1449/1

SULIT 1449/1 Matematik Kertas 1 2014

1 . 1 "4 Jam

MAJLIS PENGETUA SEKOLAH MENENGAH MALAYSIA

CAWANGAN NEGERI SEMBILAN

PROGRAM PENINGKATAN AKADEMIK TINGKATAN 5

SEKOLAH-SEKOLAH MENENGAH NEGERI SEMB.LAN 2014

MATEMATIK

Kertas 1

Satu jam lima belas minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1.

Kertas soalan ini adalah dalam dwibahasa.

2.

Soalan dalam bahasa Inggeris mendahului so alan yang sepadan dalam bahasa Melayu.

3.

ealon dikehendaki membaca maklumat di halaman belakang kertas so alan ini.

Kertas soalan ini mengandungi 29 halaman bercetak. 1449/1 © 2014 Hak Cipta Ml'SM

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MATHEMATICAL FORMULAE RUMUS MATEMATIK The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.

Rumus-rumus berikut boleh membantu and(l merifawab soalan.Simbol-simbol yang diberi adalah yang biasa digunakan.

RELATIONS PERKAITAN I.

10.

Pythagoras Theorem Teorem Pithagoras Z Z e = a + bZ

11.

peA)

12.

peA')

2.

3.

(am)' = am" A-I _

5.

6.

n(S)

(d

1 ad -be -e

Distance 1 Jarak

=)(x

= n(A)

2 -

xI)z

+ (yz - YI)z

Midpoint 1 Titiktengah

XZ YI + (X,Y) = (Xl +2 ' 2 7.

Average speed

8.

Mean

Yl.)

= 1- peA)

13.

14.

distance travelled

= - - .---~

m=

Y - intercept

x - intercept pintasan-y pintasan-x

m = - -=---- - - ­

time taken jarak yang dilalui Puratalaju = .::..-_~-----,o..-_~

masa yang diambil

sum of data

= -----­

number of data

hasil tam bah nilai data Min = - - - - - - -­ bilangan data 9.

1"1 lV

ean

Min

sum of (classmark x frequency) = ---'---------'--~ sum of frequencies

_ hasil tambah (nilai titik tengah kelas x kekerapan)

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hasil tam bah kekerapan

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SHAPE AND SPACE

BENTUK DAN RUANG 1. Area of trapezium

Luas trapezium

..!. x

=

hasH tami~ah dua sisi selari x tinggi

..!. x

=

sum of parallel sides x height

2

2

= nd Vlitan bulatan = nd = 2nj

2. Circumference of circle

2nr

n?

3. Area of circle =

Luas bulatan

=

n/

=

= 2rrrh Luas permukaan melerigkung silinder = 2njt

4. Curved surface area of cylinder

5. Surface area of sphere

= 4n?

Luas permukaan sfera = 4n/

= cross sectional area x length---­

6. Volume of right prism

Isipadu prisma tegak

=

luas keratan rentas x panjang

= nr2h

7. Volume of cylinder

Isipadu silinder = n/t 8. Volume of cone

· d u Jw n 1szpa

=

=

1 3

2

-nr h

1 .2t -n} 3

9. Volume of sphere

· du sJera ,.{; = -n}

4 .3 1szpa 3

1

10. Volume of right pyramid

- x base area x height 3

Isipadu piramid tegak= .!. x luas tapak x tinggi

3

11. Sum of interior angles of a polygon

HasH tam bah sudut pedalaman poligon

0

= (n- 2) x 180

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arc length angle subtended at centre 12. - - - - - " ' - - - - - = circumference of circle 360' panjang lengkok sudut pusat --'------......::......-::"-------'=' " - -

lilitan bulatan

13 .

