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NAME: _________________________ MARKS:

__________

CLASS: __________

SMK PEREMPUAN METHODIST, PULAU PINANG

PEPERIKSAAN PERTENGAHAN TAHUN 2013

____________________________________________________________________________

_________

MATHEMATICS

PAPER 1

FORM FOUR

1 HOUR 15 MINUTES

____________________________________________________________________________

_________

DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO

1. Answerall questions.

2. Each question is followed by four choices of answers A, B, C and D.

3. For each question, choose one answer only.

5. The diagrams given are not drawn according to scale unless stated.

6. A list of formulae is given.

7. Non programmable scientific calculator is allowed.

____________________________________________________________________________

_________

This paper consists of 3 printed pages.

Written by: Ms. Tan Phei Ling

Checked by: Pn. Ng Guat Hwa

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6 Express 3248 as a number in base five.

A 22445B 44225C 13225D 22315

7 Diagram 2 shows a regular pentagonABCDE.DEFis a straight line andEA =EF

B

AC

yo

xo

F E D

Diagram 2

The value ofx + y is

A 108

B 126

C 144

D 162

8 In Diagram 3,PSR is a tangent to the circle at point S and QT = QS.

R

S T

52o

yo

P

Q

Diagram 3

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Find the centre of the enlargement

A ( 10 , 1 )

B ( 5 , 2 )

C ( 2 , 3 )

D ( 1, 5 )

11 Given that tan = 2.1445 and 180 360o . Find the value of .Diberi bahawa tan = 2.1445 dan 180

o 360

o. Carikan nilai .

A 65o

B 115o

C 245o

D 295o

12 In Diagram 6 QRSis a straight line.Dalam Rajah 6, QRS ialah garis lurus . Q

8 cm6 cm

R

P

o

Diagram 6Rajah 6 S

What is the value of cos ?Apakah nilai kos ?

A 45

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SULIT 1449/2

B 3

5

C3

5

D4

5

13 Diagram 7 shows the graphs y = sinx and y = cosx for 180o

x 360o

Rajah 7 menunjukkan graf y = sin x dan y = kos x untuk 18 00

x 3600.

y

1

180o

1

270o

P( ,

0.7071)

Diagram 7Rajah 7

x

360o

Pis an intersection point of the graph y = cosxo

and y = sinx . They-coordinate of

P

is 0.7071 . Find the value of .

P ialah titik persilangan bagi graf y = kos xo

dan y = sin x. Koordinat-y bagi P ialah 0.7071 .

Cari nilai .

A 45

B 135

C 225

D 250

14 Diagram 8 shows a cuboid with horizontal basePQRS. PointsL ,MandNare themidpoints ofUR , TS and UR respectively.

Rajah 8 menunjukkan sebuah kuboid dengan tapak PQRS. Titik L , M dan N ialah titik tengah bagi

UR, WP dan TS masing-masing.

T U

W N LV

M RS

PQ

Diagram 8Rajah 8

Name the angle between planeMRUand planeRSTU.

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SU L I T

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SULIT 1449/2

A MRSB MRNC MLND MUT

15 Diagram 9 shows two vertical towers,KL andMN, on a horizontal plane. The angle

of elevation of vertexMfrom vertexKis 48.Rajah 9 menunjukkan dua tiang tegak. KL dan MN pada satah mengufuk. Sudut dongak puncakMdari puncak K ialah 48o. M

K

8 m

L 6 m N

Diagram 9Rajah 9

Calculate the angle of depression of the baseN from the vertex K.

Hitung sudut tunduk tapak N dari puncak K

A 12 33

B 23 25

C 36 10

D 48 23

16 In the Diagram 10,PQ andRSare two vertical pillars standing on horizontal ground.

The angle of elevation ofQ from S is 22.Dalam Rajah 10 ,PQ danRS adalah dua tiang tegak berdiri pada permukaantanah. Sudut dongak titik Q dari titik S ialah 22

o

Q

h mS

2 m

Calculate the value ofh.Hitung nilai h

P 8 m RDiagram 10

Rajah 10

A 3.23

B 5.23C 19.83

D 21 83

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SU L I T

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SULIT 1449/2

17 Which of the following graphs represents the function y =x 2 + 4 ?Graf manakah yang mewakili fungsi y =x

2+ 4 ?

