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1 4 4 9 / 1

MATHEMATICS PKer t a s 1

September 20111 jam

M AT H E M AT I C S

Tingkatan LimaKe r t a s 1

Satu Jam Lima Belas Minit

JANGAN BUKA KERTAS SOALAN SEHINGGA DIBERITAHU

1 Kertas soalan ini ada lah d a la m d w i ba h a sa2. Soalan dalam Bahasa Inggeris mendaului soalan yang sepadan

dalam Bahasa Melayu.3 Calon d ikehendak i m e m b a c a maklumat di ha laman akhir

Kertas ini mengandungi 20 halaman bercetak

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N M

N O K A D P E N G E N A L A N

1449 2

MATHEMATICS PK e r t a s 2

S E P T 2 11

2— ja m Dua jam tiga puluh minit

J N G N B U K K E R T S S O L N I N I S E H I N G G D I B E R I T H U

Tulis n a m a d an n o m b o r k a d

pengenalan anda pada ruanganyang disediakan

Ker ta s s o a l a n

d w i b a h a s a

i n i a d a l a h d a l a m

Soalan dalam bahasa Inggerismendahului soalan yang sepadandalam bahasa Melayu

alon dibenarkan menjawabkeseluruhan atau sebahagian soalansama ada dalam bahasa Inggerisatau bahasa Melayu

a l o n d ikehendak i m e m b a c a

m klum t di halaman belakangkertas s o a l a n i n i

ntuk Kegunaan Pemeriksa

K od P e m e r i k s a

Bahagian Soalan M a r k a hP e n u h

Markah

Diperoleh

A

1 3

2 4

3 3

4 6

5 4

6 6

7 4

8 6

9 6

1 5

11 5

B

12 1 2

13 12

14 1215 12

16 1 2

Jumlah

K er ta s s oa la n ini mengandungi halaman bercetak

1449/2 © 2 Hah ipla PS Pahang

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SULIT 1449/1(PP)

1449/1(PP)MATHEMATICSKertas 1Sept 2011Peraturan

Pemarkahan

MAJLIS PENGETUA SEKOLAH MENENGAH MALAYSIACAWANGA NEGERI PAHANG

PEPERIKSAAN PERCUBAANSIJIL PELAJ ARAN MALAYSIA 2011

MATHEMATICS

Kertas 1

PERATURAN PEMARKAHAN

UNTUK KEGUNAAN PEMERIKSA SAHAJA

Peraturan pemarkahan ini mengandungi 2 halaman bercetak

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SULIT 2 1449/1(PP)

Question Answer Question Answer1 B 21 B2 A 22 C3 D 23 B4 C 24 A5 B 25 C6 A 26 C7 A 27 C8 A 28 A9 C 29 B

10 C 30 D11 B 31 C12 B 32 B13 B 33 A

14 A 34 C15 C 35 B16 C 36 B17 A 37 D18 B 38 D19 D 39 A20 D 40 C

END OF MARKING SCHEMEPERATURAN PEMARKAHAN TAMAT

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SULIT 1449/2(PP)

[Lihat halaman sebelah]1449/2(PP) © 2011 Hak Cipta MPSM Cawangan Pahang SULIT

1449/2(PP)MathematicsKertas 2Sept 2011Peraturan

Pemarkahan

MAJLIS PENGETUA SEKOLAH MENENGAH MALAYSIACAWANGA NEGERI PAHANG

PEPERIKSAAN PERCUBAANSIJIL PELAJARAN MALAYSIA 2011

MATHEMATICS

Kertas 2

PERATURAN PEMARKAHAN

UNTUK KEGUNAAN PEMERIKSA SAHAJA

Peraturan pemarkahan ini mengandungi 13 halaman bercetak

http://edu.joshuatly.com

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SULIT 2 1449/2(PP)

1449/2(PP) © 2011 Hak Cipta MPSM Cawangan Pahang SULIT

SECTION A [52 MARKS]

Question Solution and Marking Criteria Marks1 (a) K1 3

(b)

Note: If ' ′ ∪ correctly shaded, award K1

K2

2777

722

32 ´´´´

h´´´´ 777

2231

7777

2232 ´´´´ + h´´´´ 77

722

31

=1232

10=h cm

K1

K1

K1

N1

4

3 Ð TPQ or Ð QPT

69

tan =q or equivalent

56 .31 o or 56 o 19¢

P1K1

N1

3

P Q R

P Q R

P Q R


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SULIT 3 1449/2(PP)