=- ----"-:_­ 0

360

area of sector angle subtended at centre = 360' area of circle luas sektor sudut pusat = 360 0 luas bulatan

PA' 14. Scale factor, k = - ­

PA

. PA' Faktor skala, k = - ­ PA

. ' 15. kea of image = k?x area of object Luas imej =!l- x luas objek

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Answer all questions Jawab semlla so alan 1

Round off 7126 correct to three significant figures.

Bundarlwn 7126 betul ,kepada tiga angka bererti.

2

3

A

712

B

713

C

7120

D

7130

7.83 x 9.45 .

1.13

A

6.54 x 10'

B

6.55 x l0'

C

6.54 X 10 - 1

D

6.55 X 10- 1

Given that x = 2.13 X 10 4 and y = 1.07 X 10 3 , express x + 5y in standard form.

Diberibahawa x=2.13 x I04 dan y=1.07 x 10 3 , unglwplwn x+ 5ydalambentuk piawai.

4

A

2.67 x 10 3

B

2.67 X 10 4

C

7.48 x 10 3

D

7.48 x 10 4

111012 + 11012 = A

1000002

B

1000102

C

1010102

D

1011102

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Given that 568 < X8 < 61s, the possible values of X is

5

Diberi bahawa 568 < Xs < 618, nilai-nilai yang mungkin bagi X ialah

6

A

56,57

B

57,58

C

57,60

D

58,60

In Diagram 1, JKLMNP is a regular hexagon. Dalam Rajah 1, JKLMNP ialah heksagon sekata.

M

J

N

Diagram 1 Rajah 1

Find the value of x .

Cari nilai x .

A

20

B

30

C

50

D

60

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In Diagram 2, JKLMNT is a regular hexagon. KLP and LMQ are straight lines. Dalam Rajah 2, JKLMNT ialah sebuah heksagon sekata . KLP dan LMQ adalah garis lurus.



K~____~L~______-,~P



J

T

Q

Diagram 2 Rajah 2 Find the value of x + y .

Cari nilai x + y .

A

105

B

115

C

125

D

185

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In Diagram 3, JKL is a common tangent to the circles with centre 0 and P, at point J and K respectively. ROQPL is a straight line. Dalam Rajah 3, JKL ialah tangen sepunya kepada bulatan berpusat 0 dan P, di titik J dariX masing-masing. ROQPL ialah garis lurus.

R

L

Diagram 3 Rajah 3

Find the value of x. Cari nilai x.

A

26

B

29

C

38

D

52

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In Diagram 4, MFHK is a square drawn on square grids.

Dalam Rajah 4, MFHK ialah segi empat sarna dilukis pada grid segi empat sarna.

G

F

~

l~

E

/ M

V

IH

~V

V

V

'"

/ J

~

~ 11

I."

Diagram 4 Rajah 4

Find the correct pairing of object, the line of reflection and its image.

Cari pasangan objek, paksi pantulan dan imejnya yang betul.

A B C D

Object! Objek EFP MEP PGH PLM

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Line of reflection Paksi pantulan GL .. FK EJ MH

Image imej PJK PFG PLK PGF

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Diagram 5 shows five diagrams drawn on square grids.

Rajah 5 menurifukkan lima rajah dilukis pada grid segi empat sama.

, "

~

/I VH

V ~~

~" 1

I'"

~

17. \u

I

~

I

1 I

I

I

I

~ -.........: ~

i

Diagram 5 Rajah 5 Which ofthe"pentagons A, B, Cor D, is an ,image of pen tag OIl R under a rotation in a certain point?

Antara pentagon A, B, C atau D, yang manakah imej bagi pentagon R di bawah suatu putaran pada pusat tertentu?

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In Diagram 6, KJM and LKN are two

Dalam Rajah 6, KJM dan LKN

bersudut tegak.

