math p2 mid year mlk09 dgn skema pdf june 7 2009-7-25 am 435k

8/6/2019 Math p2 Mid Year Mlk09 Dgn Skema PDF June 7 2009-7-25 Am 435k

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SULIT 1449/2

UJIAN PENGESANAN PERTENGAHAN TAHUN

SIJIL PELAJARAN MALAYSIA 2009

This question paper consists of 23 printed pages.

MATHEMATICSPaper 2

Two hours and thirty minutes

DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE

TOLD TO DO SO

1. This question paper consist two section: Section A and Section B.

Answer all question in Section A and Section B.

2. This question paper is bilingual.

3. Write your answers in the spaces provided in the question paper.

4. Working step must be written clearly.

5. Diagram given is not according to scale unless stated.

6. Marks for each question are given in bracket.

7. A list of formulae is given in pages 2 and 3.

8. Non programmable scientific calculator are allowed.

9 This question paper must be hand up at the end of the exam.

Section Question Fullmark Marksobtained

A

1 3

2 4

3 4

4 5

5 5

6 5

7 6

8 6

9 6

10 4

11 4

B

12 12

13 12

14 12

15 12

Total

1449/2

Mathematics

Paper 2

May

2009

NAME :..

FORM:

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SULIT 1449/2

MATHEMATICAL FORMULAE

The following formulae may be helpful in answering the questions. The symbols given are the

ones commonly used..

RELATIONS

1nmnm

aaa

2nmnm

aaa

3mnnm aa )(

4

ac

bd

bcadA

11

5 SnAn

AP)(

)(

6 )(1)'( APAP

72

12

2

12 )()(Distance yyxx

8 Midpoint ,

2,2),(2121 yyxx

yx

9 Average speed =takentime

travelleddistance

10 Mean =dataofnumber

dataofsum

11 Meansfrequencieofsum

frequency)markof(classsum

12 Pythagoras Theorem222

bac

1312

12

xx

yym

14erceptint

erceptint

x

ym

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SULIT 1449/23

SHAPES AND SPACE

1 Area of trapezium = 2

1

sum of parallel sides height2 Circumference of circle = rd 2

3 Area of circle =2

r

4 Curved surface area of cylinder = rh2

5 Surface area of sphere =2

4 r

6 Volume of right prism = cross sectional area length

7 Volume of cylinder = hj2

8 Volume of cone = hr2

3

1

9 Volume of sphere =3

3

4r

10 Volume of right pyramid = 3

1

base area height

11 Sum of interior angles of a polygon = (n 2) 180

12o

360

centeratsubtendedangle

circleofncecircumfere

lengtharc

13 o360

centreatsubtendedangle

circleofarea

sectorofarea

14 Scale factor, k =PA

PA'

15 Area of image = k2 area of object

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SULIT 1449/24

Section A

[52 marks ]

Answerall questions in this section.

1 The Venn diagram in the answer space shows sets P, Q and R. Given that the universalset = P Q R.

Gambar rajah Venn di ruang jawapan menunjukkan set P, Q dan R. Diberi set semesta

= P Q R.

On the diagram provided in the answer spaces, shadePada rajah di ruang jawapan, lorekkan

(a) the set (Q R)'b) the set (R P) Q .

[3 marks][3 markah]

Answer /Jawapan :

a)

(b)

P

Q

R

P

R

Q

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SULIT 1449/25

2 Calculate the values ofm and n that satisfy the following simultaneous linear equations :Hitung nilai m dan n yang memuaskan persamaan linear serentak berikut:

1032 nm

14 nm

[4 marks][4 markah]

Answer /Jawapan :

3 Using factorization, solve the following quadratic equation:Menggunakan pemfaktoran, selesaikan persamaan kuadratik berikut

121

73 2

x

xx[ 4 marks ]

[ 4 markah]

Answer /Jawapan :

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SULIT 1449/26

4 Diagram 1 shows a composite solid form by the combination of a cuboid and a right

cone. Rajah 1 menunjukkan sebuah gabungan pepejal yang dibentuk daripada cantuman sebuah kuboid dan

sebuah kon tegak.

Given that the volume of the composite solid is 10473

1cm

3and the height of the right

cone is 7 cm. Using =7

22, calculate

Diberi bahawa isipadu gabungan pepejal itu ialah 10473

1cm

3dan tinggi kon tegak ialah 7 cm.