4 (a) (i) And P1 6(ii) Or P1

(b) If 3p > 12 , then p > 4If p > 4 , then 3p > 12

P1P1

(c) 2n 3 – 3 where n = 3, 4, 5, 6, …

Note:

2n3 – 3 only2n3 – 3 n = 3, 4, 5,… award K12n3 - 3 n= 1, 2 ,3 ,4 ,…

K1N1

5 612 -=+ y x or 82 += y x or equivalent

NoteAttempt to equate the coofficence one the unknowns, award K1

1414 =- y or 77 = x or equivalent

OR

÷÷ø

öççè

æ-÷

÷

ø

ö

çç

è

æ

-úûù

êëé -´-´

=÷÷ø

öççè

æ

2

81

31

24

)2(31

)41(

1 x

x or equivalent

(K2)

6= x 1-= y

Note:

÷÷ø

öççè

æ-

=÷÷ø

öççè

æ

1

6

y

x as final answer, award N1

K1

K1

N1 N1

4

6 (a) 9= y P1 6(b)

c+= )9)(31

(9 or )9)(31

(9 -=- x y or equivalent

631 += x y or equivalent

)631

(0 += x

18-= x

K1K1

N1

K1

N1


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SULIT 4 1449/2(PP)


7 01572 2 =-+ y y 0)5()32( =+- y y or equivalent

OR

)1(2

)3)(1(4)2()2( 2 --±-= y __K1

5-= y

23= y or 1.5

Note:Accept without “ = 0”.Accept three terms on the same side, in any order

Accept )5(23

+÷øö

çèæ

- y y with 5,23

-= y for Kk2

Accept � −32 ( + 5 ) ℎ =32

,−5 Kk 2 Accept answer from three correct term without factorisation forKk2

K1K1

N1

N1

4

8 (a) 11-= p 1=q

Note:

)2)(4()3)(1(

1

--=

p or 11

1- award P1

P2P1

6

(b)÷÷ø

öççè

æ-

=÷÷ø

öççè

æ÷÷ø

öççè

æ- 18

1

34

21

y

x

÷÷øö

ççèæ-÷

÷øö

ççèæ

---

--=÷÷ø

öççèæ

18

1

14

23

)2)(4()3)(1(1

y

x

or ÷÷ø

öççè

æ-÷

÷ø

öççè

æ

18

1

matrix

inverse

3-= x 2= y

K1

K1

N1 N1


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SULIT 5 1449/2(PP)


Note:

Do not accept ÷÷ø

öççè

æ-

=÷÷ø

öççè

æ

34

21

matrix

inverse // ÷÷

ø

öççè

æ=÷÷

ø

öççè

æ

10

01

matrix

inverse .

÷÷ø

öççè

æ-

-=÷÷ø

öççè

æ

2

3

y

x as final answer, award N1 .

Do not accept solutions solved not using matrix method.9 (a)

14147

2236030 ´´´ or 1414

722

36090 ´´´

( ) 14147

2236030

14147

2236090

1414 ´´´+´´´´

93.33 cm 2

K1

K1

N1

6

(b)14

722

236030 ´´´ or 14

722

236090 ´´´

( )14141414147

2223609014

7222

36030 ++++´´´+´´´

85.33 cm

Note:Accept p for K mark.Correct answer from incomplete working, award Kk2

K1

K1 N1

10 (a) {MA, MT, MH, MS, AM, AT, AH, AS, TM, TA, TH, TS, HM,HA, HT, HS, SM, SA, ST, SH}

Note :Two wrong listing ---award P1

P2 6

(b) (i) {AM, AT, AH, AS}

204=

K1

N1

(ii) {MT, MH, MS, TM, TH, TS, AM, AT, AH, AS, HM, HT, HS,SM, ST, SH}

5

4

20

16or =

K1

N1

11 (a)1001524

--

109-=

K1

N1

5


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SULIT 6 1449/2(PP)


(b) ( ) 130621

45.121 =´´++ uu

20=u

Note:

( )41521

u+- or 621 ´´ u --- award K1

K2

N1

SECTION B [48 MARKS]

Question Solution and Marking Criteria Marks12 (a) (i) (7, 7) P1 12

(ii) (2, 8) P1(iii) (9, 4)

Note:Point (9, 4) marked or (3 , 0) seen or (3, 0) marked, award P1

P2

(b) (i) (a)

(b)

