Midyr Exam F4 P1 2016

8/15/2019 Midyr Exam F4 P1 2016

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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

3472/1 © 2016 Hak Cipta Panitia Matematik SMKTJJ2 SULIT

NAMA ) ****************** TINGKATAN ) ......................

8/15/2019 Midyr Exam F4 P1 2016


8/15/2019 Midyr Exam F4 P1 2016


SULIT 3 3472 / 1

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=


8/15/2019 Midyr Exam F4 P1 2016


SULIT 4 3472 / 1

#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


8/15/2019 Midyr Exam F4 P1 2016


SULIT + 3472 / 1

% 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

*


8/15/2019 Midyr Exam F4 P1 2016


8/15/2019 Midyr Exam F4 P1 2016


8/15/2019 Midyr Exam F4 P1 2016


SULIT $ 3472 / 1

?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


8/15/2019 Midyr Exam F4 P1 2016


SULIT , 3472 / 1

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/

?4 marks@3472/1 © 2016 Hak Cipta Panitia Matematik SMKTJJ2 SULIT

8/15/2019 Midyr Exam F4 P1 2016


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


8/15/2019 Midyr Exam F4 P1 2016


SULIT 11 3472 / 1

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/


8/15/2019 Midyr Exam F4 P1 2016


SULIT 12 3472 / 1

?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


(- 2, q

x

8/15/2019 Midyr Exam F4 P1 2016


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


8/15/2019 Midyr Exam F4 P1 2016


SULIT 14 3472 / 1

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


8/15/2019 Midyr Exam F4 P1 2016


SULIT 1+ 3472 / 1

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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Midyr Exam F4 P1 2016