Menggunakan =7

22, hitung

(a) the volume, in cm3, of the cuboid.

isipadu, dalam cm3, kuboid itu,

(b) the radius, in cm, of the cone. [5 marks]jejari, dalam cm, kon itu. [5 markah]

Answer /Jawapan :

(a)

(b)

Diagram 1Rajah 1

3 cm18 cm

16 cm

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SULIT 1449/27

5 (a) Complete the box in the answer space with and / orLengkapkan ruangan yang disediakan pada ruang jawapan dengan dan/ atau

(i) This statement is TRUE.Pernyataan ini adalah BENAR

3 5 = 8 3 + 5 = 8

(ii) This statement is FALSE.Pernyataan ini adalah PALSU

4 < 5 4 < 5

(b) (i) Complete the conclusion in the following argument:Lengkapkan kesimpulan dalam hujah berikut

Premise 1: All factor of 6 is factor of 24.Premis 1 : Semua faktor bagi 6 adalah faktor bagi 24.

Premise 2: 3 is factor of 6.Premis 2 : 3 ialah faktor bagi 6.

Conclusion: .Kesimpulan

(ii) Make a general conclusion by induction for the sequence

3, 9, 19, 33, .. which follows the pattern below :Buat satu kesimpulan secara aruhan bagi senarai nombor

3, 9, 19, 33, ............ yang mengikut pola berikut :3 = 1 + 2(1)

2

9 = 1 + 2(2)2

19 = 1 + 2(3)2

33 = 1 + 2(4)2

[5 marks][ 5 markah]

Answer /Jawapan :

(a) (i)

3 5 = 8 3 + 5 = 8

(ii)

4 < 5 4 < 5

(b) (i) Conclusion/Kesimpulan :

.

....

(ii) ..

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SULIT 1449/28

6 In Diagram 2, PQRS is a parallelogram . O is the origin and R lies on the x axis .

Dalam Rajah 2 PQRS ialah segiempat selari. O ialah asalan dan R terletak di atas paksi- x.

Given that PS = 4 unit and the gradient SR =3

1,

Di beri bahawa PS = 4 unit dan kecerunan SR =3

1

FindCari

a) the the coordinates of the point Rkoordinat titik R

b) the equations of the straight line PQpersamaan garislurus PQ

[ 5 marks ][5 markah]

Answer /Jawapan :

(a)

(b)

R

Diagram 2Rajah 2

x

Q

P

S(0,-3)

O

y

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SULIT 1449/29

7 Diagram 3 shows semicircle PQR of centre P and sector PKR of centre M.Rajah 3 menunjukkan sebuah semibulatan PQR berpusat di P dan sektor PKR berpusat di M.

Given that PQ = 28 cm and QPR = 140o. Using =7

22, calculate

Diberi bahawa PQ = 28 cm dan QPR = 140o. Dengan menggunakan =

7

22, hitung

(a) the perimeter, in cm, of the shaded regionperimeter, dalam cm, kawasan berlorek

(b) the area, in cm2, of the shaded region

luas, dalam cm2, kawasan berlorek

[6 marks][6 markah]

Answer /Jawapan :

(a)

(b)

P

Q

K

MR

Diagram 3Rajah 3

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SULIT 1449/210

8 (a) Given that matrix M=

13

21and MN=

10

01.

Find matrix N.

Diberi matriks M =

13

21dan MN =

10

01.

Carikan matriks N.

(b) Write the following simultaneous linear equations as matrix equation:Tulis persamaan linear serentak berikut dalam bentuk persamaan matriks:

33

82

vu

vu

Hence, using the matrix method, calculate the value of u and of v.Seterusnya, menggunakan kaedah matriks,hitung nilai u dan nilai v.

[ 6 marks]

[6 markah]

Answer /Jawapan :

(a)

(b)

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SULIT 1449/211

9 (a) State three inequalities except y 0 which satisfy the shaded region in Diagram 4.Nyatakan tiga ketaksamaan selain dari y > 0 yang memenuhi rantau berlorek dalam Rajah 4.

[3 marks][3 markah]

(b) On the graph provided in the answer space, shade the region which satisfies the three

inequalities 6,2 yxxy and 6y .Pada graf yang disediakan di ruang jawapan, lorek rantau yang memenuhi tiga ketaksamaan

yxxy ,2 6 dan 6y .

[3 marks][3 markah]

Answer /Jawapan :

(a) .

.

.