V: Reflection in the line 2= x

Note:The word “reflection” is seen --- award P1

W: Enlargement centre A or (1, 1) with scale factor 2

Note:P2: Enlargement centre N or Enlargement scale factor

of21

P1: Enlargement

P2

P3

(ii) 2218 ´ 18218 2 -´=

= 54

K1K1

N1


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SULIT 7 1449/2(PP)


13 (a) 6.67-13.33

K1K1

12

(b) Graph

§ Axes drawn in correct directions uniform scale for

44 ££- x and 531 ££- y § All 7 points and *2 points correctly plotted or the curve passes through the points for 5.34 ££- x and

2020 ££- y § A smooth and continuous curve without any straight line and

passes through all 9 correct points using the given scale for 44 ££- x and 2020 ££- y .

Note:§ 7 or 8 points correctly plotted, award K1§ Ignore curve out of range

P1

K2

N1

(c) (i) 11.5 10.5 y- £ £ - P1(ii) 4.15.1 -££- x

Note:§ Allow P marks if values of x and of y are shown on the

graph.§ Values of x and y obtained by calculation, award P0§ Or from wrong graph, award P0

P1

(d) Identify equation 23 +-= x y or yx x x -=- 23 2 Straight line 23 +-= x y correctly drawn

Values of x :2.23.2 -££- x , 9.28.2 ££ x

Note:§ Allow N marks if values of x are shown on the graph§ Values of x obtained by calculation, award N0

K1K1

N1N1


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SULIT 8 1449/2(PP)


-4 -3 -2

- 5

10

- 15

-1

20

1 2 3

y

4- 0

---5

- 10

-15

-20

Graph for Question 13Graf untuk Soalan 13


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SULIT 9 1449/2(PP)


Question Solution and Marking Criteria Marks14 (a)

Class Interval: (II to VII)Frequency: (I to VII)Midpoint: (I to VII)

Note: Allow one mistake in frequency for P1

Class interval Frequency Midpoint15 – 19 3 1720 – 24 7 2225 – 29 15 27

30 – 34 11 3235 – 39 7 3740 – 44 12 4245 – 49 5 47

P1P2P1

12

(b) 25 - 29 P1

(c)

Mean =( ) ( ) ( )

51271115734754212377

32112715227173

++++++´+´+´+

´+´+´+´

= 32.67

K2

N1(d) Refer graph

§ Axes drawn in correct direction, uniform scale for 44 ££ x and 2020 ££- y

§ *7 bars correctly drawn

Note: 5 or 6 bars correctly drawn , award K1

P1

K2 N1

(e) Any correct information from the histogram drawn N1


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SULIT 10 1449/2(PP)


Graph for Question 14Graf untuk Soalan 14

Money spent17 22 27 32 37 42 47

2

4

6

8

14

10

12

16

frequency


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SULIT 11 1449/2(PP)


Question Solution and Marking Criteria Marks15 (a)

Correct shape with rectangle PQRT and semicircle RST All solid lines.

PQ < QR Measurements correct to ± 0.2 cm (one way) and

Ð P , Ð Q , = 90 o ± 1 o

K1K1

N1

12

P Q

RT

S


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SULIT 12 1449/2(PP)


(b) (i)

Correct shape with rectangles APED and PQVQAll solid lines.

AP = PQ < QV EV < UV

Measurements correct to ± 0.2 cm (one way) andAll angles at vertices of rectangles = 90 o ± 1 o

K1K1

N2

(ii)

Correct shape with rectangles QRWV and RSXW All solid lines.( Ignore PE and EF)Correct trapezium PTFE with PE and EF dashed lineQR >QV >RS , RF =FW Measurements correct to ± 0.2 cm (one way) andAll angles at vertices of rectangles = 90 o ± 1 o

K1

K1

K1 N2

A P Q

D E

U V

QR

WV

S

X

E F

E F


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SULIT 13 1449/2(PP)

16 (a) 25 o E Note: 25 o or ° , award P1

P2 12

(b) P1

N1N1

(c) Location of Z ( 60 o S , 25 o E )

(180 – 60 – 60) × 60= 3600 nm

K1 N1

(d) Distance = 650 ×60 = 3900 nm

´´= 60cos603900 q = 130q

Longitude P = 360 – 155 – 130= E °75

K1 N1K1K1

N1

END OF MARKING SCHEME PERATURAN PEMARKAHAN TAMAT

mm pahang spm 2011

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