A y B y

Ox 4

4

Ox

C

y

D

y

Ox

4

4 xO

18 Given thatx is an integer, find all the values ofx that satisfy both of the inequalities

2x + 3 7 and 5x + 3

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SULIT 1449/2

20 Express3 +n

n

4 n

n2

as a single fraction in its simplest form.

Ungkapkan3 + n

n

4 n

n2

sebagai pecahan tunggal dalam bentuk terendah.

3 +n 2A

4 n

3n +n 2B

4 n

C3 + 3 n

4 n3

+n

2

D4 n

21 Given that5m n

6= 4 , then n =

Diberi5m n

= 4, maka n =6

A ( 5 m 24 )2

B 25 m + 24C 25 m

2 24

25

D m +4

6

22 Given that 4 (1 y ) = 3y 10

find the value ofy.

Diberi bahawa 4 (1 y ) = 3y 10, carikan nilai y.

A 7

B 5

C 4

D 2

237

3x5 can be written as

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A7

x5

3

B7

x5

3

C 21x5

D 21x5

24 Simplify 3 h2

5 h h 4 .

A 8h8

B 8h7

C 15h1

D 15h7

25 List all the integersx that satisfy the inequalities 8 + 3x

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Diagram

12

The mode is

A July

B August

C September

D November

27 Table 1 shows the cumulative frequency of scores obtained by a group of students in

a certain games .

Score of studentsSkorpelajar

1 2 3 4 5 6

Cumulative frequencyKekerapan longgokan

3 10 p 28 40 42

Table 1

If the mode score is 3 , the minimum value ofp is

A 12

B 13

C 15

D 23

28 Diagram 13 shows the graph ofy =a xn + 2 . What are the values of a and n ?.

y

y =a xn

+ 2

2

-1x

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Diagram 13

A a = 2, n = 2

B a = 2, n = 2

C a = 2, n = 3D a = 2, n = 3

29 Given that the universal set = {x : 10 x 30 ,x is an integer}.SetP= {x :x is an even number}

Set Q = {x :x is a number such that the sum of its digits is less than 5}

List all the elements of set PQ.

A { 14, 16, 18, 24, 26, 28, 30 }

B { 16, 18, 24, 26, 28, 30 }

C { 10, 12, 20, 22, 30 }

D { 16, 18, 24, 26, 28 }

30 Diagram 14 is a Venn diagram showing the elements of the universal set, , setMandN

M

N

Diagram 14

Rajah 14

Which set represents the shaded region?Set manakah yang mewakili kawasan berlorek?

A MN

B MN

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C MN

D MN

31 Diagram 15 shows two straight lines, QR andRS, drawn on Cartesian plane.R lies on

thex-axis.

y

S( 9, 4 )

Q ( 0 , 3 )

O R

Diagram 15Rajah 15

x

Given OR = 2OQ, find the gradient ofRS.

A 34

B4

3

C1

2

D 1

2

32 Diagram 16 shows a straight lineKL on a Cartesian plane.

y

K

2x + 5y = 10

L ( h , 3 )

Find the value ofh.

x0

Diagram 16

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A 5

2

B 2

5C 2

D 5

33 The coordinates of G is (0, 6) and the gradient of the straight line GHis 2

. Find3

the x- intercept ofGH.

A 9

B 1

C 4

D 9

34 A box contains 20 blue cards and some red cards. A card is chosen at random from

the box . The probability of choosing a blue card is5

.7

Find the number of red cards in the box .

Sebuah kotak mengandungi 20 keping kad biru dan beberapa keping kad merah . Sekeping kad

dipilih secara rawak daripada kotak itu .Kebarangkalian sekeping kad merah dipilih ialah5

.7

Cari bilangan kad merah dalam kotak itu .

A 8

B 15

C 28

D 35

35 Table 2 shows the distribution of a group of 120 students in two societies.Jadual2 menunjukkan bilangan 120 murid dalam dua buah persatuan.