L

Given that-sinyo

13

Dibert bahawa sin yO A

18

B

23

C

31

tan

the length of JKL. . tan

1, cari panjang bagi JKL ,

D

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Diagram 7 shows a graph of trigonometric function. The equation of the function is

Rajah 7 menunjukkan graf bagi suatu fungsi trigonometri. Persamaan bagi f ungsi itu ialah

y

1

--+-~~--~~----~----~---+

x

Diagram 7 Rajah 7

A

y

=

cosxo

R. __ y.= sin XO

13

C

y

cos 2x0

D

y

sin 2x0

Givensinxo =-sin37°and

Diberi sin

Xo

= - sin 37 dan

A

217°, 307°

B

233°, 307°

C

217°,323 0

D

233° ,323°

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0

00~x~360°.Findthevaluesofx . oo~

x ~ 360°. Cari nilai-nilai bagi x.

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Diagram 8 shows a right prism with a horizontal base JKLM, JPSM is a uniform cross section of the prism. Point T, Nand U are midpoints of PQ, JK and ML respectively. Rajah 8 menurljukkan sebuah prisma tegak dengan tapak mengufuk JKLM JPSM ialah keratan rentas seragam prisma itu. Titik T, N dan U iulah titik-litik tengah bagi PQ, JK dan ML masing-masing.

Q

Pr----.---<

~~---------- --------------- L

u

//.iI / /

J

Diagram 8 Rajah 8 Name the angle between the line TL and the base JKLM. Namakan sudut di antara garis TL dan tapak JKLM A

LTLK

B

LTV

C

LTLU

D

LTLN

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In Diagram 9, J, K and R are three points on the horizontal plane. Point Land Mare the top of a vertical lamp post and a vertical coconut tree respectively.

Dalam Rajah 9, J, K dan R ialah tiga titik pCida salah mengufuk. Titik L dan M ialah puncak sebalang liang /ampu legak dan sebalang pokok kelapa tegak masing­ masing.

M

L

Lamp post Tiang lampu

Coconut Tree Pokok Kelapa

J

K

R

Diagram 9 Rajah 9 Name the angle of depression of K from L.

Namakan sudut tunduk K dari L.

A

LLMK

B

LJLK

C

LMLK

D

LLKM

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Diagram 10 shows a vertical flat and two cars, P and Q on a horizontal plane. Rajah 10 menunjukkan sebuah rumah pangsa tegak dan dua huah kereta, P dan Q di atas satah mengufuk.

P

Q

Diagram 10 Rajah 10

Raman sitting at the balcony. Given that the distance SP=PQ. The height of RS is

90 m. The angle of depression of the car P from Raman is 56°.

Calculate the distance, in m, of SQ .

Raman duduk di balkoni. Diberijarak SP=PQ . Iinggi RS ialah 90 m. Sudut tunduk

kereta P dari Raman ialah 56°.

Hitungjarak, dalam m, bagi SQ.

A

87.79

B

108.56

C

121.42

D

160.91

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Diagram 11 shows three points, p, Q an d R on a horizontal plane.

Rajah 11 menunjukkan tiga tUik, P, Q dan R pada suatu satah mengufuk.

North Utara

Q

R Diagram 11

Rqjah 11

Given that the bearing of R from Pis ]25 0 and PR=PQ. Find the bearing of R

from Q.

Diberi bahawa bearing R dari P ialah 125° dan PR=PQ. Cari bearing R dari Q.

18

A

105 0

B

110 0

C

135 0

D

170 0

Express in general form for (2x -1)

3

7 (x - 4)

(2x-l) Ungkapkan dalam bentuk am bagi --3-

A

2X2 -6x+25=O

B

2X2 - 6x - 17 = 0

C

2X2 - 9x + 25 = 0

D

2X2 - 9x - 17 = 0

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=

7 (x - 4)

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In Diagram 12, N is the North Po le and S is the South Pole.

Dalam Rajah 12, U ialah Kutub V! aru dan S ialah Kutub Selatan.

lV/V

Greenwich Meridian

S

350

Diagram 12 Rajah 12

.

Find the difference between the longitudes M and P.

Cari perbezaan antara longitud M dan P .