(b)

x + y = 6

y = 2x

y

Ox

y

x

y = x

x + y = 5

0

Diagram 4Rajah 4

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SULIT 1449/212

10 Diagram 5 shows twelve labeled cards which are placed in an empty box.Rajah 5 menunjukkan dua belas kad berlabel yang dimasukkan ke dalam sebuah kotak kosong.

A card is chosen at random from the box.

Find the probability that

Satu kad dipilih secara rawak daripada kotak itu.

Cari kebarangkalian

(a) the card labeled with vowel is chosen.kad berlabel dengan vokal dipilih

(b) the card labeled E is chosen.kad berlabel E dipilih.

(c) the non-vowel card is chosenkad berlabel bukan vokal dipilih

[ 4 marks][4 markah]

Answer /Jawapan :

(a)

(b)

(c)

P

C

CIO L E

STEDA

Diagram 5Rajah 5

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SULIT 1449/213

11 Diagram 6 shows a right prism with a horizontal rectangular base RSTU.Rajah 6 menunjukkan sebuah prisma tegak dengan tapak segiempat tepat RSTU.

(a) Name the angle between the line QS and the plane PQUT.Namakan sudut di antara garis QS dengan satah PQUT.

(b) Calculate the angle between the line QS and the plane PQUTHitung sudut di antara garis QS dengan satah PQUT

[ 4 marks][4 markah]

Answer /Jawapan :

(a)

(b)

QP

T

S R

U

6 cm

7 cm

8 cm

Diagram 6Rajah 6

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SULIT 1449/214

Section B

[48 marks]

Answer all questions from this section.Jawab semua soalan dalam bahagian ini.

12 (a) Complete Table 1 in the answer space for the equation 30123 xxy by

writing down the values of y when x = 2 and x = 2.5. [2 marks]

Lengkapkan Jadual 1 di ruang jawapan bagi persamaan 30123

xx y dengan menulis nilai-

nilai y apabila x = 2 dan x = 2.5. [2 markah]

(b) For this part of the question, use the graph paper provided on page 16.

You may use a flexible curve rule.

Untuk ceraian soalan ini, gunakan kertas graf yang disediakan pada halaman 16.

Anda boleh guna pembaris fleksibel.

Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw

the graph of 30123 xxy for 5.25.4 x . [4 marks]

Menggunakan skala 2 cm kepada 1 unit di paksi-x dan 2 cm kepada 5 unit pada paksi-y, lukis graf

bagi 30123

xxy untuk 5.25.4 x . [4 markah]

(c) From the graph in 12(b), findDari graf 12(b), cari

(i) the value ofy when x = 1.5nilai y apabila x = 1.5

(ii) the value ofx when y = 25 [2 marks]nilai x apabila y = 25 [2 markah]

(d) Draw a suitable straight line on the graph in 12(b) to find all the values ofx which

satisfy the equation 010173 xx for 5.25.4 x .

State these values ofx. [4 marks]

Lukis satu garis lurus yang sesuai pada graf di 12(b) untuk mencari semua nilai x yang memuaskan

persamaan 010173

xx untuk 5.25.4 x . Nyatakan nilai-nilai x itu.

[4 markah]

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SULIT 1449/215

Answer /Jawapan :

(a)

x 4.5 4 3 2 1 0 1 2 2.5

y 7.1 14 39 41 30 19 14

Table 1Jadual 1

(b) Refer graph on page 16Rujuk graf pada halaman 16

(c) (i) x =

(ii) y =

(d) x = , .

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SULIT 1449/216

Graph for Question 12

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SULIT 1449/217

13 (a) Transformation G is a reflection in the straight line x = 1. Transformation

T is a translation

6

2. Transformation K is an anticlockwise rotation of o90

about the centre (3, 0).

Penjelmaan G ialah satu pantulan pada garis lurus x = 1,

Penjelmaan Tialah satu translasi

6

2. Penjelmaan K ialah putaran 90

oarah lawan jam pada

pusat ( 3 , 0).

State the coordinates of the image of point (5, 2) under each of the following

transformations:

(i) G,

(ii) TG,

(iii) KT.

[5 marks][5 markah]

(b) In Diagram 8, triangle LMN is the image of triangle RMS under transformation V.

Triangle LQP is the image of triangle LMNunder transformation W.Dalam Rajah 8, segitiga LMN ialah imej bagi segitiga RMS di bawah transformasi V. Triangle

LQP ialah imej bagi segitiga LMN di bawah transformasi W.

(i) Describe in full the transformationHuraikan selengkapnya penjelmaan

(a) V,

(b) W.