BoysLelaki

GirlsPerempuan

Mathematics SocietyPersatuan Matematik 35 20

English SocietyPersatuan B. Inggeris

40 25

Table 2Jadual2

A student is chosen at random from the group to raise up the flag.

What is the probability that a girl from the English society will be chosen ?Seorang murid dipilih secara rawak daripada kumpulan itu untuk menaikkan bendera.

k h k b k l d d h k d l h ?

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SU L I T

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SULIT 1449/2

A5

9

B5

13

C9

24

D5

24

36 A container holds 20 bars of chocolate with raisins and nuts. A bar of chocolate is

picked at random from the container. The probability of picking a bar of chocolate

with raisins is3

.5

How many bars of chocolate with nuts are there in the container ?Sebuah bekas mengandungi 20 bungkus coklat yang terdiri daripada coklat berkismis dan

berkacang. Sebungkus coklat dipilih secara rawak daripada bekas itu. Kebarangkalian bahawacoklat itu

3berkismis ialah . Berapakah bilangan bungkus coklat berkacang dalam bekas itu?

5

A 2

B 8

C 12

D 17

37 It is given thaty

25 .

Diberi bahawa y

1and y = 4 when x = 9 . Calculate the value ofy whenx =

x

1dan y = 4 apabila x = 9. Hitungkan nilai y apabila x = 25

x

A12

5

B4

15

C1

12

D1

60

38 Table 3 shows two sets of values ofp , q and rwhich satisfy r pq .Jadual3 menunjukkan dua set bagi nilai p, q dan r yang memuaskan r pq .

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SULIT 1449/2

p1

2

1

3

q 6 w

r 45 25

Calculate the value ofw.

A 5

B 15

C 45

D 135

Table 3Jadual3

439

7 1 + 3

1

2 5

1A

2 0

2 8 5 1 4

B 8 5 7 2

C 8

7D

5 2

4 5

40 Calculate the values ofm and of n in the following matrix equation .

m 10

4 2

3 12 4 =

5 1 2 1 1 n

A m = 1 , n = 3

B m = 1 , n = 2

C m = 4 , n = 3

D m = 4 , n = 1

END OF QUESTION PAPER

1449/2 2010 Hak Cipta JPM [Lihat halaman sebelah

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SULIT 1449/2

1 D 11 D 21 A 31 B

2 D 12 B 22 D 32 A

3 A 13 C 23 B 33 D

4 A 14 C 24 D 34 D

5 A 15 A 25 A 35 B

6 C 16 B 26 B 36 B

7 B 17 B 27 D 37 A

8 D 18 A 28 C 38 A

9 D 19 D 29 A 39 B

10 A 20 B 30 C 40 C

1449/2Mathematics

Paper 2

May

2010

NAME :...

FORM: 4

SEKOLAH MENENGAH SAINS MUZAFFAR SYAHAYER KEROH, 75450 MELAKA

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Section Question Fullmark

Marksobtained

A

1 3

2 4

3 4

4 3

5 4

6 5

7 6

8 6

9 6

10 5

11 6

B

12 12

13 12

14 12

15 12

Total

SULIT 1449/2

PEPERIKSAAN AKHIR SEMESTER 1

2010

MATHEMATICS

Paper 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 questions in Section A and in Section B.

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

3. Working step must be written clearly.

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

5. Marks for each question are given in bracket.

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

8. Non programmable scientific calculator is allowed.

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

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SULIT 1449/2

This question paper consists of 21 printed pages.

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2 2

x

14

S UL IT 1449/1

MATHEMATICAL FORMULAE

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

1 ama

n =am+n

RELATIONS

2 am an =amn

3 (am

)n =a mn

4 A1 =

1 db

adbc c a

P(A) =n(A)

5n(S)

6 P(A' ) =1P(A)

7 Distance = (x2

x1

)

+(y2

y1)

