,ai5ni,ai x jika
( ) 9= x f
/
?3 marks@(ns$er B ja$apanA
4 is !ien ha he )union
( ) 125 −= x x f an"
( ) .4 x x g = <in" he aluie o)
( )3 fg .
*iberi baha+a fungsi
( ) 125 −= x x f
dan
( ) .4 x x g = "ari ni,ai
( )3 fg
/
?3 marks@
(ns$er B ja$apanA
+
Di%eri )un!si
( ) 13 += x x g
"an )un!si !u%ahan
( ) 26 −= x x gh
* ari
Gi6en the functi)n
( ) 13 += x x g
and the c)m&)site functi)n
( ) 26 −= x x gh
4 find
a
( ) xh
*
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?3 marks@
(ns$er B ja$apanA
1% Di%eri sau puna a"alah "ua kali puna 'an! sau la!i %a!i persamaan kua"raik
243 2 =− x &x
* ari nilainilai &.
Gi6en that )ne r))t is t+ice the )ther f)r the %uadratic e%uati)n
243 2 =− x &x
4 find the
6a,ues )f &/
?3 marks@
(ns$er B ja$apanA
11
Di%eri persamaan kua"raik
( ) 01262 =+++ & x x
mempun'ai "ua puna 'an!
sama* ari nilai & "an punan'a.
Gi6en the %uadratic e%uati)n
( ) 01262 =+++ & x x
has t+) e%ua, r))ts4 find the 6a,ue )f
& and its r))t/
?3 marks@
(ns$er B ja$apanA
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12
Di%eri063 2 =++ h x x
mempun'ai "ua puna %er%eEa* ari jula nilai h.
Gi6en063 2 =++ h x x
has t+) different r))ts4 find the range )f 6a,ues )f h/
?3 marks@
(ns$er B ja$apanA
13
Cien ha 2 x2
+ x−1=0 is a Fua"rai eFuaion an" G is one o) is roos. Sho$
ha 2 β3+3 β
2=1 .
*iberi2 x
2+ x−1=0
ia,ah &ersamaan kuadratikdan G ia,ah satu dari&ada
&uncanya/ Tunjukkan baha+a 2 β3+3 β
2=1 .
?3 marks@
(ns$er B ja$apanA
14
Hn!kapkan )un!si kua"raik
( ) 432 2 −+= x x x f
"alam %enuk
( ) % & xa ++ 2
* "i
mana a* & "an % a"alah pemalar.
7x&ress the %uadratic functi)n
( ) 432 2 −+= x x x f
in the f)rm
( ) % & xa ++ 2
4 +here a4 &
and % are c)nstants/
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SULIT 1% 3472 / 1
(ns$er B ja$apanA
1+
<un!si kua"raik( ) % &x x xh ++= 2
mempun'ai nilai minimum 6 apa%ila2−= x
.
ari nilai & "an nilai %.
The %uadratic functi)n
( ) % &x x xh ++= 2
has a minimum 6a,ue )f 8 +hen
2−= x/ Find
the 6a,ue )f & and )f %/
?3 marks@
(ns$er B ja$apanA
1'
<un!si kua"raik( ) 22 6 & x x x f ++−=
* "en!an kea"aan & ialah pemalar mempun'ai
nilai maksimum 13. ari nilainilai %a!i &.
The %uadratic functi)n
( ) 226 & x x x f ++−=
4 +here & is a c)nstant4 has a maximum 6a,ue
)f 9:/ Find the 6a,ues )f &/
?3 marks@
(ns$er B ja$apanA
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17
ari jula nilai > %a!i
( )( ) 621 >−− x x
.
Find the range )f 6a,ues )f x f)r +hich
( ) ( ) 621 >−− x x
/
?3 marks@
(ns$er B ja$apanA
1$
/ajah %eriku menunjukkan !ra) %a!i )un!si kua"raik
( ) ( ) % xa x f +−= 23
.
The diagram sh)+s the gra&h )f the %uadratic functi)n
( ) ( ) % xa x f +−= 23
/
-en!kun! erse%u mempun'ai iik minimum
( )8* −h
"an men'ilan! paksi y pa"a
iik
( )10*0
. ari nilai h* % "an a.
The cur6e has a minimum &)int
( )8* −h
and it intersects the y5axis at the &)int
( )10*0
/ Find the 6a,ue )f h4 )f % and )f a/
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?4 marks@
(ns$er B ja$apanA
1,
/ajah %eriku menunjukkan !ra) %a!i )un!si kua"raik
( ) ( ) 92 −+−= & x x f
.