(ii) Given that LMN represents a region of area 2unit21 , calculate the area, in2unit , of the region represented by MQPN.

Diberi bahawa LMN mewakili luas 21 unit2, hitungkan luas, dalam unit

2 , kawasan yang

diwakili oleh MQPN.

[7 marks][7 markah]

L

N

M

S

R

P

Q

Diagram 7Rajah 7

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SULIT 1449/218

Answer /Jawapan:

(a) (i)

(ii)

(iii)

(b) (i) (a) V :......

....

(b) W : ...

.

(ii)

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SULIT 1449/219

14 Table 2 shows the distribution of the height of 40 students in a school.Jadual 2 menunjukkan taburan kekerapan bagi tinggi 40 orang pelajar di sebuah sekolah

Height (cm)

Tinggi (cm)

Frequency

Kekerapan135 139 2

140 144 5

145 149 8

150 154 10

155 159 7

160 164 4

165 169 3

170 174 1

Table 2Jadual 2

(a) State the modal class for the data in the Table 2 [1 mark]Nyatakan kelas mod bagi data yang diberi dalan Jadual 2 [1 markah]

(b) (i) Construct a cumulative frequency table for the data in Table 2Binakan satu jadual kekerapan longgokan bagi data dalam Jadual 2

[3 marks][3 markah]

(ii) For this part of the question, use the graph paper provided on page 21.Untuk ceraian soalan ini, guna kertas graf yang disediakan pada halaman 21.

Using the scale of 2 cm to 5 cm on the x-axis and 2 cm to 5 students on

the y-axis, draw an ogive for the data.Dengan menggunakan skala 2 cm kepada 5 cm pada paksi x dan 2 cm kepada 5 orang

pelajar pada paksi-y, lukiskan satu ogif bagi data di atas.

[5 marks][5 markah]

(c) From the graph, findDaripada graf itu, carikan

(i) median

(ii) interquartile range julat antara kuartil

[3 marks][3 markah]

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SULIT 1449/220

Answer /Jawapan :

(a)

(b) (i)

Height (cm)Tinggi (cm)

FrequencyKekerapan

Upper boundarySempadan atas

Cumulative

frequencyKekerapan

longgokan

135 139 2

140 144 5

145 149 8

150 154 10155 159 7

160 164 4

165 169 3

170 174 1

(ii) Refer graph on page 21

(c) (i)

(ii)

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SULIT 1449/221


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SULIT 1449/222

15 (a) Given that y varies directly as w3

and inversely as x . Diberi bahawa y berubah secara langsung dengan w

3dan secara songsang dengan x .

Given y = 5 when w = 2 and x = 8 .Diberi y = 5 apabila w =2 dan x = 8

Determine the variation constant, k. Hence, express y in terms of w and x.Tentukan nilai pemalar, k. Seterusnya, nyatakan y dalam sebutan w dan x

[ 3 marks ]

[3 markah]

(b) Given thatr

qp

3

, p = 16 when q = 2 and r= 9

Diberi bahawar

qp

3

, p = 16 apabila q = 2 dan r= 9

CalculateHitungkan

(i) the value of p when q = 6 and r= 81nilai p apabila q = 6 dan r = 81

(ii) the value of r when p = 36 and q = 3nilai r apabila p = 36 dan q = 3

[4 marks]

[4 markah]

(c) In Diagram 8, MN, PQ and RS are three vertical poles on the horizontal ground.Dalam Rajah 8, MN, PQ dan RS adalah tiga tiang tegak di atas tanah rata.

(i) Find the angle of depression ofMfrom Q.Cari sudut tunduk M dari Q.

(ii) If the angle of elevation of S from Q is 59o, find the distance between S and R.

Jika sudut dongakan S dari Q ialah 59o, cari jarak di antara S dan R.

[ 5 marks]

[5 markah]

N

R

S

M

Q

P

21 cm

15 cm 17 cm

Diagram 8Rajah 8

8 cm

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SULIT 1449/223

Answer /Jawapan :

(a)

(b) (i)

(ii)

(c) (i)

(ii)

END OF QUESTION PAPER

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JABATAN PELAJARAN MELAKA

UJIAN PENGESANAN PERTENGAHAN TAHUNSIJIL PELAJARAN MALAYSIA 2009

MMAATTEEMMAATTIIKK

KKEERRTTAASS 11 11444499//11


JAWAPAN

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MMAATTEEMMAATTIIKK


1 B 11 D 21 B 31 D

2 A 12 B 22 D 32 A

3 A 13 C 23 B 33 C

4 A 14 C 24 B 34 D

5 B 15 A 25 D 35 D

6 C 16 D 26 A 36 C

7 B 17 C 27 B 37 C

8 B 18 B 28 A 38 B

9 D 19 D 29 D 39 B

10 D 20 D 30 D 40 B

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MARKAH MAKSIMUM BAGI KERTAS INI : 100 MARKAH