(x,y) =x1 +x2 ,y1 +y2 8 Midpoint , 2 2

9 Average speed =distance travelled

time taken

10 Mean =sum ofdata

number ofdata

11 Mean =sum of(class markfrequency)

sum of frequencies

12 Pythagoras Theorem

c2 =a2 +

b2

m =y

2y

1

132 x1

m =y int erceptx int ercept

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S U L IT

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S U LI T 24

SHAPES AND SPACE

1449/1

11 Area of trapezium =

2 sum of parallel sides height

2 Circumference of circle = d= 2r

3 Area of circle = r2

4 Curved surface area of cylinder = 2rh

5 Surface area of sphere = 4r2

6 Volume of right prism = cross sectional area length

7 Volume of cylinder = r2h

8 Volume of cone =1

r2 h3

9 Volume of sphere =4

r3

3

10 Volume of right pyramid =1

base area height3

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

arc length12

circumference of circle=angle subtended at center

360o

area of sector

=angle subtended at centre

13 area of circle 360o

PA'14 Scale factor, k=

PA

15 Area of image = k2 area of object


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S U LIT 25 1449/1


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S U LI T 26

Section A[52 marks ]

Answerall questions in this section.

1449/1

1 On the graph in the answer space, shade the region which satisfy the three inequalities

y x , x 2 and y < 5 [3 marks ]Pada graf yang disediakan di ruangan jawapan , lorekkan rantau yang memuaskan ketiga-

tiga ketaksamaan :y x , x 2 and y < 5

Answer :

y

6x= 2

5

4

3y =x

2

1

0 1 2 3 4 x

2 Calculate the value of p and of q that satisfy the following simultaneous linear

equations:

Hitung nilai p dan nilai q yang memuaskan persamaan linear serentak berikut:

1p +2q = 5

4

Answer :

p +4q =8 [4 marks]


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S U LIT 27 1449/1

3 Solve the quadratic equation:Selesaikan persamaan kuadratik berikut:

3x =2(x + 4)

x[ 4 marks]

Answer :

4 Diagram 4 shows a cuboid with TUVW as the horizontal base . L, Mand Nare themidpoints ofPS, QR and UVrespectively.

Rajah 4 menunjukkan sebuah kuboid dengan tapak mengufuk TUVW. L, M dan N adalah titik

tengah bagi PS, QR dan UV masing-masing.

P Q

L M

TS U

RN

W Diagram 4 V

Rajah 4

Given WT= 8 cm, WV= 12 cm and QU= 4 cm.Identify and calculate the angle between the plane LVUand the plane QRVU.

Diberi WT = 8 cm, WV= 12 cm dan QU = 4 cm.

Kenal pasti dan hitungkan sudut di antara satah LVU dengan satah QRVU.

Answer:

[3 marks]


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S U LIT 28 1449/1

5 Diagram 5 shows a solid in the shape of a right pyramid. Vis vertically above the square

baseJKLM. A cylinder with radius 3 cm and height 6 cm is taken out of the solid.Rajah 5 menunjukkan sebuah pepejal berbentuk sebuah piramid tegak. V terletak tegak di atas tapak

segi empat sama JKLM. Sebuah silinder yang berjejari 3 cm dan tinggi 6 cm dikeluarkan daripada

pepejal itu.

V

M L

J KDiagram 5

Jadual5

Given JK= 8 cm and the height of the pyramid is 12 cm, calculate the volume, in cm3,

of the remaining solid. ( Use = 3.142 ) [4 marks]Diberi JK = 8 cm dan tinggi piramid ialah 12 cm, hitungkan isipadu, dalam cm

3, pepejal yang tinggal

itu. ( Guna = 3.142 )

Answer:


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S U LIT 29 1449/1

6 In Diagram 6, O is the origin. Straight line SR is parallel to straight linePQ. The equation

of straight line SR is y =3

x 2 .4

Dalam Rajah 6, O ialah asalan. Garis lurus SR adalah selari dengan garis lurus PQ. Persamaan garis

lurus SR ialah y =3

x 2 .4

y Q ( 8 , 9 )

P

xO R

SDiagram 6

Rajah 6

FindCari

a) the coordinates of pointRkoordinat titik R

b) the equation of the straight linePQ

persamaan garis lurus PQ.

Answer:

(a)

[ 5 marks ]


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S U LIT 30 1449/1

(b)

7 Diagram 7 shows sectorMPQ, sectorMSTand semicircle PQR with centreM.Rajah 7 menunjukkan sebuah sektor MPQ, sektor MST dan semibulatan PQR berpusat di M.