The diagram sh)+s the gra&h )f a %uadratic functi)n
( ) ( ) 92 −+−= & x x f
/
-en!kun! erse%u mempun'ai iik minimum
( )%*2−* "i mana % ialah pemalar.
'aakan
The cur6e has a minimum &)int
( )%*2− 4 +here % is a c)nstant/ State
;a< nilai %a!i &1 the 6a,ue )f &4
;b< nilai %a!i %1 the 6a,ue )f %4
;c< persamaan paksi simeriB the e%uati)n )f the axis )f symmetry/
?3 marks@
(ns$er B ja$apanA
a
%
2% ( se o) e>aminaion marks x1* x2* x3* x4* x5* x6 has a mean o) 5 an" a san"ar"
"eiaion o) 1.5.
Satu set markah &e&eriksaan x9 4 x3 4 x: 4 x= 4 x> 4 x8 mem&unyai min > dan sisihan &ia+ai 9/>/
=ah mark is muliplie" %' 2 an" hen 3 is a""e" o i. <in" )or he ne$ se o) marks
Setia& markah didarab dengan 3 dan seterusnya tambah :/ "ari ni,ai baru markah untuk
a meanB min*
% ariane B arians ? : marks 1 markah@
(ns$er 1 Aa+a&anB
3472/1 © 2016 Hak Cipta Panitia Matematik SMKTJJ2 SULIT
(- 2, q
x
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SULIT 13 3472 / 1
a
%
21 ( se o) ei!h num%ers has a mean o) 10.
Satu set ,a&an n)mb)r mem&unyai min 9C
a <in" ∑ x B
"ari ∑ x
% Ihen a num%er k is remoe" )rom he se* he ne$ mean is 11. <in" he alue
o) k
$&abi,a suatu n)mb)r k dike,uarkan dari&ada set itu4 min baharu ia,ah 99/ "ari ni,ai k
? : marks 1 markah@
(ns$er 1 Aa+a&anB
a
%
22 &he se o) )ie posiie ine!ers has a mo"e o) 6* a mean o) 8 an" a me"ian o) 7. -is
"o$n he possi%le )ie posiie ine!ers.
Suatu set terdiri dari&ada ,ima integer &)sitif mem&unyai m)d 84 min 0 dan median D/
Senaraikan ,ima integer &)sitif tersebut yang mungkin/
? : marks 1 markah@
(ns$er 1 Aa+a&anB
23 Cien ha a se o) num%ers is 4* 9* 15* 20* 11* 16* 18* 14.
*iberi satu set data bern)mb)r 4* 9* 15* 20* 11* 16* 18* 14.
<in"B "ari
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a ran!e 1 ju,at4
% inerFuarile ran!eB ju,at antara kuarti,
? : marks 1 markah@
(ns$er 1 Aa+a&anB
a
%
24 ( se o) "aa onsiss o) )ie num%ers. &he sum o) he num%ers is 62 an" he sum
o) he sFuares o) he num%ers is 786. &he $o ne$ num%ers* 9 an" 13* are
a""e" o he se o) "aa.
Satu set data terdiri dari&ada ,ima n)mb)r/ Easi, tambah n)mb)r5n)mb)r itu
ia,ah 83 dan hasi, tambah kuasa dua n)mb)r5n)mb)r itu ia,ah D08/ *ua n)mb)rbaru4 dan 9: te,ah ditambah ke&ada set data itu/
a Sae he mean )or he seen num%ers*
Nyatakan min bagi tujuh n)mb)r itu4
% Deermine he san"ar" "eiaion )or he seen num%ers.
Tentukan sisihan &ia+ai bagi tujuh n)mb)r itu
?4 marks@
(ns$erB Aa+a&anB
2+ &he a%le sho$s he )reFuen' "isri%uion o) he sores o%aine" %' a su"en in a
!ame.
Aadua, di ba+ah menunjukkan taburan kekera&an sk)r yang di&er),eh se)rang &e,ajar
da,am suatu &ertandingan/Sore B Sk)r 0 1 2 3
<reFuen' B Kekera&an 3 4 5 x
a ) he mean sore is 2* )in" he alue o) x.
Aika sk)r min ia,ah 34 cari ni,ai x/
% ) he me"ian sore is 2* )in" he ran!e o) alues o) x.
Aika sk)r median ia,ah 34 cari ju,at ni,ai x/ ?4 marks@
(ns$erB Aa+a&anB
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20.
6, 6, 7, 8, 13 or 6, 6, 7, , 12 or 6, 6, 7, 10, 11
6, 6, 7, !, "
#n$%er $&o%$ mo' 6 an' me'ian 7 an'
x+y 21
#n$%er $&o%$ mo' 6 or me'ian 7 or x
*0
3
+2
+1
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