20

A

105°

B

110°

C

115°

D

125°

1+ 2m as a SIng . I ' In . .ltS Slmp . 1est clorm. Express -3- - --"2 e f ractlOn 2-m

4-m

3 1+ 2m

Ungkapkan - - 2 sebagai satu pecahan tunggal dalam bentuk termudah. 2-m 4-m A

5+rn (2-rn)(2+m)

B

5-rn

(2 - m)(2 +m)

C

5 + 3m

(2 - m)(2 + m)

D

5(1 + m)

(2 - rn)(2 + rn)

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2 x- I

3

Given that - - =- x+ !

, find the value of

x ,

. x, D I'b en' b ah awa - 2- = - 3- , can"m/Gl' b agl x - I x +l

22

A

2

B

3

C

4

D

5

5 can be wntten ' as 2x

-3

5 boleh ditulis sebagai 2x 3

23

A

5 -3 -x

B

5 3

-x

C

IOx 3

D

IOx- 3

2

2

Ringkaskan

x

2m 2



9m- 3

6m

3n

B

D

(3m'niJ'

'

n

A

C

2m 2 9m- 3

(3m-'niJ' x

Simplify

­

m

2n

3m

6n

m

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It is given that 1 < p ::; 8 and - 6 < q < - 3 where p and q are integers. Find the maximum value of p - q.

Diberi bahawa I < P ::; 8 dan - 6 < q < - 3 dengan keadaan p dan q ialah integer. Cari nilai terbesar hagi p - q.

25

A

10

B

11

C

13

D

14

Table 1 is a cumulative fl'equency table which shows the mark of 30 pupils in a quiz.

Jadual 1 ialah jadual kekerapan longgokan yang menunjukkan markah bagi 30 orang murid dalam suatu kuiz.

.

Marks!

Markah Cumulative frequency/

Kekerapan Longgokan

0

1

2

3

4

5

2

7

14

25

29

30

Table 1

Jaduall Find the mode.

Cari mod.

A

2

B

3

C

4

D

5

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Diagram 13 is a pie chart which shows the number of students in four courses in a college. It is given tha the mUllb r of students of engineering course and Infonnation Technology course are 36 and 24 respectively.

Rajah 13 ialah carta pai yang menunjukan bilangan pelajar bagi empat kursus di sebuah kale}. Diberi bilangan pelajar bagi kursus Kejuruteraan dan kursus Teknologi Maklumat ialah 36 dan 24 orang masing-masing.

Engineering / Kejuruteraan

60°

Sains

Diagram 13 Rajah 13 Find the number of student of Science course.

Cari bi/angan pe/ajar bagi kursus Sa ins.

A

22°

B

40°

C

44°

D

72°

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The line graph in DiagTam 14 shows the sale of cupcakes by Salmah in a week.

Gra! garis dalam Rajah 14 menunjukkan jualan kek cawan oleh Salmah dalam seminggu. 8 ~------------------------------------------~--------,------~

7 -----------------------------6

-----------------------------------------.~------~

I

I

I I I I

:

t

:

4 I

31---r-----

I

I

___ L ____ _ I I I I

I

I :

2 7---~-----~------,------T------r------~----I I I I

o +-__~__~--~--~----~--~--~__~--~--~----L---~--~--~ Mon/tsn

Tue/Set

Wed/Rob

Thurs/Kha

Fri/Jum

Sat/Sob

Sun/Ahod

Day Had

Diagram 14 Rajah 14 The profit from each cupcake is 3 cent. Calculate the total profit of cupcakes sales in a week.

Keuntungan daripada setiap kek cawan ialah 3 sen. Hitungjumlah keuntungan jualan kek cawan dalam seminggu. A

RM 920

B

RM 960

C

RM 1060

D

RM 1202

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22

Which graph represents y

=

1449/1

i - 2x .