T

Q

P M R S

Diagram 7Rajah 7

Given thatPS =3PM, MQ = 7 cm and QMR = 120o. Using =22

, calculate7

Diberi bahawa PS = 3PM, MQ = 7 cm dan QMR = 120o. Dengan menggunakan =22

, hitung7

(a) the perimeter, in cm, of the whole diagramperimeter, dalam cm, seluruh rajah.

(b) the area, in cm2

, of the shaded regionluas, dalam cm

2, kawasan berlorek

[6 marks]

Answer:

(a)


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S U LIT 31 1449/1

(b)

8 (a) Inverse matrix of 1 3 is 1 n 3 .4 2 m 4 1

Matriks songsang bagi1 3

ialah1 n 3 .

4 2 m 4 1Find the value ofm and ofn.Cari nilai m dan nilai n.

(b) Using matrices, calculate the value ofx and ofy that satisfy the following

simultaneous linear equations:Menggunakan kaedah matrik, hitung nilai x dan nilai y yang memuaskan persamaanlinear serentak berikut:

x 3y = 5

4x 2y = 10 [ 6 marks ]

Answer :

(a)

(b)


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S U LIT 32 1449/1

9 (a) State three inequalities which satisfy the shaded region below.Nyatakan tiga ketaksamaan yang memenuhi rantau berlorek di bawah.

y

y = 2x + 1

x0

2y = x 4[3 marks]

Answer:

(a) ( i) ..

(ii)

(iii) .

(b) The Venn diagrams in the answer space show setA, set B and set C, such that

the universal set =AB C.Gambar rajah Venn di ruang jawapan menunjukkan set A, set B dan set C dengan keadaan

set semesta =AB C.


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B C

B C

S U LIT 33 1449/1

On the diagrams in the answer space, shade the set [3 marks]Pada rajah di ruang jawapan, lorek set

(i) A B '(ii) (A B) C

Answer:

A(i)

(ii)A

10 (a) Diagram 10 shows thirteen labeled cards which are placed in a box .Rajah 10 menunjukkan tigabelas kad berlabel yang dimasukkan ke dalam sebuah kotak.

P E R P E N DDiagram 10

Rajah 10

L A R

A car d is chosen at random from a box. By listing the possible outcomes of theevent , find the probability thatSatu kad dipilih secara rawak dari kotak itu. Dengan menyenaraikan semua kesudahan

yang mungkin, cari kebarangkalian bahawa

(i) the card labeled with vowel are chosen.kad berlabel dengan vokal dipilih

(ii) the card labeled with R is chosen.

kad berlabelR dipilih.

(b) Table 10 shows the marks scored by 140 students in a Mathematics tests.Jadual10 menunjukkan markah yang di perolehi oleh 140 murid dalam ujian Matematik.

Marks Number of Students

51 55 11

56 60 45

61 65 67


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S U LI T 34

66 70 17

Table 10Jadual10

A students is selected at random from the group.Seorang murid dipilih secara rawak daripada kumpulan itu.

Find the probability that the mark is :Cari kebarangkalian bahawa markahnya ialah:

(i) in the class interval 61 65dalam selang kelas 61 65

(ii) less than 61 marks.kurang dari 61

1449/1

[ 5 marks]Answer:

(a)

(i)

(ii)

(b) (i)

(ii)

11 (a) Complete the statement below using the quantifier all or some to form a true

statement.

Lengkapkan pernyataan berikut dengan menggunakan pengkuantiti semua atau sebilangan,

untuk membentuk suatu pernyataan yang benar.

quadratic equations have different roots.

persamaan kuadratik mempunyai punca - punca yang berlainan.

(b) Complete the premise in the following argument:

Lengkapkan premis dalam hujah berikut:

Premise 1 : If setP is a subset of setQ, then PQ =P.

Premis 1 : Jika set P adalah subset bagi set Q , maka PQ =P.

Premise 2 /Premis 2 : .


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S U LI T 35

Conclusion : Set P is not a subset of setQ.