No Peraturan Pemarkahan Markah

1 (a)

(b)

Note : R P seen give 1 mark

1

2

3

2 4m 6n = 20 @equivalent

7n = 21 @ equivalent

n = 3

m =2

1

1

1

1

1

4

3 3x2 5x 12 = 0

(3x + 4) ( x 3) = 0

3,3

4 xx

1

1

1,14

4 (a) 18163

864 cm3

(b) 77

22

3

1 2 r

3

110477

7

22

3

131618

2 r

5 cm

1

1

1

1

1

5

P

Q

R

P

Q

R

MATHEMATICS 1449 / 2

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5 (a) (i) or(ii) and

(b) (i) 3 is factor of 24(ii) 1 + 2n

2; n = 1,2,3,

Note : 1 + 2n2 only award 1 mark

11

12

5

6(a)

3

1

0

03

xor

x

3

3

1 @ equivalent

( 9, 0)

(b) P(0,1) @ mPQ =3

1

c )0(311

13

1 xy

1

1

1

1

1 5

7(a) 28

7

222

360

140 @ 14

7

222

360

180

287

222

360

140 + 14

7

222

360

180 + 28

91264 @

94140 @ 140.44

(b) 2287

22

360

140 atau 214

7

22

360

180 @ equivalent

228

7

22

360

140 214

7

22

360

180 @ equivalent

9

5852@

9

2650 @ 650.22

1

1

1

1

1

1 6

8(a)

7

1

7

372

71

Note :

13

21

7

1@

13

21

32)1(1

1award 1 mark

2

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(b)

3

8

13

21

v

u

38

1321

71

vu

u = 2

v= 3

1

1

1

1 6

9 (a) 5xxy

5 yx

11

1

1

2

6

10 (a)125

(b)12

2

(c) 1 12

5

12

7

1

1

1

1 4

11 (a) TQS

(b) 22 68 or 10

tan =10

7

= 35

1

1

1

1

4

Line y = 6 (solid ordashed)

Region correctlyshaded

Note: Any 2 vertexshaded correctly

award 1 mark0 6

y

y =2 x

x

6

x + y = 6

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12 (a) 46 , 15.63

(b) Refer to graph

Uniform scale and correct axisPlot all points correctly

Smooth curve

(c) (i) y = 15.5 0.5

(ii) x = 3.7 0.1 , 0.4 0.1

(d) y = 5x + 20

Draw line y = 5x + 20

x = 4.4 0.1, 0.6 0.1

1 ,1

1

21

1

1

1

1

1,1 12

13 (a) (i) ( 3, 2)(ii) ( 1, 4)

(iii) (7, 4)

(b) (i) (a) V : Rotation, 180o , at centre M

Note : 1. Rotation only award 1 mark

2. Rotation , 180o

only or Rotation at centre M only award2 marks

(b) W : Enlargement with scale factor = 3

at centre L

(ii) 32 21

168

1

1

2

3

3

1

1 12

14 (a) 150 154

(b) (i)

Upper Boundary Cumulative Frequency

139.5 2

144.5 7

149.5 15

154.5 25159.5 32

164.5 36

169.5 39

174.5 40

1

1,1

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(ii) Refer to graph

Uniform scale and correct axis

Using upper boundary as x axis

Plot point (134.5, 0)Plot all points correctly

Smooth ogive

(c) (i) 151.5

(ii) 158 147

11

1

1

1

21

1

1

1 12

15 (a)8

)2(5

3k

k= 5

x

wy

35

(b) k= 6

(i)81

)6(6 3p

= 144

(ii)4

81

(c) (i) 15

8

tan = 28.1O

(ii)17

95tanx

x = 28.29

RS = 28.29 + 836.29

1

1

1

1

1

1

1

1

1

1

11 12

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x

y

45

40

35

30

25

20

15

10

5

-5

-10

50

0123 1 2 3x45

X

X

x

x

x

x

x

x

x

x

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x

x

x

x

x

x

x

xx

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math p2 mid year mlk09 dgn skema pdf june 7 2009-7-25 am 435k

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