Graf manakah yang mewakili y = x 2 - 2x .

y

A

---~.----f-"'"

x

y

B

--'\;---------=+-~I___---.x

c

- - - + - - - - - ; -..... x

o

y

D

-~---+--~f__.

-2

o

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X

2

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Given that the universal set, .; = { x : lOS x S 30, x is an integer}. Set P = { x : x is a multiple 00} and set Q = {x: x is an odd number} . Find n( P n Q )'. Diberi bahawa set semesta, .; = { x : 10 S x S 30, x ialah integer}. Set P = {x: x ialah gandaan 3} dan set Q = {x: x ialah nombor ganjil}. Cari n(P

30

A

11

B

15

C

18

D

21

n Q) '.

Diagram 15 shows a Venn diagram with the universal set'; ={Fonn Five students}. Set P = {Members of Police Cadet}, set R = {Members of the Red Crescent Society} and set S =:: {Members ofSt. John Club} . Given that n(P) n(P

=::

35, n(R) = 46, n(S) = 28,

n R) = 10 and n(.;) = 105.

Rajah 15

menunjukka~

gambarajah Venn dengan set semesta .; = {Murid Tingkatan

Lima}. Set P = {Ahli-ahli pasukan Kadet Polis}, set R

=

{Ahli-ahli pasukan Bulan

Sabit Merah} dan set S = {Ahli-ahli pasukan St. John}. Diberi bahawa n(P) n(R) = 46, n(S) = 28, n(P

n R)

=

10 dan n«()

=

=

35,

105.

R

S

Diagram 15 Rajah 15 Find the number of Form Five students who are not a member of any three societies. Cari bilangan murid Tingkatan Lima yang bukan ahli bagi mana-mana tiga persatuan itu.

A

4

B

5

C

6

D

7

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y

Q ( 6,4 )

P

----------------~~--~----------~x

o

Diagram 16 Rajah 16 In Diagram 16, the gradient ofline PQ is

l . Find the x-intercept of the straight line 2

PQ.

Dalam Rajah 16, kecerunan garis PQ ialah A

-1

B

-2

C

-3

D

-4

~

. Cari pintasan-x bagi garis lurus PQ.

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Diagram 17 shows a straight line PQ with equation y = 2x + 8. QR is parallel to the x-axis and the distance is 6 unit. Find the gradient of PRo Rajah 17 menunjukkan garis lurus PQ yang mempunyai persamaan y = 2x + 8 . QR adalah selari dengan paksi-x danjaraknya ialah 6 unit. Cari kecerunan PRo y }-------"7'

P

0

R

x

Diagram 17 Rajah 17

A

4 5

B

5

4

C D

33

4

4

Given that the probability of choosing a boy at random from a group of student is ~. 11 Ifthere are 28 girls in the group, find the total number of students in the group.

Diberi kebarangkalian untuk memilih secara rawak seorang lelah dari sekumpulan murid ialah

tl.

Jika terdapat 28 orang perempuan di dalam kumpulan murid itu,

carijumlah murid di dalam kumpulan terse but.

A

16

B

44

C

56

D

64

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Diagram 18 Rajah 18 Diagram 18 shows 10 cards labelled with letters which are put in a box. A card is drawn at random from the box. State the probah,ility that the card drawn is not a '> vowel.

Rajah 18 menunjukkan 10 keping kad berlabel dengan huru!yang dimasukkan ke dalam sebuah katak. Sekeping kad dipilih secara rawak dari katak itu. Nyatakan kebarangkalian bahawa kad yang dipilih itu bukan vokal. A

B

c D

35

3 10 2

5

3

5

7

10

A box contains red and blue marbles. Farid has many trials to choose a marble at random. The probability that Farid choose a red marble I} . In 800 trials chosen 16 randomly, how many times does Farid choose the blue marble?