Kesimpulan : Set P bukan subset bagi set Q.

1449/1

(c) Write down two implications based on the following sentence.

Tuliskan dua impikasi berdasarkan ayat di bawah.

x3

= 125 if and only isx = 5

x3

= 125 jika dan hanya jika x = 5

(d) Make a general conclusion by induction for the number sequence 2, 10, 24, ... whichfollows the pattern :

Answer:

Buat satu kesimpulan umum secara aruhan bagi urutan nombor 2, 10, 24, .. yang mengikut pola berikut :

7 = 3(2)1

+ 1

14 = 3(2)2

+ 2

27= 3(2)3

+ 3

... = ........... [6 marks]

(a)

(b) Premise 2 : .............

(c) Implication 1 : .

Implication 2 : ....

(d) .

Section B

[48 marks]


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S U LI T 36

Answer all questions from this section.

1449/1

12. (a) Table 12 in the answer space shows the values ofx and ofy for the equation

y =4

.

xFind the value ofp and ofq. [2 marks]

Jadual12 di ruang jawapan menunjukkan nilai nilai x dan y bagi persamaan

Cari nilai bagi p dan q.

y =4

.x

(b) For this part of the question, use the graph provided on page 15. You may use a

flexible curve rule.

Untuk ceraian soalan ini, gunakan kertas graf yang disediakan pada halaman 15. Anda

boleh menggunakan pembaris fleksible.

By using a scale of 2 cm to 1 unit on the both axes, draw the graph of y =4

xfor

0.5 x 6 .

Dengan menggunakan skala 2 cm kepada 1 unit pada kedua dua paksi , lukis graf bagi fungsi

y =4

xuntuk 0.5 x 6 . [4 marks]

(c) Using the graph drawn in 12(b), findMenggunakan graf yang dilukis di 12(b), carikan

(i) the value of x when y = 5.4nilai x apabila y = 5.4

(ii) the value of y when x = 4.5

nilai y apabila x = 4.5 [2 marks]

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

satisfy the equation 7x 2x 2 =4

for0.5 x 6 .

State these values ofx [4 marks]Lukiskan satu garis lurus yang sesuai pada graf anda untuk mencari nilai nilai x yang

memuaskan persamaan 7x 2x 2 =4

bagi 0.5 x 6 .

Nyatakan nilai-nilai x tersebut .


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S U LIT 37 1449/1

Answer :

(a)

x 0.5 1 1.5 2 2.5 3 4 5 6

y 8 4 2.67 2 p 1.33 1 q 0.67Table 12Jadual12

p =

q =

(b) Refer graph on page 15.

(c) (i) x = .

(ii) y = ..

(d) x = . , .


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S U LIT 38 1449/1

Graph for Question 12


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S U LIT 39 1449/1

3 13 (a) Transformation Tis a translation and transformationPis an anticlockwise

2

rotation of 90 about the centre ( 1 , 2 ).

3 Penjelmaan Tialah translasi dan penjelmaanPialah putaran 90 ikut arah lawan jam pada

pusat ( 1, 2 ).

2

State the coordinates of the image of point ( 0 , 6 ) under each of the followingtransformations:

Nyatakan koordinat imej bagi titik( 0, 6 ) di bawah setiap penjelmaan berikut:

(i) P,

(ii) PT,

(iii) T2. [5 marks]

(b) Diagram 13 shows three quadrilaterals, ABCD, EFGH andJKLM, drawn on a

Cartesian plane.

Rajah 13 menunjukkan tiga sisiempat, ABCD, EFGH dan JKLM, dilukis pada suatu satah Cartesan.

y

C

D

6 4

8

6B

4

A2

2 O

K

L

F G

H M

E

Jx

2 4 6 8

Diagram 13Rajah 13


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S U LIT 40 1449/1

(i) JKLM is the image ofABCD under the combined transformation VU.Describe in full the transformations:

JKLM ialah imej bagi ABCD di bawah gabungan penjelmaan

VU. Huraikan selengkapnya:

(a) U,

(b) V.

(ii) It is given that quadrilateralABCD represents a region of area 32 cm2.

Calculate the area ,in cm2, of the region represented by the shaded region

Diberi bahawa sisiempat ABCD mewakili suatu kawasan yang mempunyai keluasan 32

cm2. Hitungkan luas, dalam cm

2, kawasan yang diwakili oleh rantau berlorek.

[7marks]

Answer:

(a) (i)

(ii)

(iii)

(b) (i) U :...

(ii) V : .....


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S U LIT 41 1449/1

..

(c)

14 The data in Diagram 14 shows the body weight, in kg, of 32 children in a kindergarten.Data dalam Rajah 14 menunjukkan timbangan berat , dalam kg, bagi 32 murid dalam sebuah tadika.

28 11 23 27 20 15 30 24

27 25 17 19 16 23 25 26

29 17 23 12 20 21 23 28

29 19 33 24 23 24 25 31

Diagram 14Rajah 14

a) Based on the data in Diagram 14 and by using the class interval of 3, completeTable 14 in the answer space..

Berdasarkan data dalam Rajah 14 dan dengan menggunakan selang kelas 3, lengkapkan Jadual

14 di ruangan jawapan..


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S U LI T 42

b) Based on Table 14 in (a), calculate the mean weight, in kg.Berdasarkan Jadual 14 di (a), hitungkan min berat, dalam kg.

1449/1

c) By using a scale of 2 cm to 3 kg on the horizontal axis and 2 cm to 1 child on thevertical axis, draw a histogram for the data.

Dengan menggunakan skala 2 cm kepada 3 kg pada paksi mengufuk dan 2 cm kepada 1murid pada paksi mencancang, lukiskan satu histogram bagi data tersebut

(d) State one information obtained based on the histogram in 14(c).Nyatakan satu maklumat berdasarkan histogram di 14(c)

Answer :(a)

Class interval Frequency Midpoint

10 12

.

Table 14Jadual 14

(b)

(d) ..........................................................................................................................................


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S U LI T 43

Graph for Question 14

1449/1


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S U LIT 44 1449/1

15 (a) Given that m varies directly as the cube of n and m = 36 when n = 2, express

m in term ofn . Hence, find the positive value of n when m = 288.Diberi bahawa m berubah secara langsung dengan kuasa tiga n dan m = 36 apabila n =

2, ungkapkan m dalam sebutan n. Seterusnya carikan nilai n apabila m = 288.

[3 marks]

(b) Table 15 shows the relation between three variables, p , q and r.Jadual15 menunjukkan hubungan antara tiga pembolehubah p, q dan r.

p q r

3 6 2

8 25 y

6 w 3

Given that p

Table 15

Jadual 15

q, calculate the values of w and ofy.

r2

Diberi bahawap

q , hitungkan nilai-nilai w dan y. [5 marks]r

2

(c) In Diagram 15, QRSis a straight line.Dalam Rajah 15, QRS adalah garis lurus.

Q 4 cm P

3 cm

R

o

SDiagram 15

Rajah 15

FindCari

(i) the value of cos ?

nilai kos

(ii) PRS [4 marks]


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laman sebelah[Lihat h

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S U LIT 45 1449/1

Answer :

(a)

(b)

(c) (i)

(ii)

END OF QUESTION PAPER

1449/1 2010 Hak Cipta JPM a

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S U LIT 46 1449/1

JABATAN PELAJARAN MELAKA

PEPERIKSAAN SELARAS PERTENGAHAN TAHUNSIJIL PELAJARAN MALAYSIA 2010

JAWAPAN

MMATEATEMMATATIIKK

KERTASKERTAS 22 14491449/2/2


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S U LIT 47 1449/1

MATHEMATICS 1449 / 2

MARKAH MAKSIMUM BAGI KERTAS INI : 100 MARKAH

No Peraturan Pemarkahan Markah

1 yx= 2

6

5

Liney = 5

4Correctly shaded

3y =x

2

1

0 1 2 3 4 x

1

2

3

2 p + 8q = 20 @ equivalent4q = 12 @ equivalent

q = 3

p = 4

11

1

1 4

3 3x2 2x 8 = 0

(3x + 4) (x 2) = 0

x =4

,x =23

1

1

1,14

4 LNM

tan

=

12

4 = 71.57 or 71o 34'