Sebuah kotak mengandungi guli berwarna merah dan biru. Farid membuat beberapa percubaan memilih guli secara rawak. Kebarangkalian Farid memilih guli merah ialah .!...!. . Dalam 800 percubaan memilih secara rawak, berapa kalikah Farid 16 memilih guli biru?

A

250

B

350

C

500

D

550

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Given that m varies directly as (n 2 + 3) and m ofm when n = 5.

= 10 when n = 1. Calculate the value

Diberi bahawa m berubah secara langsung dengan (n 2 + 3) dan m = 10 apabila n = 1. Hitung nilai m apabi/a n = 5.

37

A

14

B

28

C

50

D

70

••

Given that p varies inversely as q" and p n when p

=6

when q

= 1. Calculate the value of

= 48 and q = 2.

Diberi bahawa p berubah secara songsang dengan qn dan p = 6 apabi/a q Hitung nilai n apabila p

38

A

3

B

2

C

-2

D

-3

=

48 dan q

=

=

1.

2.

It is given that x varies directly as the cube root of y and inversely as the square of

z. Find the relation between x, y and z. Diberi bahawa x berubah secara langsung dengan punca kuasa tiga y dan secara songsang dengan kuasa dua z. Cari hubungan antara x, y dan z.

A

x oc

B

x oc

C

x oc

y3

Fz if; Z2

D

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39

[ 3 1~) + [_°2 :) [-32 6)4 13-9 A [-43 B

C

D

40

1449/1

=

:)

[-3 :)

-2 [~1 :) [-43 1:)

Given 1 Diberi :

[:

-53)[~1)=[~n

Find the value of x.

Cari nilai x.

A

-2

B

-1

C

1

D

2

END OF QUESTION PAPER

KERTAS SOALAN TAMAT

1449/1© 2014 Hak Cipta MPSM

[Lihat halamall sebelah SULIT

SULIT

29

1449/1

INFORMATION FOR CANDIDATES ltfAKLUMAT UNTUK CALON

1.

This question paper consists of 40 questions. Kertas saalan ini mengandungi 40 saalan.

2.

Answer all questions . Jawab semua saalan.

3.

Answer each question by blackening the correct space on the answer sheet. Jawab dengan menghitamkan ruangan yang betul pada kertas jawapan.

4.

Blacken only one space for each question. Bagi setiap saalan hitamkan satu ruangan sahaja.

5.

If you wish to change your answer, erase the blackened mark that you have made. Then blacken the space for the new answer. Sekiranya anda hendak menukarkan jawapan, padamkan tanda yang telah dibuat.Kemudian hitamkan jawapan yang baru.

6.

The diagrams in the questions provided are not-drawn·to scale unless stated. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan.

7.

A list offonnulae is provided on pages 2 to 4. Satu senarai rumus disediakan di halaman 2 hingga 4.

8.

You may use a non-programmable scientific calculator. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh dipragram.

1449/1

© 2014 Hak Cipta MPSM

SULIT

1449/1 Matematik Kertas 1 2014

MAJLIS PENGETUA SEKOLAH MENENGAH MALAYSIA CAWANGAN NEGERI SEMBJLAN PROGRAM PENINGKATAN AKADEMIK TINGKATAN LIMA

SEKOLAH-SEKOLAH MENENGAH NEGERI SEMBILAN 2014

MATEMATIK

Kertas 1

PERATURAN PEMARKAHAN

PROGRAM PENINGKATAN AKADEMIK TINGKATAN LIMA SEKOLAH-SEKOLAH MENENGAH NEGERI SEMBILAN 2014

MATEMATIK Kertas 1 1. D

11. D

21. D

31. B

2. B

12. A

22. A

32. A

3. B

13. C

23. D

33. B

4. C

14. D

24. C

34. C

5. C

15. C

25.B

35. A

6. B

16. C

26. B

36. D

7. C

17. D

27.B

37. D

8. A

18. D

28. A

38. B

9. C

19. C

29.C

39. A

10.D

20. A

30. C

40.

A

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