1

2

1

4


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S U LIT 48 1449/1


51

3 3.142 8 812

3.142336

1 3.1428 8 12 3.14233 6

386.33

1

1

11

4

63

(a) 10 =4

x 2

x =8

3

(b) m =3

4

9 =3 (8)+c or c = 34

y =3

x +34

1

1

1

1

1 5

7(a)

1202

2214 @

602

22 7

360 7 360 7120

222

14 +60

222

7 + 21 + 14360 7 360 7

215@ 71

2@ 71.67

3 3

(b)120

22

142 , atau @ equivalent360 7

(120

22

142120

22

72 ) +60

22

72 @

equivalent360 7 360 7 360 7

539 2

1

1

1

1

1

1

6

8(a) m = 10, n = 2

1

n 3

1

2 3

Note : = award 1 markm 4 1 1 (2) (3) 4 4 11 3 x 5

(b) = 4 2 y 10

x 1 2 35 = y (1 (2) 3 4) 4 110 x = 2 y = 1

1,1

1

1

1, 1 6


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CB


9 (a) 2y x 4y < 2x + 1y

1

(b) (i) A

B C

A

1

11

1

2

6

10 (a) {P, E, R, N, D, I, C, U, L, A, R}

(i)5

13

(ii)2

13(b) (i)

67

140

(ii)56

or2

140 5

1

1

1

1

1

5

11

(a) Some

(b) PQ P

(c) If x3

= 125, thenx = 5

Ifx = 5, thenx3 = 125

(d) 3n2

n ; n = 1,2,3,4,

Note : 1 + 2n2

only award 1 mark

1

1

1

1

1, 1

6

S U LIT 49 1449/1

(ii)


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Class

interval

Frequency Midpoint

10 12 2 1113 15 1 14

16 18 3 17

19 21 5 20

22 24 8 23

25 27 6 26

28 30 5 29

S U LIT 50 1449/1


12 (a) p = 1.6 , q = 0.8

(b) Refer to graph

Uniform scale and correct axis

Plot all points correctly

Smooth curve

(c) (i) x = 0.8 0.1(ii) y = 0.9 0.1

(d) y = 2x 7 @ 2x 7 =4

x

Draw line y = 2x 7x = 2.7 0.1, 0.7 0.1

1 ,1

1

21

1

1

1

1

1,1

12

13 (a) (i) (3, 7)(ii) (6 , 5)

(iii) (12 , 4)

(b) (i) (a) U : Reflection ,x = 1.

Note : Reflection only award 1 mark

(b) W : Enlargement with scale factor = 3 ,

at centre (5 , 4)

Note : 1. Enlargement with scale factor = 3 only @ Enlargement atcentre (5 , 4) award 2 marks2. Enlargement only award 1 mark

(ii) 32 32

32 32 32

256

12

2

2

3

11

112

14

(a)

1, 2, 1


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S U LIT 51 1449/1


31 33 2 32

2

1

12

1

1

(b)2(11) + 1(14) + 3(17) + 5(20) + 8(23) + 6(26) + 5(29) + 2(32)

3223

(c) Refer to graphUniform scale and correct axis,

Eight bars correctly drawn..

Using upper boundary or class interval or midpoint asx axis

(d) Any correct information from the histogram. 12

15 (a) 36 = k(2)

3

or k =9

2

288 =9

n3

2n = 4

(b) k= 2

(i) 8 =2(25)

y2

y = 5

2

(ii) 6= 2w32

w = 27

(c) (i) RP= 5

cos RPQ =3

5

cos = 3

5(ii) = 126.87

o

1

11

1

1

1

11

1

1

1

1

12


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S U LI Ty

52Graph for Question 12

1449/1

1

x0 1 2 3 4 5 6

xx

1 x

x

x

2 x

x

3

4 x

5

6

7

8 x


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S U LI T 53Graph for Question 14

1449/1

9

8

7

6

5

4

3

2

1

01449/1

112010 Hak

Cipta1J4PM

17 20 23[L

2ih

6at halam

2a9n

sebelah 32

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